THE UNIVERSITY OF CALGARY

Avalanche Prediction for Persistent Snow Slabs

by

James Bruce Jamieson

A DISSERTATION

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL ENGINEERING

CALGARY, ALBERTA

November, 1995

 James Bruce Jamieson 1995 ABSTRACT

Two field tests of snow slab stability, the shear frame test and the rutschblock test, were studied at avalanche forecasting areas in British Columbia and Alberta during the winters of 1992-93 to 1994-95. Field work focused on persistent weak snowpack layers consisting of surface hoar or faceted crystals that are the failure planes for most fatal slab avalanche accidents in Canada. The shear frame test was refined through field and finite element studies. Effects of different frame designs were identified. Shear strength measurements were shown to decrease as the distance between the frame and the weak layer decreased. Field studies of the effect of loading rate and shear frame area on shear strength confirmed previous studies. Using different shear frame operators did not affect the resulting strength measurements provided the operators maintained consistent technique. One particular shape of fracture surface was associated with significantly higher strength measurements. The strength measurements from the first two tests proved to be more variable than measurements from subsequent tests on the same weak layer. Shear frame stability indices for natural avalanches and for skier-triggered dry slab avalanches were refined by incorporating an adjustment for normal load that depended on microstructure of the weak layer. The stability index for skier triggering was further refined by adjusting for the distance the skis penetrate the snow surface. Skier stability indices based on shear frames tests at both avalanche slopes and safe study sites were correlated with skier-triggered dry slab avalanches. When compared with other forecasting variables, the skier-stability index based on study site tests ranked first or second in predictive value. Closely spaced rutschblocks on nine avalanche slopes were used to identify snowpack and terrain factors that affect rutschblock results. The frequency of skier-triggered avalanches for common rutschblock scores in the avalanche start zones was determined and shown to be similar to a Swiss study in a different snowpack. For a given rutschblock score, persistent slabs were triggered more frequently than non-persistent slabs.

v Limitations of shear frame stability indices and rutschblock tests related to slope inclination and terrain were identified.

v ACKNOWLEDGEMENTS

I am indebted to Colin Johnston for the advice and discussions that guided this investigation and for reviewing the chapters of this dissertation thoroughly and quickly. For financial support for the entire research project, I am grateful to Canada’s Natural Sciences and Engineering Research Council, Mike Wiegele Helicopter Skiing (MWHS), Canadian Mountain Holidays (CMH), and members of the BC Helicopter and Snowcat Skiing Operators' Association. For their commitment to the research project and willingness to sort out the inevitable difficulties, my thanks to Mike Wiegele and Bob Sayer from Mike Wiegele Helicopter Skiing, to Mark Kingsbury, Walter Bruns, Colani Bezzola, Rob Rohn and Bruce Howatt from Canadian Mountain Holidays, to Clair Israelson, Tim Auger, Marc Ledwidge, Gerry Israelson, Dave Skjönsberg, Bruce McMahon and Terry Willis from the Canadian Parks Service, and to Jack Bennetto, John Tweedy, Peter Weir and Gordon Bonwick from the BC Ministry of Transportation and Highways. For their expertise and field work at various times during the recent winters, I am grateful to Leanne Allison, Peter Ambler, Roger Atkins, Ken Black, James Blench, Jeff Bodnarchuk, Alex Brunet, Andrew Bullock, Steve Chambers, Peter Clarkson, Sam Colbeck, Aaron Cooperman, Alan Evenchick, Jamie Fennell, Sylvia Forest, Michelle Gagnon, Will Geary, Jeff Goodrich, Sue Gould, Brian Gould, Jim Gudjonson, Todd Guyn, Reg Hawryluk, Mike Henderson, Larry Hergot, Jim Haberl, Rob Hemming, Karsten Heuers, Jill Hughes, Gerry Israelson, Dena Jansen, John Kelly, Troy Kirwan, Karl Klassen, Marc Ledwidge, Garth Lemke, Janet Lohmann, Kevin Marr, Greg McAuley, Rod McGowan, Tony Moore, Al McDonald, Bruce McMahon, Derek Peterson, Cathy Ross, Ken Schroeder, Lisa Palmer, Simon Parboosingh, Lisa Richardson, Peter Schaerer, John Schleiss, Mark Shubin, Bert Skrypnyk, Dave Smith, Alex Taylor, Ty Trand, Julie Timmins, John Tweedy, Scott Ward, Rupert Wedgewood, George Weetman, Barry Widas, Terry Willis, Adrian Wilson, Percy Woods, Chris Worobets, Kobi Wyss, and Linda Zurkirchen. My apologies to anyone I may have omitted.

vii My thanks for helpful discussions on field work, the mountain snowpack and avalanches to Sam Colbeck, Bert Davis, Paul Föhn, Jill Hughes, Clair Israelson, Gerry Israelson, Dave McClung, Ron Perla, Peter Schaerer, Chris Stethem, Martin Schneebeli, Jürg Schweizer and the guides at Canadian Mountain Holidays and Mike Wiegele Helicopter Skiing. Jill Hughes helped compile the data. Peter Schaerer, Jürg Schweizer and Alaa Sherif each paraphrased sections of papers from German. Bert Davis got me interested in classification trees and provided useful advice on Chapter 9. Martin Schneebeli provided helpful comments on Chapters 5 and 7. Julie Lockhart proofread the entire manuscript. Thanks to Chris Stethem for the photo of Ron Perla at the cracked bed surface in Chapter 8, and to Jill Hughes and Mark Shubin for the photos of snowpack tests in Chapter 1. During this project, I was encouraged by many people including Alan Dennis, Jim Bay, Jack Bennetto, Colani Bezzola, Bob Day, Phil Hein, Clair Israelson, Brian Langan, John Morrall, Chris Stethem, Adrian Wilson, Jackie Wilson, my family and especially Julie Lockhart. My thanks to all who contributed to, or supported, this endeavour.

vii TABLE OF CONTENTS Approval Page ...... iii Abstract ...... v Acknowledgements ...... vii Table of Contents ...... ix List of Tables ...... xiii List of Figures ...... xv List of Symbols ...... xxi 1 INTRODUCTION ...... 1 1.1 Effects of Avalanches ...... 1 1.2 Avalanche Hazard Mitigation ...... 2 1.3 Mountain Snowpack ...... 3 1.4 Snow Metamorphism ...... 4 1.5 Failure of Snow Slopes ...... 8 1.6 Weak Snowpack Layers ...... 9 1.7 Avalanche Forecasting ...... 11 1.8 Computer Assisted Forecasting ...... 16 1.9 Atypical Snowpack Characteristics of Accident Avalanches ...... 17 1.10 Skier-Triggering of Persistent Weak Layers ...... 18 1.11 Snow Profiles and Snowpack Tests ...... 19 1.12 Objective and Outline ...... 22 2 LITERATURE REVIEW ...... 25 2.1 Introduction ...... 25 2.2 Slab Failure ...... 25 2.3 Shear Frame ...... 27 2.4 Slope-Specific Stability Indices ...... 32 2.5 Extrapolated Stability Indices ...... 36 2.6 Flaws in Weak Layers and Spatial Variability of Stability Indices ...... 39 2.7 Rutschblock ...... 41 2.8 Summary ...... 44 3 METHODS ...... 47 3.1 Study Areas and Co-operating Organizations ...... 47 3.2 Sites for Snowpack Tests ...... 49

ix Table of Contents, continued 3.3 Equipment ...... 51 3.4 Measurement of Slab Weight per Unit Area ...... 53 3.5 Shear Frame Tests ...... 54 3.6 Rutschblock Test ...... 57 3.7 Comparison of Rutschblock and Shear Frame Tests ...... 59 3.8 Avalanche Activity ...... 61 4 FIELD STUDIES OF THE SHEAR FRAME TEST ...... 65 4.1 Introduction ...... 65 4.2 Statistical Distribution ...... 65 4.3 Variability and Number of Tests for Required Precision ...... 69 4.4 Fracture Surface ...... 71 4.5 Loading Rate ...... 73 4.6 Test Sequence Variability ...... 75 4.7 Effect of Delay ...... 76 4.8 Frame Placement ...... 77 4.9 Variability Between Operators ...... 79 4.10 Size Effects ...... 81 4.11 Effect of Normal Load ...... 83 4.12 Frame Design ...... 86 4.13 Summary ...... 92 5 FINITE ELEMENT STUDIES OF THE SHEAR FRAME TEST . . .. 95 5.1 Introduction ...... 95 5.2 The Model and Assumptions ...... 95 5.3 Basic Stress Distribution ...... 98 5.4 Effect of Frame Placement on Stress Distribution ...... 100 5.5 Effect of Frames Placed in Hard and Soft Slabs ...... 101 5.6 Effect of Spacing Between Cross-members ...... 102 5.7 Effect of Cross-Member Height ...... 103 5.8 Summary ...... 105 6 SHEAR FRAME RESULTS AND STABILITY INDICES ...... 107 6.1 Introduction ...... 107 6.2 Shear Strength of Weak Layers Related to Density ...... 107

ix Table of Contents, continued 6.3 Shear Strength of Weak Layers Related to Hand Hardness ...... 114 6.4 Characteristics of Persistent Slab Avalanches ...... 116 6.5 Predicting Natural Avalanches on Test Slopes ...... 121 6.6 Predicting Natural Avalanches of Persistent Slabs on Surrounding Slopes. 125 6.7 Predicting Skier-Triggered Avalanches on Test Slopes ...... 138 6.8 A Skier Stability Index for Soft Slabs ...... 141 6.9 Predicting Skier-Triggered Avalanches on Surrounding Slopes ...... 147 6.10 Summary ...... 156 7 RUTSCHBLOCK RESULTS ...... 159 7.1 Introduction ...... 159 7.2 Site Selection and Rutschblock Variability on Test Slopes ...... 159 7.3 Rutschblocks on Skier-Tested Avalanche Slopes ...... 169

7.4 Relationship Between Rutschblock Scores and SK from Adjacent Shear Frame Tests ...... 173 7.5 Estimating Daniels Strength from Rutschblock Scores ...... 178 7.6 Relating Rutschblock Scores to Skier-Triggered Dry Slabs in Surrounding Terrain ...... 180 7.7 Summary ...... 182 8 FALSE STABLE PREDICTIONS ...... 185 8.1 Introduction ...... 185 8.2 Case Studies ...... 185 8.3 Characteristics Associated with False Stable Predictions ...... 190

8.4 Remote Triggering and Transitional Stability for SK ...... 190 8.5 An Alternative Failure Mode for Primary Fractures ...... 191 8.6 Summary ...... 193 9 APPLICATIONS OF SHEAR FRAME STABILITY INDICES TO AVALANCHE FORECASTING ...... 195 9.1 Introduction ...... 195 9.2 Forecasting Variables for Natural Avalanches of Persistent Slabs ...... 198 9.3 A Multivariate Forecasting Model for Natural Avalanches Involving Persistent Slabs ...... 202 9.4 Forecasting Variables for Skier-Triggered Avalanches of Persistent Slabs .. 211

xi Table of Contents, concluded 9.5 A Multivariate Forecasting Model for Skier-Triggered Avalanches Involving Persistent Slabs ...... 214 9.6 Summary ...... 220 10 CONCLUSIONS ...... 223 10.1 Field and Finite Element Studies of the Shear Frame Test ...... 223 10.2 Shear Strength of Weak Layers ...... 225 10.3 Shear Frame Stability Indices ...... 225 10.4 Rutschblock Results ...... 227 10.5 False Stable Predictions ...... 228 11 RECOMMENDATIONS FOR FURTHER RESEARCH ...... 229 REFERENCES ...... 231 A ESTIMATING DENSITY FROM MICROSTRUCTURE ...... 247 A.1 Introduction ...... 247 A.2 Hand Hardness ...... 247 A.3 Mean Densities by Microstructure and Hand Hardness ...... 247 B ERROR ANALYSIS FOR STABILITY INDICES ...... 253 B.1 Sources of Variability ...... 253

B.2 Variability for Index SN ...... 254

B.3 Variability for Index SK ...... 255 C EXAMPLE OF FIELD NOTES ...... 257

xi LIST OF TABLES

No. Title Page 1.1 Forecasting Example Using Simplified Checklist ...... 14 2.1 Possibilities for Primary Fracture ...... 26 2.2 Field Studies of Shear Frame Stability Indices ...... 33 3.1 Study Sites and Locations ...... 48 3.2 Avalanche Size Classification ...... 63 4.1 Normality of Large Sets of Shear Frame Tests ...... 66 4.2 Number of Shear Frame Tests for Required Precision ...... 71 4.3 Assessment of Common Shapes of Fracture Surfaces ...... 72 4.4 Mean Shear Strength for Various Loading Times ...... 74 4.5 Effect of Test Sequence on Variability ...... 76 4.6 Effect of Delay on Shear Strength ...... 77 4.7 Effect of Frame Placement on Shear Strength ...... 78 4.8 Effect of Different Operators on Shear Strength ...... 80 4.9 Effect of Shear Frame Area on Mean Strength and Variance ...... 82 4.10 Effect of Normal Load on the Daniels Strength ...... 84 4.11 Shear Frame Specifications ...... 87 4.12 Effect of Shear Frame Design on Mean Strength ...... 89 5.1 Material Properties for Finite Element Model ...... 96 5.2 Finite Element Models of the Shear Frame Test ...... 96 6.1 Strength-Density Regressions by Microstructure ...... 109 6.2 Comparison of Avalanche Reports and Investigations from Columbia Mountains 1990-95 ...... 117 6.3 Characteristics of Investigated Dry Slab Avalanches from Columbia Mountains 1990-95 ...... 118 6.4 Percentage of Slabs that Failed for Skier Stability Indices ...... 145

7.1 Skier Stability Index SK from Shear Frame Tests Adjacent to Rutschblock Tests for Persistent and Non-Persistent Microstructures ...... 175

7.2 Skier Stability Index SK from Shear Frame Tests Adjacent to Rutschblock Tests on Slopes of at Least 20° ...... 177 7.3 Relative Frequency of Skier-Triggered Dry Slab Avalanches in Surrounding Terrain within one Day of Rutschblock Tests on Study Slope ... 181

xiii List of Tables, concluded 8.1 False Stable Predictions ...... 191 9.1 Spearman Rank Correlations Between Forecasting Variables and the Daily Maximum Size of Natural Avalanches Involving Persistent Slabs ...... 199 9.2 Classification Trees for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Purcell Mountains ...... 206 9.3 Contingency Table for Natural Slab Avalanches Involving Persistent Slabs in the Purcell Mountains ...... 207 9.4 Classification Trees for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Cariboos and Monashees ...... 209 9.5 Contingency Table for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Cariboo and Monashee Mountains ...... 210 9.6 Spearman Rank Correlations Between Forecasting Variables and the Daily Maximum Size of a Skier-Triggered Persistent Slab ...... 212 9.7 Classification Trees for Daily Maximum Size of Skier-Triggered Persistent Slabs in the Cariboos and Monashees, 1992-93 to 1994-95...... 216 9.8 Contingency Table for Daily Maximum Size of Skier-Triggered Persistent Slabs in Cariboo and Monashee Mountains, 1992-93 to 1994-95...... 217 9.9 Classification Trees Results for Daily Maximum Size of Skier-Triggered Persistent Slabs in the Purcell Mountains, 1992-93 to 1994-95...... 218 9.10 Contingency Table for Daily Maximum Size of Skier-Triggered Persistent Slab in Purcell Mountains, 1992-93 to 1994-95...... 220 A.1 Density of Layers Grouped by Hand Hardness and Microstructure ...... 248 A.2 Regression Parameters for Estimating Density from Resistance and Microstructure ...... 251

xiii LIST OF FIGURES

No. Title Page 1.1 Avalanche fatalities in Canada, 1980-1995...... 1 1.2 Surface hoar on tree and snow surface...... 4 1.3 Rounding metamorphism...... 5 1.4 Faceting metamorphism...... 6 1.5 Avalanche path consisting of start zone, track and runout...... 8 1.6 A point release avalanche...... 8 1.7 A small slab avalanche showing the crown fracture...... 9 1.8 Recently deposited snow layers including a thick weak layer of low density snow and a thin weak layer of surface hoar...... 9 1.9 Crown fracture showing failure plane of surface hoar at base of slab...... 10 1.10 Importance of forecasting data...... 13 1.11 Microstructure of failure plane for fatal slab avalanche accidents in Canada, 1972-91 ...... 18 1.12 Testing hand hardness during a snow profile observation...... 19 1.13 The shovel shear test used primarily to identify weak snowpack layers...... 20 1.14 Compression test...... 20 1.15 Shear frame test ...... 21 1.16 Rutschblock test showing displaced block...... 22 2.1 Slab nomenclature...... 26 2.2 Shear frame showing rear cross-member and two intermediate cross-members that distribute the load ...... 29 2.3 Underside view of finger-fin frame...... 30 2.4 Cross-section of slab showing location of peak shear stress induced by static skier...... 35

2.5 Avalanche activity and concurrent values of S35 from Cariboo and Monashee Mountains, 1990-92...... 38 2.6 Rutschblock test ...... 41 2.7 Percentage of slab avalanches and concurrent rutschblock scores ...... 42 2.8 Rutschkeil test ...... 42 2.9 Cord-cut rutschblock ...... 43 3.1 Location of study sites and mountain ranges...... 47

xv List of Figures, continued 3.2 Mt. St. Anne Study Plot at 1900 m in the Cariboo Mountains...... 49 3.3 Field staff approaching a small slab avalanche...... 50 3.4 Field staff approach a 1.6 m crown fracture for profiles and stability tests..... 51 3.5 Equipment used for shear frame tests and measurement of slab weight per unit area...... 52 3.6 Rutschblock saws...... 54 3.7 Shear frame test...... 56 3.8 Rutschblock isolated on the sides by shovelled trenches...... 57 3.9 Rutschblock isolated on the sides and upper wall by cord cutting...... 57 3.10 Rutschblock test showing displaced block...... 59 4.1 Shapiro-Wilk test for normality for 28 sets of shear frame data...... 67 4.2 Frequency distributions for 8 sets of shear frame tests for which p < 0.05 from Shapiro-Wilk test for normality...... 68 4.3 Frequency distribution for coefficients of variation of shear strength...... 70 4.4 Effect of loading time on shear strength for 10 experiments with various manual loading rates...... 74 4.5 Effect of sequence number on standard deviation...... 76 4.6 Effect of normal load on strength from previous studies...... 84 4.7 Measured and predicted effect of normal load on Daniels strength...... 85 4.8 Shear frames used for comparative studies of frame design and size effects...... 86 4.9 Twelve strength comparisons of short frame with standard frame...... 90 5.1 Geometry and loading for finite element model of standard shear frame placed 3 mm above weak layer...... 95 5.2 Finite element mesh for snow in left compartment and underlying weak layer and substratum ...... 98 σ 5.3 Stress contours for xz for standard frame placed in soft superstratum 3 mm above weak layer...... 99 σ 5.4 Shear stress XZ in weak layer for standard frame placed 3 mm above σ weak layer representing average XZ of 1.0 kPa...... 99 σ 5.5 Shear stress XZ in weak layer for standard frame placed in weak layer and 3 mm above weak layer...... 100 σ 5.6 Distribution of XZ for the standard frame placed in soft and hard superstrata. In both cases, the frame is 3 mm above the weak layer...... 101 List of Figures, continued

xv σ 5.7 Distribution of XZ for 5-cross-member and standard frame...... 102 σ 5.8 Distribution of XZ in weak layer for standard and short frames placed 3 mm above the weak layer...... 104 σ 5.9 Distribution of XZ in weak layer for standard and short frames placed 1 mm into the weak layer...... 104 6.1 Daniels strength for weak layers by microstructure and density...... 110 6.2 Normalized regression variance for Group I and II microstructures...... 111 6.3 Shear strengths from present study compared with those from Perla and others (1982) for four common microstructures...... 113 6.4 Shear strength by hand hardness for common microstructures...... 114 6.5 Shear strength plotted against scaled hand hardness for decomposed and fragmented particles and for faceted grains...... 116 6.6 Cross section of typical dry slab avalanches. Layer thicknesses are measured vertically...... 119 6.7 Relative frequency of microstructures for superstratum, weak layer and substratum of dry slab avalanches in Columbia Mountains, 1990-95...... 119 6.8 Resistance for superstratum, weak layer and substratum of dry slab avalanches in Columbia Mountains, 1990-95...... 121

6.9 Values of SN for slopes that did and did not avalanche naturally...... 122 6.10 Stability trend for natural avalanches on surface hoar buried 19 January 1993. in the Purcell Mountains...... 130 6.11 Stability trend for surface hoar layer in the Purcell Mountains buried 10 February 1993...... 131 6.12 Stability trend for a layer of surface hoar buried 6 February 1994 in the Purcell Mountains...... 132 6.13 Stability trend for a layer of surface hoar buried 29 December 1993 in the Cariboo and Monashee Mountains near Blue River, BC...... 133 6.14 Stability trend for a layer of surface hoar buried 5 February 1994 in the Cariboo and Monashee Mountains near Blue River, BC...... 134 6.15 Stability trend for a layer of surface hoar buried 7 January 1995 in the Cariboo and Monashee Mountains near Blue River, BC...... 135 6.16 Stability trend for a layer of facets formed in October 1993 in Jasper National Park...... 136 6.17 Stability trend for a layer of surface hoar buried 8 February 1994 in Jasper National Park...... 137

6.18 Stability index SS for skier-tested avalanche slopes...... 139 List of Figures, continued

xvii 6.19 Effect of ski penetration on skier-induced stress...... 142 6.20 Profiles of averaged densities for high and low density slabs from the Columbia Mountains...... 143 6.21 Skiing penetration for mean slab density and estimated density at 0.3 m . .... 144

6.22 Skier stability index SK for skier-tested avalanche slopes...... 146 6.23 Skier stability trend for surface hoar layer buried 18 January 1993 in the Purcell Mountains...... 149 6.24 Skier stability trend for surface hoar layer buried 10 February 1993 in the Purcell Mountains...... 149 6.25 Skier stability trend for surface hoar layer buried on 6 February 1994 in the Purcell Mountains...... 150 6.26 Skier stability trend for surface hoar layer buried 7 January 1995 in the Purcell Mountains...... 151 6.27 Skier stability trend for surface hoar layer buried 6 February 1995 in the Purcell Mountains...... 152 6.28 Skier stability trend for surface hoar layer buried 10 February 1993 in the Cariboos and Monashees near Blue River, BC...... 153 6.29 Skier stability trend for the surface hoar layer buried 29 December 1993 in the Cariboo and Monashee Mountains near Blue River, BC...... 154 6.30 Skier stability trend for the surface hoar layer buried 5 February 1994 in the Cariboo and Monashee Mountains near Blue River, BC...... 155 6.31 Skier stability trend for the surface hoar layer buried 7 January 1995 in the Cariboo and Monashee Mountains near Blue River, BC...... 156 7.1 Rutschblock scores from Mt. St. Anne in the Cariboo Mountains, east aspect, 1900 m on 13 February 1991...... 160 7.2 Rutschblock scores from a northwest facing slope in Miledge valley in Cariboo Mountains on 6 March 1991...... 161 7.3 Rutschblock scores from Mt. St. Anne in the Cariboo Mountains, north aspect, 1900 m on 6 April 1991...... 162 7.4 Rutschblock scores from a northeast-facing slope in Miledge valley in the Cariboo Mountains on 7 January 1992...... 163 7.5 Rutschblock scores from a north-facing slope in Miledge valley in the Cariboo Mountains on 19 January 1992...... 164 7.6 Rutschblock scores from a north-facing slope in Miledge valley in the Cariboo Mountains on 3 February 1992...... 165

xvii List of Figures, continued 7.7 Rutschblock scores on Mt. St. Anne in the Cariboo Mountains, northeast aspect, 1900 m on 29 February 1992...... 166 7.8 Rutschblock scores on a northeast-facing slope in the Monashee Mountains on 31 March 1992...... 167 7.9 Rutschblock scores on a northeast-facing slope in the Monashee Mountains on 7 April 1992...... 168 7.10 Relative frequency of skier-triggered slabs on skier-tested avalanche slopes from Föhn (1987b) and present study...... 170 7.11 Relative frequency of skier-triggering for persistent and non-persistent slabs on skier-tested avalanche slopes...... 171 7.12 Slab thicknesses of persistent and non-persistent skier-tested slabs...... 173

7.13 Normalized deviations of SK from mean values for particular rutschblock scores...... 176 7.14 Mean, standard deviation and standard error for median rutschblock scores from adjacent tests...... 178 7.15 Daniels strengths estimated from rutschblock scores plotted against measured Daniels strengths from adjacent shear frame tests...... 179 7.16 Relative frequency of one or more skier-triggered avalanches in surrounding terrain within one day of study-slope rutschblock results ...... 182 8.1 Cross-section of test site, crown fracture and bed surface at slab avalanche on Mt. Albreda in the Monashee Mountains ...... 186 8.2 Remotely triggered slab avalanche in the Purcell Mountains on 24 February 1994...... 188 8.3 Cross-sections of snowpack at trigger point, profile site on propagation path and crown for a remotely triggered slab avalanche ...... 188 8.4 Cracks in bed surface at Whistler Mountain, February 1979...... 193 9.1 Box plots of the daily maximum size of natural avalanche involving a persistent slab against various forecasting variables ...... 201 9.2 Classification tree for daily maximum size of natural avalanches of persistent slabs in the Purcell Mountains using forecasting variables but

excluding SN38...... 205 9.3 Classification tree for the daily maximum size of natural avalanches of persistent slabs in the Purcell Mountains based on data from the winters of 1992-93 to 1994-95...... 206 9.4 Classification tree for the daily maximum size of natural avalanches of persistent slabs in the Cariboo and Monashee Mountains based on 150 days from the winters of 1992-93 to 1994-95...... 210

xix List of Figures, concluded 9.5 Box plots of the daily maximum size of a skier-triggered persistent slab against various forecasting variables showing median (small rectangle), lower and upper quartiles (box) and minima and maxima (whiskers)...... 213 9.6 Classification tree for the daily maximum size of skier-triggered persistent slab in the Cariboo and Monashee Mountains based on data from the winters of 1992-93 to 1994-95...... 215 9.7 Classification tree for the daily maximum size of skier-triggered persistent slabs in the Purcell Mountains using meteorological forecasting

variables but excluding SK38...... 218 9.8 Classification tree for the daily maximum size of skier-triggered persistent slabs in the Purcell Mountains using meteorological forecasting

variables and including SK38...... 219 A.1 Density by hand hardness for six common classes of microstructure...... 249 C.1 Example of field notes for profile, shear frame tests and rutschblock test. .... 258

xix LIST OF SYMBOLS

α angle between snow surface and peak shear stress due to skier, etc. max λ fractional settlement φ normal load adjustment for shear strength ρ average slab density ρ 0 estimated snow density at surface ρ 30 estimated snow density at 0.30 m below surface ρ density of ice (917 kg/m3) ice σ stress σ V vertical stress due to overburden σ XZ shear stress parallel to snow surface ∆σ XZ shear stress parallel to snow surface due to artificial load such as a skier ∆σ 'XZ shear stress parallel to snow surface due to a skier, adjusted for ski penetration σ ZZ normal stress perpendicular to snow surface Σ shear strength Σ 2 100 shear strength measured with a 0.01 m shear frame Σ 2 250 shear strength measured with a 0.025 m shear frame

Σφ shear strength adjusted for normal load

Σ∞ Daniels strength (shear strength of an arbitrarily large specimen) * Σ∞ Daniels strength estimated from rutschblock score Ψ angle between snow surface and horizontal

A, a, B empirical constants b shear frame width d shear frame depth df degrees of freedom D difference in strength measurements F F statistic g acceleration due gravity (9.81 m/s2) h slab thickness (measured vertically) List of Symbols, continued

xxi hSZ slab thickness in start zone HN height of snowfall between consecutive morning weather observations HNW water equivalent of height of precipitation (ran and snowfall) between consecutive morning weather observations HS height of snowpack (measured vertically) HST height of storm snowfall (measured vertically) HSTW water equivalent of height of presipitation during storm L line load due to skier MN1 size class of largest natural slab avalanche from previous day MN2 sum of size classes of largest natural slab avalanche from previous two days MS1 size class of largest skier-triggered slab avalanche from previous day MS2 sum of size classes of largest skier-triggered slab avalanche from previous two days MxN size class of largest natural slab avalanche on forecast day MxS size class of largest skier-triggered slab avalanche on forecast day n, N number of data p probability associated with a statistic, significance level P precision expressed as a fraction of the mean PB barometric pressure PF foot penetration

PK average of ski penetration while standing and after two jumps on same spot, estiamte of maximum penetration of skis during skiing r correlation coefficient R Spearman rank correlation coefficient R2 coefficient of determination RH relative humidity s standard deviation se standard error (standard deviation of the mean) S stability index for natural slab avalanches calculated for a specific start zone, includes frame size adjustment and normal load adjustment for granular snow

S35 stability index for natural slab avalanches calculated for 35° slopes, includes frame size adjustment and normal load adjustment for granular snow S' stability index for slab avalanches triggered by a skier, etc., includes frame size adjustment and normal load adjustment for granular snow List of Symbols, concluded

xxi SN stability index for natural avalanches calculated for a specific start zone, includes frame size adjustment and normal load adjustment for granular snow

SN38 stability index for natural slab avalanches calculated for 38° slopes, includes frame size adjustment and microstructure-dependent effect of normal load on weak layer

SK stability index for skier-triggered slab avalanches calculated for specific start zone, includes adjustments for ski penetration, frame size and microstructure-dependent effect of normal load on weak layer

SK* mean value of SK for a particular rutschblock score

SK38 stability index for skier-triggered slab avalanches calculated for 38° slopes, includes adjustments for ski penetration, frame size and microstructure- dependent effect of normal load on weak layer t students t-statistic T classification tree T' classification sub-tree Ta air temperature at time of weather observation Tmin minimum air temperature in 24 hours prior to morning weather observation Tmax maximum air temperature in 24 hours prior to morning weather observation u standard normal variable v vertical co-ordinate measured downwards from snow surface V coefficient of variation w distance between shear frame cross-members x downslope co-ordinate (parallel to snow surface) y cross-slope co-ordinate z slope-perpendicular co-ordinate measured downwards from snow surface

xxiii 1 1 INTRODUCTION 1.1 Effects of Avalanches

In Canada, most avalanches have no effect on people, structures or roads. The vast majority start in the backcountry without human involvement and come to rest without encountering people or human artefacts. Only when avalanches have the potential to affect people, structures or transportation facilities is there a hazard. Avalanches and closures for avalanche control delay traffic on highways and the cost of such delays is substantial. Morrall and Abdelwahab (1992) estimate the cost of a two hour closure at Rogers Pass at $50,000 to $90,000 depending on the proportion of heavy vehicles in a traffic volume of 350 vehicles/h in each direction. Blattenberger and Fowles (1995) estimate the cost of a one day closure of the Little Cottonwood Highway in Utah at US$1,410,370. The annual cost of traffic delays due to avalanche hazards far exceeds the cost of property damaged by avalanches which averaged less than $350,000 per year in Canada during the period 1970 to 1985 (Schaerer, 1987, p. 6). During the years 1972 to 1995, avalanche fatalities in Canada averaged eight per year and increased gradually as indicated by the five-year moving average in Figure 1.1. This dissertation focuses on predicting avalanche hazards to backcountry recreationists who account for approximately 96% of the 127 fatalities in Figure 1.1, the remainder occurring in residential areas or transportation Figure 1.1 Avalanche Fatalities in Canada, 1980-1995. corridors. (Schaerer, 1987; Canadian Avalanche Centre) 2 1.2 Avalanche Hazard Mitigation

Avalanche hazards to structures, dwellings and transportation corridors are often mitigated by zoning—placing the elements at risk in zones where avalanche return intervals are acceptably long or expected impact pressures are sufficiently small. When this is not adequate, the hazard can be further mitigated by supporting structures in avalanche start zones designed to prevent most avalanches from starting, costing approximately $1,000,000 per hectare (Mears, 1992, p. 44-45) and used mainly in Europe where population centres occur in mountain areas and in Japan where use of explosives is very restricted, defence structures usually designed to divert avalanches, such as splitting wedges, diversion berms and snow-sheds over highways or rail lines, or to slow avalanches, such as retarding mounds (McClung and Schaerer, 1993, p. 225-234), and avalanche forecasting and control programs often involving closures of affected areas during which avalanches are released by explosives. In Canada, diversion berms are used for some minor highways but major reinforced concrete defence structures such as snow-sheds are only economically justifiable for major highways such as the Trans-Canada Highway through Rogers Pass. Avalanche forecasting and control programs for transportation corridors typically close the corridor for periods of less than a few hours during which unstable snow is released with explosives, often delivered from helicopters or from road level with artillery. Roads with low traffic volumes sometimes remain closed for a day or more while storm snow stabilizes naturally, or control teams wait for suitable weather before placing explosives from helicopters. Avalanche hazards to lift-based ski areas are also managed with forecasting and control programs. When control is deemed necessary by the forecaster, many areas are stabilized with explosives before the ski area opens for the day; other areas may remain closed for part or all of the day while slopes are stabilized. Explosives are often placed from the ground or a helicopter, or by an “avalauncher” which uses pressurized gas, a 3 pressure vessel and barrel to propel explosives to avalanche start zones usually less than 1 km away. Backcountry recreational operations including helicopter skiing, snowcat skiing and ski touring manage avalanche hazards primarily by avoiding terrain where and when hazardous avalanches are probable. Since such operations use vast mountain areas (1,000-6,000 km2), explosives are not used, or are limited to testing for unstable snow and to stabilizing a few selected slopes. When large avalanches are not expected, selected slopes are often test-skied by ski guides, releasing unstable snow as small avalanches. In Canada, avalanche forecasting is common to hazard management programs for railways, highways, lift-based ski areas, commercial backcountry recreational operations and parks. Avalanche forecasting is introduced in Section 1.7 following sections on the mountain snowpack, snow metamorphism, weak snow layers and failure of snow slopes.

1.3 Mountain Snowpack

Snow crystals form in the atmosphere either by sublimation of water vapour, initially onto small particles (freezing nuclei), and/or by accretion of super-cooled water droplets (rime). Variations in temperature and supersatuation within the atmosphere result in different shapes of crystals which, when precipitated, are often recognizable as different layers of precipitation particles (Class PP). Stellar crystals with six arms are a common form. When rime obscures the original form of precipitation particles, the resulting grains are called graupel. When not broken by wind, precipitation particles are often 1-6 mm in length or diameter. When first deposited, dry layers of unbroken crystals typically have a density of 40-120 kg/m3. Alternatively, turbulence may fragment the crystals and deposit very fine particles (< 1 mm) into relatively dense layers (> 140 kg/m3). During generally clear weather, water vapour may sublime as surface hoar (frost) directly onto objects and the snow surface (Figure 1.2). When buried by subsequent snowfalls, layers of surface hoar sometimes remain weak for a month or more, often

This dissertation uses the classification of the Canadian Avalanche Association (CAA, 1995) which closely follows the definitions of Colbeck and others (1990). 4 playing an important role in avalanche formation. The properties of new snow layers vary over mountain terrain. A particular snow storm may deposit a dry layer at higher elevations and a wet layer at lower elevations where the ambient temperature was warmer. Commonly, more snow falls at higher elevations than at lower elevations. Alternatively, a single snow storm may deposit a denser wind-packed layer at higher elevations than at lower elevations where calmer conditions prevailed. Further, wind may deposit little or no snow on windward slopes (and sometimes remove previously deposited snow from windward slopes), depositing much of the Figure 1.2 Surface hoar on tree and snow surface. snow on leeward slopes.

1.4 Snow Metamorphism

Once on the ground, the properties of snow layers change over time, partly reflecting changes in microstructure which consists of ice grains and bonds between them. There are three main metamorphic processes that change the microstructure, and consequently, the mechanical properties of layers: rounding and faceting which occur in 5 dry snow (≤ 0°C) and melt-freeze metamorphism that occurs when the snow temperature cycles above and below 0°C.

1.4.1 Rounding In the absence of a sufficiently strong temperature gradient, particles reduce their specific surface, primarily by ice-to-vapour-to-ice sublimation and evolve toward more rounded equilibrium forms (Colbeck, 1983). Precipitation particles with initial dendritic forms decompose into smaller particles (Figure 1.3), followed by the growth of the larger particles at the expense of the smaller particles which disappear over time. Typically, particle Figure 1.3 Rounding metamorphism. Water convexities suffer a net loss of mass vapour sublimates as ice onto concave surfaces resulting in intergranular bonds and eventually and concavities a net gain. Since in rounded equilibrium forms. contact points between grains are effectively concavities, bonds grow between grains resulting in strengthening of the layer. Layer density also increases. Although this is a dry snow process (≤ 0°C), the metamorphic rate increases with temperature. In the seasonal snowpack, rounded grains (Class RG) are usually 0.2-1.0 mm in diameter. At an intermediate stage when the precipitation particles are still recognizable (Figure 1.3), the particles are called partly decomposed (Colbeck and others, 1990). Such particles are grouped with wind-broken particles into a class called decomposing and fragmented precipitation particles (Class DF). 6

1.4.2 Faceting (Kinetic Growth) Driven by a sufficiently strong temperature gradient, there is a net directional flow of water vapour, usually upwards since many layers are warmer on top (Figure 1.4). Under these conditions, ice generally sublimates from the top of a crystal and water vapour deposits as ice on the bottom of a crystal above. Larger grains grow at the expense of smaller grains. At the intermediate stage when flat (faceted) faces but no striations are apparent, the grains are called faceted crystals (Class FC). In the seasonal snowpack, faceted Figure 1.4 Faceting metamorphism. crystals are typically 0.5-2 mm in size, although The transfer of water vapour under a smaller faceted crystals may form near the snow sufficiently strong temperature gradient results in the progressive surface (Colbeck and others, 1990). shape changes. When kinetic growth continues, depth hoar (Class DH) consisting of striated crystals and subsequently skeletal forms including cup-, column- and plate-shaped crystals are apparent (Akitaya, 1974). Crystals are often 2-6 mm in length and may exceed 10 mm. Prior to the formation of skeletal forms, strength usually decreases (Akitaya, 1974; Bradley and others, 1977a, b; Adams and Brown, 1982; Armstrong, 1980, 1981) except for relatively dense layers (> 300 kg/m3) (Akitaya, 1974; Perla and Ommanney, 1985). The advanced skeletal forms are often stronger than the non-skeletal, striated forms. The temperature gradient is increased and hence the faceting process is augmented adjacent to layers of low permeability such as crusts (Seligman, 1936, p.70; Adams and Brown, 1982; Moore, 1982; Colbeck, 1991).

1.4.3 Melt-freeze A snow layer at 0°C may contain liquid water due to melting or rain. Under such conditions, small grains disappear, larger grains grow rapidly until they reach 1-2 mm, 7 bonding and strength decrease, and density decreases (Male, 1980). Commonly, draining limits the liquid water content to approximately 8%. Under these conditions, the grains arrange into clusters held together by surface tension of the liquid water. Regardless of the liquid content, once wet snow layers freeze, they strengthen and form crusts. Since the present study is entirely restricted to dry snow, only the crusts are of interest.

1.4.4 Effect of Temperature Gradient on the Strength of Dry Snowpacks Rounding and faceting processes compete in dry snow layers, and layers showing evidence of both processes are common. Faceting dominates if the temperature gradient exceeds a critical level and rounding dominates below this level (de Quervain, 1958). Although field workers often use 10°C/m as a rough estimate of the critical temperature gradient (Armstrong, 1981, Colbeck, 1983), it varies considerably and is affected by the temperature, density and permeability (Armstrong, 1980, 1981; Perla and Ommanney, 1985). A positive temperature gradient (warmer above) is caused by diurnal warming, a warm front or warm snow falling on a cooler snow surface. However, during much of the winter in western Canada, positive temperature gradients are usually restricted to surface layers and are replaced by a negative gradient (cooler above), sometimes within a few hours and almost always within a few days, due to the upward flow of heat from the ground toward the cooler snow surface. Also, where the snowpack thickness exceeds 1 m, the ground-snow interface stays close to 0°C in temperate latitudes. To consider the effect of temperature gradient and snow metamorphism on the strength of snow layers, generalizations are necessary. Assuming an air temperature below freezing, the magnitude of the average temperature gradient through the snowpack is increased where the snowpack thickness is reduced, or when the air temperature is reduced. In areas where the snowpack thickness is less than 1 m and the air temperature is less than -10°C for an extended period, faceting often dominates and weak layers are common. These conditions occur during early and mid-winter in many areas of the Rocky Mountains, and in isolated areas of the Columbia Mountains, such as where the wind has reduced the snowpack thickness. Alternatively, in most areas of the Columbia Mountains 8 where the snowpack thickness typically exceeds 2 m during mid-winter, rounding dominates, causing most layers to strengthen. During warmer weather in the spring, rounding and melt-freeze processes affect most layers in both ranges. The rounding process tends to strengthen and stabilize the weak layers that formed during the winter. Melt-freeze cycles alternately weaken and strengthen layers, often diurnally.

1.5 Failure of Snow Slopes

Many, but not all, avalanche paths can be divided into a start zone where avalanches Figure 1.5 Avalanche path consisting initiate, a track where only a few small avalanches of start zone, track and runout. stop, and a runout zone where the larger avalanches decelerate (Figure 1.5). Avalanches release from snow slopes in two distinct ways. When a small amount of cohesionless snow—typically the size of a snowball—slips and begins to slide down a slope setting additional snow in motion, it is called a point release or loose snow avalanche (Figure 1.6). Alternatively, when a plate or slab of cohesive snow begins to slide as a unit before breaking up, it is called a slab avalanche (Figure 1.7). Following a slab avalanche, a distinct fracture line or crown fracture is visible at the top of the avalanche. Slab avalanches will only occur when there is a weak layer under the cohesive layers that make up the slab. Slab avalanches, which are Figure 1.6 A point release avalanche. 9 generally larger than point release avalanches, are the focus of this study. Natural avalanches start without any human-related trigger such as a skier, hiker, explosive, over-snow vehicle, etc. Avalanches triggered by the fall of a cornice—a sometimes massive chunk of wind-packed snow from a Figure 1.7 A small slab avalanche showing the crown fracture. ridge top—are not considered natural avalanches in this dissertation as in NRCC/CAA (1989) since cornice falls are often more powerful than many human-related triggers. Only natural and skier-triggered avalanches are considered.

1.6 Weak Snowpack Layers

In Canada, most fatalities are caused by dry slab avalanches (Jamieson and Johnston, 1992a), and the failures that release such avalanches start and propagate in weak layers (e.g. McClung, 1987). Identifying weak layers (Figure 1.8) is fundamental to identifying unstable slabs Figure 1.8 Recently deposited snow layers including a so that they can be avoided. thick weak layer of low density snow and a thin weak layer of surface hoar. 10 Since weak layers are common in the Rocky Mountains throughout much of the winter, the snowpack is generally less stable than in the Columbia Mountains (where most of the commercial backcountry skiing in western Canada occurs). Weak layers can either be precipitated, form on or near the snowpack surface as surface hoar or faceted crystals, or form at depth as faceted crystals or depth hoar. Precipitated weak layers usually consist of large stellar-, needle-, or plate-shaped crystals, which may remain weaker and lower in density than adjacent layers during the early stages of rounding (Figure 1.8). Such weak layers generally stabilize within a few days of deposition and are subsequently termed non-persistent. While such layers were the failure plane for some fatal avalanches involving amateur decision-makers with widely varying levels of avalanche skills, Jamieson and Johnston (1992a) found no reports of fatal avalanches involving such layers where professionals made the decisions regarding access to avalanche terrain. In general, professionals have the techniques and experience to manage avalanche hazards due to non-persistent weak layers. Cooling periods as short as a single cold, clear night can produce weak layers on and near the snow surface. Strong near-surface temperature gradients due to such cooling can cause small faceted crystals to grow within the top 20 mm of the snowpack. In areas with little or no wind, surface hoar crystals can grow on the snow surface. Layers of surface hoar and/or faceted crystals that form near the surface are important in the present study since, when buried by subsequent snowfalls, they can remain weak (persist) sometimes for a month or more, and form the failure plane for some slab avalanches (Figure 1.9). Since these weak layers form on the surface, they can be identified by the date they were buried. Prolonged periods of cold Figure 1.9 Crown fracture showing failure plane weather, especially where the of surface hoar at base of slab. 11 snowpack is relatively thin, can create thick layers of depth hoar and faceted crystals. Since this faceting process is faster at the base of the snowpack where the snow temperature is generally warmer, depth hoar is most common at, but not restricted to, the base of the snowpack. Weak layers of surface hoar, faceted crystals and depth hoar are termed persistent weak layers. They accounted for the majority of avalanche fatalities in Canada from 1972 to 1992 (Jamieson and Johnston, 1992a). The thickness of a weak layer plays an important role in slab failure. In Bader and Salm’s (1990) slab failure model, the shear strain rates necessary for propagation are only possible where strain is concentrated in thin weak layers. This is supported by an extensive field study in Switzerland, where 60% of weaknesses that failed in slab avalanches or stability tests were so thin they were classified as weak interfaces, and the remaining 40% averaged 11 mm in thickness (Föhn, 1993). While these studies do not preclude an important role for thick weak layers, they emphasize that slab failures often start in weak layers so thin that they may be difficult to observe in the snowpack.

1.7 Avalanche Forecasting

Avalanche forecasts refer to the likelihood and size of avalanches, usually in terms of avalanche hazard, avalanche danger or snow stability for areas of terrain that vary from an entire mountain range to a specific slope. Since forecasts are constantly being refined, the temporal extent of the forecast is usually limited. In Canada, large-scale forecasts for a mountain range (bulletins) are usually valid for 1-7 days “unless conditions change”. Rather than attempt to predict the likelihood of avalanches following a change in weather, forecasters prefer to issue a new bulletin or advisory. For backcountry and lift-based skiing operations, the forecasts, often called snow stability evaluations, are prepared each morning. Avalanche forecasting is inherently multivariate. Atwater (1954) proposed a list of 10 factors, some of which are quantifiable such as snowfall depth, precipitation rate and air temperature, and some qualitative factors such as the character of the snow surface 12 prior to the storm. The exact list of factors has evolved (e.g. CAA, 1994) and varies according to the type of forecasting operation, be it a highway, lift-based ski area or backcountry program, and with the individual forecaster (LaChapelle, 1980). However, the factors can be grouped by the entropy (or noise or disorder) of the information. Avalanche activity and stability tests are low entropy information since they pertain directly to slope stability; snowpack observations such as profiles identifying snow layers are medium entropy information; and weather measurements that are less directly related to slope stability are high entropy information (LaChapelle, 1980). These groups are also called Class 1, 2 and 3, respectively (McClung and Schaerer, 1993, p. 124). The importance of forecasting data depends not only on its entropy, but also on how far from the relevant terrain it was obtained (Figure 1.10). In Canada, meteorological measurements are available from other avalanche safety operations in the same range, perhaps 100 or more km away, by an evening exchange of weather, snowpack and avalanche information, a weather station often within 10 to 100 km, and sometimes from a regularly accessed study site with basic weather instruments within 10 km of the relevant start zones. In addition to weather measurements, snowpack observations, stability tests and reports of avalanche activity are exchanged every evening between approximately 50 different forecasting operations in western Canada. Further, each operation records snowpack observations, stability tests and avalanche activity within their forecast area daily. However, backcountry operations and lift-based ski areas generally access study sites and start zones more frequently than highway forecasting operations, particularly those highway operations in the Coast mountains where short-term weather trends often have a dominant effect on avalanche activity. Terrain plays an important role in avalanche forecasting. Mesoscale avalanche forecasts for areas typically 10-100 km across, such as parks, summarize avalanche conditions with general reference to terrain inclination, elevation and orientation to wind or sun. Forecasts for lift-based ski areas and highways are concerned with specific start 13

Figure 1.10 Importance of forecasting data increases with proximity to forecast area and with decreasing entropy of information. The present study concentrates on stability tests in study sites and start zones. zones. Backcountry skiing operations must select terrain on the microscale with due consideration to local terrain features since the distance between safe and unsafe terrain may be less than 50 m. Such precise terrain selection is the most detailed application of the same information also used by other forecasting operations. However, while local terrain features complicate site selection and interpretation for snowpack observations and stability tests (Chapters 7 and 8), terrain features on the same scale can be used advantageously by ski guides to select safe routes. As shown in Figure 1.10, a simple snowpack observation in or near an avalanche start zone such as noting that a weak layer exists 0.4 m below the surface can be more important than an accurate measurement of wind speed or precipitation from a weather station 10 km away. Consider the following simplified example of the forecasting process for a backcountry skiing operation, based loosely on the Canadian Avalanche Association’s 14 Table 1.1 Forecasting Example Using Simplified Checklist Factor Data Stability? Import- Confid- ance? ence? I Avalanche Activity and Stability Tests Yesterday, many slopes were Avalanche skier-tested. Two small slabs were N High High Activity skier-triggered, 1 on a NE-facing slope near treeline and 1 on a N-facing slope above treeline. A stability test resulted in a “moderate” Stability Tests failure1 on a layer of surface hoar N High Low 0.4 m below the surface near tree line on an E-facing slope. II Snowpack Observations A layer of 4 mm surface hoar found Profile 0.3 m below surface in study plot N High High profile. Overall hardness2 of slab has increased in last 2 days. Settlement 0.33 m of snow from the last storm has ? High High settled to 0.30 m in the last 2 days Temperature buried surface hoar is at -5°C ? Low Mod. Temp. Gradient approximately -5°C/m in slab N High Mod. Snowpack Height 1.80 m in study plot ? Low High II Meteorological Observations Precipitation None in last 2 days Y Low High Precipitation Rate nil Y Low High Wind Speed averaged 20 km/h last night, no Y High Low noticeable drifting Wind Direction West ? Low Low Air Temperature Yesterday’s max. temp. was -12°C, ? Mod. High overnight min. temp. was -19°C Weather Forecast Warming to -5°C N High Mod. 3-5 cm of snow starting this afternoon Y High Low 1 “Moderate” manual force was required to induce failure. Stability tests are described further in Section 1.11. 2 Hardness is assessed on an ordinal scale outlined in Appendix A. The hardness of a layer or slab is relevant in various ways. It is relevant in this example because harder slabs tend to result in wider and often larger avalanches. 15 stability evaluation checklist (CAA, 1994) . In the morning, the forecaster makes abbreviated notes of the relevant data for avalanche activity and stability tests (Class I data), snowpack observations (Class II data) and meteorological observations (Class III data) as in column two of Table 1.1. The forecaster would then mark a “Y” for the factors that are contributing to stability, an “N” for the factors that are contributing to instability and a “?” for factors with unclear or mixed effects. In this case, the lack of precipitation in the last two days and the wind which was too light to cause drifting favour stability, whereas limited avalanche activity (two small skier-triggered slabs), a stability test that failed on a surface hoar layer, a profile in a study plot that found the surface hoar under a stiffening slab, and forecast warming above the maximum temperature of the previous day are indicating instability. Although the labelling of contributions to stability or instability is simplistic, the primary value of such a checklist is in ensuring that the forecaster reviews and assesses the various factors. Forecasters then consider the importance of the various factors (low, moderate or high in Column 4 of Table 1.1) for the planned skiing and the type of avalanche activity expected. Usually informally, forecasters also assess their confidence in the factors (low, moderate or high in Column 5 of Table 1.1). Factors in which the forecaster has high confidence in the observations and considers important are used to select skiing terrain for the day; in this case the avalanche activity, the profile and the forecast warming would probably lead the forecaster to exclude large avalanche slopes above and below treeline. If there are important factors for which the forecaster has little confidence in the available observations, the terrain selection might be even more restricted and the forecaster would specify field tests and observations for field work during the day to improve confidence in some of the important factors. In this example, the forecaster can do little about the lack of confidence in the amount of forecast snowfall, but concerns about drifting might be reduced by observations from a ridge-top and/or helicopter during the day, and additional profiles and stability tests near and above tree-line might be assigned to the technicians and guides to better determine where the buried layer of surface hoar exists. Since surface hoar 16 is more common in sheltered areas below tree-line than above, further field work might find suitable areas above tree-line for skiing on subsequent days. Finally, forecasters might identify the conditions that would cause them to re-assess the forecast. For example, a forecaster might ask the technicians to report back if natural avalanches or substantial drifting are observed. In this example, the forecaster's request for additional data, especially snowpack and stability tests in and near avalanche start zones illustrates the fact that forecasts are iterative and are constantly being refined (LaChapelle, 1980). Also, snow stability—even in this simplified example—cannot be separated from terrain parameters such as the direction a slope faces (aspect) or elevation band (above or below tree-line). Some observations such as the “moderate” shear on surface hoar help the forecaster build an intuitive, deterministic model; others such as wind direction pertain to the spatial distribution of snowpack properties (Buser and others, 1985).

1.8 Computer Assisted Forecasting

Avalanche forecasting models may be either based on rules developed by experts (e.g. Giraud, 1993; Schweizer and Föhn, 1995) or based on data. Data-based models include discriminant analysis (Judson and Erikson, 1973; Bovis, 1977; Obled and Good, 1980), time series analysis (Salway, 1976), nearest-neighbours (Buser, 1983; Buser and others, 1985; Buser, 1989; McClung and Tweedy, 1994; Kristensen and Larsson, 1995; Blattenberger and Fowles, 1995), ordinary and logistic regression (Blattenberger and Fowles, 1995), neural networks (Schweizer and others, 1994; Stephens and others, 1995) or classification trees (Davis and others, 1993; Boyne and Williams, 1993; Davis and Elder, 1994, 1995). Nearest neighbour models compare recent values of a set of meteorological and snowpack variables with the values of the variables on past days within the data base. The avalanche activity on days with similar conditions (nearest neighbours) can be used to estimate a probability of avalanching. However, in operational testing, forecasters show less interest in the probability and more interest in the avalanche activity on days with 17 similar conditions (Buser, 1983). Specifically, a nearest neighbour model might identify that present conditions are similar to some avalanche conditions that occurred prior to the forecaster’s employment in the area. By assessing avalanche activity on similar days, forecasters can anticipate avalanche activity by size, aspect and elevation using their experience. Nearest neighbour models have been successfully tested in forecasting operations in Switzerland (Buser, 1989) and Canada (McClung and Tweedy, 1994). A related non-parametric method, the classification tree algorithm, uses past data to build a hierarchy (or tree) of two-way decisions involving the forecasting factors. The terminal nodes (or leaves) of the tree are the predicted levels of avalanche activity. Classification trees are used in Chapter 9. Non-parametric methods work with a mix of quantitative and qualitative data, do not require normalizing transformations of non-normal data, and are sensitive to non-monotonic relations between the forecasting variables and avalanche activity variable. In contrast to data-based models, knowledge-based models (expert systems) do not require an extensive data set. After interviewing experts, rules are constructed to reflect their logic (McClung, 1995). Such systems can use both qualitative data such as the character of the snow surface prior to the recent storm and quantitative data such as meteorological variables. A recent expert system (Schweizer and Föhn, 1995), correctly estimated the level of avalanche danger on a 7-level scale in the Alps near Davos on 73% of days during the three winters, and was within one level of the verified avalanche danger on 98% of days. This dissertation focuses not on forecasting models but on stability indices for both terrain-selection decisions and mesoscale forecasts. Such indices can be incorporated into data-based models once there are sufficient data, or into knowledge-based models.

1.9 Atypical Snowpack Characteristics of Accident Avalanches

Based on reports of fatal avalanches in Canada between 1972 and 1991, Jamieson and Johnston (1992a) estimate that 99% were slab avalanches, 87% were dry, and 93% were triggered by people, mostly skiers. These characteristics are reflected in the present 18

Figure 1.11 Microstructure of failure plane for fatal slab avalanche accidents in Canada, 1972-91 (Jamieson and Johnston, 1992a). The pie charts are based on 34 of 45 accidents with amateur decision-makers and 16 of 17 with professional decision-makers for which the failure plane was reported.

study which is restricted to dry slab avalanches and emphasizes skier-triggered avalanches over naturally occurring avalanches. Although most slab avalanches start in weak layers consisting of precipitation particles or partly decomposed precipitation particles, most fatal avalanches start in weak layers with persistent forms such as surface hoar (Figure 1.11), faceted crystals and depth hoar. Such crystals are slow to change shape and gain strength when subjected to rounding metamorphism. As a consequence of their persistence, they remain weak when deeply buried by subsequent snowfalls, and their failures result in thick—often large—slab avalanches.

1.10 Skier-Triggering of Persistent Weak Layers

In a laboratory study of shear strength under various constant strain rates, the ductile-brittle transition for manufactured depth hoar was between 8 x 10-5 and 2 x 10-4 s-1 (Fukuzawa and Narita, 1993). In a similar study of rounded grains, the ductile-brittle transition was 4 x 10-4 to 8 x 10-4 s-1 (Narita and others, 1992). This implies that rounded grains can be sheared 4 to 5 times faster than depth hoar before brittle fracture. Since 19 skiers are believed to directly trigger brittle failure (Schweizer and others, 1995), depth hoar which exhibits brittle failure for a wider range of strain rates is more sensitive to skier-triggering than rounded grains. Although there are no published laboratory or field studies for shear tests of surface hoar, a ductile-brittle transition similar to that of depth hoar and consequent sensitivity to skier-triggering are expected.

1.11 Snow Profiles and Snowpack Tests

This section introduces the snow profile and four snow pack tests commonly used in Canada and elsewhere. The last two tests described, namely, the shear frame test and the rutschblock test, are the focus of this dissertation

1.11.1 Snow Profile The snow profile is a systematic observation of snowpack layers (CAA, 1995) made in a pit dug where the snowpack was undisturbed. Identification of weak layers is a primary objective of snow profiles. The information recorded for each layer commonly includes grain type and size (microstructure), resistance to penetration, liquid water content and density, along with a temperature profile. “Hand hardness” is a simple and widely used measure of resistance to penetration (Figure 1.12, Appendix A). Interpretation of snow profiles requires training and experience. Mechanical tests such as the shovel test (Figure 1.13) and Figure 1.12 Testing hand hardness during a snow profile observation. Ruler is used to identify position and thickness compression test of layers. Thermometers are used to measure snow surface (Figure 1.14) are often the temperature in shade and a temperature profile through the snowpack. In this photo, snowpack layers were revealed by final stage of a profile. See brushing. (M. Shubin photo) 20 CAA (1995) for a detailed descriptions of these tests.

1.11.2 Shovel Shear Test For the shovel test, slope-parallel manual force is applied to a shovel placed behind a column of snow and progressively increased to apply shear stress to the weak layers (Figure 1.13). Failures more than 0.2-0.3 m below the bottom of the shovel blade are more likely due to bending rather than to shear (Schaerer, 1989, 1991; CAA, 1995). Although the force required to cause planar failures 0.2 m or less below the bottom of the shovel are rated “very

Figure 1.13 The shovel shear test used primarily to identify weak snowpack layers. (J. Hughes photo)

easy”, “easy”, “moderate” or “hard”, the test is used primarily to identify weak snowpack layers rather than to quantify their strength. The force rating cannot be directly related to avalanching since it does not consider the downslope shear stress due to the weight of the slab on slopes or due to other triggers such as skiers.

1.11.3 Compression Test For the compression test (Figure 1.14),

Figure 1.14 Compression test. Failures a sequence of vertical blows of increasing force are visible on the smooth walls of the is applied by the hand to a shovel blade placed column. (J. Hughes photo) 21 on top of a column of snow and the force required to cause visible failure is rated “very easy”, “easy”, “moderate” or “hard”. Experience in the Canadian Rocky Mountains suggests that increased tapping force correlates with decreased slab avalanching due to triggers such as skiers or explosives (CAA, 1995).

1.11.4 Shear Frame Test Various shear frame tests have been used in Switzerland and Canada since the 1960’s (Roch, 1966a, b; Schleiss and Schleiss, 1970). After the weak layer to be tested has been identified in a profile or by another snowpack test, overlying snow is carefully removed to within 15-50 mm of the weak layer (Figure 1.15). A sheet metal frame, usually slightly trapezoidal and usually with two or more intermediate cross-members is placed in the snow above the weak layer so that the lower edge of the frame is close to—typically 0-10 mm above—the weak layer to be tested. Commonly, the operator slides a blade around the frame to make sure that the frame is not adhering to the surrounding snow. A force gauge that records the maximum force is attached to a hook or cord on the front of the frame and manual force is applied to cause a shear failure in the weak layer. Details of the technique are described in Section 3.3. The shear strength, obtained by dividing the maximum force recorded by the

Figure 1.15 Shear frame test. (J. Hughes photo) 22 gauge by the area of the frame, is used in various formulas for stability indices which are summarized in Section 2.4.

1.11.5 Rutschblock Test The rutschblock (“glide” block) test is a slope stability test first used by the Swiss army to find weak snowpack layers (Föhn, 1987b). On an undisturbed slope preferably inclined at 25° or steeper, a column of snow 2 m wide (across the slope) and 1.5 m down-slope is isolated from the surrounding snowpack by shovelling or cutting with a cord, saw or tail of a ski (Figure 1.16). The block is progressively loaded in seven steps by a skier as described in Section 3.6. The rutschblock score is simply the loading step (1-7) at which a weak layer in the column fails, allowing the upper portion of the column (the Figure 1.16 Rutschblock test showing displaced block. (M. Shubin photo) block) to displace downslope. Further details on the rutschblock technique and method of scoring are described in Section 3.3.

1.12 Objective and Outline

The objectives of this dissertation are: to improve shear frame stability indices, and to investigate the merit of shear frame stability indices and rutschblock scores for assessing the stability of slabs overlying persistent weak layers which cause most fatal avalanches in Canada. 23 Although naturally occurring slabs are considered, the emphasis is on skier-triggered slabs, which are the primary concern in backcountry skiing. Chapter 2 reviews relevant literature on the rutschblock and shear frame tests and on shear frame stability indices. Chapter 3 describes the shear frame and rutschblock testing techniques. Field and finite element studies of the shear frame test are summarized in Chapters 4 and 5, respectively. Chapter 6 summarizes the results of field studies relating shear frame stability indices from avalanche start zones and safe study sites to avalanche activity. Similar field studies relating rutschblock results to avalanche activity are presented in Chapter 7. Case studies of 5 skier-triggered avalanches at which the shear frame stability index for skier triggering and/or the rutschblock test incorrectly indicated stability are presented in Chapter 8, and used to draw conclusions about the limitations of stability tests and about primary failures on shallow slopes. Chapter 9 develops multivariate forecasting models based on classification trees to assess whether shear frame stability indices and rutschblock scores can improve forecasting based on meteorological variables alone. The conclusions and recommendations are presented in Chapters 10 and 11, respectively. 24

25 2 LITERATURE REVIEW 2.1 Introduction

This dissertation focuses on shear frame stability indices and rutschblock tests for assessing the stability of dry slabs overlying persistent weak snowpack layers, with an emphasis on skier-triggered slabs. Before reviewing research on these stability tests, slab failure models are summarized in Section 2.2 and the effects of shear frame size, design and normal load on shear strength are reviewed in Section 2.3. Two types of shear frame stability indices are considered: slope-specific stability indices obtained using shear frame tests on avalanche slopes which assess the stability of the tested slope (Section 2.4), and extrapolated stability indices obtained at safe study sites (level or sloping) which assess avalanche activity in surrounding terrain (Section 2.5). While the site-specific stability indices have been used by researchers to assess the predictive value of the indices and spatial variability of stability within avalanche start zones (Section 2.6), extrapolated stability indices are used for operational forecasting and are undergoing refinement by researchers. Research on the rutschblock test technique and assessments of correlations with avalanche activity are reviewed in Section 2.7.

2.2 Slab Failure

Before a slab can release as an avalanche, fractures must occur in the weak layer at the base of the slab and around the slab at the crown, flanks and stauchwall (Figure 2.1). Bucher (1948) proposed that the primary failure that initiates avalanche release could start in four different ways as summarized in Table 2.1. Failure could occur in any of these locations whenever stress exceeds strength. Until 1970, opinions of researchers varied regarding which of the four cases in Table 2.1 was most common, and consequently most important. Haefeli (1963, 1967) emphasized crown tension fracture (Case 3) but did not verify his hypothesis with field

26

Table 2.1 Possibilities for Primary Fracture (Bucher, 1948) Case Location Fracture Associated Conditions 1 central area of slab shear in weak layer “loose” weak layers or surface (neutral zone) hoar 2 central area of slab compression at base of depth hoar at base of snowpack (neutral zone) snowpack 3 crown region tension through slab fresh storm snow (slab boundary) 4 flank region shear through slab infrequent (slab boundary)

data. Bradley (1966) and Bradley and Bowles (1967) focused on compressive failures of thick layers of depth hoar (Case 2). Bradley and Bowles (1967) provided limited field data to support a correlation between the ratio of resistance-to-vertical-penetration to vertical stress due to slab weight and avalanching initiated by the collapse of thick depth hoar layers in a Continental snowpack, similar to that of the Canadian Rocky Mountains. Roch (1966a) emphasized basal shear failure (Case 1) and supporting field data are discussed in Section 2.3. In a variation of Case 1, Perla and LaChapelle (1970) argued that the first fracture was in tension at the crown but that the tensile stress at the crown was caused by a loss of shear support (ductile failure) in the weak layer. This emphasis on ductile Figure 2.1 Perspective diagram showing slab nomenclature, shear failure was orthogonal axes for x, y and z co-ordinates, slope inclination from supported by the horizontal, Ψ, and slab thickness, h, measured vertically.

27 McClung’s (1977, 1979) laboratory studies of snow under slow shear deformation. Recent slab failure models (McClung, 1981, 1987; Bader and Salm, 1990) have focused on shear failure and propagation within the weak layer at the base of the slab (Case 1). Although research has not proven that primary tensile fracture at the crown (Case 3) and primary shear fracture at a flank (Case 4) do not occur, such methods of initiating slab failure lack supporting field data and have not attracted recent interest. The primary compressive failures reported by Bradley and Bowles (1967) and field workers in areas with depth hoar layers may not be in conflict with the model of shear failure and propagation within weak layers developed by Bader and Salm (1990). Their model requires high shear stress concentrations and high shear strain rates which are more likely in thin weak layers and at interfaces than in thick weak layers associated with primary compressive failures by Bradley (1966) and Bradley and Bowles (1967). Further, reports of substrata consisting of relatively weak depth hoar (that did not release) extending to the crown fracture (T. Auger, personal communication) suggest that, regardless of the character of the primary failure, the subsequent fracture propagates along the interface. Current research on slab failure and field studies of stability indices, including this dissertation, are based on primary shear failure of the weak layer (Case 1). Primary compressive failures are revisited in Chapters 7 and 8, for areas with thick layers of depth hoar, and on shallow slopes where compressive stress exceeds shear stress.

2.3 Shear Frame

Shear frames have become the most common device for testing the shear strength of weak snowpack weak layers. An alternative, the rotary shear vane similar to that used for testing soils has been used to test homogeneous snow layers (Keeler and Weeks, 1967; Martinelli, 1971; Perla and others, 1982; Brun and Rey, 1987). The shear vane test is faster than the shear frame test since it can be pushed into the snow with a shaft and hence does not require removal of most of the snow above the test layer. However, since the bottom of the vanes cannot be consistently positioned in or near thin weak layers, it was deemed unsuitable for the present study.

28

2.3.1 Shear Frame Size For many materials, mean strength decreases with the cross-sectional area or volume of the specimen since larger specimens can contain larger flaws (Griffith, 1920). For shear frame tests, the area of the fracture surface is equal to the area of the frame, and consequently a decrease in mean strength is expected with an increase in frame area. Roch (1966a, 1966b) introduced the shear frame for measuring the shear strength of weak snow layers. He used a frame with an area of 0.01 m2. Perla (1977) compared mean strengths from frames with areas of 0.01, 0.025, 0.05, 0.10 and 0.25 m2. In each of 7 comparisons based on 100 paired tests with frames of different areas, the larger frame gave a lower mean strength than the smaller frame. Stethem and Tweedy (1981) also found that a larger frame (0.025 m2) resulted in a lower mean strength compared to a smaller frame (0.01 m2). In four of five comparisons with frames ranging from 0.01 to 0.25 m2, Föhn (1987a) found mean strengths for the larger frame were lower than for the smaller frame. Sommerfeld (1973), Sommerfeld and others (1976), Sommerfeld and King (1979), and Sommerfeld (1980) proposed that size effects in shear frame tests could be explained by Daniels’ (1945) thread bundle statistics. Using this theory, Föhn (1987a) compiled his results with those of Perla (1977) and Sommerfeld (1980) to obtain a curve of correction factors. For frames larger than 0.3 m2, mean shear strengths asymptotically approached the strength of an arbitrarily large specimen. This asymptote, called the Daniels strength, can be obtained by multiplying the mean strength obtained with a particular area of frame by the appropriate correction factor. For frames with areas of 0.01, 0.025 and 0.05 m2, the correction factors are 0.56, 0.65 and 0.71 respectively (Sommerfeld, 1980; Föhn, 1987a). Although very large frames may seem advantageous, frames larger than 0.1 m2 are less practical because: the necessary manual pull forces cannot be applied consistently and smoothly by a single operator, curvature of thin weak layers which is common in avalanche starting zones makes aligning large frames more difficult, and

29 for shear frame tests on steep slopes, adjustments to the shear strength for the slope-parallel force due to the weight of the frame and snow in the frame would become increasingly important. Three sizes of smaller frames (0.01, 0.025 and 0.05 m2) are in use. Perla and Beck (1983), Sommerfeld (1984) and Jamieson and Johnston (1993a) prefer a 0.025 m2 frame. Föhn (1987a) prefers a 0.05 m2 frame and Schaerer (1991) prefers the 0.01 m2 frame used at Rogers Pass and Kootenay Pass. 2.3.2 Shear Frame Design To distribute the applied stress more evenly through the snow layer being tested, Roch’s (1966a) frame had two intermediate cross-members. The relatively rigid outer frame distributes the manually applied load onto the rear cross-member and the two intermediate cross-members. The lower tip of each of the active surfaces (cross-members) creates a shear stress concentration in the snow layer. Perla and Beck (1983) stated that the stress concentrations are influenced by the ratio of the height of the cross-member, d, to the length of the snow sub-specimen in front of the cross-member, w (Figure 2.2). In a field comparison, they decreased d/w from 0.75 to 0.37 by increasing the number of intermediate cross-members from 2 to 5 and found that mean strength measurement was reduced by 15%. Further, they stated that increasing d/w should increase the normal load (and hence increase the strength) and might contribute to disturbance of the weak layer when the frame is inserted (Perla and Beck, 1983). Roch’s (1966a) 0 .01 m2 frame had 3 active cross-members and a d/w ratio of Figure 2.2 Shear frame showing rear cross-member and two intermediate 0.75. Perla and Beck (1983) and cross-members that distribute the load.

30 Sommerfeld (1984) retained the slightly trapezoidal shape and three active cross-members but preferred frames with an area of 0.025 m2. Perla and Beck (1983) maintained the d/w ratio of 0.75 whereas Sommerfeld (1984) reduced the frame height to obtain a d/w ratio of 0.4. In contrast to the shear frames with compartments, Brown and Oakberg designed a frame which distributed the load more evenly using thirty-two 10 mm wide fins anchored to a plate on top of the 0.01 m2 shear frame shown in Figure 2.3 (Lang and others, 1985). The fins were approximately 10 mm apart and extended 17 mm down into the 25 mm high frame. Lang and others (1985) used the frame for five sets of 10 tests on a particular surface hoar layer that ranged in strength from 0.03 to 0.35 kPa over a 40 day period, but reported that the surface hoar layer was sometimes too weak to test. Maximum variability Figure 2.3 Underside view of finger-fin frame. Load is distributed onto 32 finger-fins, each extending 17 mm was reported to be less than into the 25 mm high frame. 0.20 kPa for 10 tests on the same day. No comparison of this frame with conventional compartmental frames was found in the literature. Föhn (1987a) used a 0.05 m2 frame with cross-members and a d/w ratio of 0.64. This “Swiss” frame is constructed of 1.5 mm stainless steel and is four times as heavy as the 0.025 m2 frame adopted as a standard for the present study. Using compartmental frames, Perla and Beck (1983) report an increase in strength with frame weight. No comparison of the Swiss frame with other frames was found in the literature.

31 Field comparisons between various frames, including those that varied in cross-member height and spacing between cross-members, are presented in Chapter 4. Finite element studies of shear stress for various frame designs are presented in Chapter 5.

2.3.3 Effect of Normal Load on Shear Strength The shear strength of granular materials generally increases with normal load. For failures due to yielding, a linear increase with normal load is commonly modelled with the Mohr-Coloumb failure criteria (Holtz and Kovacs, 1981, p. 453.). However, since most shear frame tests are pulled fast enough to cause brittle fractures (Section 4.5), a linear Mohr-Coloumb effect should not be assumed (de Montmollin, 1982). To assess the effect of normal load on shear strength, Roch (1966b) experimented with weights placed on top of shear frames. He measured an increase in shear strength with an increase in the normal load. Perla and Beck (1983) also reported an increase in shear strength with frame weight but questioned whether this normal load effect was due to “internal friction”, an inertial effect associated with the rapid pull on the frame, or ploughing of the weighted frame in the substratum. Assuming the normal load effect was due to internal friction, φ, Roch (1966a, b) expressed the adjusted shear strength as Σ Σ + σ φ φ = ZZ (2.1) where the shear strength, Σ, is the maximum pull force divided by the area of the shear ρ frame and the normal stress on the weak layer due to the slab of density, , slab thickness, h (measured vertically) on a slope of inclination, Ψ, is σ ρ 2Ψ ZZ = gh cos (2.2) Roch (1966b) found that the internal friction term φ depended on strength and 2 Σ microstructure. Using a 0.01 m frame to obtain a strength, 100, he determined empirical formulas for φ for several different microstructures φ Σ , σ ) Σ σ fresh snow ( 100 ΖΖ = 0.1 + 0.08 100 + 0.04 ZZ (2.3a) φ Σ , σ ) Σ rounded grains ( 100 ΖΖ = 0.4 + 0.08 100 (2.3b) φ Σ , σ ) Σ σ facets and depth hoar ( 100 ΖΖ = 0.8 + 0.08 100 - 0.01 ZZ (2.3c).

32 Perla and Beck (1983) argued that the normal adjustment was not “crucial” since the coefficient for the correlation between their unadjusted stability index (Section 2.5) σ and the normal load ZZ was only r = -0.44 for 23 slab avalanches. However, the significance of this correlation is p < 0.04 indicating that the correction for normal load may have merit. Field data and analysis of normal load effects from the present study are presented in Section 4.11. 2.4 Slope-Specific Stability Indices

Field studies of stability indices obtained from shear frame tests at avalanche start zones and assessed using the avalanche activity of those start zones are reviewed in this section. The indices vary depending on whether they include stress due to artificial triggers in the denominator, and adjust for normal load due to the slab, or the size of the frames (Table 2.2). Assuming that most slab failures start with shear failure of the weak layer, Roch (1966a) began field studies of slab stability based on a stability index Σ100 +σzz φ(Σ100, σzz) SRoch = (2.4) σxz σ where XZ is the shear stress in the weak layer due to the weight of the overlying slab. From statics, the shear stress due to the slab (Figure 2.1) is σ ρ Ψ Ψ XZ = gh sin cos (2.5)

Near 35 avalanches, Roch (1966a) found that the index SRoch ranged from 0.76 to 7.5, averaged 2.05 and had a standard deviation of 1.20. (He believed that when slopes

avalanched with SRoch > 2, the primary fractures must have been tensile fractures at the crown—exceptions to the more common shear failures within weak layers.) However,

Roch did not compare values of SRoch from slopes that had avalanched with slopes that had not. Also, although he reported the trigger for each of the avalanches, he did not separate the 24 naturally triggered avalanches from the 11 artificially triggered avalanches in his analysis, even though the denominator of the strength/stress index (Eq. 2.4) did not include the superimposed stress of artificial triggers such as skiers or explosives.

33

Table 2.2 Field Studies of Shear Frame Stability Indices Study True Adjust for Adjust for Include Artificial Index Size Effects Normal Load Stress Slope-Specific Stability Indices Roch (1966a, b) Y N Y3 N Perla (1977) Y N2 N2 N Sommerfeld and King (1979) Y Y N N Conway and Abrahamson YN Y N (1984) Föhn (1987a) Y Y Y3 Y Conway and Abrahamson YN Y Y (1988) Föhn (1989) Y Y Y3 Y Jamieson and Johnston YY Y3 Y (1995a) Extrapolated Stability Indices1 Schleiss and Schleiss (1970) N N N N Stethem and Tweedy (1981) N N2 NN2 Jamieson and Johnston YY Y3 natural av. only (1993) Jamieson and Johnston YY Y3 Y (1995a) 1 Study relates stability parameter from shear frame tests at safe study site to avalanche activity in surrounding terrain. 2 Effect studied but not incorporated into stability index/ratio. 3 Applied normal load adjustment for granular snow to weak layers with various microstructures.

2 Σ Using a 0.025 m shear frame to obtain a measure of shear strength, 250, Perla Σ /σ (1977) used the ratio 250 XZ (without the normal load correction) for field studies of slab stability. For 80 slab avalanches, the ratio ranged from 0.19 to 6.4, averaged 1.66 and had a standard deviation of 0.98. He believed that the large standard deviation cast doubt on the usefulness of the ratio for stability evaluation. However, Perla did not compare values

34 Σ /σ of 250 XZ on slopes that had avalanched with values on slopes that had not, and did not report the type of trigger for the avalanches. On eight slopes that had recently avalanched, Sommerfeld and King (1979) measured the shear strength of the failure plane with a 0.025 m2 frame. They adjusted the Σ shear strength (without the normal load correction) 250 for size effects to obtain the

Daniels strength of an arbitrarily large specimen, Σ∞. Remarkably, in five of the eight Σ /σ cases, the ratio ∞ XZ was between 0.97 and 1.04. However, in the remaining three cases, the ratios were 0.83, 1.68 and 2.47. Further, they only tested eight slopes, and did not include the stress due to skiers or explosives in the stress term (denominator of stability index) although two of the slopes were triggered by skiers and three were triggered by explosives. Conway and Abrahamson (1984) used a different technique for their shear frame tests. Working on avalanche slopes, they isolated a vertical column of snow and embedded the shear frame on top of the column, which in some cases extended over 1 m above the weak layer. While this technique includes the inherent effect of normal load on the weak layer and is independent of shear frame size, pulling the frame downslope superimposes substantial bending stress on the shear stress in the weak layer. Eight slabs that avalanched yielded stability indices that averaged 1.57 with a standard deviation of 1.29 in contrast to 18 slabs that did not avalanche where the stability index averaged 4.25 with a standard deviation of 2.78. This is the first comparison of stability indices on slopes that did and did not avalanche, and the results indicate the merit of stability indices for discriminating between stable and unstable slopes, despite the effect that bending may have had on the results. Föhn (1987a) combined Roch’s (1966a, b) normal load adjustment with Sommerfeld and King’s (1979) size correction to obtain a stability index for natural avalanches Σ∞ +σ φ S = zz (2.6) σxz ∆σ and added the term XZ for the artificially induced stress into the denominator of Equation 2.6 to obtain an index for artificially triggered avalanches

35 Σ∞ +σ φ S = zz (2.7) σxz +∆σxz By assuming isotropy and linear elastic behaviour and ignoring deviatoric stress gradients, ∆σ Föhn derived formulas for estimating XZ for a walker, a skier, a “snowcat” and a 1 kg Ψ ∆σ explosive. For a skier on a slab of thickness h on a slope of inclination , XZ is 2L cos α sin α2 sin(α +Ψ) ∆σ = max max max (2.8) xz πh cosΨ α where L is the line load due to a skier (500 N/m) and max is the angle from the snow surface to the peak shear stress (Figure 2.4) tabulated by Föhn (1987a) for common values Ψ ∆σ of . For a skier on a 38° slope, XZ simplifies to 0.14/h kPa where h is in m. Föhn’s ∆σ (1987a) formula for XZ, the slope-parallel static stress induced by a skier, was verified by Schweizer’s (1993) finite element model and approximately by field measurements. Using a load cell buried at various depths between 0.1 and 0.6 m under a level snow surface, Schweizer and others (1995) showed that calculated normal stress due to a static skier agreed well with the normal stress generated by skiers pushing vertically downwards with their legs. Also, Schweizer and others (1994) showed that the stress on the load cell depended on the properties of the slab, a factor that is ignored in analytical formulas for skier induced stress used by Föhn (1987a) and Jamieson and Johnston (1995a). Using S for natural avalanches and S' for slabs triggered mainly by skiers or explosions, Föhn rated the combined “success” of S and S' for discriminating between snow slopes that had, and had not avalanched. S or S' is rated successful where the index is less Figure 2.4 Cross-section of slab showing location than 1 and the slab released, or is of peak shear stress induced by static skier.

36 greater than 1.5 where the slab did not release. Values of S or S' between 1 and 1.5 were considered to indicate transitional stability and were excluded from the success score. The success score for S combined with S' for 110 avalanche slopes was 75% (Föhn 1987a). Since avalanche forecasting typically relies on at least 10 factors (Section 1.7), a single variable capable of predicting the stability of 75% of avalanche slopes is promising. Föhn (1987a) along with Roch (1966a) and Jamieson and Johnston (1993a, 1995a) applied Roch’s normal load correction for granular snow (Eq. 2.3b) to all weak layers, independent of their microstructure. To account for the fact that skis penetrate into soft snow, often by as much as 0.3-0.5 m, thereby decreasing the distance from the skis to the weak layer and increasing the skier-induced stress, Jamieson and Johnston (1995a) adjusted Föhn’s (1987a)

skier-stability index S' to allow for ski penetration to obtain SK and related it to avalanche activity on persistent weak layers. Based on an additional winter of field data since submission of Jamieson and Johnston (1995a), this adjustment is refined in Chapter 6 and the refined index is assessed using a larger set of avalanche data. While the ability of slope-specific stability indices to discriminate between stable and unstable slopes has been established (Conway and Abrahamson, 1984; Föhn, 1987a, Jamieson and Johnston, 1995a), most avalanche forecasting and control programs do not have the resources to do shear frame tests in more than 1 or 2 avalanche start zones—and it is not always safe to do so. Consequently, the application of shear frame results to such operations requires that stability indices be extrapolated to surrounding terrain from shear frame tests at sites that are generally safe to access.

2.5 Extrapolated Stability Indices

While a slope-specific stability index depends on the slope inclination of the start zone, an extrapolated stability index intended as a predictor of avalanche activity in surrounding terrain should apply to start zones with various slope inclinations. Either the index can be calculated for a minimum or average inclination, or the trigonometric functions of slope inclination can be dropped, resulting in an expression of the form

37 Σ/ρgh—which is the ratio of slope-parallel shear strength to vertical stress due to the weight of the slab. Historically, this ratio has been called the stability factor (Schleiss and Schleiss, 1970; Salway, 1976; Stethem and Tweedy, 1981; NRCC/CAA, 1989; Jamieson and Johnston, 1993a). However, since Σ/ρgh is not a stability factor or stability index as defined in some engineering texts, the Canadian Avalanche Association now refers to Σ/ρgh as the Stability Ratio (CAA, 1995). Jamieson and Johnston (1993a) showed that when stability indices such as Föhn’s S are calculated for a constant slope angle, they are approximately proportional to ratios of the form Σ/ρgh. Consequently, ratios of the form Σ/ρgh are included as shear frame stability indices in this study. Since 1963, the avalanche control program for the Trans-Canada Highway through Σ ρ Σ Rogers Pass has used ratio 100/ gh, where 100 is the shear strength measured with a 0.01 m2 frame, as an index of stability for avalanche paths that can affect the highway (D. Skjönsberg, personal communication). Schleiss and Schleiss (1970) report that snow Σ ρ stability in nearby start zones is critical when the ratio 100/ gh (measured in a level study plot) is less than 1.5. Further south in the Selkirk Mountains, the avalanche control program for the highway through Kootenay Pass uses the same ratio and critical level (J. Tweedy, personal communication). Σ ρ Σ ρ Stethem and Tweedy (1981) report 100/ gh and 250/ gh values of 0.97 and 1.02, respectively, measured in a level study plot near the time that natural avalanches released, and 1.87 and 1.29, respectively, when avalanches were artificially triggered. The higher values for artificially triggered slabs supports the use of a term for artificially induced stress in the denominator of stability indices, the magnitude of which will depend on the type of trigger (skier, explosive, etc.). To extrapolate from representative study slopes to surrounding avalanche slopes,

Jamieson and Johnston (1993a) calculated S35 which is simply Föhn’s S (Eq. 2.6) calculated for a 35o slope, an inclination typical of many avalanche starting zones. Based on 70 test days over three winters in the Cariboo and Monashee Mountains (Fig. 2.5),

Jamieson and Johnston chose the critical value of S35 empirically, weighting days with dry slab avalanches more than days without such avalanches. Transitional stability was defined

38

Figure 2.5 Avalanche activity and concurrent values of S35 from Cariboo and Monashee Mountains, 1990-92. (After Jamieson and Johnston, 1993a) Only class 1.5 and larger natural avalanches (CAA, 1995) are included since smaller natural avalanches are not reported consistently, and do not pose a serious threat to skiers.

as the band of S35 values within ±10% of the critical value. S35 scored a success when one

or more dry natural slab avalanches were reported with 15 km of the study site and S35

was below the transition band, or no dry slab avalanches were reported and S35 was above

the transition band. Based on this criterion, S35 correctly predicted avalanche activity on

75-87% of the 70 test days, depending on whether S35 was measured at a level plot or an inclined study slope, and whether natural dry slab avalanches with estimated dates were

included or excluded. For S35 measured in a level study plot, the avalanche activity, including avalanches with estimated dates, is shown in Figure 2.5. Most of the failure planes for the avalanches in this study were within the more

recent storm snow. S35 has not been assessed for the deeper, more persistent weak layers typical of most fatal avalanches. Also, Jamieson and Johnston applied Roch’s normal load correction for granular snow (Eq. 2.3b) to all weak layers, independent of their microstructure. Jamieson and Johnston (1995a) used Ψ = 35° in the equation for the slope specific

equation, SK, (Section 2.4) to obtain an extrapolated index for skier stability, SK35. A

39 refinement denoted by SK38 which differs from SK35 in slope inclination and normal load adjustment based on recent studies in the Columbia Mountains (Section 4.11), is assessed using a larger data set than previously available in Chapter 6.

2.6 Flaws in Weak Layers and Spatial Variability of Stability Indices

Snowpack properties, including the mechanical properties of weak layers, vary within avalanche start zones. For natural avalanches that release under their own weight, Bader and Salm (1990) argued that the critical shear strain rate for propagation could only be achieved at flaws in weak layers with insufficient shear strength to resist the shear stress of the overlying slabs. Such flaws have been called shear bands, slip bands, or slip surfaces (Palmer and Rice, 1973; Rice, 1973, Singh, 1980; McClung, 1981; McClung, 1987), deficit zones (Conway and Abrahamson, 1984) and super-weak zones (Bader and Salm, 1990). Most of the theoretical models of snow-slab failure (Singh, 1980; McClung 1981; McClung, 1987) are based on fracture mechanical models for clay slab failures (Palmer and Rice, 1973; Rice, 1973). According to the analytical and finite element model of Bader and Salm (1990), super-weak (deficit) zones can grow over periods of up to 60 minutes prior to reaching a critical size (5-30 metres in downslope length) beyond which brittle fractures release the slab. If super-weak zones can exist for such periods of time, then field tests of snow stability may, potentially, verify the theory. Based on shear frame tests spaced along a 15 m wide part of a crown, Conway and Abrahamson (1984) report that their stability index varied from < 1 to 3.6. Also, for shear frame tests down a 50 m long portion of a flank at a second avalanche, the index varied from < 1 to 2.3. Shear frame tests for which the weak layer fractured before the pull could be applied were assigned a stability index < 1 whereas Föhn (1989) (and presumably other authors) rejected tests involving “pre-fractures”. Conway and Abrahamson used stability indices with values < 1 as evidence of super-weak (deficit) zones, although such results only occurred where the weak layer fractured before the pull was applied to the frame (Föhn, 1989).

40 In a subsequent study of 5 slopes, Conway and Abrahamson (1988) used Vanmarke statistics to determine a probability distribution for the super-weak areas of five slopes, four of which avalanched and one which fractured locally. Since each of the slopes had a 95% probability of including a deficit zone at least 2.9 m long, they concluded that small deficit zones could determine the stability of avalanche slopes. Föhn (1989) countered this idea by pointing out that greater variability for stability indices—due to the presence of super-weak zones—than for other snowpack properties has not been detected, neither his nor Conway and Abrahamson’s (1984, 1988) data provide evidence of deficit areas for natural avalanches (S < 1) if specimens that fractured before the frame was pulled are rejected, small deficit zones for artificial triggers (S′ < 1) exist on slopes that could not be triggered, and stability tests at a single point in an avalanche start zone have proven to be useful indications of stability and this would not be true if small deficit zones determine the stability of avalanche slopes. Also, Jamieson and Johnston (1995a) report that 17 of 23 (83%) slopes on which

SK < 1 were skier triggered, and 14 of 17 (72%) slopes on which SK > 1.5 were not skier-triggered. It is unlikely that stability tests from a single pit (area 2 m2) in an avalanche start zone (area 100-20,000 m2) could have such predictive value if small deficit zones determine stability. Additional field data to support the merit of tests for skier-stability at a single location in an avalanche slope are presented in Chapters 6 and 7. Also, the spatial variability of stability tests for skiers is documented for 9 slopes in Chapter 7. However, no field study of natural avalanches has disproven Bader and Salm’s (1990) assertion that shear strain rates necessary for propagation can only be achieved at the stress concentration around super-weak (deficit) zones. On the other hand, there is no field evidence that super-weak zones can gradually grow in length to over 10 m during periods of up to 60 minutes as calculated by Bader and Salm (1990). However, the fact

41 that skiers can produce dynamic stresses in weak layers comparable to the static stresses due to the weight of the slab and to the shear strength of weak layers, indicates that super-weak zones are not necessary for skier-triggering (Schweizer and others, 1995). Figure 2.6 Rutschblock test. 2.7 Rutschblock

The rutschblock test (Figure 2.6) is a slope stability test first used by the Swiss army to find weak snowpack layers (Föhn, 1987b). Unlike the shear frame test, it does not require extensive training or specialized equipment such as force gauges. The lower wall of the column is exposed by digging a pit in the snowpack. The sides and upper wall can be isolated from the surrounding snowpack by shovelling, cutting with cords, skis, or large saws. The block is loaded in seven steps by a skier. The rutschblock score is simply the loading step at which a weak layer in the column fails, allowing the upper portion of the column (the block) to displace downslope. Further details on the rutschblock technique are presented in Section 3.3.2. Although the rutschblock test and variations of it have been promoted by earlier publications in German (e.g. Munter, 1973), its popularity in North America follows Föhn’s (1987b) paper in English. In a study involving rutschblock tests on 150 avalanche slopes, Föhn compared each of the seven rutschblock scores with the relative frequency of slab avalanches (Figure 2.7). The percentage of slab avalanches decreased with increasing rutschblock score. However, since 10-15% of the slopes with the highest rutschblock scores avalanched, the rutschblock test did not, by itself, indicate that a particular slope was stable. This limitation of the rutschblock test is, according to Föhn, due to imprecise site selection. Since rutschblock scores vary on any particular avalanche slope, one or two

42 tests may miss the least stable part of a slope. Föhn emphasized that factors such as snow profiles and weather must be used along with rutschblock tests to assess slab stability. Whitmore and others (1987) attempted to compare the rutschblock test to other “level-type tests” such as the shovel shear test. In 16 cases, individual rutschblocks were Figure 2.7 Percentage of slab avalanches and concurrent rutschblock scores (after Föhn, 1987b). compared with 1-4 level-type tests. There were insufficient data for conclusions since only 16 rutschblock tests were made and the rutschblock scores only varied from 5 to 7. Nevertheless, the authors did develop a preference for the rutschblock because of the variability of results of the lever-type tests. Munter (1991, p. 93-102) compared the rutschblock test to a variation with a wedge-shaped block called the rutschkeil (Figure 2.8). When a cord is used to cut the sides and upper wall, the rutschkeil test is usually faster than the rutschblock test. Munter also finds the rutschkeil “more sensitive” than the rutschblock since the block can be loaded more gently by a skier moving onto the block from the side, Figure 2.8 Rutschkeil test (after Munter, whereas the rutschblock requires a skier to 1991).

43 step down onto the block from above. However, this difference seems unimportant since both Munter (1991) and Föhn (1987a) considered the slope to be unstable whether the block moves before stepping onto the block or while stepping onto the block. One disadvantage of the rutschkeil test involves the variable area of the failure surface. Experience with wedge-shaped blocks during the winters of 1989-90 to 1990-91, shows that sometimes the whole wedge displaces indicating a shear failure over an area of 3 m2 and sometimes only the portion of the wedge downslope of the skier displaces indicating a shear failure over an area of approximately 1.8 m2 and a fracture of unknown character under the skis. (This problem is reduced for the rutschblock since the block is loaded closer to the upper wall.) Further, since the skis extend 0.1 to 0.2 m on both sides of the wedge, the skier load is carried partly by the wedge being tested and partly by the surrounding snowpack. Also, the portion of the skier load carried by the snow surrounding the wedge depends on factors unrelated to stability, including the compressibility of the snow and the length and stiffness of the skis. This problem and the variability of the area of the shear failure surface make the rutschkeil test less suited to research on snow stability than the rutschblock test. Munter (1991, p. 90) reported that a 5° decrease in slope inclination tends to increase the rutschkeil score by approximately one step, but did not provide supporting data. Although there are differences in the loading steps for the rutschkeil and rutschblock test, Jamieson and Johnston (1993b) provided field data and a simple numerical technique to indicate that a 10° decrease in slope inclination tends to Figure 2.9 Cord-cut rutschblock (after Jamieson and Johnston, 1993b).

44 increase the rutschblock score by one step. However, this general effect was only significant on 10 of 24 slopes, probably due to natural variability of snowpack properties and the non-linear increase in stress with rutschblock loading steps reported by Schweizer and others (1995). Jamieson and Johnston (1993b) found that the time required to perform a rutschblock could be reduced by approximately half by using a ski or specialized saw to cut the sides and upper wall of the rutschblock. Provided no knife-hard crusts exist in the slab to be cut, 4-6 mm knotted cords can also be used (Figure 2.9). Based on 21 comparisons between adjacent tests using these alternative block-cutting techniques, Jamieson and Johnston were unable to detect any significant effect of the block-cutting technique on the resulting rutschblock scores provided the width of the block flared as shown in Figure 2.9. In a study of 36-67 rutschblock scores on six uniform slopes that varied in slope inclination by less than 10°, Jamieson and Johnston (1993b) found that one rutschblock test has an approximately 67% probability of giving the median score for the slope and 97% probability of giving a score within 1 step of the slope median. The probability of the median score of 2 independent tests being within ½ step of the slope median is approximately 91%.

2.8 Summary

2.8.1 Slab Failure Most cases of snow slab failure begin with a shear failure within the layer or weak interface (e.g. McClung, 1987), although limited field data suggest that slab failure can also start with a compressive (collapse) failure where thick weak layers exist in the snowpack (Bradley and Bowles, 1967). For natural avalanches, shear failures start at flaws in weak layers, grow in a ductile manner (Bader and Salm, 1990) and propagate rapidly when they reach a downslope length of approximately 2-60 m. In contrast to natural avalanches, skiers can directly trigger brittle fractures in buried weak layers (Föhn, 1987a; Schweizer and others, 1995).

45

2.8.2 Shear Frame Sommerfeld (1980) and Föhn (1987a) determined correction factors for shear frames with areas in the practical range of 0.01 to 0.05 m2. These correction factors allow stability indices and associated critical values to be calculated and compared on the same basis regardless of the size of the frame employed to test the weak snow layer. However, mean strength determined with a shear frame is affected by the spacing between fins and perhaps by the height of the fins. Little is known about the effects of these design factors. Hence, present shear frame design is arbitrary rather than optimal. 2.8.3 Shear Frame Stability Indices The ability of shear frame stability indices (based on the ratio of shear strength to shear stress) to discriminate between stable and unstable slopes is evidence that slab failure frequently begins with shear failure within the tested weak layer. Since the shear frame stability indices rely on brittle failure of small specimens, whereas slab failure for natural avalanches begins with a ductile failure of a very large specimen, critical levels of such indices for natural avalanches must be determined empirically. Slope specific stability indices such as S and S' can discriminate between stability and instability for approximately 75% of avalanche slopes (Föhn, 1987a). Since most accident avalanches in Canada involve failure planes that consist of persistent grain structures, the critical levels of the stability indices for persistent snowpack weak layers should be determined. Extensive or frequent testing of avalanche start zones is impractical for most backcountry forecasting operations, so extrapolated (mesoscale) stability indices need to be calibrated for deeper layers involving persistent snowpack weaknesses.

46

2.8.4 Rutschblock Föhn (1987b) showed that slab avalanching becomes progressively less likely as scores from rutschblock tests on the avalanche slopes increase, and he proposed a practical interpretation of rutschblock scores. A correlation between rutschblock scores on safe study slopes and avalanche activity in surrounding terrain has not been established. Jamieson and Johnston (1993b) determined the precision of 1 or 2 rutschblock scores for a uniform slope, and showed that an increase in slope inclination of 10o tends to decrease the rutschblock score by 1 step. This allows rutschblock scores to be estimated for steeper avalanche starting zones from tests on less steep and safer sites nearby 47 3 METHODS 3.1 Study Areas and Co-operating Organizations

Persistent weak layers do not occur every winter in every mountain region. To ensure sufficient data were obtained and to ensure that the results would be widely applicable, eight locations in four different mountain ranges (Table 3.1, Figure 3.1) were selected in co-operation with participating private or public sector organizations. During the winters of 1992-93 to 1994-95, seasonal research technicians were based at Bobby Burns Lodge (operated by Canadian Mountain Holidays) and at Mike Wiegele Helicopter Skiing in Blue River, BC. The five public sector participants were Banff National Park (BNP), Jasper National Park (JNP), Glacier National Park (GNP), Yoho National Park (YNP) and BC Ministry of Transportation and Highways (MoTH) at Kootenay Pass. Wardens from the Banff, Jasper and Yoho National Parks, staff from Glacier National Park’s Snow Avalanche Warning Section (SRAWS) and avalanche technicians from Kootenay Pass made measurements approximately once per week during the winters of

1992-93 and 1993-94. Figure 3.1 Location of study sites and mountain ranges. 48

Table 3.1 Study Sites and Locations Location Main Study Sites Co-operating Organization Columbia Mountains Cariboo Mountains near Mt. St. Anne Mike Wiegele Blue River, BC Helicopter Skiing Monashee Mountains near Sams Mike Wiegele Blue River, BC. Helicopter Skiing Bobby Burns Mountains in Pygmy, Rocky, Elk, Canadian Mountain the Purcell Range near Vermont Holidays Parson, BC Rogers Pass in Selkirk Roundhill on Mt. Fidelity Glacier National Park, Mountains, BC Parks Canada Kootenay Pass in Selkirk East Peak B.C. Ministry of Mountains, BC Transportation and Highways Rocky Mountains Banff National Park, Bow Summit on Icefields Banff National Park, Alberta Parkway Parks Canada Jasper National Park, Parker’s Ridge on Icefields Jasper National Park, Alberta Parkway Parks Canada Yoho National Park, BC Schaffer Bowl, Lake Yoho National Park, O’Hara and Wapta Lake Parks Canada

The majority of the data were collected in the Cariboo and Monashee Mountains near Blue River, BC, the Purcell Mountains near Bobby Burns Lodge, and in the Selkirk Mountains near Rogers Pass and Kootenay Pass. These 4 ranges are part of the Columbia Mountains where the snowpack at tree line usually exceeds 2 m in thickness throughout the winter. Under these conditions, the average temperature gradient throughout the snowpack is sufficiently low that thick weak layers of depth hoar are rare. Persistent weak layers usually consist of surface hoar or faceted crystals. While buried layers of surface hoar are usually less than 15 mm in thickness, layers of faceted crystals sometimes exceed 0.5 m in thickness. As will be shown in Section 6.4, the weak layers that cause many slab 49 avalanches in the Columbia Mountains are less than 25 mm in thickness. Both natural and skier-triggered avalanches from the Columbia Mountains are used in this study. The balance of the data is from the Rocky Mountains where the snowpack at tree line usually averages 1-1.5 m during the winter. Thick weak layers of faceted crystals and depth hoar are common in the lower half of the snowpack during most winters. Almost all avalanche data from the Rocky Mountains used in this study are for natural avalanches.

3.2 Sites for Snowpack Tests

In this study and in most forecasting operations, snowpack observations and tests are made at avalanche start zones and at study sites. Level study sites are referred to as study plots. Study sites are generally not threatened by avalanches except, perhaps, under unusual conditions.

3.2.1 Study Plots and Slopes

Study sites are chosen in consultation with the co-operating organization (Table 3.1) to ensure that general snowpack conditions at the site are representative of the snowpack conditions common in surrounding avalanche terrain. Study sites are also chosen for their uniform snowpack, a consideration that precludes the use of sites subject to substantial amounts of drifting snow. This criterion results in a necessary difference between study sites which are generally sheltered from the wind, and start zones, many of which are exposed to drifting. A typical study plot is shown in Figure 3.2. Study sites are visited routinely, usually once or more Figure 3.2 Mt. St. Anne Study Plot at 1900 m in the Cariboo Mountains. per week, and the snowpack tests 50 are related to avalanche activity in surrounding terrain, including avalanche activity that may occur days after the visit to the study site.

3.2.2 Site Selection in Avalanche Start Zones Unlike study sites where snowpack tests are related to avalanche activity, often many km away, tests in avalanche start zones are only related to avalanche activity in the tested start zone. In avalanche start zones, snowpack tests are made at a site judged typical of the start zone. Figure 3.3 Field staff approaching a small slab avalanche in the Purcell Mountains. This site selection requires experience since the snowpack is usually more variable in avalanche start zones than in study sites. Also, tests are usually completed within an area of 2-4 m2 whereas start zones range in area from 100 to 20,000 m2. Site selection often includes probing to establish uniformity of depth and of major layers, and sometimes preliminary profiles of the snowpack to establish the extent of the weak layer. Snowpack tests are made after the slope has released naturally or been ski-tested. If a slab is successfully skier-triggered, then the area remaining for testing the undisturbed snowpack is reduced. In some instances, no area that is typical of the undisturbed snowpack remains after the avalanche. Field staff are shown approaching a small and large avalanche in Figures 3.3 and 3.4, respectively. 51

Figure 3.4 Field staff approach a 1.6 m crown fracture in the Cariboo Mountains for profiles and stability tests.

3.3 Equipment

Equipment used for shear frame tests is shown in Figure 3.5. The outer frame and intermediate fins of the shear frames consist of stainless steel or aluminium sheet metal. Most shear frames including the standard frames used for this study are a few mm wider at the front than at the back to reduce friction between the sides of the frame and adjacent snow. Following experimentation with different materials and construction techniques during 1990-92, the shear frames used from 1993-95 consisted of a stainless steel outer frame with 0.6 mm cross fins affixed with silver solder (Figure 3.5) . The lower edges of the frames were sharpened to reduce the force required to push the frame into the snow above the weak layer (superstratum) and consequently to reduce the possibility of disturbance of the weak layer. After the frame is placed in the snow above the weak layer, a blade (Figure 3.5) is passed around the frame to ensure that the frame is not adhering to the surrounding snow. 52

Figure 3.5 Equipment used for shear frame tests and measurement of slab weight per unit area.

Force gauges with capacities of 25, 50, 100 and 250 N are used depending on the areas of the frame and the expected strength of the weak layer to be tested. Between 10% and 100% of their capacity, the gauges are rated accurate to within 1% of the capacity. Setting a switch on the gauge causes it to record the maximum force. Thermometers were used to measure the temperature of the weak layer. For most profiles at study sites, the snow temperature was measured every 0.1 m from the surface to below the weak layer being tested. Digital thermometers with a thermister in the tip of the metal shaft (Figure 3.5) were used during the winters of 1993-94 and 1994-95. The density gauge and small digital scale, or sampling tube and force gauge, were used to measure the slab weight per unit in two different ways as described in the next section. For most rutschblock tests, the column of snow was isolated from the surrounding snowpack on both sides and at the upper wall with a specialized saw (Figure 3.6). The 53 saws were all constructed of 3.2 mm aluminium and the teeth were offset to cut a 10 mm gap in hard snow. Most of the saws were 1.3 m long and jointed so they could be disassembled for transport by skiers with backpacks.

Figure 3.6 Rutschblock saws.

3.4 Measurement of Slab Weight per Unit Area

Slab weight per unit area was measured for every set of shear frame tests by one of two methods. In the “core sample” method, the sampling tube was pushed vertically down through the snow from the surface to the weak layer. A small plate was slid over the bottom of the tube during extraction from the snowpack. The snow in the tube was then deposited into a light plastic bag. If the slab height exceeded the length of the tube, subsequent samples were taken directly below the previous sample until the weak layer was reached. To obtain an average weight, the procedure was usually repeated several times before the bag was weighed by suspending it from a vertically held force gauge. For thin slabs, additional samples were required to ensure the weight of the core samples exceeded 10% of the force gauge’s capacity. Dividing the weight by the 0.0028 m2 cross-sectional area of the tube and by the number of cores yields the slab weight per unit area, denoted by ρgh in this dissertation. Avalanche workers usually refer to the slab weight per unit area as the load on the weak layer. 54 The second method of measuring load requires that the layers be identified. A sample of each layer was taken with a 93 mm long cylindrical sampler with a diameter of 37 mm and a volume of 1 x 105 mm3. The sampler was inserted vertically into layers thicker than 0.1 m, and horizontally into thinner layers. These samples were either weighed using the gravity balance or by placing the snow in a plastic bowl on the small digital scale (Figure 3.5) which had been tared with the empty bowl. The slab weight per unit area is simply the sum over the layers of the product of density, layer thickness and acceleration due to gravity. The advantages of the layer-by-layer density method are: field workers can mentally calculate the density from the weight (by shifting the decimal point) and repeat the sample if the density seems questionable, and the density of the individual layers can be correlated with other properties such as resistance, as was done for hand hardness (Appendix A). The core sample method is faster and potentially more accurate since the volume of snow that is weighed is larger. However, two accuracy problems were identified with the core sample method. Sometimes on slopes operators do not hold the tube vertically before pushing it down through the slab. This can be mitigated if a second person, standing back several metres, carefully watches and corrects the orientation of the tube. The second problem occurs when crusts overlie soft snow layers within the slab. Under these conditions, the descending tube will often break the crust into pieces larger than the cross-section of the tube, and the softer snow below will be pushed ahead of and away from the descending tube, resulting in under-sampling. When time permitted and crusts were not a problem, both methods were used and the results averaged.

3.5 Shear Frame Tests

The main advantages of the shear frame test method are: it is conceptually simple, the strength of very thin layers can be determined, 55 the frame and force gauge are small enough and light enough to be carried in a backpack in the field, and the frame and force gauge are relatively inexpensive (< $800).

Its disadvantages include: placing the frame on thin, often delicate weak layers requires considerable manual skill, weak layers underlying a crust often cannot be tested since pushing the frame through the crust may fracture the weak layer, the results depend on the design of the frame (Perla and Beck, 1983), and load is applied manually and the results depend on the loading rate (Perla and Beck, 1983; Föhn, 1987a). Studies of these last three limitations are discussed under Size Effects (Section 4.10), Frame Design (Section 4.12) and Loading Rate (Section 4.5). Variability between operators is discussed in Section 4.9.

3.5.1 Technique Before the shear frame test is performed, the weak layer is identified with a profile of snow layers, a tilt board test, a shovel test, or a rutschblock test, all of which are described in Observation Guidelines and Recording Standards for Weather, Snowpack and Avalanches (CAA, 1995). Overlying snow is removed, leaving approximately 40-45 mm of undisturbed snow above the weak layer (Figure 3.7). The shear frame with sharpened lower edges is then gently inserted into the undisturbed snow so that the bottom of the frame is—preferably—within 2-5 mm, of the weak layer (Perla and Beck, 1983). In practice, the strengths of the weak layer and the snow above the weak layer (the superstratum) influence the distance between the weak layer and the bottom of the frame. If the superstratum is not much harder than the weak layer then the shear frame must often be placed very close to, or into, the weak layer to avoid a fracture in the superstratum rather than in the weak layer when the frame is pulled. Alternatively, if the superstratum is very hard, then the weak layer may pre-fracture, that 56 is, fracture during frame placement. Under such conditions, frames must be placed 5-10 mm above the weak layer and occasionally higher. The effect of frame placement more or less than the recommended 2-5 mm is discussed in Sections 4.8 and 5.4. After the frame is placed, a thin blade is passed around the sides of the frame to ensure that surrounding snow is not in contact with, and possibly bonding to, the frame. This cut must extend to the weak layer to ensure that a known area is tested. The force gauge is attached to the cord linking the two sides of the frame and is pulled smoothly and quickly (< 1 s) Figure 3.7 Shear frame test. (J. Hughes usually resulting in a planar failure in the photo) weak layer just below the base of the frame. Tests in which half or more of the fracture surface deviated beyond the active weak layer were rejected. Shapes of fracture surfaces and treatment of data with non-planar fracture surfaces are discussed in Section 4.4. Shear strength is determined by dividing the maximum load on the force gauge by the area of the frame, usually 0.025 m2. Average shear strengths of weak layers were based on sets of at least 7 shear frame tests during the winters of 1990-93. During the winters of 1994 and 1995, the usual number of tests in study sites was increased to 12 to reduce the standard error of shear strength. 57 3.6 Rutschblock Test

3.6.1 Rutschblock Technique A pit at least as deep as any potential failure planes—often 1-1.5 m deep—is excavated with a shovel. The wall of the pit that faces down-slope is extended by shovelling until it is at least 2 m across the slope (Figure 3.8). Figure 3.8 Rutschblock isolated on the sides by The sides of the block can be shovelled trenches. either cut or shovelled, the latter method requiring more time. If the sides of the block are to be shovelled, then two 1.5 m long parallel marks extending up the slope from the pit wall and 2 m apart are made on the snow surface with a ski or ruler. After shovelling trenches just outside these marks, the upper wall is cut with the tail of a ski or a cord. If the side walls are to be cut with a ski, ski-pole, cord or saw, then the marks for the side walls are 2.1 m apart at the pit wall and 1.9 m apart at the up-slope end of the marks (Figure 3.9). This flaring of the block reduces the potential for friction at the sides of the block that could affect the rutschblock score. After the side walls are cut with a ski-pole, saw or tail of a ski by a Figure 3.9 Rutschblock isolated on the sides and person standing outside the upper wall by cord cutting. 58 dimensions of the column, then the upper wall is cut by the same method. However, if a cord is used, then the side walls and upper wall can be cut simultaneously by extending the cord from the pit, up one side of the column, around ski-poles or avalanche probes at the upper corners and down the other side to the pit (Figure 3.9). Two operators in the pit, one holding either end of the cord, alternately pull their end of the cord to “saw” both side walls and the upper wall. An 8 m length of 4-6 mm cord with simple knots tied every 0.3 m successfully cuts a wide variety of snow layers except for melt-freeze crusts of “knife” hardness.

3.6.2 Loading Steps and Rutschblock Scores Rutschblock scores range from 1 to 7. Scores of 1-6 correspond to the first loading step that produces a slope-parallel failure of the block. A score of 7 indicates that none of the 6 loading steps caused a slope-parallel failure. The following sequence of loading steps, except for the “soft slab” variation of step 6, is similar to the steps described by Föhn (1987a): Step 1: An undisturbed column of snow is isolated by shovelling or cutting as described above.

Step 2: The skier approaches the block from above and gently steps down onto the upper part of the block (within 0.35 m of the upper wall).

Step 3: Without lifting the heels, the skier drops from a straight leg to a bent knee position, pushing downwards and compacting surface layers.

Step 4: The skier jumps upwards, clear of the snow surface, and lands on the compacted spot.

Step 5: The skier jumps again and lands on the same compacted spot.

Step 6: For hard or deep slabs, the skier removes the skis and jumps on the same spot. For softer slabs where jumping without skis might penetrate through the slab, the skis are kept on, the skier steps down another 0.35 m—almost to mid-block—and pushes downwards once then jumps at least three times 59

3.6.3 Failure Mode For rutschblock scores of 1 or 2 and sometimes for scores of 3 or higher, the entire block displaces as shown in Figure 3.10. However, when the loading steps of 4, 5 or 6 are applied to softer slabs, the fracture often extends from the operator’s skis down to the weak layer and along the weak layer to the pit, leaving a part of the block undisplaced. In such cases, the area of the shear failure is less than 2 m2. However, this reduction in area is minimized by loading the rutschblock near the upper wall as shown in Figures 3.8, 3.9 and 3.10. Figure 3.10 Rutschblock showing displaced block (M. Shubin photo) 3.7 Comparison of Rutschblock and Shear Frame Tests

The rutschblock method can test a 2 m2 area of snowpack in 10-20 minutes whereas a set of 7-12 shear frame tests in a 2 m2 pit typically requires 30-45 minutes, including slab weight measurements. A rutschblock test can be interpreted immediately whereas computing a stability index from shear frame tests requires a hand-held calculator or written calculations. Further, a displaced rutschblock is often a convincing indication of instability whereas a shear frame stability index is “just a number”. 60 Although site selection for any stability test requires experience, the rutschblock test requires less practice and less specialized equipment (the large saw is optional) than the shear frame test. The shear frame test can only be used after the weak layer has been identified, whereas the rutschblock test identifies weak layers and rates their stability. However, the “ski-penetration problem” may cause the rutschblock test to overlook weak layers or incorrectly rate their stability. This problem occurs when the operator's skis penetrate very close to, or through, weak layers during the loading steps (Jamieson and Johnston, 1993b). After a shallower slab has displaced, allowing the operator's skis to penetrate the slab more deeply and increasing the skier-induced stress, the rutschblock test may not yield a valid score for deeper weak layers. This can be a substantial limitation if the stability of deeper weak layers is important, or as was often the case in the present study, the primary objective of the test. The rutschblock test is not a reliable test for weak layers deeper than 1 m whereas the shear frame test can be applied at any depth. Jamieson and Johnston (1993b) found a significant effect of slope inclination on rutschblock score only for 10 of 24 slopes and Schweizer and others (1995) doubt that a rutschblock score can be adjusted for slope inclination due to the non-linear loading steps. This is in contrast to shear frame stability indices which can calculated for a wide range of slope inclinations. Not only can the slope inclination be changed, but the slab density and slab thickness can be readily changed to estimate the stability where conditions are different. Shear frame stability indices for skiers are calculated for a static skier and may not represent the dynamic shear stress due to skiing or, in the worst case, the impact of a falling skier. On the other hand, the same set of shear frame and slab weight measurements can be used to calculate stability indices for triggering due to slab weight (natural trigger), a skier, over-snow vehicle, explosive, etc. 61 The stiffness of superstratum influences slab failure by imposing stress and strain concentrations on the weak layer. The rutschblock test includes this real stress and strain concentration whereas the shear frame test obscures this effect by imposing a stress concentration due to the fins and dimensions of the frame on the weak layer. Also, pushing the frame into a hard superstratum sometimes fractures the weak layer, making valid shear frame tests impossible. Selecting the best test method based on the comparisons summarized above depends on the objective. The present research study uses both rutschblock and shear frame tests in avalanche start zones and in study sites. However, for avalanche forecasting programs, some general preferences can be summarized. Both the shear frame test and rutschblock test are well suited to study sites. However, the shear frame stability indices have advantages for extrapolation to surrounding terrain since they can be calculated for different slope inclinations, slab densities and slab thicknesses as well as for different triggers (natural, explosive, etc.). The ability to calculate shear frame stability indices for different triggers is less important for forecasting programs concerned primarily with skier-triggered avalanches. While stability tests at study sites are applied to surrounding terrain, tests in avalanche start zones are more often applied locally. For many forecasting programs, the speed and simplicity of the rutschblock test are substantial advantages in start zones. Based on the literature summarized in Table 2.2, operational use of the shear frame—which dates back to 1963—has been restricted to study sites.

3.8 Avalanche Activity

For the present study, avalanche occurrences were compiled by type of release (slab or loose), size, type of trigger (natural, cornice or skier-released, etc.), moisture content (dry, moist or wet), aspect, elevation and location (CAA, 1995) using mainly information obtained from ski guides operating in the forecast area. On a given day the portion of the total operating area observed for avalanche occurrences varied from 0 to 40% depending on visibility conditions, number of guides skiing (typically 5-12) and their operating locations. The research team also compiled occurrence data for slopes visible from near 62 the study sites, in particular on days during bad weather when helicopter skiing operations were grounded. Some avalanche occurrence data are unavoidably influenced by weather and operational factors. Typically, this happened when, for one or more days after an occurrence, visibility was limited or there was no helicopter skiing near the location of the avalanche. Some crown fractures and/or deposits from natural avalanches were estimated to be 1 or more days old when they were first observed. Consequently, for most of these avalanches, the date of occurrence was estimated. In a determination of critical values of stability indices, Jamieson and Johnston (1993a) found that excluding avalanches with estimated dates had little effect on the critical values. In Chapters 6 and 7, the stability parameters are related to natural avalanche activity including avalanches with estimated dates. Fortunately, for skier-triggered avalanches the dates of occurrence are known. For the purpose of the present study, natural avalanches are defined as those that release without an external trigger such a skier, explosive or falling chunk of cornice. Cornice-triggered avalanches are not considered natural avalanches in the present study since many falling chunks of cornice are powerful triggers that can release relatively stable slabs. Distinguishing cornice-triggered avalanches from natural avalanches is consistent with the NRCC/CAA (1989) definition of natural avalanches and with Roch’s (1981) definition of an intrinsic trigger, but inconsistent with the CAA (1995) definition. Slab avalanches triggered by explosives and helicopters were recorded but there were too few of these avalanches to use in the analysis. In Canada, avalanches are classified by size based on destructive potential (Table 3.2; CAA, 1995). A class 1 avalanche is “relatively harmless to people”, whereas a class 2 avalanche can “injure, bury or kill a person”. A class 3 avalanche can “bury and destroy a car, destroy a small building, damage a truck or break a few trees”. The destructive potential for larger avalanches is given in Table 3.2. Half sizes, such as 1.5, are used for avalanches that appear to fall between two size classes. Most reported avalanches were within 15 km of the study sites, but some were more than 30 km away. 63

Table 3.2 Avalanche Size Classification (CAA, 1995) Size Class Destructive Potential 1 Relatively harmless to people. 2 Could injure, bury or kill a person. 3 Could bury and destroy a car, destroy a small building, damage a truck or break a few trees. 4 Could destroy a railway car, large truck, several buildings, or a forest area up to 4 hectares. 5 Could destroy a village or 40 hectares of forest. 64

65 4 FIELD STUDIES OF THE SHEAR FRAME TEST 4.1 Introduction

Shear strength, as measured with a shear frame, depends on the material properties of the snow layer being tested. However, the results of shear frame tests may also be affected by or related to factors such as: manual loading rate, different operators, test sequence since the operator may refine the manual loading rate or the frame placement while repeatedly testing the same layer, delays between placing the frame and applying the load, shape of the fracture surface, normal load on the weak layer, distance between the bottom of the frame and the weak layer, cross-sectional area of frame, and design of frame including height of frame and number of load-carrying cross-members. The effects of these factors are assessed in this chapter after examining the statistical distribution and variability of shear strength measurements.

4.2 Statistical Distribution

Strengths determined from shear frame tests can be considered continuous, and certainly they have the properties of interval data. Analyses of such data are facilitated if the data are normally distributed. To assess the normality of shear frame results, 28 sets of 30 or more tests with standard frames from the winters of 1991-95 are summarized in Table 4.1. The Shapiro-Wilk test is presently the preferred test for normality (Shapiro and others, 1968; Statsoft, 1994, p. 1412). For four of the 28 sets of shear frame tests tabulated in Table 4.1, the hypothesis of normality is rejected at the 1% level (p < 0.01). An additional four sets could be rejected at the 5% level (p < 0.05). The values of p for the 28 large sets

66 Table 4.1 Normality of Large Sets of Shear Frame Tests Date Microstructure Mean Coef. No. of (of most common Strength of Tests Shapiro-Wilk grains in weak layer) Var. Test1 (kPa) V n W p 91-12-19 decomposed & frag. 0.301 0.167 30 0.891 0.002 91-12-20 precip. particles 0.345 0.100 36 0.984 0.913 91-12-21 decomposed & frag. 0.525 0.084 32 0.913 0.015 92-02-11 decomposed & frag. 1.096 0.108 38 0.824 1x10-5 92-02-14 surface hoar 0.386 0.083 30 0.931 0.059 92-02-17 surface hoar 0.645 0.129 30 0.958 0.320 92-04-10 facets 0.614 0.195 32 0.972 0.615 93-02-06 surface hoar 2.129 0.199 32 0.987 0.963 93-02-13 surface hoar 3.181 0.144 32 0.970 0.568 93-02-24 surface hoar 0.476 0.141 32 0.948 0.150 93-03-03 surface hoar 0.615 0.147 30 0.962 0.394 93-03-16 facets 2.157 0.172 31 0.940 0.098 93-04-01 facets 2.208 0.179 30 0.979 0.824 94-03-30 graupel 4.013 0.123 30 0.952 0.222 94-12-04 graupel 0.931 0.135 30 0.973 0.673 94-12-15 decomposed & frag. 0.219 0.135 30 0.908 0.014 94-12-29 graupel 1.432 0.197 30 0.891 0.005 95-01-04 graupel 2.124 0.160 30 0.950 0.201 95-01-29 surface hoar 1.294 0.199 30 0.921 0.033 95-02-09 surface hoar 3.71 0.090 33 0.888 0.002 95-02-22 surface hoar 1.874 0.118 30 0.947 0.160 95-02-28 surface hoar 3.035 0.083 36 0.968 0.457 95-03-07 surface hoar 4.185 0.075 30 0.970 0.594 95-03-24 graupel 2.764 0.150 30 0.923 0.038 95-03-28 graupel 3.597 0.10 30 0.977 0.770 95-03-29 surface hoar 5.921 0.09 30 0.963 0.408 95-01-23 surface hoar 4.139 0.097 30 0.964 0.444 95-01-29 surface hoar 1.204 0.109 33 0.962 0.352 1 Rows for which p ≤ 0.05 are marked in bold.

67 of shear frame tests are plotted against mean shear strength in Figure 4.1 using international symbols (Colbeck and others, 1990) to distinguish the microstructure. No systematic effect of mean shear strength on p is apparent in Figure 4.1. However, p < 0.05 for all four sets of tests on decomposed and fragmented precipitation particles. The frequency histograms and associated normal distributions for the eight sets for which p < 0.05 are presented in Figure 4.2. All exhibit central tendency; however, four are skewed right and two are skewed left. Since the hypothesis of normality cannot be rejected for 20 (p < 0.05) to 24 (p < 0.01) of the 28 data sets, the shear frame data are assumed to be normally distributed. However, further studies of decomposed and fragmented precipitation particles would be worthwhile.

Figure 4.1 Shapiro-Wilk test for normality for 28 sets of shear frame data.

68

Figure 4.2 Frequency distributions for 8 sets of shear frame tests for which p < 0.05 from Shapiro-Wilk test for normality.

69 4.3 Variability and Number of Tests for Required Precision

The spatial variability of shear strength of a particular weak layer throughout an area such as an avalanche start zone is certainly relevant to stability evaluation, but digging numerous pits in every start zone or study plot of concern requires too much time for any avalanche forecasting operation. Safety concerns also limit access to avalanche start zones. Hence, the variability reported for the present studies and for previous studies (except for Sommerfeld and King, 1979) is for repeated shear frame tests of a particular weak layer in a single pit, usually within 30-60 minutes. Shear frame tests are usually made in one or two rows across the slope and the area tested by 7 to 12 shear frame tests is usually less than 0.5 m by 2 m. The coefficient of variation is the preferred measure of variability for snow strength since it is less dependent on mean strength than the standard deviation which increases with mean strength (Keeler and Weeks, 1968; Jamieson, 1989). Previously reported coefficients of variation for 0.01, 0.025 and 0.05 m2 shear frame tests are typically 0.25 but range from 0.18 to 0.62 (Perla, 1977; Sommerfeld and King, 1979; Föhn, 1987a; Schaerer, 1991). The highest values of 0.54, 0.52 and 0.62 were reported by Sommerfeld and King (1979) who tested the failure plane at up to three sites along crown fractures. During the winters of 1989-90 to 1994-95, 809 sets of six or more shear frame tests (with areas of 0.01, 0.025 or 0.05 m2) were made in study sites chosen partly for uniformity of snowpack (Section 3.2.1), and in avalanche start zones where greater variability is expected. For these 809 sets, the coefficients of variation ranged from 0.03 to 0.66 with a mean of 0.152 (Figure 4.3). At level study plots (inclination <3°) chosen for a uniform snowpack, the coefficients of variation from 342 sets of six or more tests ranged from 0.03 to 0.46 with a mean of 0.144. In avalanche start zones with inclinations of at least 35°, the coefficients of variation from 114 sets of six or more tests ranged from 0.04 to 0.54 with a mean of 0.178. The remaining 353 sets are from sites, mainly study slopes, with slope inclinations between 3° and 34°.

70

Figure 4.3 Frequency distribution for coefficients of variation of shear strength.

The present study’s coefficients of variation are generally lower than previous studies. This may be due to: reduced disturbance of the weak layer due to the use of relatively shear frames constructed of relatively thin sheet metal with sharpened lower edges, consistently fast loading resulting in fractures within 1 s, the generally consistent snowpack of the Columbia Mountains where most of the tests were done, or the field practice of rejecting tests that do not fail on the intended layer, or show definite evidence of disturbance such as pine needles or an animal track in the fracture surface. (Tests were not rejected due to surprisingly low or high pull forces.) The number of tests, n , required to obtain precision, P , can be estimated from the coefficient of variation, V, by solving

2 n = (tp;n-1 V/P) (4.1)

Table 4.2 shows the number of tests for V = 0.15 which is typical of study plots in the present study, V = 0.18 which is typical of start zones in the present study and

71

Table 4.2 Number of Shear Frame Tests for Required Precision Required Significance No. of Shear Frame Tests Precision Level Coef. of Var. Coef. of Var. Coef. of Var. P p 0.15 0.18 0.25 0.05 0.10 26 37 70 0.05 0.05 36 52 98 0.05 0.01 64 90 170 0.10 0.10 8 11 19 0.10 0.05 11 15 26 0.10 0.01 19 25 45 0.15 0.10 5 6 9 0.15 0.05 6 8 13 0.15 0.01 10 13 22

V = 0.25 which is typical of previous studies. For any particular level of precision, the number of tests increases with the coefficient of variation. The reduced variability from the present study results in fewer tests being necessary to achieve a required precision. This an important point for avalanche safety operations because a greater number of tests would require a larger pit and more time, and could be operationally impractical.

4.4 Fracture Surface

During the winters of 1991-95, 703 sets of shear frames tests were made with standard 0.025 m2 frames for a total of 8468 tests. The shape of the fracture surfaces were classified with the standard descriptors (Table 4.3) for 6951 tests, and 5757 of these (83%) exhibited smooth planar fracture surfaces. Shapes that occurred less than 10 times are excluded from Table 4.3 and this analysis. To compare the strength measurements associated with planar fracture surfaces Σ with measurements associated with other shapes of fracture surfaces, each strength, i, was converted to standard normal

ui =(Σi − Σ)/sΣ (4.2) Σ where and sS are the mean and standard deviation for the particular set of shear frame

72

Table 4.3 Assessment of Common Shapes of Fracture Surfaces Sample t-test Descriptor Description of Fracture n Mean St. tp Surface Dev. (kPa) (kPa) C smooth, planar 5757 -0.02 0.95 - - SBD divot under rear compartment, 200 0.02 0.93 -0.66 0.51 divot < 5 mm deep MBD divot under rear compartment, 154 0.09 0.90 -1.46 0.15 divot 5-10 mm deep BBD divot under rear compartment, 131 0.41 0.93 -5.19 7E-07 divot > 10 mm deep W 1 wave per compartment, 243 0.01 0.94 -0.54 0.59 waves 5-10 mm deep SW 1 wave per compartment, 77 0.03 0.85 -0.54 0.59 waves < 5 mm deep SIR irregularities < 5 mm deep 44 0.13 0.9 -1.09 0.28 IRR irregularities 5-10 mm deep 114 0.10 0.96 -1.28 0.20 LC fractured deeper at right or 31 0.27 0.87 -1.84 0.07 left side SH small hump, height < 5 mm 22 -0.25 1.04 1.04 0.31 STP stepped between 2 fracture 21 0.31 0.94 -1.60 0.12 planes BC back divot extends beyond 14 -0.11 1.30 0.26 0.80 rear compartment

tests. Combining the normalized values from the 703 sets gives an aggregate set of 8468 values with mean 0 and standard deviation 0.95. This aggregate set is then partitioned by fracture descriptor so the set of values with a particular fracture descriptor can be compared with the set of 5757 values with planar fractures using a two-tailed t-test for unequal sample sizes and unequal variances. Representing the sets of planar and non-planar fracture surfaces with the subscripts 1 and 2 respectively, the calculated value for t (Mattson, 1981, p. 430) is =( − ) ( 2 + 2 )1/2 t u1 u2 / s1/n1 s2/n2 (4.3)

73 where the number of degrees of freedom is

2 2 2 4 4 df = (se1 + se2 ) / (se1 /n1+se2 /n2) (4.4) and the standard error is se = s/ n (4.5) For each comparison, calculated values of t and the total probability associated with both tails, p, are shown in Table 4.3. The only shape of fracture descriptor that has strength measurements significantly different from planar fractures are those with a back divot under the rear compartment that is more than 10 mm deep. Such fractures only occur when the bed surface is not appreciably stronger than the weak layer being tested, typically when both the weak layer and the bed surface consist of facets or depth hoar. This condition is most common in the Rocky Mountains where entire sets of shear frame tests may result in fractures with deep back divots. For future studies in which minimal variability is important, shear frame tests with such fracture surfaces should be rejected. However, this rejection may not be practical in the Rocky Mountains where deep back divots are common and imperfect data may be better than none for avalanche forecasting.

Table 4.4 Mean Shear Strength for Various Loading Times Date Microstructure Loading Time to Failure (s) 0-0.5 0.6-1.0 1.5-3.0 3.5-6.0 6.5-9.0 9.5-15 15.5-30 90-01-28 decomposed/frag. - 0.37 0.34 0.44 - - - 90-01-20 rounded grains 0.35 0.38 0.39 0.39 0.32 - 0.41 90-01-28 decomposed/frag. - 0.4 0.43 0.34 - - - 90-01-20 rounded grains 0.42 0.44 0.5 0.53 0.58 0.51 - 90-01-21 decomposed/frag. 0.51 0.52 0.51 - 0.6 - - 90-01-28 rounded grains - 1.11 1.2 1.31 1.48 - - 90-01-29 decomposed/frag. - 1.23 1.45 1.51 1.38 1.8 - 90-01-22 rounded grains - - 1.98 1.91 2.07 - - 90-01-21 rounded grains 1.75 2 2.09 2.33 - 2.54 - 90-01-20 rounded grains 2.32 2.9 2.87 3.23 2.83 3.1 4.7

74 4.5 Loading Rate

In a laboratory study of depth hoar under various constant displacement rates, Fukuzawa and Narita (1993) found a ductile-brittle transition between 8 x 10-5 s-1 and 2 x 10-4 s-1. In ductile-brittle transition, as loading times to failure decreased from 3 to 1.5 s, strengths were reduced by approximately 35%. Figure 4.4 Effect of loading time on shear strength However, in the brittle range as for 10 experiments with various manual loading loading times decreased from 1.5 s rates. to 0.2 s, strengths were only reduced a further 12%. For in situ shear frame tests of snowpack layers, the load is applied manually with a force gauge that records the maximum force. Shear strength measured with a shear frame depends on the rate at which the manual load is applied. Perla and Beck (1983) found the strength was reduced by 25% when loading times were reduced from approximately 30 s to approximately 3 s. To minimize rate effects, recent field studies (Föhn, 1987a; Jamieson and Johnston, 1993a) chose to load shear specimens to failure within 1 s. The effect of loading rate on shear strength was studied by attempting to apply the load at various constant rates and measuring the loading time with a stop-watch. Loading times are partitioned into 7 intervals and for each interval in which there were at least three results, the mean strength is reported in Table 4.4 and plotted in Figure 4.4. For strengths less than 1 kPa, shown in the first five rows of Table 4.4, there is no apparent

75 effect of loading time on strength. However for four of the five series with strengths greater than 1 kPa (shown in the last 5 rows of Table 4.4), there is an increase in strength with a increase in loading times (decrease in loading rate). Since persistent weak layers typically have a shear strength of less than 2 kPa and critically weak persistent layers typically have a strength less than 1 kPa, shear frames were loaded to failure in less than 1 s for all shear frame results presented in subsequent chapters and in the other field studies of the shear frame test outlined in this chapter. This minimizes the effect of loading rate on strength and is consistent with the laboratory study of Fukuzawa and Narita (1993).

4.6 Test Sequence Variability

Schaerer (personal communication) has suggested that the first shear frame test in a set of tests on a particular weak layer be rejected since the operator requires at least 1 test to learn the optimal loading rate and frame placement with respect to the weak layer. To determine if variability is greater for initial tests than for subsequent tests, 703 sets of 2 or more tests with the standard 0.025 m2 frame are used. The strength from each test is normalized using the mean and standard deviation from each set (Eq. 4.2). The combined set of normalized strengths is then partitioned by sequence number. The means and standard deviations of the set of first tests, set of second tests, etc. and including the set of third to seventh tests are shown in Table 4.5. The standard deviations of these sets are plotted in Figure 4.5. Increased variability on the first and second tests in a sequence is apparent in Figure 4.5. The significance of the apparent increase in variability is assessed by comparing the variance of the set of first tests with the variance of the set of third to seventh tests with an F test.

2 F = (s1/s3-7) (4.6) This value of F is 1.45 which is significant at the 10-4 level. Similarly, when the variance of the set of second tests is compared with the variance of the set of third to seventh tests, F = 1.14 which is marginally significant (p = 0.03). Hence for future studies in which

76 minimal variability is important, the first and perhaps the second test in a set should be rejected.

Table 4.5 Effect of Test Sequence on Variability Sequence No. of Tests Mean St. Dev No. in Set 1 703 -0.004 1.111 2 703 -0.008 0.985 3 702 0.007 0.903 4 701 0.06 0.943 5 696 0.001 0.91 6 691 0.048 0.92 7 674 0.005 0.93 3-7 3464 0.024 0.921

Figure 4.5 Effect of sequence number on standard deviation.

4.7 Effect of Delay

Shear frames are usually pulled within 5-10 s of the frame being placed in the snow above the weak layer. Occasionally the frame remains placed for up to 60 seconds while the force gauge is being zeroed, cleaned of snow, ice or moisture. To assess the effect of

77 such delays, alternating tests were performed on 30 March 1995 at the Mt. St. Anne Study Plot. This weak layer was susceptible to changes in strength because the weak layer was relatively warm (-3.7oC), the air was unusually warm (+7oC) and the microstructure was non-persistent (partly decomposed precipitation particles and rounded grains) and consequently capable of metamorphic and strength changes faster than most layers in the present study. Tests with the usual 5-10 s delay were alternated with tests with a 3 minute delay until 14 pairs were obtained. The hypothesis that there was no difference in strength was assess with a two-tailed t-test for matched pairs

t = Dn/sD (4.7) where D and sD are the mean and standard deviation of the differences in strength respectively. The comparison was repeated with a 3 kg mass on top of the shear frame. In each case, there was no significant difference in strength (p > 0.14) as shown in Table 4.6. Apparently, delays of up to 3 minutes do not affect the strength measured with a shear frame. This would also be true for persistent layers, the mechanical properties of which are, by definition, slower to change than non-persistent layers.

Table 4.6 Effect of Delay on Shear Strength Load on Top No Delay 3 Min. Delay Difference t-test for Paired of Shear Tests Frame Mean Coef. of Mean Coef. of Mean Coef. of No. of (kg) Var. Var. Var. Pairs tp (kPa) (kPa) (kPa) 0 2.74 0.13 2.73 0.18 -0.01 39.5 14 0.09 0.926 3 3.59 0.05 3.41 0.11 -0.18 2.04 14 1.56 0.143

4.8 Frame Placement

When a shear frame is loaded, stress concentrations occur in the snow at the lower edges of the cross-members. Placing the lower edges closer to a weak layer should result in lower strength measurements due to increased stress concentrations in the weak layer. Recommended distances between the bottom edges and the weak layer include “< 5 mm

78 but not through the weak layer” (Perla and Beck, 1983), “just above” (Sommerfeld, 1984; Schaerer, 1991), “a short distance above” (NRCC/CAA, 1989), and “a few mm above” (CAA, 1995). To assess the effect of the distance between the lower edges of the frame and the weak layer, four sets of 14 to 33 alternating pairs were made during the winter of 1994-95 with a standard 0.025 m2 frame. Each pair consisted of a test with the lower edges placed in the weak layer and one with the lower edges placed above the weak layer. When the lower edges were placed in the weak layer the strength was reduced by 12%, 13% and 20% compared to strengths obtained with the lower edges 2-5 mm above the weak layer (Table 4.7). This strength reduction was 41% when the lower edges were placed in the weak layer compared to strengths obtained with the lower edges 10 mm above the weak layer. In every comparison, the strength reduction was significant (p < 10-5) based on two-tailed t-test for matched pairs (Eq. 4.7). To reduce stress concentrations, it is clearly advantageous to place the frame above the weak layer. However, this is not always practical since it will sometimes result in a failure within the snow above the weak layer (superstratum). This is most common when the superstratum is comparable in strength to the weak layer. Resulting fracture surfaces may be “wavy” or “irregular”. When failures occur in the snow above the weak

Table 4.7 Effect of Frame Placement on Shear Strength Above Weak Layer In Weak Difference t-test for Pairs Date / Layer Microstructure Dist. Mean C. of Mean C. of Mean C. of No. of tp above Var. Var. Var. Pairs (mm) (kPa) (kPa) (kPa) 94-12-16 10 0.80 0.16 0.46 0.24 -0.33 -0.54 14 6.9 1x10-5 rounded facets 95-01-29 2-5 1.29 0.20 1.04 0.17 -0.26 -0.95 30 5.7 3x10-6 surface hoar 95-1-23 2-5 4.14 0.11 3.65 0.13 -0.49 -1.14 30 4.8 4x10-5 surface hoar 95-1-29 2-5 1.20 0.10 1.06 0.11 -0.15 -1.00 33 5.7 2x10-6 surface hoar

79 layer, usually the only feasible way to test the weak layer is to place the lower edges of the frame in the weak layer. Fortunately, weak layers of surface hoar commonly result in planar fractures when the shear frame is placed above the weak layer. Occasionally, the superstratum is so hard that it fractures prematurely when the operator pushes the frame into the weak layer. Such “pre-fractures” can sometimes be avoided by pushing the frame only to within 10-20 mm of the weak layer. These “high” placements may result in higher strengths due to reduced stress concentrations in the weak layers or, conceivably, lower strengths due to bending. However, there is no evidence of reduced strength in the one set of shear frames placed 10 mm above the weak layer (Table 4.7). The sensitivity of shear strength to the distance that the frame is placed above the weak layer represents a limitation of the shear frame test. Until there are further studies of this effect, it is recommended that, whenever possible, the shear frame should be placed 2-5 mm above the weak layer, and that whenever snowpack conditions necessitate that the distance between the frame and the weak layer be more or less than the nominal 2-5 mm, the distance should be recorded. In subsequent chapters, results based on shear frames placed more or less than the recommended 2-5 mm above the weak layer are included.

4.9 Variability Between Operators

The results of shear frame tests can vary between operators because the frame is placed manually and the load is applied manually. Also, operators vary in their ability to locate very thin weak layers but their skills improve with training and experience over one or more winters. Operator variability was studied by alternating operators while testing the same layer on the same day. Using the difference in strength measurement between adjacent tests with alternating operators, D, the hypothesis that D = 0 is tested with a two-tailed t-test (Eq. 4.7). The results of 20 comparisons are summarized in Table 4.8 which includes a column for the mean loading time since many of these sets of shear frame tests involve

80

Table 4.8 Effect of Different Operators on Shear Strength Mean Operator 1 Operator 2 Difference t-test Date Micro- Load Mean Mean Mean Coef. No. structure Time Strength Strength of of tp ± S.D. ±S.D. Var. Pairs (s) (kPa) (kPa) (kPa) 90-01-15 decomp./frag. 1.4 1.10±0.10 1.19±0.23 -0.09 -1.9 7 1.38 0.218 90-01-15 graupel 1.7 3.40±0.39 3.01±0.31 0.38 1.6 9 1.87 0.099 90-01-31 rounded 1.3 1.69±0.31 1.60±0.22 0.09 3.8 8 0.74 0.485 90-03-02 decomp./frag. 1.0 1.64±0.24 1.58±0.18 0.06 4.8 17 0.86 0.403 90-03-02 decomp./frag. 1.3 4.12±0.47 3.90±0.50 0.21 1.9 19 2.30 0.034 90-03-04 decomp./frag. 0.9 2.23±0.23 2.11±0.28 0.12 2.0 22 2.29 0.032 90-03-04 decomp./frag. 1.0 2.07±0.17 2.11±0.28 -0.04 -7.7 22 0.61 0.550 90-03-04 decomp./frag. 1.1 2.23±0.23 2.07±0.17 0.16 1.4 22 3.25 0.004 90-03-05 rounded 1.0 7.70±0.76 7.22±0.64 0.48 2.3 12 1.54 0.153 90-03-05 rounded 1.1 8.04±1.37 7.20±0.67 0.83 1.9 11 1.74 0.112 90-03-05 rounded 1.1 8.04±1.37 7.65±0.78 0.39 2.5 11 1.30 0.222 90-03-05 rounded 1.0 2.44±0.37 2.52±0.29 -0.08 -4.5 14 0.83 0.420 90-03-05 rounded 0.9 2.44±0.37 2.52±0.47 -0.08 -4.0 14 0.93 0.368 90-03-05 rounded 0.9 2.52±0.47 2.52±0.29 0.00 134.1 14 0.03 0.978 90-03-06 precip. part. 0.6 0.18±0.04 0.19±0.04 -0.01 -7.3 16 0.55 0.591 90-03-06 precip. part. 0.5 0.18±0.04 0.18±0.04 0.00 10.7 16 0.38 0.713 90-03-06 precip. part. 0.4 0.19±0.04 0.18±0.04 0.01 5.1 16 0.78 0.446 90-03-27 rounded 0.6 2.24±0.45 2.24±0.50 0.00 370 31 0.02 0.988 91-03-30 decomp./frag. < 1 0.69±0.07 0.67±0.09 0.01 7.0 31 0.8 0.430 91-03-30 decomp./frag. < 1 2.03±0.31 2.05±0.20 -0.03 -10.8 27 0.48 0.633

loading times greater than 1 s. The hypothesis was rejected at the 1% level (p < 0.01) for one comparison involving 22 pairs and for two additional experiments at the 5% level (p < 0.05). In the comparison that a significant difference was detected (p < 0.01), one operator was tapping the frame into place with the blade used to cut around the frame while the other was using the standard technique of pushing it into place by hand. When

81 the tapping was discontinued, no significant operator effects (p > 0.05) were detected with this operator. Since the one experiment with p < 0.01 can be explained and marginally significant operator effects (0.01 < p < 0.05) only occurred in 2 of 19 experiments, different operators are not considered to be a source of variability for the relatively small sets of 7-12 shear frame tests used in subsequent chapters, since the operators received training and supervision in the early stages of their work.

4.10 Size Effects

Mean shear strengths measured with the shear frame decrease with increasing frame size (Perla, 1977; Sommerfeld, 1980; Föhn 1987a). This was verified at Mt. St. Anne in the Cariboo Mountains, where comparisons were conducted using shear frames with areas of 0.01, 0.025 and 0.05 m2. In each comparison, shear tests with the standard frame (area 0.025 m2) were alternated with tests with the non-standard frame (area 0.01 or 0.05 m2). Mean differences between adjacent tests, D , and the coefficient of variation of the difference, VD, are reported in Table 4.9. Except for the comparison on 1993-03-16, the larger frame had a lower mean strength than the smaller frame. The hypothesis that there is no difference in strength is assessed with a t-test (Eq. 4.7). The probability that there is no difference between mean strengths measured with the standard and non-standard frames, based on a two-tailed t-test, is p. For 7 of 9 comparisons, the larger frame had a significantly lower mean strength than the standard frame (p < 0.05). On 1990-04-04, there was no significant difference in mean strengths (p = 0.41). There was one unexpected and unexplained result. On 1993-03-16, the 0.05 m2 frame had a significantly increased strength compared to the 0.025 m2 frame (p = 2x10-4). Nevertheless, for eight of nine comparisons the larger frame had a lower mean strength and for seven of these, the difference was significant. For strength tests of brittle materials, variability is expected to decrease with increasing sample size. However, Schaerer (1991) did not find the difference in variability among frames with areas of 0.01, 0.025 and 0.05 m2 to be significant. The data in Table 4.9 are used to assess the effect of frame area on variability with the F test:

82

Table 4.9 Effect of Shear Frame Area on Mean Strength and Variance Date Std. Frame Test Difference Variance Frame No. Mean Coef. Area Coef. of Mean Coef. t-test F-test Strength of of Pairs of 2 (kPa) Var. (m ) Var. (kPa) Var. tpFp 90-02-15 0.691 0.17 0.01 0.12 39 0.23 0.7 8.86 9E-11 0.513 0.979 90-02-25 0.791 0.14 0.01 0.24 32 0.12 1.74 3.2 0.003 2.885 0.002 90-03-17 2.111 0.19 0.01 0.18 54 0.45 1.17 6.22 8E-08 0.875 0.686 90-04-04 3.082 0.16 0.01 0.24 24 0.14 5.72 0.84 0.41 2.218 0.031 90-04-06 3.852 0.13 0.01 0.16 26 0.30 2.30 2.18 0.039 1.526 0.149 91-12-21 0.531 0.08 0.05 0.13 32 -0.08 -0.94 -5.92 2E-06 2.493 0.007 92-02-17 0.642 0.13 0.05 0.11 30 -0.15 -0.46 -11.6 2E-12 0.704 0.825 92-04-10 0.613 0.2 0.05 0.14 32 -0.08 -1.51 -3.70 8E-04 0.52 0.963 93-03-16 2.164 0.17 0.05 0.17 31 0.33 1.31 4.19 2E-04 0.922 0.587 93-04-01 2.214 0.18 0.05 0.16 30 -0.24 -1.71 -3.16 0.004 0.815 0.708 1 decomposed and fragmented precipitation particles 2 surface hoar 3 precipitation particles 4 faceted crystals

2 F = (stest/sstd) (4.8) where s is the standard deviation for a sample of tests with a particular frame. For six of the nine comparisons summarized in Table 4.9, variability decreased with increased frame size. However this decrease was only significant for two comparisons (p < 0.03). On 1991-12-21, the 0.05 m2 frame showed a significant increase in variability compared to the 0.025 m2 frame. It appears comparisons involving a greater number of alternating tests would be required to determine if the effect of frame size on variability is significant. To eliminate the effect of frame size from shear strength measurements and relate shear frame results to much larger areas relevant for slab failure Sommerfeld (1973, 1980) and Sommerfeld and King (1979) proposed that shear strength could be corrected based

83 on Daniels (1945) statistics. Based on a compilation of field studies (Föhn, 1987a), the

2 Daniels strength, Σ∞, for any loaded area larger than about 0.5 m , is Σ Σ ∞ = 0. 65 250 (4.9) and Σ Σ ∞ = 0.56 100 (4.10) Σ Σ 2 2 where 250, and 100 are the shear strengths measured with a 0.025 m and 0.01 m shear frame respectively. For the studies of persistent instabilities reported in subsequent chapters, a 0.025 m2 frame was used for almost all shear tests. On occasions when a force gauge with sufficient capacity was not available, a 0.01 m2 frame was used. The Daniels strength is used for all results presented in subsequent chapters.

4.11 Effect of Normal Load

For granular materials, shear strength generally increases with normal load, and for failures due to yielding, this effect is commonly modelled by the Mohr-Coloumb failure criterion (de Montmollin, 1982). For brittle fractures, the effect can be empirically Σ modelled in terms of shear strength, , and normal load, sZZ (Roch, 1966b) Σ Σ σ φ Σ σ φ = + zz ( , zz) (4.11) φ Σ where ( ,szz) is the normal load adjustment. By placing weights on top of shear frames, Roch (1966b) and Perla and Beck (1983) observed increased strength with increased normal load (Figure 4.6). Roch (1966b) determined empirical equations for the normal load adjustment for fresh snow, rounded grains and faceted grains (Eq. 2.3a, b, c). The previous studies did not provide any results for the effect of normal load on surface hoar which is very important to avalanche forecasting in western Canada. During the winter of 1995, the shear strength was measured for three persistent layers and one non-persistent layer (Table 4.10). For each layer, 6-14 shear frame tests were made in a

84

Figure 4.6 Effect of normal load on strength from previous studies. The ordinate shows the Daniels strength since Roch (1966a) used a 0.01 m2 frame and Perla and Beck (1983) used a 0.025 m2 frame.

Table 4.10 Effect of Normal Load on the Daniels Strength Normal Rounded Facets Surface Hoar Rounded Decomposed and Stress Surface Hoar Fragmented σ ΖΖ Particles (kPa) N Daniels N Daniels N Daniels N Daniels Strength Strength Strength Strength Mean ± S.E. Mean ± S.E. Mean ± S.E. Mean ± S.E. (kPa) (kPa) (kPa) (kPa) 0 6 0.61 ± 0.02 7 2.31 ± 0.12 8 3.52 ± 0.11 14 1.78 ± 0.06 0.12 6 0.62 ± 0.04 7 2.51 ± 0.06 8 3.49 ± 0.13 0 - 0.39 6 0.68 ± 0.03 7 2.55 ± 0.08 8 3.46 ± 0.10 0 - 1.18 6 0.70 ± 0.07 7 2.63 ± 0.08 8 3.65 ± 0.15 14 2.33 ± 0.03

level study plot with no added normal load and with weights of mass 0.3, 1 and 3 kg placed on top of a standard shear frame. The resulting mean Daniels strengths are shown in Table 4.10 and plotted against the normal stress in Figure 4.7. The normal stress is calculated from the added weights and does not include the mass of the frame or the snow in the frame which typically total

85

Figure 4.7 Measured and predicted effect of normal load on Daniels strength.

0.3-0.4 kg. For the three persistent layers, the increase in strength is comparable to the standard errors, and the correlation between the increase in strength and the normal load is not significant (N = 9, r = 0.43, p = 0.24). This is in contrast to the 0.55 kPa (31%) increase in strength of the decomposed and fragmented particles. Since the increase in strength for an increase in normal load is not significant for persistent layers, no adjustment for normal load (φ = 0) is applied to persistent layers in subsequent chapters. Further studies are required to determine if there is a small but significant effect of normal load on the strength of persistent weak layers. For non-persistent layers, stability indices are calculated in subsequent chapters using the following equations taken from Roch (1966a) and adjusted to Daniels strength. For precipitation particles φ(Σ σ Σ σ ∞, zz) = 0.08 ∞ + 0.056 + 0.022 zz (4.12) and for decomposed and fragmented precipitation particles as well as for rounded grains φ(Σ σ Σ ∞, zz) = 0.08 ∞ + 0.224 (4.13)

86 As shown in Figure 4.7, Equation 4.13 increases too quickly for the persistent weak layers summarized in Table 4.10 but provides an acceptable prediction for the normal load effect on the strength of the layer of decomposed and fragmented particles.

4.12 Frame Design

To distribute the applied stress more evenly through the snow layer being tested, Roch’s (1966a, b) frames had two intermediate cross-members (fins). The relatively rigid outer frame distributes the manually applied load equally onto the rear cross-member and the two intermediate cross-members. The lower tip of each of these active cross- members creates a shear stress concentration in the weak snow layer. These stress concentrations are influenced by the ratio of the height of the cross-member, d, to the length of the snow sub-specimen in front of the cross-member, w (Figure 4.8). Perla and Beck (1983)

Figure 4.8 Shear frames used for comparative studies of frame design and size effects.

87 suggested that by decreasing the d/w ratio, stress concentration at the lower tip of the cross-member is increased, and that increasing d/w will increase the normal load and may contribute to increased disturbance of the weak layer when the frame is inserted . Roch’s (1966a) 0.01 m2 frame had 3 active cross-members and a h/w ratio of 3:4. Perla and Beck (1983) and Sommerfeld (1984) preferred frames with an area of 0.025 m2 but retained the three active cross-members and the slightly trapezoidal shape designed to minimize friction between the frame and the snow on either side. Perla and Beck (1983) maintained the d/w ratio of 3:4 (Table 4.11). Using 0.025 m2 frames, the following effects were studied by alternating tests with standard and non-standard frames on the same layer: distance between cross-members (w = 31 mm compared with standard w = 52 mm) reduced frame height (d = 20 mm compared with standard d = 40)

Table 4.11 Shear Frame Specifications Frame Area No. of Cross- Dist. Frame Material Frame Mass Identifier (m2) Active Member Between Width Thickness Material of Cross- Height Cross- to Frame Members Members Length d w Ratio (mm) (mm) (mm) (kg) standard 0.025 3 40 52 1:1 0.6 st. steel 0.20 short 0.025 3 20 52 1:1 0.6 st. steel 0.12 5-fin1 0.025 5 40 31 1:1 0.6 st. steel 0.30 100 0.01 3 25 35 1:1 0.8 st. steel 0.09 500 0.05 4 40 53 1:1 0.8 st. steel 0.48 Swiss 0.05 5 30 47 4:5 1.5 st. steel 0.87 finger-fin 0.025 32 30 18 1:1 0.6 st. steel 0.30 1 Also referred to as the 5-cross-member frame

88 4.12.1 Reduced Distance Between Cross-Members

The effect of reduced distance between fins was studied by alternating tests with a 5-cross-member frame (w = 31) with tests using a standard frame (w = 52 mm, 3 active cross-members). In each of the five comparisons (Table 4.12), the mean strength measurement was reduced by 16-26% by decreasing the distance between cross-members and the difference was significant (p < 10-6 ). Similarly, Perla and Beck (1983) reported a 15% reduction in strength measurement when the distance between cross-members was reduced from approximately 50 mm (3 active cross-members) to approximately 30 mm (5 active cross-members). Increasing the number of cross-members increases the number of stress concentrations resulting in reduced strength measurements.

4.12.2 Reduced Frame Height

The effect of reduced frame height (d = 20 mm) was compared with standard height frames (d = 40 mm) by alternating tests on particular weak layers. The resulting differences in mean strength measurement are both positive and negative. Only after considering whether the frame was placed in or above the weak layer, did a pattern become apparent (Figure 4.8). For the eight comparisons in which both the standard and the short frame were placed in the weak layer, t-tests showed the mean strength measurements to be not significantly different in four comparisons, and that the mean strength measurement with the short frame was significantly greater than the mean strength measurement with the standard frame in the other four comparisons (Figure 4.9). Greater strength measurement for the short frame when both frames are placed in the weak layers is difficult to explain. When both the standard and short frame were placed above the weak layer, the mean strength measurement with the short frame was less than the mean strength measurement with the standard frame in each of the four comparisons and the difference was significant for three of the four comparisons. The reduced strength measurement with the short frame is probably due to increased stress concentrations associated with the shorter cross-members (Perla and Beck, 1983). Two points are important to interpret these potentially confusing results:

89

Table 4.12 Effect of Shear Frame Design on Mean Strength Std. Frame Test Frame Difference t-test Date Microstructure Mean C. I.D. C. Mean C. No. Str. of (Table of of of tp (kPa) Var. 4.11) Var. (kPa) Var. Pairs 92-02-14 surface hoar 0.39 0.08 5-fin 0.14 -0.07 -0.78 30 7.02 1.0E-07 93-02-13 surface hoar1 3.18 0.14 5-fin 0.18 -0.56 -1.04 32 5.45 6.0E-06 93-02-24 surface hoar 0.48 0.14 5-fin 0.15 -0.08 -0.96 32 5.88 1.7E-06 95-02-22 surface hoar, 1.87 0.12 5-fin 0.09 -0.29 -0.84 30 6.56 3.5E-07 facets 95-03-07 surface hoar1 4.18 0.08 5-fin 0.16 -1.09 -0.58 30 9.48 2.2E-10 91-12-20 precip. particles2 0.34 0.10 short 0.11 0 -38.4 36 0.16 0.88 93-02-24 surface hoar2 0.48 0.14 short 0.13 0.02 3.94 32 1.44 0.16 93-03-03 surface hoar, 0.61 0.15 short 0.16 0.11 1.31 30 4.19 2.4E-04 facets2 94-03-30 graupel2 4.01 0.12 short 0.18 0.87 1.04 30 5.27 1.2E-05 94-12-04 graupel2 0.93 0.14 short 0.11 0.02 8.09 30 0.68 0.50 95-01-04 graupel2 2.12 0.16 short 0.19 -0.09 -5.19 30 1.06 0.30 95-02-09 surface hoar 3.71 0.09 short 0.14 -0.09 -6.55 33 0.88 0.39 95-03-01 surface hoar 3.3 0.10 short 0.1 -0.24 -1.65 31 3.36 2.1E-03 95-03-24 graupel2 2.76 0.15 short 0.14 0.38 1.54 30 3.55 1.3E-03 95-03-28 graupel2 3.6 0.10 short 0.13 0.34 1.56 30 3.51 1.5E-03 95-03-29 surface hoar 5.92 0.09 short 0.13 -0.19 -3.33 30 1.64 0.11 95-03-17 surface hoar1 3.29 0.11 short 0.12 -0.3 -1.69 26 3.01 0.01 92-03-27 precip. particles 0.31 0.11 Swiss 0.12 0.13 0.59 14 6.3 2.7E-05 92-04-10 facets 0.61 0.2 Swiss 0.24 0.39 0.53 32 10.6 8.1E-12 94-03-30 graupel2 4.01 0.12 Swiss 0.21 0.42 2.49 30 2.2 0.04 95-02-28 surface hoar 3.03 0.08 finger- 0.11 0.49 0.83 36 7.26 1.8E-08 fin 95-03-18 graupel2 1.55 0.10 finger- 0.09 0.88 0.37 10 8.64 1.2E-05 fin 1 rounding or surface hoar crystals apparent 2 bottom of frame placed in weak layer

90

Figure 4.9 Twelve strength comparisons of short frame with standard frame. Significance levels less than 0.1 are shown.

Frames can usually be placed above the weak layer for the persistent weak layers that are so important to avalanche forecasting. For such frame placements, the short frame resulted in strength reductions of only 2% to 9%. The difference in mean strength measurement was only significant for one of five comparisons for mean strengths below 2.6 kPa. This lower range is particularly relevant to avalanche forecasting since the mean strength for the critically weak layers that released 38 of the 40 skier-triggered slabs tested with a standard frame (Chapter 7) was less than 1.6 kPa. Also, the front cross-member (that does not directly apply load to the specimen) of the short frame was observed to bend frequently when testing stronger layers. A thicker, stiffer front cross-member would reduce bending but could contribute to weak layer disturbance during frame placement. This bending problem combined with the fact that operators found the short frame difficult to place with respect to the weak layer question the merit of further studies with the short frame.

91 4.12.3 The Swiss Shear Frame

The Swiss shear frame used by Föhn (1987a) differs in every dimension and proportion from the others listed in Table 4.11. Most noticeably, the sheet metal is 2.5 times the thickness of the standard frame and the weight more than four times that of the standard frame. In three comparisons in which tests with the 0.05 m2 Swiss frame were alternated with the 0.025 m2 standard frame, the mean strength measurements obtained with the Swiss frame were 10%, 42% and 63% greater than the strength measurements obtained with the standard frame (Table 4.12). Such increases cannot be explained simply by the increase in normal load due to the mass of the Swiss frame since such increases would range between 1 % and 14% according to Eq. 4.12. The Swiss frame requires considerably more insertion force because it has more cross-members of thicker metal than the standard frame. The disturbance due to pushing the thicker cross-members through the snow and close to the weak layer could cause additional bonding and perhaps a measurable strength increase due to “fast metamorphism” (Gubler, 1982; de Montmollin, 1982) caused by the additional pressure on the weak layer.

4.12.4 The Finger-Fin Shear Frame

Lang and others (1985) used a very different shear frame for a study of surface hoar. The 0.01 m2 frame was designed by R.L. Brown and R. Oakberg to reduce stress concentrations by eliminating the active cross-members and using 32 “finger-fins”, each 10 mm wide, extending down from a top plate. Further, the fins were 8 mm shorter than the side walls to ensure that the fins did not penetrate into the weak layer. For comparison with the standard 0.025 m2 frame, a 0.025 m2 version of Brown and Oakberg’s finger-fin frame was built (Figure 4.6). Each of the 32 fins were 17 mm wide, 30 mm long and were 10 mm shorter than the sides of the frame. On 28 February 1995 and 18 March 1995, the frame resulted in higher mean strength measurements (Table 4.12), presumably due to the reduced stress concentrations. However, on 18 March

92 1995, it took 30 attempts to get 10 fractures on the weak layer being tested. The other 20 tests were rejected because the fracture occurred near the bottom of the finger-fins in the snow above the weak layer. There was no problem with the standard frame. A similar problem occurred on 24 March 1995, when no fractures occurred in the weak layer being tested during 14 attempts. Again, the standard frame produced consistent planar fractures. As discussed in Section 4.8, snowpack conditions often dictate that the shear frame be placed a certain distance above the weak layer, usually 0-10 mm. Since the finger-fin frames are designed to locate the fin-tips 8-10 mm above the weak layer, they cannot test as many weak layers as the standard compartmental frame.

4.13 Summary

Shear strength measurements from shear frame tests are assumed to be normally distributed since only 4 to 8 of 28 sets of 30 or more tests show evidence of non-normality (Section 4.2).

Coefficients of variation for shear frame tests average 0.15 and 0.18 from level study plots and avalanche start zones respectively (Section 4.3). These values are less than the 0.25 reported in previous studies and result in a reduced number of tests to achieve a particular level of precision.

Shear frame tests that result in divots more than 10 mm deep under the rear compartment of the frame yield strength measurements significantly greater than tests with planar fractures (Section 4.4). No significant effect could be detected for 10 other common shapes of fracture surfaces.

Shear frame strengths tend to increase at slower loading rates. However, the effect of loading rate on strength is reduced for loading times less than 1 second, and is negligible for mean strengths less than 1 kPa (Section 4.5). This is consistent with a laboratory study (Fukuzawa and Narita, 1993) using constant displacement rates that found brittle fractures and a reduction in strength of only 12% when loading times were reduced from 1.5 to 0.2 seconds.

93 The first two tests in a set of tests are more variable than subsequent tests and could be rejected to improve within-set variability (Section 4.6).

Although not recommended, delays of up to 3 minutes between placing the frame and pulling the frame do not appear to affect the resulting shear strength measurements (Section 4.7).

Placing the bottom of the frame in the weak layer results in lower strengths than placing the bottom of the frame a few mm above the weak layer (Section 4.8). Frame placements 2-5 mm above the weak layer usually result in planar fractures, but frames must sometimes be placed in the weak layer or more than 5 mm above it to obtain planar (shear) failures.

With consistent technique, there is no apparent difference in mean strength measurements obtained by different experienced shear frame operators (Section 4.9) using the same approximate loading rate and technique for placing the frame.

Shear frames with larger areas result in lower mean strengths than smaller frames (Section 4.10) as shown in previous studies. Although strength measurements obtained with larger frames usually show reduced variance compared to smaller frames, the reduction is not statistically significant. Based on the work of Sommerfeld (1980) and (Föhn, 1987a), strength measurements obtained with 0.01 m2 and 0.025 m2 frames are adjusted to the equivalent strength of a very large specimen, called the Daniels strength. In subsequent chapters, the strength measurements obtained with the 0.025 m2 standard frame are multiplied by the appropriate adjustment factor, 0.65, to obtain the Daniels strength.

Persistent weak layers of surface hoar and rounded facets do not show a significant strength increase with increased normal load. This is in contrast to the increase reported by Roch (1966b) for depth hoar and for non-persistent microstructures (Section 4.11). No adjustment for normal load (φ = 0) is applied to the strength of persistent weak layers in subsequent chapters. If a weak normal load effect exists for persistent layers—and more extensive field studies are recommmended—then the

94 stability indices in subsequent chapters for thick, dense slabs overlying persistent weak layers may be conservative.

Decreasing the distance between active cross-members while keeping the overall dimensions of the frame constant increases the number of stress concentrations and reduces the mean shear strength measurement (Section 4.12).

Decreasing the height of the active cross-members has an inconsistent effect, tending to increase the strength measurement when the bottom of the frame is placed in the weak layer and decrease the strength measurement when the bottom of the frame is placed above the weak layer. However, this study was complicated by bending of the front cross-member of the shorter frame and by difficulty placing the shorter frame.

The relatively heavy Swiss shear frame results in increased shear strength measurements compared to the 0.025 m2 shear frame used as a standard in the present study (Section 4.12.3).

The finger-fin shear frame results in decreased shear strength measurements due to reduced stress concentrations but restricts the operator's ability to place the frame a certain distance above the weak layer (Section 4.12.4), a practice that is often required to obtain planar fractures in particular weak layers.

95 5 FINITE ELEMENT STUDIES OF THE SHEAR FRAME TEST 5.1 Introduction

Although sloping snowpacks have been studied with finite element models (Curtis and Smith, 1975; Singh, 1980; Bader and others, 1989; Bader and Salm, 1990; Schweizer, 1993), a literature review revealed no finite element models of the shear frame test. In fact, neither analytical nor finite element models for the stress distribution have dealt with the effect of cross-member height or spacing between cross-members proposed by Perla and Beck (1983). In this chapter, a simple finite element model is developed and used to qualitatively assess the effect on the shear stress distribution due to: the stiffness of the snow within the frame, the placement of the shear frame with respect to the weak layer, and cross-member height and spacing between cross-members.

Figure 5.1 Geometry and loading for finite element model of standard shear frame placed 3 mm above weak layer.

5.2 The Model and Assumptions

The basic geometry of the two dimensional model is shown in Figure 5.1. The models consist of three isotropic layers: the snow within the frame (superstratum), the weak layer and the bed surface (substratum). The superstratum is modelled as either part 96 of a soft slab (~200 kg/m3) or part of a hard slab (~400 kg/m3). The weak layer is modelled as a 2-mm thick softer layer (~160 kg/m3). Material properties for the three layers were chosen from Mellor’s (1975) compilation of snow properties and are shown in Table 5.1. In four of the six models summarized in Table 5.2, the bottom of the frame is 3 mm above (ab) the weak layer. In the remaining two models, the bottom of the frame is 1 mm into the 2-mm thick weak layer.

Table 5.1 Material Properties for Finite Element Model Layer Nominal Density Young’s Modulus Poisson’s Ratio (kg/m3) (MPa) Soft Superstratum 200 10 0.25 Hard Superstratum 400 100 0.25 Weak Layer 160 2 0.25 Bed Surface 200 10 0.25

Table 5.2 Finite Element Models of the Shear Frame Test Model Shear Frame Stiffness of No. of Displacement Necessary Name Frame Placement with Superstratum Elements for Average Shear Respect to E (MPa) Stress of 1 kPa (mm) Weak Layer std-ab-soft std 3 mm above 10 7 130 0.0130 std-in-soft std 1 mm into 10 6 604 0.0130 std-ab-hard std 3 mm above 100 7 130 0.0077 5-ab-soft 5-fin1 3 mm above 10 7 110 0.0115 shrt-ab-soft short 3 mm above 10 5 570 0.0136 shrt-in-soft short 1 mm into 10 5 044 0.0136 1 frame has 5 cross-members or fins

The bed surface is fixed (0 displacement) 30 mm to the right of the frame, 20 mm to the left of the shear frame and at the base 30 mm below the weak layer. The left surfaces of the snow within the frame compartments were loaded with constant displacement to the right, in preference to pressure loading which would have tended to tilt the snow in the compartments unrealistically. The constant displacement for the left surface of each 97 compartment is a consequence of assuming that the frame is rigid. The displacement was chosen to cause an average shear stress in the weak layer of 1.0 kPa which is typical of the shear strength of persistent weak layers (Table 5.2). A linear model is used since shear frame loading times (< 1 s) are well within the range associated with linear stress-strain curves and brittle failures for tension (Narita, 1980, 1983; Singh, 1980) and for shear (Fukuzawa and Narita, 1993). However, such macroscopic linear behaviour does not rule out small-scale plasticity at stress concentrations and grain boundaries. Nevertheless, linear elasticity is assumed since it is sufficient to provide qualitative comparisons of different frame designs, frame placements and material properties. Since the sides of the frame restrict expansion during loading, a two-dimensional plane strain model is used. Each element is a bi-linear quadrilateral with nodes at each corner and the midpoint of each of the four sides. Such elements require additional calculations compared to four-node quadrilateral elements but they define a quadratic shape function which allows the sides of the elements to curve during deformation. In and near the lower tips of the active cross-members and the weak layer, the elements are 1 mm by 1 mm prior to loading as shown in Figure 5.2. At the upper and lower surfaces of the model, well away from the weak layer, the size of the elements increases to 4 mm by 1 mm to reduce the number of elements and consequently the number of computations. Elements are joined at nodes, providing continuity. Boundary conditions, such as displacements, are applied at the nodes. As a consequence of the assumed linear elasticity, the peak stresses depend strongly on the size of the elements—smaller elements resulting in higher peak stresses. For the following comparisons, the same mesh of elements in and near the weak layer is used for all models. Thus, the peak stresses reflect—at least relatively—the various geometries and the material properties that are being compared. The models, material properties and boundary conditions were encoded using Patran software. Finite element calculations were done by Abaqus software. 98

Figure 5.2 Finite element mesh for snow in left compartment and underlying weak layer and substratum.

5.3 Basic Stress Distribution σ The contour plot of XZ shows a stress concentration at each of the three active cross-members plus one at the right cross-member (Figure 5.3). This rightmost stress concentration indicates the effect of cutting around the frame with a blade through the 3 mm of superstratum below the frame and into the weak layer. The stress concentration at the leftmost cross-member is partly due to the applied displacement and partly due to the blade notching the weak layer. The superposition of these two stress concentrations results in the peak stress near the leftmost (back) cross-member (Figure 5.4). This explains why fracture surfaces with divots under the left (back) compartment (Table 4.3) are much more common than divots under the middle or right (front) compartments. The stress concentration at the three active cross-members is two-lobed. These two lobes extend into the weak layer which is 3 mm below the bottom of the cross-members and can be seen as σ peaks in XZ as shown in Figure 5.4. 99

σ Figure 5.3 Stress contours for xz for standard frame placed in soft superstratum 3 mm above weak layer. Displacement is 0.013 mm to the right on the left edges of the three compartments of snow in the frame.

σ Figure 5.4 Shear stress XZ in weak layer for standard frame placed 3 mm above weak σ layer representing average XZ of 1.0 kPa. 100 5.4 Effect of Frame Placement on Stress Distribution

The distance between the weak layer and the bottom of the shear frame as recommended in Chapter 3 is 2-5 mm. However, in practice the distance necessary to achieve planar shear failures ranges between 0 and 20 mm depending the strength of the σ weak layer and the hardness of the layer above the weak layer. The distribution of XZ in the weak layer is modelled for two common frame placements: frame placed 1 mm into a 2-mm thick weak layer and 3 mm above a 2-mm thick weak layer. As shown in Figure 5.5, σ the peak values of XZ are reduced when the frame is placed 3 mm above the weak layer compared to frame placements into the weak layer. This is consistent with field studies (Section 4.8) in which frames placed in weak layers resulted in lower strengths than frames placed 2-10 mm above weak layers. The analysis confirms that the more even stress distribution when the frame is placed above the weak layer is advantageous and should be used whenever practical.

σ Figure 5.5 Shear stress XZ in weak layer for standard frame placed in weak layer and 3 mm above weak layer. 101 5.5 Effect of Frames Placed in Hard and Soft Slabs

Ideally, a strength test should depend only on the mechanical properties of the test specimen. However, practical strength tests fall short of this ideal. The shear strength measured with the shear frame test depends on factors such as the frame design, the loading rate and the distance between the frame and the weak layer. The stiffness of the snow gripped by the frame (superstratum) may also affect the distribution of shear stress of the weak layer and strength. Since the same weak layer can not be tested in situ with superstrata of varying stiffness, finite element models are used. Young’s Moduli of 10 MPa and 100 MPa are chosen to represent soft (~200 kg/m3) and hard slabs (~400 kg/m3). For both models, the shear frame is 3 mm above a 2-mm thick σ weak layer. As shown in Figure 5.6, the distribution of XZ within the weak layer is more even for the hard slab than for the weak slab. The stiffer slab results in reduced stress peaks which would tend to increase the measured strength of the weak layer. Although the difference in stress distributions due to the varied stiffness of the superstratum is much less than the difference caused by placing the shear frame above or into the weak layer

σ Figure 5.6 Distribution of XZ for the standard frame placed in soft and hard superstrata. In both cases, the frame is 3 mm above the weak layer. 102 (Figure 5.6), the stiffness of the snow gripped by the frame is one more factor that can affect the measured strength of a weak layer.

5.6 Effect of Spacing Between Cross-members

In the field study summarized in Section 4.12, increasing the number of active cross-members from three to five while keeping the other dimensions of the frame constant consistently reduced the measured strength of the weak layer. To compare with that field study, a shear frame test with a 5-cross-member frame was also modelled with finite elements. For standard and 5-cross-member models (Figure 5.7), the slab was soft (E = 10 MPa) and the frames were 3 mm above the 2-mm thick weak layer. The σ distribution of XZ for both the standard frame and the 5-cross-member frame are shown in σ Figure 5.7. For the 5-cross-member frame, XZ has two more peaks, but all peaks are reduced in magnitude compared with those caused by the standard frame. Based on the assumption that the strength is determined by the peak stress, the reduced peaks

σ Figure 5.7 Distribution of XZ for 5-cross-member and standard frame. 103 associated with the 5-cross-member frame would suggest increased strength rather than decreased strength as measured in the field. There are at least two possible explanations: The assumption of strength being determined by peak stress is too simplistic. Specifically, the linear elastic model ignores plasticity in the snow near the lower edges of the cross-members. Although the peak stresses are reduced with the 5-cross-member frame, the number of peaks is increased by two. Thus the probability of a stress concentration due to a cross-member being near a flaw in the weak layer is increased. A more detailed model based on elasto-plasticity, or a non-continuum model based on a probabilistic distribution of bonds and “chains” (Kry, 1975; Gubler, 1978) is beyond the scope of this study.

5.7 Effect of Cross-Member Height σ The effect of cross-member height was assessed by comparing the distribution of XZ within the weak layer for the standard frame (40 mm cross-members) with the short frame (20 mm cross-members). The shear stress distribution is plotted in Figure 5.8 for both frames placed 3 mm above the 2 mm thick weak layer, and in Figure 5.9 for both frames placed 1 mm into the 2 mm-thick weak layer. In both cases, the difference between the stresses induced by the standard and short frame is minimal. This is consistent with the field studies (Section 4.12.2) which only detected a significant difference for 1 of the 5 comparisons with mean strengths less than 2.5 kPa. However, it is in contrast with Perla and Beck (1983) who proposed that reducing the frame height while keeping the distance between cross-members constant would concentrate the shear stress closer to the cross-members. This effect is not apparent in Figure 5.8 or 5.9. σ For particular material properties and geometry of the model, XZ is proportional to the displacement due to the assumption of linear behaviour. Thus, for average shear strength values in the 2.5 to 6 kPa range in which the in situ comparisons (Section 4.12.2) detected a significant effect of cross-member height, the model would also predict the same stress distribution for the short and standard height frames. Similarly, if the Young’s 104

σ Figure 5.8 Distribution of XZ in weak layer for standard and short frames placed 3 mm above the weak layer. The line for short frame is shifted 5 mm to the left for clarity.

σ Figure 5.9 Distribution of XZ in weak layer for standard and short frames placed 1 mm into the weak layer. The line for short frame is shifted 5 mm to the left for clarity. 105 Moduli for the superstratum, weak layer and substratum are scaled while maintaining the σ 10:2:10 ratio (Table 5.1), then XZ will also be scaled by the same factor for the models with short and standard frame heights. Hence, the finite element model does not show any σ substantial effect of frame height on XZ. This is consistent with the explanation offered in Section 4.12.2 that the measured difference between short and standard frames for relatively strong weak layers may be due to increased bending of the cross-members in the short frame.

5.8 Summary

There are stress concentrations associated with the active cross-members and with the notching of the weak layer caused by cutting along the front and back of the frame with a blade. However, such cutting is essential to ensure that a specimen of known size, free from restraint by the adjacent snowpack, is tested.

The stiffness of the snow within the frame influences stress concentrations and consequently the measured strength of the weak layer a few mm below the frame, although other factors such as the distance between the bottom of the frame and the weak layer may have a greater effect on stress concentrations, and consequently, on measured strength.

Placing the frame 2-5 mm above the weak layer reduces stress concentration and is recommended whenever practical.

The finite element model for the 5-cross-member frame shows two additional stress concentrations compared to the model for the standard 3-cross-member frame. However, the peak stresses for the 5-cross-member frame are reduced compared to the standard frame. Since the measured strength with the 5-cross-member frame is not increased compared to the standard 3-cross-member frame (Section 4.12.1), either strength is not determined simply by peak stress or the assumption of linear elasticity is too simplistic to model the stress concentrations at the lower edges of the cross-members. 106 According to the finite element models for frames placed 3 mm above the weak layer and for frames placed 1 mm into a 2-mm thick weak layer, the distribution of shear stress within the weak layer is not substantially affected by reducing cross-member height from 40 mm to 20 mm.

107 6 SHEAR FRAME RESULTS AND STABILITY INDICES 6.1 Introduction

While the emphasis in this chapter is on relating stability indices to natural and skier-triggered dry slab avalanches, Sections 6.2 and 6.3 relate the shear strength of weak layers to density and hand hardness. Before assessing a stability index for natural avalanches based on detailed on-site investigations by researchers, this limited set of investigated avalanches is shown to be similar to a much larger but less detailed set of avalanches reported by ski guides for the Columbia Mountains (Section 6.4).

Shear frame stability indices, SN and SN38 are assessed for natural avalanche activity on test slopes and in surrounding terrain in Sections 6.5 and 6.6, respectively. Shear frame stability index SS is related to skier-triggered slab avalanche activity on test slopes in

Section 6.7 and refined to obtain the stability index SK in Section 6.8. An “extrapolated” variation of SK called SK38 is assessed for skier-triggered slab avalanche activity in Section 6.9.

6.2 Shear Strength of Weak Layers Related to Density

The shear strength of dry snow is strongly related to density (e.g. Keeler and Weeks, 1968; Keeler, 1969; Mellor, 1975; Perla and others, 1982) and microstructure (e.g. Keeler and Weeks, 1968, Perla and others, 1982; Föhn, 1993). While laboratory studies have identified a decrease in the tensile strength of dry snow with an increase in temperature (Roch, 1966b; Narita, 1983), such an effect has proven difficult to identify in field studies of shear strength (Perla and others, 1982) or tensile strength (Jamieson, 1989). Although liquid water content also affects strength (e.g. Brun and Rey, 1987), it is not a factor in the present study which is restricted to dry snow. Grain size is not considered a predictor of strength since previous field studies have not established a significant effect (Perla and others, 1982; Jamieson, 1989; Föhn, 1993).

108 Perla and others (1982) reported shear strength of weak layers as a function of density but many density samples included snow from adjacent layers since the weak layers where thinner than their density sampler (20 mm). Föhn (1993) reported the shear strength of weak layers and interfaces but did not relate shear strength to density, presumably since many of the weak layers were too thin to be sampled for density. Further, since the failure planes for slab avalanches are often interfaces (Föhn, 1993), it would seem that density samples of failure planes and hence a relationship between the shear strength of failure planes and density are impossible. However, for approximately 17% of the failure planes tested with shear frames in the present study, the grains at the failure plane were indistinguishable from an adjacent layer (superstratum or substratum), and the adjacent layer was thick enough (> 35 mm) for density sampling. The shear strength of these weak planes is related to the density of the indistinguishable adjacent layers in this section. Since surface hoar is always too thin for density sampling and always distinct from adjacent layers that are thick enough for density sampling, no data for surface hoar are included in this section. The dependence of tensile and shear strength on density is non-linear (e.g. Keeler and Weeks, 1968; Keeler, 1969; Martinelli, 1971; Mellor, 1975; Perla and others, 1982; Jamieson and Johnston, 1990). Ballard and Feldt’s (1965) theoretical model for sintering of rounded grains is inappropriate since the microstructure of many of the weak layers in the present study are not rounded and show little evidence of sintering. Also, Perla and others (1982) obtained a better fit to shear frame strengths with the relation Σ ρ/ρ B = A( ice) (6.1) ρ 3 where ice is the density of ice (917 kg/m ) and A and B are empirical constants that depend on microstructure. Since the variance of snow strength increases with the mean strength, Martinelli (1971) and Jamieson and Johnston (1990) stabilized the variance with a logarithmic transformation. A log-log transformation of Eq. 6.1 yields Σ ρ/ρ ln = ln A + B ln ( ice) (6.2)

109 For microstructure classes 1 to 5 (Colbeck and others, 1990), the empirical variables A and B and the coefficients of determination, R2, are shown in Table 6.1 for regressions of Daniels strength on density with and without the logarithmic transformation. The mean Daniels strengths are also plotted in Figure 6.1. Graupel (class 1f) is distinguished from other types of precipitation particles with a different symbol. As reported by a field study of tensile strength (Jamieson and Johnston, 1990), layers of graupel are generally weaker than other types of precipitation particles with the same density. Similarly, Figure 6.1 uses a different symbol for rounding facets (class 4c) than for other types of facets. As shown in Table 6.1, the seven mean strengths of rounding facets are not correlated with density. However, the mean strengths of the rounding facets fall within the 46 mean strengths for faceted grains, and the subclass is subsequently included within the class of faceted grains.

Table 6.1 Strength-Density Regressions by Microstructure Microstructure No. of Density Regression Regression (Colbeck and Mean ρ Σ ρ/ρ B Σ ρ/ρ ∞ = A( ice) ln ∞ = ln A + B ln ( ice) others, 1990) Strengths 3 (kg/m ) ABR2 ABR2 Precipitation 11 50-110 8.3 1.55 0.44 3.09 1.18 0.33 Particles1 (1) Graupel (1f) 3 110-235 ------Decomposed/ 65 65-270 24.9 2.07 0.67 12.8 1.74 0.42 Fragmented (2) Rounded Grains 12 105-270 12.2 1.52 0.57 10.2 1.44 0.60 (3) Faceted 46 110-330 16.4 1.94 0.35 22.3 2.25 0.57 Crystals2 (4) Rounding Facets 7 205-280 1.35 -0.10 0.00 1.15 -0.20 0.01 (4c) Depth Hoar (5) 2 250-280 ------Group I 1 (1,2,3) 88 50-270 23.0 2.00 0.73 13.7 1.76 0.63 Group II (4,5) 55 110-330 14.0 1.80 0.32 22.8 2.23 0.54 1 excluding graupel (1f) 2 excluding rounding facets (4c)

110 In the Columbia Mountains where most of the strength measurements were made, precipitation particles (class 1) generally metamorphose into decomposed grains (class 2) which in time metamorphose into rounded grains (class 3). Not surprisingly, these three microstructures show a continuous increase in strength with increasing density, and are assembled as Group I microstructures for additional regressions shown in Table 6.1. A similar trend for Group I microstructures has also been shown for tensile strength (Jamieson and Johnston, 1990). Commonly in the Rocky Mountains of western Canada and occasionally in the Columbia Mountains, faceted grains (class 4) metamorphose into depth hoar (class 5). In Figure 6.1, these two microstructures show a similar increase in strength with increasing density. They are assembled into Group II for additional regressions in Table 6.1. For the regressions of Daniels strength on density using Equations 6.1 and 6.2, the coefficients of determination for the 55 points with Group II microstructures are 0.32 and 0.54 respectively. For the 88 points with Group I microstructures, the corresponding

Figure 6.1 Daniels strength for weak layers by microstructure and density.

111 coefficients of determination are 0.73 and 0.63. Since the Group II microstructures show reduced coefficients of determination for fewer points, the mean shear strengths are clearly more variable as a function of density. This is consistent with previous studies for tensile strength (Sommerfeld, 1973; Jamieson and Johnston, 1990). As shown in Table 6.1, the log-log transformation reduces the coefficient of determination for Group I microstructures, and increases it for Group II microstructures. Since the intent of the transformation was to stabilize the variance, the preferred regression will be the one with the more consistent variance. For both regressions, the variance for five strength intervals is plotted for Group I and II in Figure 6.2. For this comparison, the variance for each interval is normalized using the total variance for the entire range of strengths. For both microstructure groups, the log-log transformation increases the normalized variance for low strengths and decreases it for high strengths. However, Group I microstructures show a more consistent variance without the transformation and the Group II microstructures show a more consistent variance with the transformation. The greatest normalized variance is, not surprisingly, for the highest strengths and there are more high strengths for Group II microstructures. Martinelli (1971) used the logarithmic transformation for strengths that ranged up to 100 kPa and Jamieson (1989) found that the transformation effectively stabilized the variance for tensile

Figure 6.2 Normalized regression variance for Group I and II microstructures.

112 strengths that ranged up to 8 kPa. For the generally low shear strengths associated with weak layers, the transformation is only effective for the highest measured strengths. Nevertheless, the preferred regressions are the ones with the most consistent variance (and highest coefficients of determination). The best fit for Group I microstructures is obtained with the regression based on Eq. 6.1 and with its logarithmic transformation (Eq. 6.2) for Group II microstructures. For the range of densities reported in Table 6.1 and Figure 6.1, the regression line for Group II microstructures falls below the line for Group I microstructures. This is consistent with field observations that faceted grains are weaker than partly decomposed and rounded grains with the same density.

6.2.1 Comparison with Previous Field Study

Perla and others (1982) also reported shear strength as a function of density for the common microstructures. Although they used a very similar frame (0.025 m2 with three active cross-members), there are several relevant differences. In the present study: The shear frames are pulled to failure within 1 s, resulting in brittle fractures —according to Fukuzawa and Narita (1993)—whereas some of Perla and others (1982) results could involve ductility since they were pulled to failure “within a few seconds”. The strengths are only plotted against density and regressed on density when the resistance and grain type of the weak plane are indistinguishable from an adjacent weak layer that is thick enough for a density sampler, whereas Perla and others (1982) took density samples centred on the weak layer and hence included snow from the layers above and below the weak layer whenever the weak layer was thinner than their density sampler. The data are exclusively for weak layers whereas most of the results from Perla and others (1982) are for homogeneous layers. Perla and others (1982) report regression parameters similar to those in Table 6.2 and based on Eq. 6.1. Their regressions for the 0.025 m2 shear frame are readily converted

113 to Daniels strength by multiplying the coefficient A in Eq. 6.1 by 0.65 (Sommerfeld, 1980; Föhn, 1987a). For the four microstructures common to Perla and others (1982) and the present study, the regressions on density are compared in Figure 6.3. As shown in Figure 6.3, Perla and others (1982) report shear strengths over a wider density range, presumably because they did not restrict their tests to weak layers. Only for layers of precipitation particles did Perla and others (1982) report lower strengths, and then only by approximately 0.1 kPa. For decomposed and fragmented precipitation particles, both studies report similar strengths, although strengths from the previous study are approximately 0.2 kPa higher for a density of 250 kg/m3. Similarly for rounded grains and faceted crystals, the strengths from Perla and others (1982) are substantially higher than those from the present study for densities greater than 250 kg/m3. Such differences are not surprising since the present study was restricted to weak layers and to loading times of less than 1 s, both of which are associated with lower strengths.

Figure 6.3 Shear strengths from present study compared with those from Perla and others (1982) for four common microstructures.

114 6.3 Shear Strength of Weak Layers Related to Hand Hardness

The most widely used measure of resistance in Canada and internationally is “hand hardness”, which results from a simple, quick and empirical test. A fist, four finger tips, one finger tip, the blunt end of a pencil or a knife tip is pushed horizontally into a snow layer while wearing gloves. The hand hardness is simply the bluntest object that can be pushed into the snow with a force of 10-15 N in Canada (NRCC/CAA, 1989; CAA, 1995) or 50 N internationally (Colbeck and others, 1990). (For the present study, the hand hardness of layers as thin as 3 mm were tested using a thin plastic ruler to compare their resistance with a thicker layer in the same pit for which the hand hardness could be determined with a fist, fingers, pencil or knife.) The levels of hand hardness are abbreviated as F, 4F, 1F, P and K. Snow layers with resistance between the five major levels of hand hardness can be qualified with a “+” or “-” sign, giving 15 levels: F-, F, F+, 4F-, 4F, 4F+, 1F-, 1F, 1F+, P-, P, P+, K-, K and K+ (CAA, 1995). Ice layers harder than “knife” are labelled I for ice. For the four most common microstructures, mean Daniels strengths are plotted for hand hardness classes of F, 4F, 1F and P in Figure 6.4. Along with each mean, “whiskers” show the range of two standard errors. An increase in variability as indicated by the standard error is apparent for increasing mean Figure 6.4 Shear strength by hand hardness for common strength. For sets of more microstructures. The number of data for each hand hardness level and microstructure are shown.

115 than 20 data there is an approximate probability of 0.95 of the population mean falling within two standard errors of the sample mean, so the means of hand hardness for two different microstructure classes differ at the 0.05 significance level when their whiskers do not overlap. The usefulness of hand hardness as an index of shear strength can be assessed from the trends evident in Figure 6.4. For each of the four classes of microstructure, mean strength increases significantly with hand hardness. Also, for hand hardness levels of F and 4F, the mean strength for decomposed and fragmented grains is significantly higher than for precipitation particles. For each of the four hand hardness levels, the mean strength for rounded grains is significantly stronger than for decomposed and fragmented grains. For hand hardness levels of F, 4F and P, the mean strength of faceted crystals is less than for rounded grains, and for 1F hardness, the reduction in mean strength for faceted crystals is not significant. Consequently, as an index of shear strength, hand hardness is best interpreted together with microstructure. Since the area of the objects being pushed into the snow does not decrease proportionally from fist to knife, hand hardness is an ordinal and not an interval measure. The CAA's geometric scale for hand hardness (NRCC/CAA, 1989; CAA, 1995) is intended to provide a graphical indication of resistance that better reflects quantitative —but more time consuming—measures of the resistance such as is obtained with the ram penetrometer (e.g. Martinelli, 1971). For this geometric scale, each major level of hand hardness is plotted at twice the hardness-value of the preceding major level. Hence, 1-finger (1F) is considered to be twice as hard as four-finger (4F) and four times as hard as fist (F), which is given an arbitrary value that allows all values to be plotted on a particular graph. Using this doubling scale and the intermediate hardness levels such as 4F+, the Daniels strength is plotted against hand hardness in Figure 6.5 for the two classes of microstructure with the most data. An approximately linear relationship is apparent between Daniels strength and scaled hand hardness, which supports the use of the doubling scale.

116

Figure 6.5 Shear strength plotted against scaled hand hardness showing approximately linear relationship for 126 layers of decomposed and fragmented particles and for 140 layers of faceted crystals.

6.4 Characteristics of Persistent Slab Avalanches 6.4.1 Comparison of Reported and Investigated Dry Slab Avalanches

Before assessing the results of shear frame tests done near recent dry slab avalanches, it is helpful to consider whether the avalanches selected for such tests are a representative sample of the dry slab avalanches of concern to backcountry avalanche forecasting. In addition to on-site investigations that included rutschblock tests and shear frame tests on the failure plane as well as measurements of slab thickness, slope angle, etc. (Appendix C), basic observations of many avalanches are available from daily occurrence reports from ski guides. These occurrence reports include estimates of slab thickness, avalanche width, slope angle, elevation, etc. and are based on a Canadian specification for reporting avalanche occurrences (CAA, 1995). In this section, the slab thickness, slab width and start zone inclinations from occurrence reports and on-site investigations are compared (Table 6.2). The occurrence reports are limited to class 2 and larger avalanches which are, by definition, large enough to injure, bury or kill a person. Smaller avalanches are not reported consistently or completely and are of lesser importance to backcountry forecasting and the present study. The avalanche occurrence reports used for Table 6.2 are

117 from the winters of 1990 to 1995 in the Cariboo and Monashee Ranges of the Columbia Mountains. Mean slab thickness and start zone inclinations from occurrence reports and investigations are compared using a two-tailed t-test for unequal sample sizes and unequal variances (Eq. 4.3). As shown in Table 6.2, there is no significant difference (p > 0.05) between the mean thickness or width of the class 2 and larger slab avalanches reported by ski guides and those investigated by researchers. However, the reported natural avalanches started in significantly steeper terrain than the investigated natural avalanches. This difference is not surprising since some natural avalanches start in very steep terrain which can be difficult or unsafe to access for investigations. Also, the investigated skier-triggered avalanches are significantly steeper than the reported skier-triggered avalanches. However, since the reported start zone inclinations are estimated and the investigated start zone inclinations are measured, the difference may simply be the result of inclinations being under-estimated. During several investigations of reported avalanches, a tendency towards under-estimated slope inclinations was noted.

Table 6.2 Comparison of Avalanche Characteristics from Occurrence Reports and On-Site Investigations Reported Dry Slab Investigated Dry Slab t-test Characteristic Avalanches1, Avalanches2 Class 2 and Larger N Range Mean±S.D. N Range Mean±S.D. tp Natural Slab Thickness (m) 286 0.1-2.0 0.53±0.32 14 0.4-1.5 0.59±0.29 -0.77 0.45 Slab Width (m) 239 8-1500 121±182 14 20-350 114±90 0.26 0.80 Start Zone Incline (o) 258 25-60 40±6.0 17 30-45 37±3.7 3.09 <10-2 Skier-Triggered Slab Thickness (m) 36 0.2-1.2 0.55±0.24 51 0.1-1.5 0.46±0.26 1.66 0.10 Slab Width (m) 28 8-400 69±78 39 2-400 59±94 0.47 0.64 Start Zone Incline (o) 33 20-45 35±5.0 51 28-48 39±4.7 -3.67 <10-3 1 Reports are from Cariboo and Monashee Mountains near Blue River, BC. 2 Investigations are from Cariboo, Monashee, Purcell and Selkirk Mountains.

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6.4.2 Characteristics of Investigated Slab Avalanches

Aside from the differences in start zone inclination, the investigated slab avalanches appear to be representative of the natural and skier-triggered slab avalanches in the Columbia Mountains. Snowpack measurements and observations from the investigations are summarized in Table 6.3 for natural and skier-triggered slab avalanches. Also, Figure 6.6 shows the thicknesses of the slab, superstratum, weak layer and substratum for the natural and skier-triggered dry slab avalanches in this study. An inclination of 38o is typical of start zones for natural and skier-triggered dry slab avalanches in this study

Table 6.3 Characteristics of Investigated Dry Slab Avalanches from Columbia Mountains 1990-95 Natural Skier-Triggered N Range Mean ± N Range Mean ± S.D. S.D. Slab Thickness (m) 14 0.37-1.5 0.59 ± 0.29 51 0.1-1.5 0.46 ± 0.26 Density (kg/m3) 10 101-259 189 ± 53 48 76-374 162 ± 70 Superstratum Thickness (m) 14 0.03-0.30 0.15 ± 0.08 45 0.01-0.35 0.11 ± 0.08 Density (kg/m3) 3 70-232 143 ± 82 14 98-300 161 ± 54 Weak Layer Thickness (mm) 41 20-30 23 ± 5 232 5-80 21 ± 16 Density (kg/m3) 2 180-230 205 ± 35 7 55-200 121 ± 49 Daniels Strength (kPa) 10 0.27-2.27 1.06 ± 0.60 48 0.04-2.123 0.57 ± 0.45 Substratum Thickness (m) 12 0.01-0.34 0.13 ± 0.12 41 0.01-0.65 0.19 ± 0.14 Density (kg/m3) 1 294 294 12 106-450 212 ± 88 1 An additional 10 weaknesses were recorded as interfaces (thickness 0 mm) 2 An additional 21 weaknesses were recorded as interfaces (thickness 0 mm) 3 Includes high strengths from some remotely triggered avalanche discussed in Chapter 8.

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Figure 6.6 Cross section of typical dry slab avalanches. Layer thicknesses are measured vertically.

(Table 6.2) and in others (Perla, 1977; Williams and Armstrong, 1984, p. 201; Föhn, 1987a). The dominant microstructures for the superstratum, weak layer and substratum are summarized in Figure 6.7. Although approximately 15% of the superstrata consisted of faceted crystals, microstructures such as rounded grains, crusts and decomposed and fragmented precipitation particles were more common. Depth hoar and surface hoar crystals were not observed Figure 6.7 Relative frequency of microstructures for superstratum, weak layer and substratum of dry slab in the superstrata. Faceted crystals avalanches in Columbia Mountains, 1990-95.

120 and surface hoar were commonly observed in the weak layers but crusts were never reported as a weak layer. Faceted crystals were more common in weak layers than depth hoar, indicating that the earlier products of kinetic metamorphism are often critically weak, a finding consistent with Bradley and others (1977a, b) and Adams and Brown (1982). The weak layers are more likely to consist of faceted crystals or surface hoar than are the superstrata, and the substrata consist of a wide assortment of microstructures. Crusts occurred more often in the substrata than in the superstrata. The microstructures of the superstrata, weak layers and substrata are shown separately for natural and skier-triggered dry slab avalanches in Figure 6.7. Less metamorphosed forms such as precipitation particles and decomposed and fragmented precipitation particles were observed more often in the superstrata of skier-triggered avalanches than in natural avalanches. The substrata for skier-triggered slabs also show the same bias toward less metamorphosed microstructures compared to natural slab avalanches. This is not surprising since skiers, and guides in particular, ski test slopes with shallower, younger slabs, and avoid slopes with deeper, older slabs that might be unstable and consequently, more dangerous. For natural avalanches, faceted crystals were found in the weak layers more often than surface hoar, whereas the opposite was true for skier-triggered avalanches. This association of surface hoar with skier triggering is consistent with a study of fatal accidents in Canada (Jamieson and Johnston, 1992a) in which 41% of the identified weak layers consisted of surface hoar. The distribution of hand hardness for the superstratum, weak layer and substratum is shown in Figure 6.8 for natural and skier-triggered dry slab avalanches in the Columbia Mountains. Although the hand hardness levels are scaled (NRCC/CAA, 1989; CAA, 1995), the distributions are summarized with the median, and 10, 25, 75 and 90th percentiles which are suited to ordinal data. For natural avalanches and skier-triggered avalanches, the mean hardness of the weak layers (4F) are less than for the superstrata (1F) or substrata (P- for natural avalanches and 1F for skier-triggered avalanches). As well, based on the CAA’s doubling scale, the hardnesses of the superstrata and the substrata are more variable than the hardness of the weak layers. Although a softer weak

121

Figure 6.8 Resistance for superstratum, weak layer and substratum of dry slab avalanches in Columbia Mountains, 1990-95. layer sandwiched between two harder layers is common for slab avalanches, similar “sandwiches” also occur in stable snowpacks. Nevertheless, recognition of such hardness sandwiches is helpful for stability evaluation (e.g. Fredston and Fesler, 1994, p. 56-57). Subsequent sections of this chapter assess shear frame stability indices for natural avalanches (Section 6.5 and 6.6) and for skier-triggered avalanches (6.7, 6.8 and 6.9).

6.5 Predicting Natural Avalanches on Test Slopes

In this section, a stability index for natural avalanches is compared with natural avalanche activity on avalanche slopes tested with the shear frame. Although it is impractical for avalanche safety operations that forecast for large backcountry areas to test weak layers in numerous starting zones with the shear frame, a comparison of avalanche activity for low and high values of the stability index is a useful way of assessing whether the index can discriminate between stable and unstable slopes (Föhn, 1987a). The slope-specific stability index for natural avalanching is

122 Σφ S = (6.3) N ρgh sin Ψ cos Ψ

where Sf is the Daniels strength adjusted for the effect of the normal load due to the overburden, r is the average slab density, h is the vertical thickness of the slab and Y is the slope inclination in the start zone. This index differs from S developed by Föhn (1987a) only in that the effect of normal load on shear strength varies with the microstructure of the weak layer, based on data presented in Section 4.11. Since the effect of normal load on persistent microstructures is taken to be negligible based on field data presented in Figure

4.7, SN is lower and hence potentially more conservative than S for persistent slabs, especially for deep slabs which apply high normal loads to the underlying weak layer. (An error analysis for this index is presented in Appendix B.) Shear frame tests were done within 2 days of 10 natural dry avalanches involving persistent slabs and one involving a non-persistent slab. The mean slab thickness of these

avalanches is plotted against the stability index SN in Figure 6.9. In each case, SN is based

Figure 6.9 Values of SN for slopes that did and did not avalanche naturally.

123 on shear frame tests of the failure plane. For comparison, Figure 6.9 also includes points from 29 persistent slabs and 33 non-persistent slabs that did not avalanche, in which case the weak layer judged most likely to fail was tested with the shear frame.

Since there is only one non-persistent slab that failed naturally, SN's ability to predict the natural stability of non-persistent slabs cannot be determined.

However, 10 of the 39 persistent slabs failed naturally. Values of SN for the 10 persistent slabs that released naturally range widely from 0.9 to 8.5. The four natural avalanches for which SN > 4 are labelled with the location in Figure 6.9. It appears that increased air temperatures contributed to the slab failures or that subsequent cooling contributed to the surprisingly high values of SN. At the Roller Coaster avalanche on 1 February 1993, a crust had developed on the surface of the slab and bed surface, indicating that at least one melt-freeze cycle had occurred after the avalanche and before the shear frame tests two days later, rendering the shear frame results questionable. The Arrowhead avalanche occurred at 2700 m elevation during marked warming and snowfall on 2 March 1994 when freezing levels and rain rose to approximately 2000 m. The tests were done a day later when the air temperature in the start zone had dropped to -6.7oC. The Elk avalanche occurred at 2500 m elevation on 4 March 1994 during an unusually warm period when the freezing level rose to 2000 m. The shear frame tests were done a day later when the air temperature had dropped to -13.5oC. Similarly the Sherbrooke avalanche occurred on 28 December 1994 when air temperatures rose to -2oC and the shear frame tests were done 2 days later when the air temperature had dropped to -21oC. The Elk and Sherbrooke avalanches occurred during warming without substantial loading and the Arrowhead avalanche occurred during warming and loading by snowfall.

Nevertheless, SN does not appear promising for predicting natural avalanches in which warming contributes to slab failure by increasing the shear strain rate without increasing the shear stress. This is not surprising since the stability index SN is a critical stress failure criterion (Eq. 6.3) whereas laboratory studies of snow in tension (Salm, 1971; Narita, 1980, 1983) show that the peak stress for ductile failure depends on the strain rate and Brown and others (1973) showed that the peak stress depends on the strain history.

124

The merit of SN for predicting natural avalanches due to loading by precipitation could also be questioned because the critical stress for ductile failure depends strongly on the strain rate which is not part of the shear frame stability index2. Yet, shear frame stability indices have already proven themselves (Schleiss and Schleiss, 1970; Föhn, 1987a; Jamieson and Johnston, 1993a) to be useful for predicting natural avalanches, most of which are caused by loading due to precipitation. However, the critical values of shear frame stability indices which are based on brittle strength of small areas are questionable since natural avalanching involves initial ductile failure of large areas. Schleiss and Schleiss (1970) found Σ/ρgh to be critical at approximately 1.5. Jamieson and Johnston (1993a) found a similar index for natural avalanching to be critical between 2.8 and 3. Further, in Föhn’s (1987a) study in the Swiss

Alps, values of SN for 18 dry slabs that failed averaged 2.3 and SN was less than 1.5 for only three of these slabs, suggesting a critical value greater than 2.3. In Figure 6.9, only 10

values of SN were obtained for persistent slabs that failed and four of these can be rejected

based on temperature effects. However, a critical value near 2 appears likely since SN < 2

for five of the six natural avalanches not attributed to warming and SN > 2 for 24 of the 29 slabs that did not avalanche naturally. The number of slabs that avalanched naturally and were tested with shear frames is very limited partly because access to fresh dry slab avalanches within a day or two of slab failure is restricted by safety considerations, helicopter logistics, poor flying weather and snowmobiling difficulties. However, the primary reason for this limitation is the fact that research technicians were directed to try to access skier-triggered slab avalanches in

2 A critical strain rate failure criterion might be more promising since, based on the work of McClung (1977) and Narita (1980), Bader and Salm (1990) showed that the critical strain rate for the low density snow associated with weak layers was approximately 10-4 s-1. However, Sommerfeld's (1979) strain gauge on an avalanche slope was removed and presumably damaged by the first avalanche. A practical strain gauge for avalanche slopes and stability index based on strain rate have not yet been developed.

125 preference to natural avalanches whenever there was a choice because skier-triggered avalanches cause many more backcountry fatalities than do natural avalanches.

The next section assesses a variation of SN using reported natural avalanche occurrences from surrounding slopes where more data were available than for investigated avalanche slopes tested with the shear frame.

6.6 Predicting Natural Avalanches of Persistent Slabs on Surrounding Slopes

In this section, natural avalanche activity over a large area is compared with a stability index measured at a safe study site. Although most of the dry slab avalanches were within 10-15 km from the study site, some were 30 km away. The study sites ranged in inclination from 0 to 32o, were rarely exposed to avalanches from slopes above, and were generally sheltered from the wind. However, aside from wind effects, sites were selected that had a snowpack similar to surrounding avalanche terrain. The study sites were near treeline and ranged in elevation from 1900 to 2300 m. Most avalanche start zones in the study areas are between 1700 and 3000 m. Most snow storms are accompanied by wind from the south, south-west or west which increases the amount of snow deposited on the north, north-east and east slopes. The inclined study sites face north, north-east and east as do many of the slide paths on which avalanches were reported. Since the objective of this section is to apply a stability index to slopes of various inclinations many km away from the study slope, a slope angle of Ψ = 38o that is typical of slab avalanche start zones (Table 6.2) is used in Eq. 6.3 to obtain SN38. Between the low values of a stability index that are associated with unstable slabs and the high values that are associated with stable slabs, there is a critical or transitional value. In practice, the transition consists of a band of values because of differences in snow conditions between avalanche starting zones and study sites and because of the variability of shear strength and overburden measurements. Since stability indices are used in conjunction with other observations, the width of the transition band is based on the

126 90% confidence band for the stability indices. The width of this band can be approximated from the shear strength measurements which are more variable than the density

measurements. Typically, values of SN38 are based on 12 shear frame tests in a study site that have an average coefficient of variation of 15% (Section 4.3). This corresponds to a 90% confidence band approximated by ±10% of the transitional value. Persistent weak layers underlying thick slabs generally change in strength more slowly than persistent weak layers underlying shallow slabs. For this reason, persistent weak layers were tested with the shear frame approximately twice per week when the slab depths in the study sites were less than approximately 0.6 m and once per week when the persistent weak layers were more deeply buried. Dry slab avalanche activity can be compared with values of the stability index on those days that persistent weak layers were tested with the shear frame. However, avalanche activity can also be compared with stability indices between test days by linearly Σ σ ρ interpolating the strength ∞ between test days and estimating the load v = gh daily based on precipitation recorded at the nearest weather station. For example, if the shear strength and load were measured at a particular study site on the ith and kth days, then the load on the jth day is

HNWj σ =σ − + (σ −σ ) v,j v,j 1 k v,k v,i (6.4) Σi HNW where i < j < k and HNW is the water equivalent of the precipitation over the previous 24 σ σ Σ k hours. Values of ( v,k - v,i)/ i HNW vary with the study site. At Mt. St. Anne in the Cariboos, the study plot receives an average of 0.013 kPa of load in the study plot per mm of water in the precipitation gauge located 100 m away. Similarly, Sam’s study site in the Monashee Mountains receives an average of 0.015 kPa of load per mm of water in the Mt. St. Anne precipitation gauge 23 km away. In the Purcell Mountains where the height of snowfall within the previous 24 hours, HN, was used in lieu of HNW which requires a melting precipitation gauge or regular weighing of a column of snow from the previous 24 hours, 0.012, 0.016, 0.021 and 0.032 kPa of load are typically received at the Vermont (1600 m), Elk (2250 m), Pygmy (2150 m) and Rocky (1900 m) study sites respectively for

127 each cm of snowfall recorded at the Bobby Burns Lodge (1370 m). The Rocky study site is located in the Crystalline Valley which is known for heavier snowfall than nearby valleys. While precipitation and hence increase in load could be estimated daily for particular study sites based on precipitation at the nearest weather station, the changes in strength cannot be estimated based on meteorological parameters or easily measured snowpack properties. This means that at present the only way to determine a shear frame stability index is to access a study site, dig a pit and perform the shear frame tests, a practice that would be impractical for most backcountry avalanche forecasting operations to do on a daily basis. However, by interpolating load between test days, the merit of extrapolating stability indices to surrounding terrain can be assessed. Extrapolating to surrounding terrain with a stability index is not new. The highway avalanche safety programs for the Trans-Canada Highway through Rogers Pass (Schleiss Σ ρ and Schleiss, 1970) and for BC Highway 3 through Kootenay Pass use the ratio 100/ gh for surrounding terrain. However, neither program has been able to verify the merit of this ratio mainly because operational staff only perform the shear frame tests when other forecasting factors indicate low stability (Salway, 1976). Jamieson and Johnston (1993a) obtained shear frame data from Mt. St. Anne during days in which dry slab avalanches were reported and days in which no such avalanches were reported. The shear frame tests were done on the weak layer that appeared to be least stable at the study site. They used Σ ρ the ratio 250/ gh as well as the index S35 which uses the normal load correction for rounded grains (Roch, 1966b; Föhn, 1987a). Using empirically chosen critical levels and a ±10% band for transitional stability, the predictive merit of the indices was indicated by the fact that the values were below the transition band on approximately 84% of days in which natural dry slab avalanches were reported and above the transition band for 73% of the days in which no natural dry slab avalanches were reported. However, that study correlated S35 for the weak layer that appeared least stable in the study plot with all dry natural slab avalanches that were reported to occur on the day of the shear frame tests. S35

128 was not interpolated between test days, and neither the tested weak layers nor the failure planes for the natural dry slab avalanches were restricted to persistent weak layers. In general, selecting a critical level that is too high will result in excessive false predictions of instability, and a critical level that is too low will result in excessive false predictions of stability. The latter type of prediction errors are called false stable predictions and are potentially far more serious because they can contribute to an unstable

slope being judged stable. In the Swiss Alps, values of SN for 18 dry slabs that avalanched naturally averaged 2.3 (Föhn 1987a), suggesting a critical value greater than 2.3. However, when extrapolating to surrounding terrain a higher critical value may be appropriate because of the greater variability in snowpack properties over larger areas and the need to reduce the proportion of false stable prediction errors. Jamieson and Johnston

(1993a) empirically determined critical values of S35 that averaged 3.0 for the level study

plot and 2.8 for a nearby study slope at Mt. St. Anne. In the following studies of SN38, a

critical value of 2.8 is used to assess the merit of SN38 for discriminating between avalanche and non-avalanche days.

Since SN38 is a ratio of shear strength to shear stress, increases in SN38 over time indicate that the shear strength of the weak layer is increasing faster than shear stress due

to slab weight, whereas decreases in SN38 indicate that the shear stress due to slab weight is increasing faster than the shear strength of the weak layer. Decreases in shear strength due to metamorphic weakening of the weak layer are not common in the Columbia Mountains and measurable decreases in load due to sublimation exceeding precipitation

are also not common; therefore most decreases in SN38 are due to increases in slab weight and shear stress caused by precipitation. Due to varying amounts of snowfall (load) between study sites and start zones, extrapolation of stability from a study site to a start zone might not seem promising. However, snow layers under heavier slabs tend to densify and strengthen faster than an initially similar layer under a lighter slab (Armstrong, 1980). This tendency reduces the differences between stability indices for particular weak layers from areas with different loads.

129 When attempting to correlate a stability index of a particular weak layer in a study site with avalanche activity over a wide area, there may be uncertainty associated with the identification of the failure plane of the avalanches. Some fresh avalanches cannot be approached safely. More often, operational staff do not have time to verify the failure plane by visiting the crown or flanks. Frequently, an observer identifies the failure plane from a distance of up to several hundred metres away based on the depth of the crown and flank fractures and on knowledge of weak layer depths from snow profiles often within a few km of the avalanche. Typically, two to four persistent weak layers are repeatedly tested with the shear frame over a period of two or more weeks each winter at each of the two main forecast areas, i.e. the Purcell Mountains near Bobby Burns Lodge and the Cariboo and Monashee Mountains near Blue River, BC. However, not all of these persistent weak layers produce sufficient avalanches for comparison with stability indices such as SN38. From those persistent layers that were monitored, there were three from the Purcell Mountains, three from the Cariboo and Monashee Mountains, and two from Jasper National Park that produced natural dry slab avalanches on at least two days. Based on testing of these eight layers, the ability of SN38 to discriminate between avalanche and non-avalanche days is assessed in the following three subsections. 6.6.1 Purcells

During the winter 1992-93, shear frame tests were done at two level study plots: Rocky at 1900 m and Pygmy at 2150 m, and at 25-35o slopes adjacent to these plots. At each of these sites a layer of surface hoar buried on 18 January 1994 was tested. Intervals between testing ranged up to 14 days, partly since a helicopter was unavailable for site access during two 1-week periods. The only natural dry slab avalanches that were reported to have started on the surface hoar layer occurred on 30 January 1993 and 4 February 1993 (Figure 6.10). Although shear frames tests had not been started yet on the surface hoar at Rocky Plot, the index SN38 was below 2.8 at Pygmy Plot, Pygmy Slope and Rocky Slope on 30 January 1993 when approximately five dry slab avalanches started on the surface hoar layer. However, by 4 February 1993 when the last avalanche started on

130 the surface hoar

layer, SN38 was below 2.8 only at the Rocky Slope. For three to four weeks, there were no natural dry slab avalanches

reported and SN38 remained above 2.8. During 6 March to 15 March, natural dry slab avalanches

occurred when SN38 was below 2.8 at

Rocky Plot, Rocky Figure 6.10 Stability trend for natural avalanches on surface Slope and Pygmy Plot. hoar buried 19 January 1993. in the Purcell Mountains. Further, during 12

February to 14 February when SN38 at Pygmy Plot, Pygmy Slope and Rocky Slope was above 2.8, no dry slab avalanches occurred. Although a few of these avalanches between 6 March and 15 March started on the surface hoar layer buried 10 February 1993, the failure plane was not reported for most of these avalanches. Note that the afternoon air temperature was above freezing at 1370 m when the avalanches occurred on 6 March and

7 March 1993. Nevertheless, based on Figure 6.10, a critical value of 2.8 for SN38 appears useful for discriminating between stable and unstable periods, even though it failed to predict the single avalanche on 4 February 1993. A second layer of surface hoar was buried at all four study sites on 10 February 1993. However, cold weather between 14 February and 26 February (Figure 6.11) caused a strong temperature gradient within the snow on top of the surface hoar, resulting in cohesionless faceted snow instead of a cohesive slab. There were numerous small loose

131 avalanches but no slab avalanches during this period. The marked decrease in SN38 at all sites on 5 March 1993 was due to heavy snowfall. During 6 March and 11 March,

SN38 was below 2.8 at all sites and dry slab avalanches occurred. Three of these were reported to have failed on the surface hoar layer. Figure 6.11 Natural stability trend for surface hoar layer No dry slab avalanches buried 10 February 1993 in the Purcell Mountains. occurred between 12 March and 15 March while SN38 increased at Pygmy Plot, Pygmy Slope and Rocky Plot and was above 2.8 at Rocky Plot. On 16 March, more than 10 dry slab avalanches started on the surface hoar and SN38 dropped below 2.8 at the three sites at which the surface hoar was still being tested as a result of renewed snowfall. As with the previous figure, a critical value of 2.8 for SN38 appears useful for discriminating between stable and unstable periods in Figure 6.11. In subsequent seasons, persistent weak layers were tested with the shear frame at Pygmy Slope and Rocky Slope. However, the testing in the level plots was discontinued because the study slopes appeared to work as well as the level plots, and because any effect of creep within the snowpack on the strength of surface hoar would better reflect the strength changes of surface hoar in start zones. In the winter of 1993-94, a layer of surface hoar and/or faceted crystals was buried on 6 February in the Purcell Mountains. A new study plot (Elk) representative of

132 shallower snowpack areas more likely to produce and retain persistent weak layers was added. The surface hoar layer was monitored with the shear frame at the Pygmy, Rocky and Elk study sites where it initially consisted of 1-2 mm faceted crystals, 2-3 mm surface hoar and 6-10 mm surface hoar, Figure 6.12 Stability trend for a layer of surface hoar buried 6 respectively. Throughout February 1994 in the Purcell Mountains.

the testing, SN38 at the Elk Plot remained above values from the Rocky and Pygmy sites (Figure 6.12). Natural dry slab avalanches were reported to have started on the surface hoar on 14 February 1994, 3 March, 4 March and

6 March. SN38 was below 2.8 at the Elk Plot when the avalanches occurred on 14 February and the air temperature at Bobby Burns Lodge was above 0°C on 3 March and 4 March

when the other avalanches occurred. However, there were many days in which SN38 from the Elk Plot was below 2.8 and no natural dry slab avalanches on the surface hoar were reported. Throughout the test period at the Pygmy site and for most of the period at the

Rocky site, SN38 was below 2.8. While SN38 from these two sites was less than 2.8 on the days that the natural dry slab avalanches were reported to have started on the surface

hoar, there were many days in which SN38 was below 2.8 and no natural dry slab avalanches were reported to have started on the surface hoar layer, so a critical value of

SN38 = 2.8 was not very effective at discriminating between stable and unstable periods.

133 6.6.2 Cariboos and Monashees near Blue River

On 29 December 1993, a layer of surface hoar was buried in the Cariboo and Monashee Mountains near Blue River, BC. However, size of the surface hoar varied considerably throughout the forecast area. At Sam’s Study Plot, the surface hoar was 2 mm in size and at the Mt. St. Anne Study Plot the surface hoar was 6-9 mm in size, larger than in surrounding terrain. Not surprisingly, SN38 for this layer was lower at the Mt. St. Anne Study Plot than at Sam’s Study Plot throughout the following 5 weeks as shown in Figure 6.13. Since these two study plots receive similar amounts of precipitation, the difference in SN38 values indicates that the 2 mm surface hoar at Sam’s Plot was substantially stronger than the 6-9 mm surface hoar at Mt. St. Anne throughout the period. During the period 1 January 1994 to 4 January 1994, natural dry slab avalanches started on the surface hoar in the Cariboo

Mountains when SN38 at both sites was at its lowest values. However, after 4

January SN38 remained below 2.8 at Mt. St. Anne and none of the natural dry slab avalanches were reported to have started on the Figure 6.13 Stability trend for a layer of surface hoar buried surface hoar. The size of 29 December 1993 in the Cariboo and Monashee Mountains near Blue River, BC.

134 the surface hoar when it was buried appears to be critical. In the Mt. St. Anne Study Plot where it was larger than

in surrounding terrain, SN38 remained low and failed to predict the absence of avalanches on the surface hoar. In Sam’s Plot, where the surface hoar was relatively

small, SN38 was above 2.8 from 1 January to 3 January when natural dry slab avalanches were starting on the surface hoar layer. Figure 6.14 Stability trend for a layer of surface hoar buried 5 February 1994 in the Cariboo and On 5 February 1994, a layer Monashee Mountains near Blue River, BC. of surface hoar was buried in the Cariboo and Monashee Mountains. Although most of the natural dry slab avalanches that started on the surface hoar occurred

when SN38 at Mt. St. Anne and Sam’s Plots was minimal (Figure 6.14), the absence of natural dry slab avalanches starting on the surface hoar after 17 February was not

predicted since SN38 remained below 2.8 throughout the period at both sites. A layer of large surface hoar was buried in the Cariboo and Monashee Mountains near Blue River on 7 January 1995. Only 3 natural dry slab avalanches were reported on this surface hoar layer and these occurred between 17 January and 19 January 1995 as

shown in Figure 6.15. Although the index SN38 reached 3.1 on 18 January, it was below 2.8 on the preceding and following days when the other avalanches started on the surface hoar layer. No other natural dry slab avalanches were reported to have started on the

surface hoar although SN38 dropped below 2.8 from 6 February to 12 February. During the

135 period from 10 January to 18

February, SN38 was generally effective at discriminating between periods with and without natural dry slab avalanches that started on the surface hoar layer.

6.6.3 Rocky Mountains

A layer of snow that fell on a crust in Jasper National Park was weakened by faceting during cold weather during Figure 6.15 Stability trend for a layer of surface hoar November and December 1993. buried 7 January 1995 in the Cariboo and Monashee Mountains near Blue River, BC. This resulted in a layer of facets approximately 0.1 m thick located approximately 0.1 m above the ground. On 6 days between 1 December 1993 and 9 January 1994 this layer was tested with a shear frame at the Sunwapta Study Plot

(2000 m). Based on these tests, SN38 ranged between 0.9 and 1.4 staying well below 2.8 (Figure 6.16). Avalanche observations were conducted along the Icefield Parkway. Natural dry slab avalanches that started in these facets were reported intermittently between 4 December 1993 and 9 January 1994 and continued after the shear frame tests on this weak layer were discontinued. Since there were many days in which SN38 < 2.8 and no avalanches occurred, SN38 did not effectively predict days without avalanches. However, the snow in the start zones in this area of Jasper National Park is strongly affected by wind whereas the Sunwapta Study Plot is sheltered from wind. Possible explanations include:

1. A stability index like SN38 based on shear frame tests in a sheltered study plot is not relevant to surrounding wind-affected start zones.

136

Figure 6.16 Stability trend for a layer of facets formed in October 1993 in Jasper National Park.

2. SN38 < 2.8 represents a condition that is necessary for natural avalanches but not sufficient.

3. The stability index, SN38, that is based on the ratio of shear strength to shear stress is better suited to the failure of thin weak layers more common in the Columbia Mountains than to the failure of thick weak layers common in the Rocky Mountains.

On 8 February 1994, a layer of surface hoar was buried in Jasper National Park (and 2-4 days earlier in the Columbia Mountains to the west). Shear frame tests were conducted on this layer in the Sunwapta Study Plot on 5 days between 10 February and 14

March 1994. During the period 10 February to 12 February, SN38 was above 2.8 and no natural dry slab avalanches were reported to have started on the surface hoar layer

(Figure 6.17). Except for 27 February, SN38 remained below 2.8 until tests were discontinued on 15 March 1994. Natural dry slab avalanches started on the surface hoar

137

Figure 6.17 Stability trend for a layer of surface hoar buried 8 February 1994 in Jasper National Park.

during 9 of the 30 days between 13 February and 15 March that SN38 was below 2.8. As with other persistent weak layers from Jasper National Park, all the avalanches occurred when SN38 was below 2.8, but there were 21 days without avalanches during which

SN38 < 2.8.

6.6.4 Summary for Natural Stability Indices

When considering the effectiveness of a stability index for discriminating between days with and days without natural dry slab avalanches, it must be noted that no single variable provides a sound basis for predicting natural dry slab avalanches. The index SN38 and the critical value 2.8 appeared to have some predictive value for the stability of the persistent weak layers buried on 18 January 1993, 10 February 1993 and 6 February 1994 in the Purcell Mountains. However, SN38 was not effective for the surface hoar layers

138 buried on 29 December 1993 and 5 February 1994 in the Cariboo and Monashee

Mountains near Blue River, BC. SN38 appeared to be a useful predictor of the natural dry slab avalanche activity for the surface hoar layer buried on 7 January 1995 in the Cariboos

and Monashees near Blue River. The effectiveness of SN38 for the Rocky Mountains remains unclear. The studies at Jasper National Park are confounded by strong wind effects in start zones. Although Schleiss and Schleiss (1970) found the ratio Σ/ρgh useful for weak layers

under the snow from the most recent storm, and Jamieson and Johnston (1993a) found S35 useful for natural dry slab avalanches, many of which started in weak layers buried only by Σ/ρ the most recent storm, SN38 which is similar to gh and S35 appears to have limited predictive value for persistent layers that remain weak for several storms. The difference probably lies in the depth and persistence of the weak layers. Persistent layers such as surface hoar and facets are the failure planes for many thick natural avalanches, whereas weak layers of precipitation particles are usually the failure plane for shallower slab avalanches mainly involving snow from the most recent storm. This supports the unproven statement by Schleiss and Schleiss (1970) that the shear frame test is most effective for weak layers of “new snow” (precipitation particles). However, few fatal avalanches start naturally; most are triggered by people (Seligman, 1936, p.336; Jamieson and Johnston, 1993b). The next three sections assess stability indices for skier triggering.

6.7 Predicting Skier-Triggered Avalanches on Test Slopes

In this section, a stability index for skier-triggering is assessed using the results of skier-testing on avalanche slopes. As in section 6.5, the failure plane or potential failure plane is tested with the shear frame at a site judged typical of the start zone. As noted in Chapter 2, Föhn (1987a) derived a stress term for the stress induced in a ∆σ weak layer by a static skier, xz, and included it in the denominator of the stability index

139 S' (Equation 2.7). Replacing the normal load adjustment in the numerator of S' by φ Σ σ ( ∞, zz) which depends on microstructure (Section 4.11) yields Σ∞ +σzzφ(Σ∞, σzz) SS = (6.5). σxz +∆σxz Slopes were skier-tested before the shear frame tests were performed. To reduce the hazard to the tester during unstable conditions and especially when the slab thickness exceeded 0.3 m, short slopes were selected. Occasionally, these short slopes “failed” but did not release an avalanche, as indicated by a tension crack through the slab near the top of the slope and a flank crack down along one or both sides of the slab. In a few cases in which the slab did not fail there were two weak layers. When time permitted, both layers were tested with the shear frame resulting in two data points for the same slope on the same day.

The slab thickness in the start zone hSZ is plotted against SS for 63 persistent slabs (square symbols) and 26 non-persistent slabs (circular symbols) in Figure 6.18. Slabs that failed are marked with filled symbols, and slabs that did not fail are marked with unfilled

Figure 6.18 Stability index SS for skier-tested avalanche slopes. Slabs triggered from more than 50 m away from the displaced slab are marked with square around the symbol.

140 symbols. Symbols indicating slabs that were remotely triggered from a distance of at least 50 m from the displaced slab are surrounded by a square.

Within the unstable range SS < 1, 81% (25/31) of the persistent slabs and 69% (9/13) of the non-persistent slabs failed. Within the band of transitional stability used by ≤ ≤ Föhn (1987a), 1 SS 1.5, 70% (7/10) of the persistent slabs and 13% (1/8) of the

non-persistent slabs failed. In the stable range, SS > 1.5, 27% (6/22) of the persistent slabs and 0% (0/5) of the non-persistent slabs failed. For persistent weak layers, the proportion of slabs that failed decreased from 81% to 70% to 27% for the stable, transitional and unstable ranges respectively. For non-persistent weak layers, the proportion of slabs that failed decreased from 69% to 13% to 0% for the stable, transitional and unstable ranges respectively. These decreases in the proportion of slab failures for increasing values of a stability index are measures of the effectiveness of the index. Prediction errors are defined as false unstable if the stability index < 1 and the slabs did not fail when skier-tested, or false stable if the stability index > 1.5 and the slab was skier-triggered. In terms of prediction errors, there were 6/31 (19%) false unstable predictions for persistent slabs and 4/13 (31%) for non-persistent slabs. Also, there were 6/22 (27%) false stable results for persistent weak layers and none (0/5) for non-persistent layers. These proportions of predictions errors are similar to the 25% reported by Föhn (1987a) for slabs with various triggers. This shows that Föhn’s (1987a) study is repeatable

and that skier-stability indices such as S' or SS are equally effective in the Columbia Mountain snowpack as in the Swiss Alps despite differences in climate and snowpack. While both false stable and false unstable results are prediction errors, it is more important to minimize false stable results than false unstable results. If a stability index like

SS strongly influenced decisions about where and where not to ski, then false stable predictions would have far greater consequences and costs (e.g. serious accidents, medical costs, legal fees, etc.) than false unstable results which would only result in stable slopes being avoided and, at worst, customer dissatisfaction. If the costs of a false stable prediction are k times greater than those of a false unstable prediction, then a slope should be avoided if the probability of a slab failure exceeds 1/(k + 1) (Blattenberger and Fowles,

141 1995a, b). Since k probably exceeds 100, slopes should be avoided that have a probability of a hazardous avalanche as low as 10-2. Although slope-specific shear frame stability indices based on shear frame tests are probably too time-consuming for backcountry skiing operations that ski many slopes per day, the success of SS (Figure 6.18) is compared with a refined stability index in the next section which is the basis for extrapolated stability indices in Section 6.9 and Chapter 9. Shear frame tests are, as a matter of practice, done where slab properties are judged typical of the start zone. For avalanches that are triggered remotely, it is possible that the snowpack properties at the trigger point differ substantially from those at the site of the shear frame tests. In particular, three of the six false stable results involve remote triggering as indicated by a square surrounding the symbol in Figure 6.18. Remote triggering is discussed further in Chapter 8.

6.8 A Skier Stability Index for Soft Slabs

One of the assumptions inherent in SS is that the skier's weight is applied at the snow surface. However, in the soft, low-density snowpack typical of the Columbia Mountains, skis typically penetrate the snow surface by 0.3 m. For ski penetration during skiing, PK, resulting in the skis being hSZ - PK above the weak layer, the stress induced by a static skier Ψ (Eq. 2.8) on a slope of inclination SZ is 2 2L cos αmaxsin αmaxsin(αmax +ΨSZ) ∆σ xz = (6.6) π(hSZ − PK)cos ΨSZ The effect of this adjustment for ski penetration on combined shear stress due to the σ ∆σ slab and skier, XZ + 'XZ is shown in Figure 6.19 for penetrations of 0.0, 0.2 and 0.4 m. Using a density at depth v (measured vertically) of 125 + 150v kg/m3 which is shown to be typical of the Columbia Mountains in the next section, the shear stress in the weak layer due to the slab of thickness h is h σxz = g sin Ψ cos Ψ ∫(125 + 150v)dv (6.7). 0 For weak layers within 0.7 m of the surface, such penetrations substantially increase the total shear stress on the weak layer (Figure 6.19), indicating the relevance of

142

modifying SS for ski penetration. Skier triggering of a slab is most likely when ski penetration is greatest. While skiing in powder snow, ski penetration

reaches a maximum, PK, when a skier pushes down with the skis between

turns. Since PK cannot readily be measured and depends on the weight of

the skier, the area and Figure 6.19 Effect of ski penetration on skier-induced stiffness of the skis as well stress. as skiing technique, it was decided to estimate the maximum penetration during skiing for an average skier. Estimation based on the resistance profile of hand hardnesses was considered, but this would have required additional measurements involving an ordinal measure of hardness, and would probably have made the stability index calculations too complicated for many hand-held calculators. For these reasons ski penetration is estimated based on slab density which was available from measurements of slab weight per unit area (load) and slab

thickness which were already required for indices such as SN and SS.

6.8.1 Density Profiles

Snow density usually increases with depth, although some wind slabs are exceptions to this generalization. Assuming a linear increase of density with depth, the density at depth v is ∆ρ ρ =ρ + v (6.8) v 0 ∆v

143 ρ where 0 is the density at the surface. This assumption of linearity was assessed using density profiles from the Columbia Mountains. From 128 profiles at least 0.5 m deep that were observed during the winters of 1993-95, there were 45 with mean slab density less than 160 kg/m3 and 42 with mean slab density greater than 200 kg/m3. For each of these groups of slabs, the densities are averaged at increments of 0.1 m between 0.1 m and 0.6 m as shown in Figure 6.20. Increases in density with depth appear linear and linear regressions yield ∆ρ/∆v = 143 kg/m4 for the low density slabs and 167 kg/m4 for the high density slabs. Since ∆ρ/∆v shows little dependence on mean slab density, a nominal value of ∆ρ/∆v = 150 kg/m4 is subsequently used for all slabs. Since the mean slab density, ρ, of an idealized slab occurs at v = h/2

∆ρ ρ=ρ + (h/2) 0 ∆v (6.9)

Using ρ from 0 Figure 6.20 Profiles of averaged densities for high and low Equation 6.10 and density slabs from the Columbia Mountains. evaluating Equation 6.9 at v = 0.3 m which is typical of skiing penetration, the density 0.3 m below the surface can be estimated ∆ρ ρ =ρ+ (0.3 − h/2) (6.10) 30 ∆v ρ σ σ ρ where the mean slab density, , is obtained from V/h where V = gh is the load (slab weight per unit area) measured with core samples or a density profile (Section 3.4).

144 6.8.2 Estimating Ski Penetration from Average Slab Density

As part of the rutschblock study (Chapter 7), measurements of ski penetration were obtained after gently stepping onto previously undisturbed snow, and after two jumps on

the same spot. The mean of these two measurements is taken as the skiing penetration, PK. Measurements were taken between the two skis near the boots. Most of the skis were 65-70 mm wide and 1.8 to 2.0 long, although occasionally skis approximately 110 mm wide were used. The field staff that did most of the ski penetration tests varied in mass from 55 to 90 kg. In Figure 6.21, these penetration measurements from 233 slabs in the Columbia Mountains and 21 slabs in the Rocky Mountains are plotted against mean slab density and the density estimated at 0.3 m. For the Rocky Mountain data, the average of the two

penetration measurements, PK, is not significantly correlated with mean slab density (R2 = 0.01, p = 0.65) or with the density estimated at 0.3 m (R2 = 0.03, p = 0.49).

However, for the Columbia Mountain data, PK is significantly correlated with mean slab density (R2 = 0.30, p < 10-4) and with the estimated density at 0.3 m (R2 = 0.50, p < 10-4).

Figure 6.21 Skiing penetration for mean slab density and estimated density at 0.3 m.

145 ρ ρ For this latter correlation, the linear regression of PK on 30 is PK = 0.55 - 0.0016 30 which is used in the next section to calculate a stability index that adjusts for ski penetration.

6.8.3 Modified Skier Stability Index

Using this stress term from Equation 6.6, a modified stability index for skier triggering is obtained Σφ SK = (6.11) σxz +∆σ xz

When the skis penetrate through the weak layer, that is PK > hSZ, SK is defined to be 0. (An error analysis for this index is presented in Appendix B.)

The slab thickness in the start zone, hSZ, is plotted against SK in Figure 6.22 for the same 63 persistent (square symbols) and 26 non-persistent slabs (round symbols) used to assess SS in Section 6.7. Within the unstable range SK < 1, 76% (31/41) of the persistent slabs and 69% (10/19) of the non-persistent slabs failed. Within the band of transitional ≤ ≤ stability, 1 SK 1.5, 75% (6/8) of the persistent slab and none (0/5) of the non-persistent slabs failed. In the stable range, SK > 1.5, 7% (1/14) and 0% (0/2) of the non-persistent slabs failed.

For their unstable, transitional and stable ranges, the predictions based on SK (which adjusts for ski penetration) and SS (which does not) are compared in Table 6.4. In the unstable range where a higher percentage of slab failures is better, the adjustment for ski penetration decreased the proportion of persistent slabs that failed from 81% to 76%. In the stable range where a lower percentage of slab failures is better, the adjustment for ski penetration reduced the proportion of persistent slabs failed from 27% to 7%.

Table 6.4 Percentage of Slabs that Failed for Skier Stability Indices Persistent Slabs Non-Persistent Slabs Index Index < 1 1 ≤ Index ≤ 1.5 Index > 1.5 Index < 1 1 ≤ Index ≤ 1.5 Index > 1.5

SS 81% 70% 27% 69% 13% 0%

SK 76% 75% 7% 53% 0% 0%

146

Although the proportion of false unstable predictions for persistent slabs increases

from 19% for SS (Figure 6.18) to 24% for SK (Figure 6.22), the proportion of false stable

predictions—which are critical—is reduced from 27% for SS to 7% for SK.

For non-persistent slabs, 16% fewer slabs fail in SK’s unstable range than in SS’s unstable range. No slabs failed in the stable range of either index.

The index SK has two advantages over SS: it is more realistic physically since it allows for ski penetration; and the number of false stable predictions which are of greatest concern is reduced with only a small increase in the number of false unstable predictions which have no serious consequences.

Figure 6.22 Skier stability index SK for skier-tested avalanche slopes.

147

Since most of the points for which SK = 0 (due to PK exceeding hSZ) resulted in slab failure, skiers appear to be efficient triggers even when the maximum penetration during skiing exceeds the thickness of the slab. The points for four dry slab avalanches that were skier-triggered from more than 50 m away from the avalanche are marked with a surrounding square. These remotely triggered avalanches are discussed in Chapter 8 where it will be argued that a fracture triggered by a skier at a localized weakness can propagate, sometimes to a nearby avalanche slope, and release a dry slab avalanches where the slab was too stable to be triggered by a skier. Since the snowpack properties at the trigger point can be very different from the properties in the start zone, SK based on shear frame tests at a well-chosen site in the start zone will occasionally yield false stable predictions. Such cases illustrate an important limitation of any stability test done where conditions are typical of the start zone, and emphasize that decisions about where or where not to ski should be based on a variety of factors and not simply on one or more stability tests in the start zone. This point is discussed further in Section 8.2 where case studies are presented for the avalanches labelled 93-03-16 and 94-02-24 in Figure 6.22.

6.9 Predicting Skier-Triggered Avalanches on Surrounding Slopes

This section is similar to Section 6.6 which attempted to relate SN38 to natural dry Ψ o slab avalanche activity in surrounding terrain. In this section, SK is calculated for = 38 to obtain a stability index SK38 which is related to skier-triggered avalanche activity in surrounding terrain. Between test days, the shear strength is interpolated linearly and the load is calculated with Equation 6.4. However, SK38 also requires the slab height between test days in order to calculate the shear stress due to the skier. On day j between test days i and k, the slab height is λ hj = hj-1(1- ) + HNj (6.12) λ ΗΝ where is the fractional settlement and j is the height of the snow that fell on day j. σ Since the load on day j is v,j which can be calculated from the precipitation at a nearby

148

weather station (Eq. 6.4), HNj is simply σ σ ρ HNj = ( v,j - v,j-1)/g HN (6.13) ρ λ This leaves the density of the new snow, ΗΝ, and settlement, , as the only ρ unknowns. For the purposes of this interpolation between test days, HN is taken to be 100 kg/m3 which is typical of recently deposited dry snow. Settlement depends on the density, temperature and microstructure of each of the slab layers. However, for simplicity

and to fit the interpolated values of hj between the measured values hi and hk, fractional settlement is calculated empirically by iteration. For the first iteration, λ = 0.03 is assumed. If the calculated slab height on day k is more than the measured height, then λ is increased by 0.003 for the next iteration. If the calculated slab height on day k is less than the measured height, then λ is reduced by 0.003 for the next iteration. Iterations are stopped when the calculated slab height on day k is within 0.02 m of the measured slab height. During the winters of 1993-95, there were five persistent weak layers that produced dry ski-triggered slab avalanches in the Purcell Mountains and four in the Cariboo and

Monashee Mountains near Blue River, BC. For these nine persistent weak layers, SK38 is related to the number of skier-triggered dry slab avalanches in the following two

subsections. SK38 is assumed to have the same band of transitional stability between 1 and

1.5 as SK.

6.9.1 SK38 for Surrounding Slopes in the Purcell Mountains On 18 January 1993 a layer of surface hoar was buried in the Purcell Mountains. This layer was tested with shear frames at the Rocky Slope, Rocky Plot, Pygmy Slope,

and Pygmy Plot until mid-March. Although SK38 remained near 1.5 at the Pygmy Slope

until 5 February, SK38 exceeded 1.5 at the Rocky Slope and Pygmy Plot on 29 January and 2 February respectively (Figure 6.23). The last skier-triggered avalanches on the surface

hoar were reported on 27 January 1995 when SK38 was between 1 and 1.5 at these three sites. Testing did not begin at Rocky Plot until 2 February 1995. No skier-triggered dry

slab avalanches were reported after SK38 exceeded 1.5 at any site. On 10 February 1993, a well-developed layer of surface hoar was buried in throughout the Columbia Mountains. Until 4 March 1993, the overlying snow was

149 generally cohesionless and

SK38 was 0 since estimated ski penetration exceeded the thickness of the slab (Figure 6.24). Although

SK38 reached 1.5 on 16 March 1993 at the Rocky Plot, it remained below 1 at the Pygmy Plot, Pygmy Slope and Rocky Plot until testing was discontinued on 16 March 1993. Intermittent skier-triggered dry slab avalanche activity Figure 6.23 Skier stability trend for surface hoar layer buried 18 January 1993 in the Purcell Mountains. was reported between 24 February and 9 March 1993. However, after March 9 the instability remained, the slab had stiffened and was capable of wide propagations, and many ski runs were avoided because of the buried surface hoar. Elsewhere in the Columbia Mountains, there were a few Figure 6.24 Skier stability trend for surface hoar layer buried 10 February 1993 in the Purcell Mountains.

150 reports of skier-triggered slab avalanches on the surface hoar through the remainder of March and into April. This surface hoar layer was considered to be the most persistent

weak layer that avalanche workers had seen in many years. Certainly SK38 from Pygmy Plot, Pygmy Slope and Rocky Slope was consistent with this perspective on the stability of this particular weak layer. On 6 February 1994, a layer of surface hoar was buried throughout the Columbia

Mountains. At the Pygmy Slope and Elk Plot, SK38 increased from 1 to 1.5 between

17 February and 22 February. SK38 was 1.5 when testing started at the Rocky Slope (Figure 6.25). Most skier-triggered dry slab avalanche activity stopped on 17 March when

SK38 climbed above 1. However, there were three ski-triggered dry slab avalanches reported to have started the surface hoar in the following 18 days. The first on 20 February was triggered by a research technician while aggressively ski-testing a steep unsupported slope. Such isolated avalanches are expected during transitional stability. On 24 February a large slab was remotely triggered at the head of the south fork of Hume Creek. Shear frame and rutschblock tests were done between the trigger point and the slab avalanche and are discussed in Section 8.2. On 7 March, a second slab was remotely triggered in the vicinity. Site-specific shear frame and rutschblock tests were done the following day and are discussed in Section 8.2. As previously mentioned, remotely Figure 6.25 Skier stability trend for surface hoar layer buried on 6 February 1994 in the Purcell Mountains.

151 triggered dry slab avalanches may not be predicted by shear frame and rutschblock tests where snowpack conditions are typical of the start zone. Hence, it is not surprising that

SK38 is also not a effective predictor of such slab avalanches. Except for these two remotely triggered avalanches, no other skier-triggered dry slab avalanches were reported to have started on the surface hoar layer when SK38 was above 1.5. During cold clear weather between 29 December 1994 and 6 January 1995, surface hoar grew throughout the Columbia Mountains at elevations below 1600 to 1800 m and at a few higher elevation sites. This layer did not form at the Pygmy (2050 m) or Elk (2250 m) sites, but did form at the Rocky Slope (1900 m) and Vermont Plot (1600 m). On 7 January, snowfall buried 3 mm surface hoar on the Rocky Slope and 10-15 mm surface hoar at the Vermont Plot, which is located at 1550 m near the bottom of a relatively dry valley. The snowpack and the surface hoar at the Vermont Plot were unlike those reported in start zones. (Shear frame tests at the Vermont Plot were primarily intended for a strength change model that is not part of this thesis.) SK38 from Vermont is included in Figure 6.26 to emphasize that SK38 must be based on shear frame tests from a study site with a snowpack that is similar to start zones. Except for one remotely triggered avalanche on 27 January, no skier-triggered dry slab avalanches on the Figure 6.26 Skier stability trend for surface hoar layer 7 January surface hoar were buried 7 January 1995 in the Purcell Mountains.

152

reported after 18 January which was the last day that SK38 at the Rocky Slope was below 1.5 (Figure 6.26). The dry slab avalanche on 27 January was remotely triggered by a group of skiers gathering at a level site to wait for a helicopter. The avalanche released below the skiers on a short slope. On 6 February 1995, a light snowfall buried a layer of surface hoar that had formed in certain locations in the Purcell Mountains but not in others. In the Elk Plot, 3-5 mm surface hoar was buried, whereas at Rocky and Pygmy Slopes, the buried surface hoar layer could not be found. Prior to February 17, less than 0.17 m of snow covered the

surface hoar at the Elk Plot, ski penetration exceeded slab thickness and consequently SK38 was 0 (Figure 6.27). Following the snowfall that started late on 16 February and continued until 19 February, the surface hoar stabilized rapidly and exceeded 1.5 on 23 February.

Two dry slab avalanches were skier-triggered prior to 17 February when SK38 was 0 and none were reported after that date. In spite of the inconsistent distribution of the surface

hoar layer, SK38 was consistent with the reported avalanche activity on the surface hoar.

Figure 6.27 Skier stability trend for surface hoar layer buried 6 February 1995 in the Purcell Mountains.

153

6.9.2 SK38 for Surrounding Slopes in the Cariboo and Monashee Mountains near Blue River, BC

On 10 February 1993 a well-developed layer of surface hoar was buried throughout the Columbia Mountains. This layer was tested with shear frames at the Mt. St. Anne Study Plot until field work was concluded on 6 April 1993. Although no skier-triggered dry slab avalanches were reported to have started on the layer after 1 March 1995 in this area (Figure 6.28), many slopes remained unstable because of this layer. Also, as the slab stiffened in March, extensive propagations were reported elsewhere in the Columbia Mountains and many slopes were avoided where profiles revealed the presence of the surface hoar. So, while SK38 was below 1 when avalanches were skier-triggered on this layer, the absence of avalanches on the surface hoar layer after 1 March does not prove that SK38 at the Mt. St. Anne study plot was too low to be of predictive value. On 29 December 1993, a surface hoar layer of varying thickness was buried in the Cariboo and Monashee Mountains near Blue River, BC. The surface hoar crystals were generally larger in the Cariboo Mountains than in the Monashee Mountains. At the Mt. St. Anne Study Plot in the Cariboo Mountains, the surface hoar crystals were particularly large (6-9 mm), whereas they were 2 mm in length at the Sam’s Study Plot in Figure 6.28 Skier stability trend for surface hoar layer buried the Monashees. No 10 February 1993 in the Cariboos and Monashees near Blue River, BC.

154 skier-triggered dry slab avalanches were reported to have started on this layer in the Monashee Mountains. The last skier-triggered dry slab avalanche reported to have started on the surface hoar occurred on 7 January

1994 when SK38 from the Mt. St. Anne Study Plot just exceeded 1 (Figure 6.29). At this

site, SK38 did not exceed 1.5 until 16 January. It Figure 6.29 Skier stability trend for the surface hoar layer appears that buried 29 December 1993 in the Cariboo and Monashee particularly large Mountains near Blue River, BC. surface hoar at Mt. St. Anne was initially very weak and unusually slow to stabilize. These results from Mt. St.

Anne and Sam’s Plot emphasis the importance of initial conditions; SK38 is most effective when the initial microstructure of the weak layer at the study site is similar to initial microstructure of the weak layer in surrounding start zones. On 5 February 1994, a layer of surface hoar was buried in the Cariboo and Monashee Mountains near Blue River, BC. This layer was tested at Sam’s Plot and the Mt. St. Anne Plot until 19 March and 22 March respectively. There were no

skier-triggered dry slab avalanches on this surface hoar layer after 18 February when SK38

at the two plots was just below 1 (Figure 6.30). SK38 exceeded 1.5 on 24 February and 4 March respectively. On 5 March in the Cariboo Mountains, a snowmobile remotely

155 triggered a dry slab avalanche on the surface hoar when SK38 was 1.57 and 1.78 at Mt. St. Anne and Sam’s Plots respectively. Although SK38 is based on the stress induced by a skier and not a snowmobile, the event does indicate that the surface hoar could still be remotely triggered. On 7 January 1995, a surface hoar layer that was widespread at elevations below 1600-1800 m was buried in the Columbia Figure 6.30 Skier stability trend for the surface hoar Mountains. This layer was layer buried 5 February 1994 in the Cariboo and monitored with the shear Monashee Mountains near Blue River, BC. frame at the Mt. St. Anne Study Plot until 18 February 1995. The last skier-triggered dry slab avalanche occurred on the 25 January, the first day that SK38 exceeded 1 (Figure 6.31). SK38 exceeded 1.5, 7 days later on 1 February 1995.

6.9.3 Summary for Skier Stability Indices

Based on the results from Figures 6.24 to 6.32, most skier-triggered dry slab avalanches on persistent layers start when SK38 for the particular persistent weak layer at a well-chosen study site is less than 1.5. Skier-triggered dry slab avalanches on persistent weak layers are more common when SK38 < 1 than when SK38 < 1.5. The three skier-triggered dry slab avalanches that occurred when SK38 > 1.5 were remotely triggered (Figures 6.25 and 6.27) and are discussed in Chapter 8.

156 Differences in initial microstructure of the persistent weak layer between two study sites do appear

to affect SK38. If buried surface hoar crystals in a particular site are substantially larger than at a second site,

then SK38 will tend to be lower at the first site and remain that way over a period of weeks (Figure 6.27 and Figure 6.31 Skier stability trend for the surface hoar layer 6.30). The same would buried 7 January 1995 in the Cariboo and Monashee Mountains near Blue River, BC. be true for start zones in a particular valley or at particular elevations.

6.10 Summary

Regressions for estimating the Daniels strength of common microstructures from density are presented in Section 6.2. For those weak layers that are too thin for density measurements, Section 6.3 shows the mean strength and variability for Daniels strength for common microstructures by classes of hand hardness.

Sections 6.4 to 6.9 relate stability indices SN, SS and SK to avalanche activity on

slopes tested with the shear frame, and SN38 and SK38 to avalanche activity on

surrounding terrain. SN, SS are similar to S and S' developed by Föhn (1987a) except

157 that a microstructure-dependent normal load adjustment is applied to the shear strength to avoid the possibility of over-estimating the stability of slopes with persistent weak layers.

Values of SN are presented for various slopes that avalanched and did not avalanche naturally in Section 6.5. For each of four slopes that avalanched with high values of

o SN, warming or ambient temperatures near 0 C are likely explanations, showing that

SN cannot predict avalanches under such conditions.

The fact that transitional stability of SN falls well above 1 implies that a critical stress failure criterion is not ideally suited to predicting natural avalanching. Although a failure criterion based on critical shear strain rate would likely be a better predictor of natural avalanching, it remains impractical since strain gauges on avalanche slopes have not survived avalanching (Sommerfeld, 1979).

SN38 is obtained by calculating SN for a 38° inclination typical of start zones. Although most natural avalanches of persistent slabs occurred on surrounding slopes when SN38 was less than 2.8, SN38 ranged widely on days without reports of natural Σ ρ avalanches of persistent slabs (Section 6.6). Since SN38 is similar to 100/ gh which has been used operationally for over 30 years and S35 which predicted avalanche activity on approximately 80% of avalanche days (Jamieson and Johnston, 1993a), the difficulty with assessing SN38 for natural avalanching of persistent slabs may lie with reporting the failure planes for natural avalanches many of which are observed from a distance.

Consistent with data from Föhn (1987a), SS < 1 indicates skier-triggering is likely, ≤ ≤ 1 SS 1.5 indicates marginal stability (approximately half of the tested slopes were skier-triggered) and SS > 1.5 indicates reduced probability of skier-triggering

(Section 6.7). However, SS ignores ski penetration which is often 0.3 m in the Columbia Mountains.

158 A practical method for estimating ski penetration based on measurements of load

and slab thickness that were already necessary for calculating SS is presented in

Section 6.8. Incorporating this estimated ski penetration into the formula for SS

results in SK which reduces the proportion of false stable predictions.

SK38 is obtained by calculating SK for a 38° inclination typical of start zones. In

Section 6.9, SK38 is shown to be better predictor of skier-triggered avalanches in

surrounding terrain than is SN38 for natural avalanches. Also, values of SK and SK38 between 1 and 1.5 correspond to transitional stability for test slopes and surrounding terrain respectively. The indicates that the critical stress failure criterion upon which

SK and SK38 are based is effective for skier-triggered avalanches.

Differences in the initial size of surface hoar crystals between two study sites affect stability. If surface hoar crystals at a particular site are substantially larger than at a second site, then stability will tend to be lower at the first site and remain that way for a period of weeks.

159 7 RUTSCHBLOCK RESULTS

7.1 Introduction

Like the shear frame stability index SK, the rutschblock test is an indicator of slab stability for skier loading. Much as SK was assessed for avalanche slopes and for study slopes in the previous chapter, rutschblock results from avalanche slopes are related to the frequency of skier-triggered slabs on the tested slopes in Section 7.3, and results from safe study slopes are related to the frequency of skier-triggered slab avalanches in surrounding terrain Section in 7.6. Site selection on avalanche slopes is very important since the snowpack on such slopes is more variable than on study slopes which are chosen for their uniform snowpack. Section 7.2 makes recommendations about site selection based on closely spaced rutschblock tests on nine slopes which, like many avalanche slopes, include trees, buried rocks, drifts and variations in slab thickness and slope inclination.

Since SK and rutschblock scores are both indicators of slab stability for skier loading, there should be a relationship between them. A linear relationship is determined in Section 7.4 based on adjacent shear frame and rutschblock tests. A breakdown in this relationship for slopes of less than 20° is used to support a hypothesis that initial failures on such low-angle slopes involve compression. In Section 7.5, the linear relationship and the equation for SK are used to illustrate a method for estimating shear strength from rutschblock scores.

7.2 Site Selection and Rutschblock Variability on Test Slopes

This section identifies some sources of variability related to terrain for the purpose of illustrating some of the limitations of rutschblock tests and making recommendations about selecting sites for rutschblock and other stability tests. Variability of rutschblock scores due to changes in slope inclination has been discussed by Jamieson and Johnston (1993b) and Schweizer and others (1995). Also, Munter (1991) has discussed similar effects for rutschkeil tests.

160 The variability of rutschblock scores is assessed from sets of closely spaced rutschblock tests on slopes with snowpack variability comparable to many avalanche slopes. During the winters of 1991 and 1992, sets of 20 to 81 rutschblock tests were done on each of nine slopes in the Cariboo or Monashee Mountains. Each slope was free of rock outcrops and abrupt inclination changes, and, except where mentioned, the failure plane (critical weak layer) was deeper than the operator’s skis penetrated after two jumps on the same spot. The set of 36 tests on 6 March 1991 and the set of 81 tests on 7 April 1992 involved two operators of similar weight and the other seven sets involved only one operator. The number of tests was limited occasionally by the amount of undisturbed snow within the boundaries of the slope and more often by helicopter and access logistics. Each set was completed within six hours. On 13 February 1991, 42 rutschblocks tests were made on an east-facing slope of Mt. St. Anne at 1900 m (Figure 7.1). The slope inclination ranged from 32° at the lowest test positions on the slope to 50° beside two drifts at the top of the slope. Except for two tests near the bottom of the slope, the failures occurred in a layer of 2-5 mm graupel under a 0.32 to 0.51 m thick slab. At the site of these two tests, a weak layer of precipitation particles 0.22 m below the surface failed at Figure 7.1 Rutschblock scores from Mt. St. Anne in the Cariboo Mountains, east aspect, 1900 m on 13 February 1991. For most loading step 6. tests with scores of six or less the slab was 0.40 to 0.50 m thick overlying 2-5 mm graupel.

161 Overall, rutschblock scores ranged from 4 to 7 with most of the scores of 7 occurring at the steep upper part of the slope where the graupel layer could not be found. It is likely that when the rounded particles of graupel precipitated, they rolled off the steeper upper part of the slope and were subsequently buried lower on the slope. This is consistent with observations that weak layers of graupel are more common in gentle and moderate terrain often used for stability tests than in start zones. In fact, graupel is not common in the failure planes of slab avalanches although in some mountain areas it is commonly reported in test profiles and identified as a weak layer by stability tests. In the Cariboo Mountains on 6 March 1991, recent snowfall on top of 2-9 mm surface hoar resulted in widespread instability. A short 25°-30° slope above a level area was selected for repeated rutschblock tests. Twenty-six of the 36 rutschblocks failed with score 3 (Figure 7.2) although scores ranged from 1 to 5. Rutschblock scores of 1 are not common but one such result occurred in the left row when the block slid as the side wall was being cut. Two of the five scores of 2 were adjacent to the test that scored 1, suggesting a particularly weak area of surface hoar. Also, the four highest scores consisting of two 4’s and two 5’s were in the top left corner of the slope. Surface hoar could not be found at the sites of the top two rutschblocks in the left row where the blocks failed on a layer of Figure 7.2 Rutschblock scores from a northwest facing slope in Miledge valley in decomposed and fragmented Cariboo Mountains on 6 March 1991. For most precipitation particles. It is likely that tests, the slab was 0.50 to 0.60 m thick and slid on surface hoar.

162 wind near the top of the slope and possibly redirected by the tree interfered with the formation of surface hoar, resulting in higher rutschblock scores than in the more sheltered parts of the slope. The 4° decrease in slope angle is a less probable explanation for the high scores in the top left portion of the slope since no comparable scores occurred at the bottom of the slope where the inclination was also 25°. As in the Figure 7.1, the rutschblock scores are higher and more variable near the top of the slope where wind effects are often more evident. On 6 April 1991, 52 rutschblock tests were made on a uniform north-facing slope on Mt. St. Anne in the Cariboo Mountains (Figure 7.3). Slope inclinations at the sites of the rutschblock tests ranged from 27° to 34° and did not show any consistent up-slope or cross-slope trends. Slab thicknesses ranged from 0.44 to 0.48 m except for the two rightmost tests in the top row where the slab thicknesses were 0.57 and 0.63 m. Underlying this slab was a layer of 1 mm decomposed and fragmented precipitation particles. The relatively consistent slab thicknesses and slope inclinations probably contributed to the low variability of rutschblock scores, most of which were 3 or 4. One exception occurred closest to the two trees where the score was 6 which supports the recommendation that tests should be at least 5 m from trees (CAA, 1995). The other exceptions occurred at seven test sites in the upper Figure 7.3 Rutschblock scores from Mt. St. Anne in the Cariboo three rows and are Mountains, north aspect, 1900 m on 6 April 1991. The slope denoted by the scores inclination ranged from 27° to 34°. The slab was approximately 0.45 m thick. All but two blocks slid on 1 mm decomposed and 2/3 or 2/4 in fragmented precipitation particles

163 Figure 7.3. At these sites, a 0.17 m slab failed first on the second loading step followed by the deeper layer on the third or fourth loading step. The scores of 3 and 4 for the deeper weak layer are questionable since ski penetration probably increased once the 0.17 m slab slid off the column. On 7 January 1992, 49 rutschblock tests were made on a relatively uniform northeast-facing slope in the Cariboo Mountains (Figure 7.4). The slope was steeper on the left side of Figure 7.4 where slope inclinations were 34°-37° compared to 30°-33° on the right side. Slab thicknesses ranged from 0.38 to 0.55 m. In the bottom four rows, the scores were all 4 with one 6. In the upper three rows, the scores were 3’s and 4’s with one 5. Slab thicknesses where the six scores of 3 occurred were generally thinner with a mean of 0.42 m and standard deviation of Figure 7.4 Rutschblock scores from a northeast-facing slope in Miledge valley in the Cariboo Mountains on 7 January 1992. 0.03 m compared to Slope inclinations ranged from 30° to 37°. The slab was 0.38 to the 41 tests with 0.55 m thick overlying 1.5 mm decomposed and fragmented precipitation particles. scores of 4 where slab thicknesses were 0.48 ± 0.03 m. Also, an intermittent thin crust was reported under the failure plane for four of the six scores of 3 and only for one test with a higher score. This stiffer substratum may have contributed to the reduced scores by increasing the shear stress gradient at the base of the weak layer (Schweizer, 1993). This set of rutschblock tests also show increased variability higher on the slope. For the test with the score of 6, no failures occurred when the operator jumped twice near the top of the block (steps 4 and 5). After these two jumps, ski penetration was

164 0.42 m and the weak layer on which most tests failed was 0.10 m deeper than the skis. However, the top 0.28 m failed when the operator stepped down towards mid-block and a second failure occurred 0.24 m deeper on the same weak layer as other tests when the operator “pushed” the skis down without jumping. The failure plane that was common in other tests was deeper than average at this site—0.52 m below the surface—however there were 18 other tests with slab thickness greater than 0.50 m so the above average thickness was not an important factor in the above average score. Since there is no apparent reason to doubt the score of 6, it is clear that scores two steps above the slope median can occur on uniform slopes. On 19 January 1992, 48 rutschblock tests were made on a less uniform north-facing slope in the Cariboo Mountains (Figure 7.5). Slope inclinations in the shaded area of Figure 7.5 were 30°-36° and 36°-43° in the unshaded area. In the less steep area (shaded), 23 rutschblocks scored 4 and four tests scored 5, whereas in the steeper area (unshaded), two tests scored 3, eight tests scored 4 and one test scored 5. The slab thickness varied from 0.25 to 0.35 m over a weak layer of Figure 7.5 Rutschblock scores from a 1-1.5 mm decomposed and fragmented north-facing slope in Miledge valley in the Cariboo Mountains on 19 January 1992. The slab precipitation particles. Ski penetration was 0.25 to 0.35 m thick overlying a weak layer after two jumps (rutschblock step 5) of 1-1.5 mm decomposed and fragmented precipitation particles. Sites where the skis ranged from 0.30 to 0.40 m. Where the penetrated the weak layer are marked “SPP”.

165 skis penetrated the weak layer, the result was rejected and the site marked with “SPP” in Figure 7.5 to denote the ski penetration problem. At most of these sites, the rutschblock failed when the operator stepped to mid-block or pushed downwards with the skis without jumping at mid-block as part of loading step 6. However, the tests were not scored as 6’s since the skis had penetrated the weak layer on step 5. Hence, careful monitoring of ski penetration can avoid rutschblock scores that are high and misleading when ski penetration approaches slab thickness. At several rutschblock sites in the steeper (unshaded) area, the snowpack which generally exceeded 2 m in the area was only 1 m thick over a buried rock. At such locations, the temperature gradient within the snowpack is increased (Gray and others, 1995) and ski penetration will increase where the snowpack has been weakened by faceting. On 3 February 1992, 44 rutschblock tests were made on a short north-facing slope in the Cariboo Mountains (Figure 7.6). Slope inclinations ranged from 27° to 35° with the steepest inclinations occurring in the middle part of the slope. Except for four tests in the top right part of Figure 7.6, each rutschblock failed on a weak layer of 2-4 mm graupel under a 0.47 Figure 7.6 Rutschblock scores from a north-facing slope in Miledge valley in the Cariboo Mountains on to 0.62 m slab. Except for the 3 February 1992. Slope inclinations ranged from 27° top right corner of the slope to 35°. Except for four tests in the top right, the slab was 0.47 to 0.62 m thick overlying a weak layer of where there were five scores of graupel. * denotes rutschblocks which failed under a 7, rutschblock scores varied shallow wind slab. # denotes a rutschblock that failed in a different weak layer.

166 from 4 to 6 without any apparent spatial trend. The scores of 7 in the top right corner are interesting. The weak layer of graupel was missing, presumably due to wind effect, so it would have been a poor place for a single test to detect this particular weak layer. While it would have been a good place to test the stability of the wind slab, many small wind slabs can be identified by their location and smooth “chalky” appearance and a site lower on the slope would have been a better place to test for most weak layers. This set of rutschblock also illustrates greater variability and some higher scores near the top of the slope. On 29 February 1992, 20 rutschblock tests were made on a northeast-facing slope in the Cariboo Mountains. The slope inclination increased from 19° at one of the lowest tests on the slope to 37° at the leftmost test near the top of the slope (Figure 7.7). All slabs failed in the same layer of surface hoar. The slab was 0.40 to 0.47 m thick except in for the top two rutschblocks where the slab was 0.65-0.70 m thick due to wind-deposited snow. For the leftmost test, the upper 0.17 m layer displaced on the loading step 6 as well as the 0.42 m slab that failed on the surface hoar layer. The increase in scores from 3 and 4 in mid-slope to 5 at Figure 7.7 Rutschblock scores on Mt. St. Anne in the the bottom of the slope may Cariboo Mountains, northeast aspect, 1900 m on 29 February 1992. Except for the two tests in the drift, be due to the decrease in slope the slab was approximately 0.45 m thick overlying 3-5 mm surface hoar.

167 inclination at the bottom of the slope (Jamieson and Johnston, 1993b). However, the two scores of 6 near the top of the slope cannot be attributed to such and effect since they occurred at the steepest sites. While the score of 6 in the top row may be due to the thicker slab, it is unclear why the score at leftmost rutschblock test is two steps above the slope median. This is another example of higher and more variable scores near the top of the slope. On 31 March 1992, 51 rutschblock tests were made on a northeast-facing slope in the Monashee Mountains. The slope inclination increased from 19°-22° for the lowest test sites to 34°-39° for the highest test sites (Figure 7.8). Except for four tests which are marked (*) in

Figure 7.8 that failed Figure 7.8 Rutschblock scores on a northeast-facing slope in on a crust 0.61-0.72 m the Monashee Mountains on 31 March 1992. Except for 4 marked tests, the slab failed on a weak layer of 1 mm faceted below the surface, all grains and 2-3 mm surface hoar. the rutschblocks failed in a weak layer of 1 mm faceted grains and 2-3 mm surface hoar. In the lower six rows, this weak layer was 0.39-0.57 m below the surface and in the top two rows it was 0.47-0.70 m below the surface. Rutschblock scores varied from 4 to 6 with no apparent spatial trends. The test in the top row marked 3/5 failed 0.16 m below the surface on step 3 and then again 0.69 m below the surface on loading step 5. Rutschblock scores are not reduced near the upper steeper part of the slope compared to their values lower on the slope. However, a reduction in scores due to increased inclination higher on the slope may have been obscured by the increased slab thickness in the same area. Whatever the cause,

168 all rutschblock scores were within ±1 step from the median score of 5. On 7 April 1992, 78 rutschblock tests were done on a northeast-facing slope in the Monashee Mountains. A 70 kg skier loaded the blocks on the left side of the slope and an 80 kg skier loaded the rutschblock on the right side of the slope. As shown in Figure 7.9, the slope inclination was 29°-36° except near the top of the slope (shaded in Figure 7.9 Rutschblock scores on a northeast-facing slope in the Monashee Mountains on 7 April 1992. The Figure 7.9) where slope blocks failed on 2-4 mm graupel under a 0.35 to inclinations were 23°-28°. The 0.50 m slab. slab thickness was 0.35 to 0.40 m in the upper less-steep part of the slope and 0.40 to 0.50 m in the lower steeper part of the slope. Rutschblock scores range from 4 to 6. However, the four tests that scored 6 were in the upper less-steep part of the slope suggesting that the decrease in slope inclination near the top of the slope had more effect on the scores that the reduction in slab thickness, which increases skier-induced stress. These scores of 6 are two steps above the slope median. Again, the highest scores and increased variability occurred near the top of the slope. Good sites for rutschblocks are those with limited variability and unlikely to yield misleading scores. It is particularly important to avoid sites that yield scores much above average since these could contribute to an unstable slope being judged stable. As shown by the high scores and increased variability of rutschblock scores near the top of a slope in

169 Figures 7.1, 7.2, 7.6, 7.7 and 7.9, the top of a slope is often not a good site for a rutschblock test. In Figures 7.1, 7.2, 7.6 and 7.7, there was no decrease in slope inclination in the upper slope where the highest scores occurred, so slope decrease was not a factor contributing to the higher scores. Possible causes for these higher scores near the top of a slope include: surface hoar crystals being smaller or absent (Figure 7.2) since surface hoar growth slows for wind speed above 2-4 m/s (Hachikubo and others, 1995) and the upper part of a slope is often more exposed to wind than lower areas of the slope, or graupel grains being blown off the upper part of a slope (Figure 7.6) or rolling off the steeper part of a slope (Figure 7.1). Alternatively, the score may be misleadingly high if a rutschblock is done where the stress induced by the skier in the weak layer is reduced as a result of the slab being locally thickened into a “pillow” by wind loading (Figure 7.7). Also, misleading rutschblock results can be associated with sites near trees (Figure 7.2 and 7.3), buried rocks (Figure 7.5) or drifts (Figure 7.7). By avoiding such sites, most rutschblock scores can be expected to be within ±1 step of the slope median. Jamieson and Johnston (1993b) estimate a 97% probability of rutschblock scores being within ±1 step of the slope median on the uniform part of a slope. However, as shown in Figures 7.2 and 7.4, scores two steps above the slope median can infrequently occur on the uniform part of a slope. The use of other—seemingly redundant—information such as snow profiles and slope tests can reduce the reliance on a rutschblock test and further reduce the probability of a unstable slope being judged stable. Finally, as discussed for Figure 7.5, failure to notice that the operator's skis have penetrated almost to, or through, the weak layer during a rutschblock test can also contribute to over-estimating slab stability.

7.3 Rutschblocks on Skier-Tested Avalanche Slopes

Rutschblock tests were made on avalanche slopes where slab conditions were judged typical of the start zone after the slopes were skier-tested. Occasionally, after a slab avalanche released, no representative site could be found near the flank or crown that

170 was representative of the start zone. Usually two or more tests were done, but occasionally there was only time or sufficient representative and undisturbed snow for one rutschblock test. Tests were done before the slab and weak layer were judged to have changed substantially, recognizing that snow properties change more quickly with warmer temperatures. Except for two slopes that were tested three days after the slab avalanche, all rutschblock tests were done within one day of the slope being skied. At slab avalanches, only rutschblock results for the failure plane were used. On one skier-tested slope that did not avalanche, two rutschblock results were obtained since there were two distinct weak layers. If the skis penetrated the failure plane prior to failure of the rutschblock, the test was rejected. The percentage of skier-triggered slabs is plotted against 63 median rutschblock scores from the present study in Figure 7.10 along with Föhn’s (1987b) results from a similar but larger study in Switzerland. Non-integer median scores such as 3.5 are rounded up. Although there are no results for median rutschblock scores of 1 in the present study, both studies show a general decrease in the percentage of skier-triggered slab avalanches as median rutschblock scores increase from 2 to 6. Approximately 15% of avalanche slopes with rutschblock scores of 7 from the Swiss study were skier-triggered and Föhn (1987b) attributes this to difficulty selecting sites that are safe yet representative. In the present study, three of ten slabs with median rutschblock scores of 7 were skier-triggered. However, the

rutschblock tests Figure 7.10 Relative frequency of skier-triggered slabs on were done near the skier-tested avalanche slopes from Föhn (1987b) and present study.

171 crown where slab conditions were judged typical of the start zone, yet two slopes were triggered where the slab was much thinner, and the other was likely triggered from a spot weaker than either the crown or the rutschblock site. These false stable results are discussed in Chapter 8. Also, the number of these false stable results may be biased upwards since field staff sought unusual and unexpected avalanches to determine the limitations of rutschblock (and shear frame) tests. In Figure 7.11, the percentage of skier-triggered slabs for the 44 slabs overlying persistent weak layers are plotted separately from the 19 slabs overlying non-persistent weak layers. While the number of results for non-persistent layers is limited, the frequency of skier-triggering is clearly less than for persistent layers. Clearly, persistent weak layers are more sensitive than non-persistent weak layers to some difference between the skier-triggering of a slab avalanche and the skier-triggering of a rutschblock. There are two obvious and related differences: unlike the portion of a slab loaded by a skier, a rutschblock is not supported laterally by the surrounding slab, and a moving skier tests a much larger area of a start zone than a skier on a rutschblock. Persistent weak layers may have more localized weaknesses (flaws) that are sensitive to skier-triggering than non-persistent layers, and/or a higher percentage of fractures in persistent weak layers may propagate over distances large enough to release slab avalanches. While the first explanation cannot be ruled out, field reports strongly link persistent weak layers with extensive propagations. This Figure 7.11 Relative frequency of skier-triggering for persistent and non-persistent slabs on skier-tested avalanche slopes.

172 association may be partly due to the brittleness of persistent weak layers (Section 1.10) and partly due to such layers remaining weak over days or weeks while the overlying slab increases in thickness and stiffness and consequently in the strain energy capacity necessary for extensive propagation (Jamieson and Johnston, 1992b). If the distribution of flaws in non-persistent weak layers is similar to that of persistent layers, then it follows that skiers are starting fractures in non-persistent weak layers but that these fractures do not propagate over distance large enough to release slab avalanches. These results indicate that the microstructure of the failure plane should be observed and reported. For example, a report of “rutschblock 4 on surface hoar” is better for predicting skier-triggered slab avalanches than a report of “rutschblock 4”. Although none of the 10 non-persistent slabs with median rutschblock scores of 4 to 7 were skier-triggered (Figure 7.11), a larger study would presumably show some skier triggering for such rutschblock results. In Figure 7.12, the percentage of skier-triggered persistent slabs decreases from 93% for median scores of 3 or less, to 60% for median scores of 3.5 to 5, to 21% for median scores of 5.5 to 7. For median rutschblock scores of 3 or less, 56% of non-persistent slabs were skier-triggered and none of the slabs with median rutschblock scores of 3.5 to 7 were skier-triggered. The slab thicknesses at the rutschblock sites are plotted against the median rutschblock scores in Figure 7.12. Slab thicknesses increase from 0.10-0.53 m for median scores of 2 to 0.42-1.65 m for median scores of 7. For the three false stable results mentioned previously (rutschblock scores of 7 near skier-triggered slabs), the thickness of the slabs at the rutschblock sites were 1.0, 1.1 and 1.65 m. These are serious prediction errors since such thick slabs often result in large destructive avalanches. For such thick slabs, skiers are not effective triggers for such deeply buried weak layers because the shear stress induced by skiers is much less than the shear stress due to the slab (Föhn, 1987a; Figure 6.19). However, these slabs are triggered from sites with snowpack conditions quite different from the rutschblock site, as discussed in Chapter 8.

173

Figure 7.12 Slab thicknesses of persistent and non-persistent skier-tested slabs. The points for some rutschblock scores are offset slightly along the abscissa for clarity. Median scores may be either integers or halves (e.g. 3.5). Data are from the Columbia and Rocky Mountains, 1992-95.

7.4 Relationship Between Rutschblock Scores and SK from Adjacent Shear Frame Tests

Rutschblock scores and shear frame stability indices such as S' (Föhn, 1987a), SS

(Jamieson and Johnston, 1993b) and SK are all indicators of slab stability for skiers. Föhn (1987a) determined a non-linear relationship between values of the skier stability index S' from shear frame tests and scores from adjacent rutschblock tests. Jamieson and Johnston

(1993b) regressed SS on rutschblock scores from adjacent tests and determined a linear relationship. In this section, relationships between SK and rutschblock scores from adjacent tests are examined for slopes with Ψ ≥ 20° and for gentler slopes with Ψ < 20°. Based on the relationship, tests on gentle slopes (Ψ < 20°) are used to discuss a failure mechanism for skier-triggering different from the shear failure typical of steeper slopes.

174 Subsequently, a relationship is established for estimating shear strength from rutschblock scores for slopes with inclinations of 20° or more. Between 1990 and 1995, 281 sets of shear frames tests were obtained for the failure planes of adjacent rutschblock tests. The median rutschblock score is based on tests usually done within 3-5 m of the shear frames tests and on the same day. Median rutschblock scores are based on three or more rutschblock tests in 46 cases, on two rutschblock tests in 171 cases and on one test in 64 cases. The primary microstructure of the weak layer was classified as persistent for 207 cases, as non-persistent for 70 cases, and as unclassified for three cases. For median

rutschblock scores from 1 to 7, the mean and standard deviation of SK are given in Table 7.1 for persistent and non-persistent microstructures. For integer-valued median rutschblock scores, calculated values of the t-statistic and significance level, p, for a

two-tailed t-test are included in Table 7.1 to compare SK for persistent and non-persistent

microstructures. The difference between the mean values of SK for persistent and non-persistent microstructures is only significant (p = 0.02) for a median rutschblock score of 6 and marginally significant (p = 0.07) for a median rutschblock score of 2. Since these

two differences have the opposite sign, a systematic difference in mean values of SK cannot be determined for persistent and non-persistent microstructures and the data are combined with the three results for unclassified microstructures in the rightmost column of Table 7.1. For slopes of less than 20°, Jamieson and Johnston (1993b) reported three values of

SS for adjacent median rutschblock scores of 4, 4 and 5. However, these three values of SS were well above the values typical for rutschblock scores of 4 and 5. To investigate this further, 10 additional sets of shear frame and rutschblock tests were done on slopes of less than 20° making a total of 13 sets of adjacent tests on gentle slopes. The front wall of the rutschblock was watched closely since displacement of slabs on such shallow slopes is often less than 20 mm. For 10 of the 13 sets of rutschblocks, fractures propagated to the front (lower) wall for loading steps of 4, 5 or 6. The remaining three sets of tests scored 7.

This effect was analyzed using the deviations of SK from the mean for particular

175

Table 7.1 Skier Stability Index SK from Shear Frame Tests Adjacent to Rutschblock Tests for Persistent and Non-Persistent Microstructures Median Persistent Non-Persistent t-test All Microstructures Rutsch- Microstructures Microstructures block No. of S No. of S tpNo. of S Score K K K Pairs Mean±SD Pairs Mean±SDPairs Mean±SD 1 1 0.03 0 - - - 1 0.03 1.5 1 0.74 0 - - - 1 0.74 2 16 0.35±0.24 8 0.17±0.14 -1.92 0.07 24 0.29±0.23 2.5 6 0.43±0.34 1 - - - 7 0.37±0.35 3 22 0.69±0.38 10 0.52±0.32 1.28 0.21 33 0.63±0.36 3.5 5 0.65±0.59 3 0.90±0.32 - 8 0.74±0.49 4 44 0.94±0.53 17 0.91±0.57 0.19 0.85 61 0.93±0.54 4.5 4 0.87±0.16 2 1.47±0.02 - - 6 1.07±0.34 5 14 1.26±0.73 7 1.21±0.37 0.18 0.86 23 1.29±0.61 5.5 5 1.02±0.53 2 0.99±0.19 - - 7 1.01±0.44 6 35 1.64±0.89 16 1.05±0.51 2.44 0.02 51 1.45±0.83 6.5 4 1.59±0.47 2 1.94±0.46 - - 6 1.70±0.46 7 50 2.40±0.98 2 1.53±0.46 1.27 0.21 52 2.36±0.98

rutschblock score, SK*, given in the rightmost column nine of Table 7.1. The normalized deviations (SK-SK*)/SK* are plotted against slope inclination in Figure 7.13. For slope inclination of at least 20° the normalized deviations scatter around 0 as expected. However, for slopes of less than 20°, 10 of the 13 deviations are greater than 0. These deviations are marked in Figure 7.13 with the median rutschblock score and the microstructure of the weak layer. This includes 8 of the 10 results for which fractures reached the front wall. Clearly, fractures started and propagated for rutschblock loading steps of 4 to 6 more often than predicted by SK. Consequently, one or more of the assumptions behind SK is inappropriate for such shallow slopes. This stability index is based on the same assumptions as S', two of which depend on slope inclination. In the derivation of S', Föhn (1987a) assumed that

176 1. the primary fracture was in shear, and 2. the principal stress due to the slab rotates to slope-parallel prior to failure. Although both assumptions are questionable for such shallow slopes, the first is particularly dubious since as the slope inclination decreases, compressive stress due to the skier will increase and shear stress will decrease, and the skier loading is probably responsible for fracture since snow is very sensitive to rapid loading (Narita, 1980, 1983; Fukuzawa and Narita, 1993) . Although in general, shear or tension is necessary for propagation, it appears that the primary fracture for skier-triggering may be caused by compression rather than shear on such shallow slopes. Since many of these weak layers are thin (e.g. surface hoar), this clarifies that the compressive failures proposed by Bucher (1948) and supported by Bradley and Bowles (1967) are not limited to thick layers of depth hoar. Skier-triggering on shallow slopes and propagation are discussed further in Chapter 8.

Figure 7.13 Normalized deviations of SK from mean values for particular rutschblock scores. These deviations do not average 0 for slopes of less than 20°. For these slope inclinations, the microstructure of the weak layer is marked: SH (surface hoar), FC (faceted crystals) and DF (decomposed and fragmented precipitation particles) along with the median rutschblock score.

177 Excluding the adjacent shear frame and rutschblock tests on slopes of less than 20°, means and standard deviations of SK for each median rutschblock score are given in Table 7.2 and plotted in Figure 7.14 along with the standard error. Except for median scores of 1.5 (for which there is only one pair), 5.5 and 6, mean values of SK increase with increasing median rutschblock scores, indicating that SK can be estimated for particular rutschblock scores. Jamieson and Johnston (1993b) used a regression to estimate SS from adjacent rutschblock scores. However, the variability of SK, as indicated by the standard deviation, increases with the mean value of SK indicating that a regression which minimizes the sum of the squared deviations would be strongly influenced by large values of SK which are more numerous and more variable. Fortunately, regression is not necessary to estimate mean values of SK from median rutschblock scores. Mean values can be read from Table 7.2 or interpolated from Figure 7.14. Interpolating between median scores of 2 and 6.5 yields

SK = 0.31 (RB - 1) (7.1)

Table 7.2 Skier Stability Index SK from Shear Frame Tests Adjacent to Rutschblock Tests on Slopes of at Least 20°

Median No. of Pairs SK Rutschblock Score Mean St. Dev. 1 1 0.03 - 1.5 1 0.74 - 2 24 0.29 0.23 2.5 7 0.37 0.35 3 33 0.63 0.36 3.5 8 0.74 0.49 4 57 0.90 0.49 4.5 6 1.07 0.34 5 21 1.20 0.56 5.5 7 1.01 0.44 6 47 1.31 0.65 6.5 6 1.70 0.46 7 48 2.25 0.82

178

Figure 7.14 Mean, standard deviation and standard error for median rutschblock scores from adjacent tests.

which is a good fit to mean values of SK except for median scores of 1.5 (for which there is only 1 point), 5.5 and 7, which is unique since rutschblock scores have an upper bound

of 7 whereas SK has no inherent upper bound.

7.5 Estimating Daniels Strength from Rutschblock Scores

It is possible to estimate Daniels strength, Σ∞, of the failure plane from rutschblock Σ score since SK is a function of ∞ (Eq. 6.11) and SK can be estimated from the median rutschblock score (Eq. 7.1). Combining equations 6.11 and 7.1 yields the estimated Daniels strength ∗ Σ σ ∆σ σ φ Σ σ ∞ = 0.31 (RB - 1) ( XZ + XZ) - ZZ ( ∞, ZZ) (7.2) which simplifies to ∗ Σ σ ∆σ ∞ = 0.31 (RB - 1) ( XZ + 'XZ) (7.3) for persistent weak layers for which φ ≅ 0 (Section 4.11).

179 There were 208 values of SK paired with median scores from adjacent rutschblocks on slopes of at least 20°. ∆σ However, XZ is not defined for 18 cases for which estimated skiing penetration reached the ≤ weak layer (h - PK 0). Surprisingly, for the Figure 7.15 Daniels strengths estimated from rutschblock ∗ scores plotted against measured Daniels strengths from remaining 190 pairs, Σ ∞ is adjacent shear frame tests. Σ not correlated with ∞ since 2 ∆σ R = 0.01. However, the problem lies with 'XZ which becomes highly variable as PK ∗ Σ Σ > approaches h (Appendix B). For the 181 pairs ( ∞, ∞) for which h - PK 0.05 m, the coefficient of determination for the correlation improves to R2 = 0.49. These 181 points ≤ are plotted in Figure 7.15. The nine points for which h - PK 0.05 m are for relatively low

Daniels strengths (Σ∞ < 1 kPa). Four of these points are plotted with a distinct symbol in Figure 7.15 and the remaining five lie above the graph since their estimated Daniels strengths are between 6 and 16 kPa. For Daniels strengths above 2 kPa, many of the estimates are too low. For Daniels strengths below 2 kPa, estimates are proportional to measured values and most fall within 0.5 kPa of the measured value. Although rutschblock tests require less training and specialized equipment than shear frame tests, the variability in the estimates, particularly for strengths above 2 kPa, undermines the usefulness of estimating Daniels strength from rutschblock scores.

180 7.6 Relating Rutschblock Scores to Skier-Triggered Dry Slabs in Surrounding Terrain

This section relates rutschblock scores on study slopes to skier-triggered dry slab avalanche activity within the forecast region, typically within 15 km of the study plot. As with the extrapolation of shear frame stability indices in Sections 6.9, this approach has two limitations: most of the avalanches are small since ski guides avoid slopes with weak layers perceived to be unstable and deep enough to produce hazardous slab avalanches, and the failure planes of the reported avalanches are usually but not always identified. In contrast to the shear frame stability indices, rutschblock scores cannot easily be interpolated between test days since adjustments for increases in load due to precipitation and decreases in slab thickness due to settlement have not been developed. Also, rutschblock scores predicted from estimated shear strengths would not be accurate (Section 7.5). Initially, the relative frequencies of one or more skier-triggered dry slab avalanches on days with results for the same failure plane from rutschblocks on study slopes were compiled. However, there was only one match, that is, a day with one or more skier-triggered avalanches and a rutschblock result for the same layer. The number of matches rose to 14 when the selection was broadened to include one or more skier-triggered dry slab avalanches that occurred within one day of the rutschblock tests. These results are summarized by study plot and persistent weak layer in Table 7.3. For each median rutschblock score, the fraction n/m indicates that on n of m days with a rutschblock result, one or more skier-triggered dry slab avalanches failed in a particular weak layer with one day of the rutschblock result for the same weak layer. However, there were insufficient data to determine if the relative frequency of skier-triggered dry slab avalanches decreased as the median rutschblock score increased for particular weak layers and specific study slopes. Hence the relative frequencies are totalled by rutschblock score for all weak layers and all study slopes in the bottom row of Table 7.3. Although this

181 totalling does not prevent the same avalanche from being counted for rutschblock results

Table 7.3 Relative Frequency of Skier-Triggered Dry Slab Avalanches in Surrounding Terrain within one Day of Rutschblock Tests on Study Slope Median1 Rutschblock Score on Study Study Slope Formation Date of Slope Persistent Weak Layer 234567 Rocky Study Slope, Purcells 6 December 1993 - - - 0/1 - 0/3 20 December 1993 - - - - 0/2 - 3/18 January 19932 - 1/1 - - 0/1 0/5 10 February 1993 - 1/1 1/2 - 0/1 - 19 December 1994 - - - - - 0/2 28 December 1994 - - - - - 0/2 6 February 1994 - - - - - 1/2 7 January 1995 - 2/2 - 0/1 1/1 0/3 25 January 1995 - - - 0/1 1/1 0/1 Pygmy Study Slope, Purcells 20 December 1993 - - 0/1 - 0/1 - 3/18 January 19932 - - 1/2 0/1 0/2 0/3 10 February 1993 - 1/2 - 0/1 - - 6 February 1994 - - 1/1 - - 1/2 Elk Study Slope, Purcells 6 February 1994 - - - 0/1 0/1 0/1 Mt. St. Anne, Cariboos and Monashees 5 February 1994 - - 1/1 - - 0/1 14 February 1994 0/1 - - - 0/1 - Sam’s Slope, Cariboos and Monashees 5 February 1994 - - - - - 1/1 All Study Slopes ------All Weak Layers 0/1 5/6 4/7 0/6 2/11 3/26 1 Non-integer median scores such as 3.5 are rounded up. 2 Failures on surface hoar layers buried 3 January and 18 January 1993 were difficult to distinguish since they were 5-10 mm apart after settlement.

182

Figure 7.16 Relative frequency of one or more skier-triggered avalanches in surrounding terrain within one day of study-slope rutschblock results for same weak layer.

from two different study slopes, it does show a general decrease in skier-triggered avalanche activity as median rutschblock scores increase on study slopes (Figure 7.16). There were at least six test days for each median rutschblock scores of 3 to 7, and except for the fact that no skier-triggered persistent slabs were reported on six days when median rutschblock scores averaged 5, a decrease in skier-triggered dry slab avalanche activity is apparent in Figure 7.16. This indicates that rutschblock tests on study slopes have predictive value for particular persistent weak layers in surrounding terrain.

7.7 Summary

Snowpack and terrain factors affecting rutschblock results are discussed in terms of variability of rutschblock scores on nine avalanche slopes. Sites near the top of slopes, near trees, over rocks and at pillows of wind-deposited snow sometimes exhibit rutschblock scores and/or failure planes quite different from the remainder of the slope. Even when avoiding such sites, rutschblock scores two steps above the slope median are possible indicating the importance of using other sources of

183 information such as avalanche activity, slope tests and profiles to confirm or raise doubts about the results of 1 or 2 rutschblock tests.

The percentage of skier-triggered persistent slabs on skier-tested avalanche slopes decreased from over 80% to 33% as median rutschblock scores increased from 2 to 5 (Figure 7.11). Three of nine skier-tested slopes with median scores of 7 for persistent slabs were skier-triggered indicating that the median score from one or two rutschblock tests is, by itself, not a completely reliable indicator of stability.

For non-persistent weak layers, no slabs were skier-triggered on 10 slopes with median rutschblock scores above 3. The frequency of avalanching for non-persistent slabs with rutschblock scores of 2, 3 and 4 was approximately the same as for persistent slabs with rutschblock scores of 4, 5 and 6 respectively. Accordingly, the interpretation of rutschblock scores should reflect the fact that persistent slabs are more likely to be skier-triggered than non-persistent slabs with the same rutschblock score.

A relationship between skier stability index SK and median rutschblock scores exists on slopes with inclinations of 20° or more. However, this relationship breaks down on slopes of less than 20° where SK usually predicts higher stability than the rutschblock. It is hypothesized that skiers can initiate compressive fractures instead of shear failures on slopes of less than 20°.

A method for predicting the Daniels strength based on rutschblock scores was investigated using on the relationship between skier stability index SK and median rutschblock scores. However, the estimates of Daniels strength are too variable to be useful for predicting stability.

Rutschblocks on safe study slopes are shown to have predictive value for the skier stability of persistent layers on surrounding slopes. However, as for rutschblock tests on avalanche slopes, the particular persistent weak layer is sometimes skier-triggered when the rutschblock score for that layer on the study slope is 7.

184

185 8 FALSE STABLE PREDICTIONS 8.1 Introduction

False stable predictions occur when a rutschblock test or shear frame stability index indicates stability for an avalanche slope that releases under snowpack conditions similar to those under which the tests were performed. The five skier-triggered slabs with rutschblock scores of 6 or 7 (Figure 7.11), and/or SK values greater than 1.3

(Figure 6.22), are the focus of this chapter. (Although SK values between 1 and 1.5 are considered transitionally stable in Chapter 7, the two slopes that avalanched with SK values between 1.3 and 1.5 are included in this chapter since they share characteristics with other false stable predictions.) Case studies are presented for the five avalanches. The terrain and snowpack characteristics common to these case studies are summarized to identify limitations of snowpack tests associated with terrain features. Also, the false stable results are used to support an argument that some primary fractures initiated by skiers involve compression.

8.2 Case Studies

8.2.1 Purcell Mountains, Malachite Valley, 27 January 1993

On 27 January 1993, a researcher on skis on a 5° slope felt a fracture in the snowpack in Malachite Valley of the Purcell Mountains. The fracture propagated 100 m to 35° slope where it released a 0.8 m slab that included 0.7 m of “1 finger- to pencil-hard” layers. The failure plane consisted of facets and surface hoar that had been buried on 18 January 1993. The slab thickness was similar at the trigger point and in the start zone. Cracks in the bed surface, both downslope and up-slope of the crown fracture, were apparent after the avalanche released, and are assumed to have occurred as part of the failure process. These cracks precluded the selection of a suitable site for rutschblock tests. Shear frame tests at a site near the crown resulted in a stability index of SK = 1.46.

186

8.2.2 Monashee Mountains, Mt. Albreda, 16 March 1993

On 16 March 1993, a slab avalanche (1.0 m thick, 30 m wide) was triggered by a skier on a 32o north-facing moraine slope at 2100 m on Mt. Albreda in the Monashee Mountains. At approximately six places, rocks and humps in the moraine were exposed in the bed surface (Figure 8.1). Cracks were observed in the bed surface between the rocky bumps in the ground surface. At the places where the snowpack was only 1 m thick prior to the avalanche, weak depth hoar surrounded the rocks and humps. The exact trigger point is not known but the slab was likely triggered near one of the rocks or humps surrounded by depth hoar. The failure plane consisted of 2-3 mm rounded facets and surface hoar from the layer of surface hoar that had been buried 18 January 1993, almost two months earlier.

Figure 8.1 Cross-section of test site, crown fracture and substratum at slab avalanche on Mt. Albreda in the Monashee Mountains that was triggered 16 March 1993.

187 When the site was reached the next day for investigation, the most representative undisturbed site was on the 25o slope approximately 2 m above the crown fracture. Due to deteriorating weather, there was only time for eight shear frame tests and one rutschblock test. (Field notes for these observations are presented in Appendix C.) At this site, which was probably within 20 m of the trigger point, both the stability index, SK = 1.82, and the rutschblock test, RB = 7, indicated stability. Hence, a stability test several metres away from a localized weak spot can be misleading.

8.2.3 Purcell Mountains, Hume Valley, 24 February 1994

On a north-facing glacier at the head of the south fork of Hume Creek in the Purcell Mountains on 24 February 1994, two researchers and a ski guide skied down gentle terrain. They stopped on a 15-20° slope just east of the glacier near rocky outcrops where a slab (approximately 0.2 m thick) lay on top of depth hoar. They felt a fracture in the shallow snowpack under their skis and heard a “whumpf” sound commonly associated with propagating fractures (snowquakes) within the snowpack (DenHartrog, 1982). Moments later they received a radio call saying that a large slab avalanche was running down the west-facing 35° slope approximately 400 m to the west (Figure 8.2). The area near the crown could not be safely accessed, so a profile was observed on the glacier approximately 150 m east of the crown where the inclination was 28° and approximately 4 m of seasonal snowpack lay on the glacier ice (Figure 8.3). The thickness of the slab at the profile site was 1.65 m, similar to the crown thickness that averaged an estimated 1.5 m. The bottom 0.7 m of the slab at the profile site consisted of “pencil- to knife-hard” layers. (Extensive fracture propagations are commonly associated with thick slabs containing such hard and stiff layers.) The failure plane consisted of 2-6 mm facets and surface hoar that had been buried on 6 February 1994.

Based on the shear frame tests at the 28° profile site, SK was 0.77. Calculated for the

38° slope of the start zone, SK was 0.66—remarkably low for such a thick slab and an outlier on Figure 6.22. It is likely that the fracture had propagated through the surface hoar layer at this profile site which was directly between the trigger point and the crown.

188

Figure 8.2 Remotely triggered slab avalanche in the Purcell Mountains on 24 February 1994.

Figure 8.3 Cross-sections of snowpack at trigger point, profile site on propagation path and crown for a remotely triggered slab avalanche at the head the south fork of Hume Valley in the Purcell Mountains on 24 February 1994.

189 Approximately 1 h had elapsed between the fracture propagation and the shear frame and rutschblock tests. During this time, the fractured surface hoar layer may have partly rebonded under the weight of the slab. Although this questionable value of SK suggests instability, the rutschblock result indicated stability. Even when three people without skis jumped on the rutschblock simultaneously, the block did not fail. This rutschblock score of 7 is not surprising since—for such deep weak layers—the stresses induced by persons on foot are small compared to the stress induced by such a thick slab (Föhn 1987a; Figure 6.19), a limitation of the rutschblock test identified in Section 7.3. It is very likely that the fracture was initiated by the skiers in the depth hoar near the rocky outcrops, propagated through the surface hoar layer in a snowpack that could not be triggered by skiers and released a large slab avalanche when it reached a slope steep enough to avalanche.

8.2.4 Purcell Mountains, Hume Valley, 8 March 1994

On 8 March 1994, a second slab avalanche was remotely triggered by skiers at the head of the south fork of Hume Creek in the Purcell Mountains. Skiers in gentle terrain on a west-facing slope at 2415 m initiated a fracture within the snowpack that propagated 60 m to a 35° slope where it released a 1.0-m-thick slab avalanche. A profile on a 14° slope at the estimated trigger point revealed a 1.0-m-thick slab of which 0.7 m consisted of “pencil-hard” layers overlying a layer of 8 mm surface hoar that had been buried on 6 February 1994. A profile near the crown was similar, showing a 0.9 m slab that included 0.75 m of “pencil-hard” layers overlying the failure plane of 1-8 mm facets and surface hoar. This is another example of a fracture that initiated in low angle terrain and propagated to a slope steep enough to slide where it released a slab avalanche. There was no suitable site for rutschblock tests near the crown. However, shear frame tests at the profile site resulted in a SK value of 1.37 for the 35° slope of the start zone.

190

8.2.5 Observation Peak, Rocky Mountains, 9 February 1995

A skier ascending a southeast-facing 20° slope at 2400 m on Observation Peak in the Rocky Mountains triggered a fracture that propagated 300 m to a 34° slope where it released a 100 m wide slab avalanche. The slab was approximately 0.5 m thick at the trigger point and 1.1 m thick at the crown where it included 1.0 m of “1-finger and pencil-hard” layers. At a 34° site near the crown, a rutschblock test indicated stability since the block did not slide after a skier jumped several times on the block (RB = 7). Hence, the slab was released by a propagating fracture triggered where the slab was less stable, but the slab remaining in the start zone could not be skier-triggered.

8.3 Characteristics Associated with False Stable Predictions

Selected snowpack and terrain characteristics for these five case studies are summarized in Table 8.1. Certain characteristics are common to these false stable predictions: In every case, the failure plane consisted of a persistent microstructure. In four of the five cases, the trigger point was more than 50 m from the avalanche, so slab conditions at the trigger point may have been very different from the start zone and the site of the shear frame and rutschblock tests. In each of these cases of remote triggering, the avalanche was triggered from a slope too shallow for a dry slab to avalanche (< 25o). In two of the four cases, the slab at the trigger point was much thinner than at the crown. In at least two cases, the fracture initiated in depth hoar near rocks. In two of five cases, obvious cracks extended through the bed surface.

8.4 Remote Triggering and Transitional Stability for SK During the winters of 1992-93 to 1994-95, shear frame and/or rutschblock tests were made at 95 skier-tested avalanche slopes. Of the five slopes that produced false stable results, four were triggered from more than 50 m away from the resulting

191

Table 8.1 False Stable Predictions Slope Slab Inclination Thickness Date Location Predictor (o) (m) Comments Trig. Start Trig. Start Point Zone Point Zone 93-01-27 Purcell Mtns., Remote trig. 100 m.

Malachite SK = 1.46 5 35 0.8 0.8 Cracks through bed Valley surface 93-3-17 Monashee Depth hoar around

Mtns., SK = 1.82 32 32 1.0 1.0 rocks at trigger point. Mt. Albreda RB = 7 Crack through bed surf. 94-02-24 Purcell Mtns., RB = 7 Depth hoar around

Hume Creek SK = 0.66 20 38 0.2 1.5 rocks at trigger point. Remote trig. 400 m.

94-03-08 Purcell Mtns., SK = 1.37 14 35 1.0 1.0 Remote trigger. Hume Creek 60 m 95-02-09 Rocky Mtns., Observation RB = 7 20 34 0.5 1.1 Remote trigger 300 m Peak avalanche. Assuming that propagating fractures (snowquakes) can advance through weak layers in which a skier could not start a fracture, it follows that skiers in the start zone = 7 where SK > 1.3 or RB may have been unable to trigger the slabs that were remotely . triggered Since the only skier-triggered slabs for which SK > 1.3 were remotely triggered, the results summarized in Figure 6.22 imply transitional stability for 1 < SK < 1.3. However, until more data are available to refine the band of transitional stability, an upper limit of 1.5 appears to provides a reasonable margin of safety. The avalanche on Mt. Albreda that was not triggered remotely is important because it illustrates that shear frame and rutschblock tests done where conditions appear typical of the start zone can incorrectly indicate stability.

192 8.5 An Alternative Failure Mode for Primary Fractures

The skier stability index, SK, is a refined version of Föhn’s (1987a) S' for skiers. Both indices are based on the ratio of shear strength to shear stress. The success of these indices for predicting slab stability for skiers (Figure 6.22) is proof that failures for most skier-triggered slabs begin with a shear failure within a thin weak layer. However, important exceptions to shear failure may occur on slopes of less than 20°

inclination. Section 7.4 shows that SK, which is based on shear failure, overestimates the stability of rutschblocks on such slopes. Presumably, the initial failures on slopes of less

than 20° that SK fails to predict involve compression. Further, all four of the remotely

triggered slabs for which SK and/or RB incorrectly indicated stability were triggered on

slopes of 20° or less. Even without specifying the failure mode on shallow slopes, SK cannot be expected to predict skier-triggered avalanches on such shallow slopes because it cannot reliably predict rutschblock failures on such shallow slopes. The rutschblock test, which is not restricted to initial shear failure, may prove useful for assessing the potential of snowpacks on such shallow slopes for initiating fractures. Certainly, the rutschblock test is capable of identifying weak layers on such shallow slopes, regardless of the failure mode. Bed surface cracks were reported in two of the four false stable results (Table 8.1). Although the bed surface was not photographed at either site, Figure 8.4 shows bed surface cracks at an avalanche at Whistler Mountain in February 1979. At the remotely triggered avalanche in the Malachite Valley on 27 January 1993, cracks through the bed surface were found well above the crown and precluded the selection of a suitable site for rutschblock tests. If such cracking were simply a consequence of the avalanche then it would likely be reported at more of the 52 investigated avalanches. However, bed surface cracks were only observed at two avalanche sites, both of which gave false stable results.

The failure of SK to predict instability at these sites, and particularly at the avalanche on Mt. Albreda which was not triggered remotely, could be explained if the initial failure involved the cracks and not shear failure in the weak plane along which the fracture

subsequently propagated. While this argument is far from conclusive, it and SK’s

193 over-estimation of rutschblock stability on shallow slopes (Section 7.4) suggest that not all cases of skier-triggering begin with shear failure of a weak layer. The bed surface cracking is consistent with a primary compressive fracture at the base of the snowpack or within thick depth hoar layers as proposed by Bucher (1948), Bradley (1966), Bradley and Bowles (1967) and Schweizer (1991). However, primary compressive fractures may not be limited to thick weak Figure 8.4 Cracks in bed surface at Whistler Mountain, layers. SK’s February 1979. Such cracks are believed to occur during slab failure. (C. Stethem photo) over-estimation of rutschblock stability on shallow slopes with weak layers of surface hoar (Figure 7.13) suggests that primary compressive failures can occur within relatively thin layers.

194 8.6 Summary

Sections 6.8 and 7.3 show that the skier stability index, SK, and rutschblock scores based on tests where conditions are judged typical of start zones (Figure 6.22 and 7.12) can predict the skier stability of most slopes. However, as the case studies illustrate, stability tests done where snowpack conditions are typical of start zone are occasionally misleading and cannot predict avalanches triggered at localized weaknesses—sometimes with dimensions of only a few metres—or remotely from sites with a less stable snowpack than the start zone. This represents an important limitation of stability tests since it is impractical to test all potential trigger points associated with a locally thin snowpack or with humps, rocks, trees or bushes under the snowpack that are within a few hundred metres of start zones. Stability tests and profiles are presently interpreted together with: a general awareness of the snow distribution, knowledge of mesoscale stability trends based on weather, study site and avalanche observations, and familiarity with the terrain. Clearly, the character of the ground-snow interface within a few hundred metres of the start zone is a relevant terrain consideration. Although this idea is not new, the case studies of false stable predictions confirm its importance. Localized weaknesses should be suspected wherever the ground surface is particularly uneven, as is common on moraines. This is particularly important when stiff slabs overlie persistent weak layers—a combination capable of extensive propagation. The more extensive the propagation, the more likely the fracture will reach a slope steep enough to avalanche. However, although a weak layer and a stiff slab are required for propagation, there is presently no practical snowpack test that indicates whether local fractures that can start near rocks, bushes or thin snowpack areas, etc. will propagate over tens or hundreds of metres, or not at all.

195 9 APPLICATIONS OF SHEAR FRAME STABILITY INDICES TO AVALANCHE FORECASTING

9.1 Introduction

In conventional avalanche forecasting, the forecaster’s experience is used to anticipate avalanche activity based on observations of weather, snowpack and past avalanches (LaChapelle, 1980; Buser and others, 1985). Some forecasting operations presently use shear frame stability indices and rutschblock tests along with other weather, snowpack and avalanche observations to make decisions. Since 1990, rutschblock tests have been adopted to varying degrees by backcountry avalanche safety programs in Canada. Although shear frame stability indices have been used for forecasting natural avalanches of storm snow and closures for timing explosive control at the highways through Rogers Pass since 1963 (D. Skjönsberg, personal communication) and through Kootenay Pass since 1980 (J. Tweedy, personal communication), such indices are presently not used by backcountry avalanche forecasting programs in Canada where skier-triggered avalanches are the greatest concern. This chapter attempts to determine if extrapolated shear frame stability indices could improve backcountry avalanche forecasting of persistent dry slabs which are the cause of most backcountry fatalities (Jamieson and Johnston, 1992a). The approach is to compare the number of days correctly forecast using SN38 and SK38 as well as conventional measurements with the number of days correctly forecast using only conventional measurements. A limitation of this approach results from the selection of conventional measurements. Quantitative meteorological measurements such as air temperature, precipitation and wind speed taken daily at fixed sites and previous avalanche activity are used. However, snowpack tests such as shovel tests, compression tests, ski tests and profiles are excluded since they are done intermittently and at varying locations. Although backcountry forecasters consider such tests to be important, they are difficult to assess systematically.

196 Sections 9.2 and 9.4 present correlations of individual forecasting variables such as previous avalanche activity, air temperature, precipitation, wind speed and shear frame stability indices with natural and skier-triggered avalanche activity, respectively. Sections 9.3 and 9.5 develop simple multivariate forecasting models for natural and skier-triggered avalanches respectively, and compare the performance of these models when shear frame stability indices are included and excluded. The analysis in each section is repeated for the Purcell Mountains near Bobby Burns Lodge and for the Cariboo and Monashee Mountains near Blue River, BC. Measurements for the meteorological variables are taken in the morning before skiing terrain is selected for the day. Interpolated values of the shear frame stability

indices, SN38 and SK38, are used between days that persistent weak layers were tested with the shear frame. All variables are related to avalanche activity for the same day. While the date of occurrence is accurately recorded for skier-triggered avalanches, the occurrence date of natural avalanches is often estimated. Avalanches that are estimated to have occurred during the night prior to morning weather observation are usually recorded as having occurred on the previous day. This is optimal since it relates avalanche activity to daily weather measurements such as 24 h maximum air temperature, 24 h snowfall, etc. Various measures of avalanche activity are possible. The daily total number of avalanches (with a maximum of 10) was used in Chapters 6 and 7. McClung and Tweedy (1994) summed the size classes for all reported avalanches. Davis and Elder (1995) compared various measures of avalanche activity including number of avalanches, sum of sizes of all avalanches, as well as the size of the largest avalanche on a given day, and found that the ranked order of forecasting variables was the same for each measure of avalanche activity. This implies that the assessment of a particular variable’s predictive value—which is an objective of this chapter—is relatively insensitive to the measure of avalanche activity. For the present data set, Spearman rank correlations between the daily number of persistent dry slab avalanches and the daily maximum size class are 0.999 for natural avalanches and 0.997 for skier-triggered avalanches for 356 days in the Cariboo and Monashee Mountains. Similarly, the correlations are 0.999 for both natural and

197 skier-triggered avalanches for 295 days in the Purcell Mountains. Such correlations may seem surprising since large avalanches are much less common than small avalanches. However, since no persistent dry slab avalanches are reported on many days, the various measures of avalanche activity primarily distinguish between days with avalanches and days without avalanches. In subsequent analyses, the daily maximum size class of natural or skier-triggered avalanches involving a persistent slab, MxN or MxS, respectively, is used as the measure of avalanche activity in part because the size of expected avalanches—especially skier-triggered avalanches—affects backcountry decisions more than the number of avalanches. For example, when class 1 avalanches (not large enough to injure a person) are expected, ski guides will intentionally trigger many slabs to stabilize slopes and, in many cases, remove the weak layer before additional snowfall builds a thicker and more destructive slab. In contrast, slopes are generally avoided on which a class 2 slab avalanche (large enough to injure, bury or kill a person) might occur. Since the forecasting model described in the next section tends not to predict levels that rarely occur, the number of levels of avalanche activity should be reduced for these analyses. For this reason, half-sizes of avalanches (CAA, 1995; Table 3.2) are rounded up to the nearest integer, and MxN and MxS are assigned a value of 3 on the rare days with a persistent slab avalanche larger than class 3. As a result of this reduction, MxN and MxS only take on values of 0, 1, 2 or 3, levels which are adequate for practical decision-making. The following analyses use the shear frame stability indices for the persistent weak layers discussed in Chapter 6, excluding those from the Rocky Mountains for which insufficient data were available. In the Purcell Mountains near Bobby Burns Lodge, the tested persistent layers were buried 19 January 1993, 10 February 1993, 6 February 1994, 7 January 1995 and 6 February 1995. In the Cariboo and Monashee Mountains near Blue River, BC, the tested persistent weak layers were buried 10 February 1993, 29 December

1993, 5 February 1994 and 7 January 1995. To obtain one daily value of SN38 and of SK38 for each of the two forecast areas, values for various persistent weak layers from different

198 study sites within a forecast area are averaged for each day. Averaging across study sites reduces the effect of an unusually weak (or strong) persistent layer at a particular study site such as occurred for the surface hoar layer buried 10 February 1993 at Mt. St. Anne (Section 6.9.2).

9.2 Forecasting Variables for Natural Avalanches of Persistent Slabs

This section presents relationships between the size class of the largest natural persistent dry slab avalanche reported on a particular day, MxN, and

the extrapolated stability index, SN38, for natural avalanches of persistent slabs, local meteorological measurements available to the forecasters and ski guides on the morning of the day, MN1 which is the size class of the largest natural persistent slab avalanche reported for the previous day, and MN2 which is the sum of the size classes of the largest natural persistent slab reported for the two previous days. The relationship between two variables may be either monotonic (increasing or decreasing) or non-monotonic, or there may be no discernible relationship. For example, a monotonic (increasing) relation would exist between wind speed and avalanche activity if increased wind speed was associated with increased avalanche activity. If more activity were associated with moderate winds than with light or strong winds, then the relationship would be non-monotonic. Monotonic relationships are assessed with Spearman rank correlations which are suited to ordinal data. Non-monotonic relationships are assessed with box graphs. Spearman rank correlation coefficients, R, are presented in Table 9.1 for MxN’s

relationship to common meteorological variables as well as to MN1, MN2 and SN38 for observations the winters of 1992-93, 1993-94 and 1994-95. These meteorological measurements include total height of the snowpack, HS, height of 24 h snowfall, HN, accumulated snowfall during a storm, HST, and foot penetration, PF, which can also be considered snowpack measurements. In the Purcell Mountains, the meteorological

199

Table 9.1 Spearman Rank Correlations Between Forecasting Variables and the Daily Maximum Size of Natural Avalanches Involving Persistent Slabs, MxN Purcell Mountains1 Cariboo and Forecasting Variables Monashee Mtns.2 NR pNR p Max. Nat. Av. on Previous Day (MN1) 294 0.03 0.61 355 0.38 <10-6 Sum of Max. Nat. Av. Previous 2 Days 293 0.21 <10-4 354 0.47 <10-6 (MN2) Barometric Pressure (BP) 261 0.04 0.51 353 -0.12 0.02 Air Temperature (Ta) 268 0.03 0.62 327 -0.01 0.87 24 hr Min. Air Temperature (Tmin) 267 0.06 0.35 332 -0.01 0.85 24 h Max. Air Temperature (Tmax) 267 0.10 0.12 334 -0.10 0.07 Wind Speed (WS) 264 0.03 0.59 258 0.05 0.38 Wind Direction (WD) 75 -0.03 0.77 258 0.10 0.13 Height of 24 h Snow (HN) 264 -0.06 0.37 - - - Height of Storm Snow3 (HST) 255 -0.03 0.61 - - - Water Equiv. of 24 h Precip.4 (HNW) - - - 323 0.15 0.01 Water Equiv. of Storm Precip.5 (HSTW) - - - 323 0.16 10-2 Height of Snowpack (HS) 268 0.02 0.77 356 0.06 0.26 Foot Penetration (PF) 263 0.03 0.60 - - - 6 Natural Stability Index (SN38) 138 -0.21 0.01 168 -0.01 0.91 1 All variables except for SN38 based on manual measurements at Bobby Burns Lodge, 1370 m at approximately 0630 h. Wind speed estimated as calm, low, moderate or strong and converted to 0, 15, 35 or 50 km/h. Wind Direction estimated using 8 cardinal directions. 2 All variables except for barometric pressure measured automatically at Mt. St. Anne, 1900 m. Air temperature, wind speed and wind direction are averaged between 0400 and 0500 h. 3 Reset to 0 after precipitation has stopped and useful settlement observations were obtained. 4 Estimated from HN when precipitation gauge not working. 5 Cumulated HNW. Reset to 0 after 24 h period ending at 0500 with less than 0.3 mm precipitation. 6 Mean of measured and/or interpolated values from various study sites and persistent weak layers. 7 R values marked in bold are significant at the 0.05 level.

200 measurements were obtained in the morning from manual weather observations at Bobby Burns Lodge (1370 m). For the Cariboo and Monashee Mountains near Blue River, BC, meteorological measurements, other than barometric pressure were obtained from an automatic weather station (1900 m) on Mt. St. Anne in the Cariboo Mountains. Barometric pressure was obtained from the weather station at the Blue River airport (678 m) and adjusted to the equivalent pressure at sea level. Storm and 24 h precipitation measurements are HSTW and HNW in mm from a gauge that melts the precipitation to determine the equivalent amount of water. Differences in the observations recorded at each area reflect differences in equipment and operational practices at the two areas.

Of the variables given in Table 9.1 for the Purcell Mountains, only MN2, and SN38 are significantly correlated (p < 0.05) with MxN. The positive correlation of MN2 with MxN is consistent with the accepted use of recent avalanche activity as a predictor of

expected avalanche activity. The negative correlation between SN38 and MxN implies that

MxN tends to increase as the natural stability index, SN38, decreases. On the many days that

no natural avalanches are reported for persistent slabs (MxN = 0), high values of SN38 are implied. The lack of correlations with the meteorological forecasting variables other than Tmax may be due to the difference in weather between the start zones, typically 1700 m to 2700 m, and the Bobby Burns Lodge which is at 1370 m in a relatively dry valley, or with difficulty identifying persistent failure planes for natural avalanches—most of which are observed from a distance. Difficulty identifying the failure plane for natural avalanches may partly explain why persistent avalanche activity on the previous two days (MN2) correlates better than activity on the previous day (MN1). In the Cariboo and Monashee Mountains near Blue River, BC, MN1, MN2, PB, HNW and HSTW are significantly correlated with MxN (p < 0.05). The strong positive correlations of MxN with MN1 and with MN2 indicate the importance of previous avalanche activity as a predictor of present natural avalanche activity. The negative correlation with barometric pressure implies that natural avalanches of persistent slabs are more common on days with low barometric pressure than for higher pressure. The positive correlations with 24 h precipitation and storm precipitation indicate that persistent

201

Figure 9.1 Box plots of the daily maximum size of natural avalanche involving a persistent slab against various forecasting variables showing median (small rectangle), lower and upper quartiles (box) and minima and maxima (whiskers). Boxes for the Purcell Mountains near Bobby Burns Lodge are unshaded and boxes for the Cariboos and Monashee Mountains near Blue River, BC are shaded. Precipitation values are height of snowfall in cm for the Purcell Mountains and height of melted precipitation in avalanches are more common for higher values of precipitation than for lower values. The correlation of MxN with SN38 is not significant which is consistent with the discussions in Section 6.6.2. Non-monotonic relationships between MxN and most forecasting variables from Table 9.1 are assessed with box graphs in Figure 9.1. Foot penetration is excluded from Figure 9.1 since the usual interpretation—deeper foot penetration is associated with larger

202 avalanches—implies a monotonic relation which was tested with the correlation in Table 9.1. Air temperature, Ta, and minimum 24 h air temperature, Tmin, are excluded since they exhibit the same general trend as Tmax which is plotted in Figure 9.1. MN1 is excluded since MN2 yields stronger correlations with MxN in both forecast areas. Height of 24 h snow, HN, and height of storm snow, HST (cm), from the Purcell Mountains are plotted along with their respective water equivalents, HNW and HSTW (mm), from the Cariboo and Monashee Mountains. Non-monotonic relations apparent in Figure 9.1 are used to select variables for a multivariate model in the next section. For each forecasting variable and each value of MxN, the median values are plotted as small rectangles and the boxes which extend from the 25th to 75th percentile include the middle half of the data. Substantial shifts in the median values or boxes for different values of MxN suggest that the variable may have predictive value. In addition to MN2, PB, HNW and HSTW which correlate with MxN in the Cariboo and Monashee Mountains (Table 9.1), Tmax, WS, WD, and HS, also show promise of being useful predictors (Figure 9.1). In the Purcell Mountains, HS and Tmax show promise as predictors. Three variables which are useful predictors for other forecasting models (e.g. Buser and others, 1987; Davis and others, 1993; McClung and Tweedy, 1994), namely, wind speed, WS, height of 24 h snowfall, HN, and height of storm snow, HST, do not appear to be promising predictors of MxN, probably because they are observed at Bobby Burns Lodge where snow and weather conditions are quite different from start zones in the Purcell Mountains.

9.3 A Multivariate Forecasting Model for Natural Avalanches Involving Persistent Slabs

9.3.1 Selection of Model

The objective of this section is to determine if the inclusion of SN38 in a multivariate forecasting model improves the performance of the model. Although nearest neighbours models have advantages (Section 1.8) for forecasting, such models are not suited to

203 assessing the importance of a particular variable since they require that the variables be weighted heuristically (Buser and others, 1985). Classification tree models are used in preference to discriminant analysis for this assessment of SN38, since such models do not require normalizing transformations, allow for complex interactions between the predictor variables, are sensitive to non-monotonic relations between the predictor variables and the response variables, and allow a categorical response variable with more than two levels for avalanche activity (Davis and Elder, 1995). Classification trees recursively split the data into two groups using various partitioning rules. Fortunately, the resulting trees tend to reflect structure in the data and are not strongly affected by the choice of partitioning rule (Breiman and others, 1984, p. 94). Although a partitioning rule based simply on the number of cases (days) misclassified is tempting, Breiman and others (1984, p. 94-98) prove otherwise. The partitioning rule of the S-Plus software that was used for these analyses is based on deviance which is a measure of a lack-of-fit of an observation to the data used to construct a particular node. Consider a day with MxN = 1 directed to a particular node of the tree. If all the data used to construct the node had MxN = 1, then the deviance for the particular day would be zero at that node. If only 60% of the observations used to construct the node had MxN = 1 then the deviance would be greater than zero according to the log-likelihood formula for deviance (Chambers and Hastie, 1992, p. 412-414). For the present data, each forecasting variable consists of ordinal (or interval) values which allows each variable, Xi, to be split using a critical value, Xic. At each split, each critical value, Xic, between sorted values of Xi is tried for each variable to find the split

Xi < Xic that partitions the data into subsets with minimal deviance. The same splitting rule is then applied to each subset. The fact that the same forecasting variable can be used recursively allows complex patterns in the data to be detected. Potentially, sets could be split until there is only one datum in each subset. However, while the initial splits reflect structure and grouping of the data (which are important), splitting into very small subsets results in fitting a tree to individual data points (which is not relevant to most problems). For the present application, splitting was stopped when

204 there were five or less days in a subset, or the set consisted of points with a single value of MxN, indicating that five or more days with the same maximum size of dry natural avalanches had been grouped together. Subsets that are not subdivided further are called terminal nodes or leaves. The measure of the lack-of-fit of a particular tree to a compatible data set is the residual mean deviance defined as the deviance summed over all the observations divided by the degrees of freedom of the tree (number of cases minus the number of terminal nodes) (Statsci, 1994, p. 12.10). Hence, the better a tree fits a data set, the less the residual mean deviance. Although the misclassification rate is the obvious measure of lack-of-fit, it ignores the fact that the probability of a particular value of the response variable, MxN at a node usually falls between 0 and 1 (Breiman and others, 1984, p. 94-98). Subsequent analyses present the lack-of-fit in terms of both the misclassification rate and the residual mean deviance.

9.3.2 Purcell Mountains

All data-based multivariate models including classification trees require large data sets (Davis and Elder, 1995). However, the size of the data set (number of days) tends to decrease as the number of variables increases since different variables often have missing

values on different days. For example, including SN38 in a model excludes those days that

neither measured nor interpolated values of SN38 were available. During the three winters that persistent weak layers were monitored in the Purcell

Mountains, measured or interpolated values of SN38 were obtained for persistent weak layers from at least one study site between 26 January 1993 and 16 March 1993, between 13 February 1994 and 21 March 1994 and between 12 January 1995 and 3 March 1995 for a total of 138 days. The daily avalanche activity for the weak layers that produced one or more dry slab avalanches is described in Sections 6.6 and 6.9. For the Purcell Mountains, the rank correlations in Table 9.1 show that MN2, Tmax

and SN38 exhibit significant monotonic relationships with MxN, and the box graphs (Figure 9.1) for PB, HS and possibly storm precipitation, HST, show non-monotonic

205 relationships to MxN. Eliminating the days for which any of these six variables had missing values yields a data set of 12 days with persistent slab avalanches (MxN > 0) and 121 days without such avalanches (MxN = 0). When the classification tree algorithm is applied to the variables MN2, HS, HST,

Tmax and PB with SN38 excluded, a tree (Model N-P-E in Table 9.2, Figure 9.2) results which misclassifies 12 days and has a deviance of 0.44. Removing the parts of the tree that do not reduce the misclassification rate (circled in Figure 9.2) reduces the number of terminal nodes to four and increases the residual mean deviance to 0.56. Following the splits (“decisions”) in Figure 9.2, MxN = 2 is “predicted” when 0.80 ≤ HS < 1.15 m and MN2 ≥ 3. (Of course, such predictions reflect the limited data set and may not fit expectations based on intuition and determinism.)

Including SN38 with MN2, HS, HST, Tmax and PB for the same set of 133 days results in Model N-P-I (Figure 9.3) which has a reduced residual mean deviance of 0.37 and a reduced misclassification rate of 11/133. Nine of 12 avalanche days are misclassified

Figure 9.2 Classification tree for daily maximum size of natural avalanches of persistent slabs in the Purcell Mountains using forecasting variables but excluding SN38. Data are from the winters of 1992-93 to 1994-95. For each split, the left branch denotes days for which the “less than” criterion is true.

206

Table 9.2 Classification Trees for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Purcell Mountains Model Cost- No. of Residual Mis- Name Forecasting Variables1 Complexity Terminal Mean classifi- Factor Nodes Deviance cation rate N-P-E HS, HST, Tmax, PB, MN2 0 14 0.44 12/133

N-P-I SN38, HS, HST, Tmax, PB, MN2 0 11 0.37 11/133

N-P-1 SN38, HS, HST, Tmax, PB, MN2 1 9 0.38 11/133

N-P-2 SN38, HS, HST, Tmax, PB, MN2 2 7 0.43 11/133

N-P-3 SN38, HS, HST, Tmax, PB, MN2 3 7 0.43 11/133

N-P-4 SN38, HS, HST, Tmax, PB, MN2 4 5 0.48 11/133

N-P-5 SN38, HS, HST, Tmax, PB, MN2 5 4 0.53 11/133

N-P-6 SN38, HS, HST, Tmax, PB, MN2 6 4 0.53 11/133

N-P-7 SN38, HS, HST, Tmax, PB, MN2 7 2 0.64 12/133 1 Variables marked in bold are selected by the classification tree algorithm from those listed and used to build the tree.

Figure 9.3 Classification tree for the daily maximum size of natural avalanches of

persistent slabs in the Purcell Mountains using forecasting variables including SN38. Data are from the winters of 1992-93 to 1994-95. For each split, the left branch denotes days for which the “less than” criterion is true.

207 and two of 121 non-avalanche days are misclassified as shown in Table 9.3. So, including

SN38 results in one more avalanche day being correctly classified. Removing the parts of the tree that do not reduce the misclassification rate (circled in Figure 9.3) reduces the number of terminal nodes to four and increases the residual mean deviance to 0.53. To determine which of the six variables are most effective at reducing the residual mean deviance, D, the tree model can be simplified by increasing the cost-complexity factor, k, and removing the least important subtrees T' with cost-complexity (Statsci, 1994, p. 12.17) defined as

DK(T') = D(T') + k · number of terminal nodes of subtree T'. (9.1) By increasing the cost-complexity factor, k, from 1 to 7, the residual mean deviance and misclassification rate increase, the number of terminal nodes decreases and the most important variables are retained at each step (Table 9.2). By this technique, the forecasting variables for MxN in the Purcell Mountains are, in decreasing predictive value, SN38, HS,

HST, Tmax, PB and MN2. Of these variables, only SN38 and Tmax showed significant monotonic relationships to MxN in Table 9.1. The second most important variable, HS, did not exhibit a significant correlation with MxN (Table 9.1) but did show a non-monotonic

Table 9.3 Contingency Table for Natural Slab Avalanches Involving Persistent Slabs in the Purcell Mountains Modelled Observed Size of Slab Avalanche Size of 023 Avalanche Excl. SN38 Excl. SN38 Excl. SN38 Incl. SN38 Excl. SN38 Incl. SN38 0 119 119 6 5 4 4 2222300 3000000 Total 121 121 8 8 4 4 Proportion 119/121 119/121 2/8 3 0/4 0/4 Correct Percent 98% 98% 25% 38% 0% 0% Correct

208 relationship to MxN (Figure 9.1) indicating the importance of non-monotonic relationships between avalanche forecasting variables.

9.3.3 Cariboo and Monashee Mountains

During the three winters that persistent weak layers were monitored in the Cariboo

and Monashee Mountains, measured or interpolated values of SN38 were obtained for weak layers that produced more than one slab avalanche between 14 February 1993 and 30 March 1993, between 30 December 1993 and 22 March 1994 and between 10 January 1995 and 18 February 1995 for a total of 168 days. The daily avalanche activity for the weak layers that produced one or more dry slab avalanche is described in Sections 6.6 and 6.9. For the Cariboo and Monashee Mountains, the variables selected based on their correlations with MxN (Table 9.1) are avalanche activity over the previous two days, MN2, barometric pressure, PB, maximum temperature, Tmax, 24 h precipitation, HNW and storm precipitation, HSTW. Wind speed, WS, and wind direction, WD, and height of snowpack, HS, are selected from the box plots in Figure 9.1. The natural stability index,

SN38, is included to determine if it has predictive value in combination with the other variables selected from Table 9.1 and Figure 9.1. Eliminating the days for which one or more of these eight predictor variables is missing reduces the data set to 94 days. Unfortunately, these data are highly unbalanced since there are only seven days with persistent avalanches. Results from the classification tree models are summarized in Table 9.4. Using the eight forecasting variables MN2, WS, Tmax, WD, HNW, HSTW, HS and PB, the classification tree algorithm selects MN2, WS, Tmax and WD as predictors for the 94 days mentioned previously (Model N-C-9E). The model achieves a misclassification

rate of 7/94 by classifying all days as non-avalanche days. Including SN38 with the other eight variables results in Model N-C-9I which also classifies all avalanche days as non- avalanche days. The data set is simply too small and too unbalanced to give interesting results.

209 Table 9.4 Classification Trees for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Cariboos and Monashees Model No. of Residual Mean Mis- Name Forecasting Variables1 Terminal Deviance classification Nodes rate N-C-9E MN2, WS, Tmax, WD, 6 0.37 7/94 HNW, HSTW, HS, PB

N-C-9I MN2, WS, SN38, Tmax, 6 0.37 7/94 HNW, HSTW, HS, WD, PB N-C-7 MN2, Tmax, HS, HSTW, 8 0.27 9/150

HNW, PB, SN38 1 Variables marked in bold are selected by the classification tree algorithm from those listed and used to build the tree.

However, the size of the data set can be increased by eliminating the variables WS and WD which are missing (due to riming problems with the anemometer and wind vane) on more days than the other variables, except for SN38 which must be included to be assessed (Table 9.1). Eliminating WS and WD increases the data set to 150 days including 13 avalanche days. Using the seven forecasting variables MN2, Tmax, HNW, HSTW, HS,

PB and SN38, the classification tree algorithm selects MN2, Tmax, HS, HSTW and rejects

SN38 along with HNW and PB for Model N-C-7 (Figure 9.4). Hence, for this larger data set, SN38 does not contribute to a reduced misclassification rate for avalanche activity. As shown in Table 9.5, all of the 137 days without avalanches and all of the four days with class 3 or larger avalanches are correctly classified. However, all of the nine days with class 1 or 2 avalanches are misclassified.

In summary, SN38 shows predictive value for natural avalanche activity in the Purcell Mountains but not in the Cariboo and Monashee Mountains. This inconsistent result is likely a consequence of the number of reports of natural avalanches of persistent slabs being limited due to difficulty approaching natural avalanches—many of which start in very steep terrain—and correctly identifying the failure plane. However, this difficulty does not apply to skier-triggered avalanches considered in the next section.

210

Figure 9.4 Classification tree for the daily maximum size of natural avalanches of persistent slabs in the Cariboo and Monashee Mountains based on 150 days from the winters of 1992-93 to 1994-95. For each split, the left branch denotes days for which the “less than” criterion is true.

Table 9.5 Contingency Table for Daily Maximum Size of Natural Avalanches of Persistent Slabs in the Cariboo and Monashee Mountains Modelled Size of Observed Size of Slab Avalanche Avalanche 012≥3 0 137 2 5 0 10000 20000 >20024 Total 137 2 7 4 Proportion 137/137 0/2 0/7 4/4 Correct Percent Correct 100% 0% 0% 100%

211 9.4 Forecasting Variables for Skier-Triggered Avalanches of Persistent Slabs

This section assesses relationships between the daily maximum size of skier-triggered persistent dry slab avalanches, MxS, and meteorological variables PB, Ta, Tmin, Tmax, WS, WD, HN or HNW, HST or HSTW, HS and PF which are available to the forecasters and ski guides on the morning of the day,

the extrapolated skier stability index SK38 for persistent slabs, MS1 which is the size class of the largest skier-triggered persistent slab on the previous day, and MS2 which is the sum of the size classes of the largest skier-triggered persistent slabs from the two previous days. As with the previous section for natural avalanches, variables are selected based on either monotonic relationships detected with correlations or with non-monotonic relationships apparent in box plots. The selected variables are used in multivariate classification trees to assess the predictive value of SK38 for forecasting skier-triggered persistent slabs. Rank correlation coefficients, R, are presented in Table 9.6 between MxS and the variables listed above based on data from the winters of 1992-93, 1993-94 and 1994-95. The meteorological variables are the same as those used for the correlations with natural avalanches in Section 9.2.

In the Purcell Mountains, MS1, MS2, BP, HN, HST and SK38 correlate significantly

(p < 0.05) with MxS. The negative correlation of barometric pressure and SK38 with MxS implies that skier-triggering of persistent slabs tends to increase as barometric pressure and SK38 decrease. The positive correlations of HN and HST with MxS imply that skier-triggering of persistent slabs tends to increase as 24 h and storm snowfall increase. In the Cariboo and Monashee Mountains, previous skier-triggered avalanche activity

(MS1 and MS2) as well as air temperature (Ta, Tmin and Tmax) and SK38 show significant

212

Table 9.6 Spearman Rank Correlations Between Forecasting Variables and the Daily Maximum Size of a Skier-Triggered Avalanche Involving a Persistent Slab Purcell Mountains Cariboo and Forecasting Variables1 Monashee Mtns. NR p N R p Max. Skier-Trig. Slab on Previous Day 294 0.14 0.02 355 0.50 <10-6 (MS1) Sum of Max. Skier-Trig. Slab on 293 0.18 10-3 354 0.54 <10-6 Previous 2 Days (MS2) Barometric Pressure (PB) 261 -0.12 0.05 353 -0.08 0.13 Air Temperature (Ta) 268 -10-3 0.98 327 -0.13 0.02 24 hr Min. Air Temperature (Tmin) 267 0.01 0.93 332 -0.12 0.03 24 h Max. Air Temperature (Tmax) 267 -0.07 0.24 334 -0.15 0.01 Wind Speed (WS) 264 0.01 0.82 258 0.05 0.44 Wind Direction (WD) 75 0.09 0.44 258 0.01 0.85 Height of 24 h Snow (HN) 264 0.15 0.01 - - - Height of Storm Snow (HST) 255 0.15 0.01 - - - Water Equiv. of 24 h Precip. (HNW) - - - 320 0.03 0.52 Water Equiv. of Storm Precip. (HSTW) - - - 320 0.04 0.44 Height of Snowpack (HS) 268 0.08 0.17 356 -0.06 0.23 Foot Penetration (PF) 263 0.08 0.20 - - - -3 -6 Skier Stability Index (SK38) 138 -0.29 <10 168 -0.49 <10 1 Variables are measured as noted in Table 9.1.

correlations with MxS (p < 0.05). Air temperature (Ta, Tmin and Tmax) and SK38 are negatively and significantly correlated with MxS. Tmax has a stronger correlation with MxS than Ta or Tmin and is used in subsequent analysis. The negative correlation may be due to factors such as an increase in skier-triggered persistent slabs during the clearing and cooling after a storm when skiing in avalanche terrain often resumes or increases, or a reduction in skier-triggered persistent slabs in late winter and spring when air temperatures rise and persistent weak layers are less common. Box graphs are presented in Figure 9.5 to assess non-monotonic relationships of the forecasting variables with MxS. MS2 is shown in the box plots although MS1 would

213 probably have worked as well since MS1 and MS2 show comparable correlation coefficients in Table 9.6. Ta and Tmin are excluded since they show similar but weaker correlations than Tmax with MxS. Foot penetration is also excluded since only a monotonic relationship is likely and the correlation with MxS is not significant (Table 9.6).

Figure 9.5 Box plots of the daily maximum size of a skier-triggered persistent slab against various forecasting variables showing median (small rectangle), lower and upper quartiles (box) and minima and maxima (whiskers). Boxes for the Purcell Mountains near Bobby Burns Lodge are unshaded and boxes for the Cariboos and Monashee Mountains near Blue River, BC are shaded. Precipitation values are height of snowfall in cm for the Purcell Mountains and height of melted precipitation in mm for the Cariboo and Monashee Mountains, 1992-93 to 1994-95.

214 HN and HST (cm) from the Purcell Mountains are plotted on the same graphs as HNW and HSTW (mm) respectively from the Cariboo and Monashee Mountains. In the Purcell Mountains, neither wind speed nor wind direction observed at Bobby Burns Lodge (1370 m) shows a relationship with MxS in Figure 9.5. Reduced barometric pressure, PB, is apparent on days with MxS = 1 compared to days with MxS = 0 and MxS > 1. Height of snowpack, HS, shows a possible relationship with MxS. Hence, PB

and HS are included with Tmax, HN, HST and SK38 in the multivariate forecasting model

for the Purcell Mountains. The graph of SK38 in Figure 9.5 shows that most persistent

slabs were skier-triggered in the Purcell Mountains when SK38 is less than 1.5, which is the

critical value determined for SK and SK38 in Sections 6.8 and 6.9 respectively. In the Cariboo and Monashee Mountains, neither the wind speed nor the wind direction show a relationship with MxS in Figure 9.5. Maximum temperature, Tmax, and

barometric pressure, PB and SK38 were selected based on their correlations with MxS in Table 9.6. This leaves 24 h precipitation, HNW, and storm precipitation, HSTW, and height of snowpack, HS, all of which show increased median values for MxS = 2 than for

lower values of MxS. Consequently, Tmax, PB, SK38, HNW, HSTW and HS are used in the multivariate forecasting model for the Cariboo and Monashee Mountains in the next

section. The graph of SK38 in Figure 9.5 shows that most persistent slabs were

skier-triggered in the Cariboo and Monashee Mountains when SK38 < 0.75. This is below the critical value of 1.5 which was generally critical for most weak layers probably because

of the very low values of SK38 for the surface hoar layer buried on 10 February 1993 at the Mt. St. Anne Study Plot (Section 6.9.2).

215 9.5 A Multivariate Forecasting Model for Skier-Triggered Avalanches Involving Persistent Slabs

9.5.1 Cariboo and Monashee Mountains

In the Cariboo and Monashee Mountains there were 150 days with no missing values for SK38, MS2, HST, BP, HS, HNW or Tmax. Excluding SK38 but including MS2, BP, Tmax, HNW, HSTW and HS, the classification tree algorithm builds model S-C-E (Table 9.7) which misclassifies MxS on 13 of the 150 days and has a residual mean deviance of 0.37. Including SK38 results in the model S-C-I which also misclassifies 13 days but reduces the residual mean deviance to 0.33. The tree for this model is shown in Figure 9.6.

The contingency tables for the tree without SK38 and the tree with SK38 are shown in

Table 9.8. The tree that includes SK38 misclassifies one less day with a class 1 skier-triggered slab than the tree that excludes SK38. As was done for natural avalanches in the Purcell Mountains, the forecasting variables can be ranked by simplifying the model and noting which variables are retained as predictors. By increasing the cost-complexity factor, k, from 1 to 17, the variables are ranked, in order of decreasing predictive value, MS2, SK38, HSTW, PB and HS

Figure 9.6 Classification tree for the daily maximum size of skier-triggered persistent slab in the Cariboo and Monashee Mountains based on data from the winters of 1992-93 to 1994-95.

216

Table 9.7 Classification Trees for Daily Maximum Size of Skier-Triggered Persistent Slabs in the Cariboos and Monashees, 1992-93 to 1994-95. Model Cost- No. of Residual Mis- Name Forecasting Variables1 Complexity Terminal Mean classificatio Factor Nodes Deviance n rate S-C-E MS2, HS, HSTW, 0 9 0.37 13/150 Tmax, PB, HNW,

S-C-I MS2, SK38, HSTW, PB, 0 9 0.33 13/150 HS, HNW, Tmax

S-C-1, 2, 3 MS2, SK38, HSTW, PB, 1, 2, 3 7 0.36 15/150 HS, HNW, Tmax

S-C-4 MS2, SK38, HSTW, PB, 4 6 0.39 15/150 HS, HNW, Tmax

S-C-5, 6, 7 MS2, SK38, HSTW, PB, 5, 6, 7 5 0.44 15/150 HS, HNW, Tmax

S-C-8 MS2, SK38, HSTW, PB, 8 4 0.49 20/150 HS, HNW, Tmax

S-C-9...16 MS2, SK38, HSTW, PB, 9-16 3 0.60 20/150 HS, HNW, Tmax

S-C-17 MS2, SK38, HSTW, PB, 17 2 0.73 29/150 HS, HNW, Tmax 1 Variables marked in bold are selected by the recursive partitioning algorithm for the model.

(Table 9.7). This approach ranks the non-monotonic relationships of HSTW and HS with MxS (Figure 9.5) higher than the monotonic relationship of Tmax with MxS (Table 9.6), indicating the importance of non-monotonic relationships in avalanche forecasting.

9.5.2 Purcell Mountains

The effect of SK38 on the misclassification rate for skier-triggered persistent slabs in the Purcell Mountains can be assessed by considering classification trees developed with

and without SK38 from the same set of days. The selection of variables for the models is based on correlations in Table 9.6 and box graphs in Figure 9.5. In Table 9.6, MS1, MS2,

PB, HN, HST and SK38 were significantly correlated with MxS (p < 0.05). In Figure 9.5,

217

Table 9.8 Contingency Table for Daily Maximum Size of Skier-Triggered Persistent Slabs in Cariboo and Monashee Mountains, 1992-93 to 1994-95. Observed Size of Slab Avalanche Predicted Size of 012 1 2 1 2 1 2 Avalanche Excl. SK38 Incl. SK38 Excl. SK38 Incl. SK38 Excl. SK38 Incl. SK38 0 114 113 6 7 1 1 102151611 2 3 22088 Total 117 117 23 23 10 10 Proportion 114/117 113/117 15/23 16/23 8/10 8/10 Correct Percent 97% 97% 65% 70% 80% 80% Correct 1 Predictions based on Model S-C-E which excludes SK38 as a forecasting variable. 2 Predictions based on Model S-C-I which includes SK38 as a forecasting variable.

Tmax appears to be of predictive value since it is generally lower on days when MxS is 1 than when MxS is 0. HS is also included since it appears greater when MxS is 1 than when MxS is 0 or 2. MS2 is included in preference to MS1 since it exhibits a stronger correlation in Table 9.4. Excluding the days in which any one of these variables is missing results in a set of 133 days, including 16 days with skier-triggered persistent slabs.

From the variables, MS2, PB, HS, HST, Tmax and HN but excluding SK38, the classification tree algorithm selects PB, HS, HST and Tmax but not HN as predictors of MxS for Model S-P-E (Table 9.9). This model has 11 terminal nodes and a residual mean deviance of 0.45. Unlike previous trees that excluded shear frame stability indices, this tree (Figure 9.7) correctly classifies some avalanche days. As shown in the contingency table (Table 9.9), this tree correctly classifies 110 of 117 non-avalanche days and 8 of 16 avalanche days for a misclassification rate of 15/133. Removing the subtrees that do not reduce the misclassification rate (circled in Figure 9.7) increases the residual mean deviance to 0.59.

218

Table 9.9 Classification Trees Results for Daily Maximum Size of Skier-Triggered Persistent Slabs in the Purcell Mountains, 1992-93 to 1994-95. Model Cost- No. of Residual Mis- Name Forecasting Variables Complexity Terminal Mean classification Factor Nodes Deviance rate S-P-E PB, HS, HST, Tmax, 0 11 0.45 15/133 HN, MS2

S-P-I SK38, PB, HST, Tmax, 0 12 0.42 12/133 HS, MS2, HN

S-P-1 SK38, PB, HST, Tmax, 1 10 0.44 12/133 HS, MS2, HN

S-P-2 SK38, PB, HST, Tmax, 2 9 0.45 12/133 HS, MS2, HN

S-P-3 SK38, PB, HST, Tmax, 3 7 0.49 12/133 HS, MS2, HN

S-P-4, 5 SK38, PB, HST, Tmax, 4, 5 5 0.57 12/133 HS, MS2, HN

S-P-6, 7, SK38, PB, HST, Tmax, 6, 7, 8, 9 4 0.64 14/133 8, 9 HS, MS2, HN

S-P-10 SK38, PB, HST, Tmax, 10 2 0.80 16/133 HS, MS2, HN 1 Variables marked in bold are selected by the classification tree algorithm from those listed for the model.

Figure 9.7 Classification tree for the daily maximum size of skier-triggered persistent slabs in the Purcell Mountains using meteorological forecasting variables but excluding

SK38. Data are from the winters of 1992-93 to 1994-95.

219

Including SK38 with the variables MS2, PB, HS, HST, Tmax and HN yields Model S-P-I which reduces the residual mean deviance from 0.45 to 0.42 and improves the misclassification rate from 15/133 to 12/133. This model correctly classifies 112 of 117 non-avalanche days and 9 of 16 avalanche days. Removing the subtrees that do not reduce the misclassification rate (circled in Figure 9.8) increases the deviance to 0.57.

Figure 9.8 Classification tree for the daily maximum size of skier-triggered persistent slabs in the Purcell Mountains using meteorological forecasting variables

and including SK38. Data are from the winters of 1992-93 to 1994-95.

Although including SK38 (Model S-P-I) improves the overall misclassification rate, it misclassifies 4 of 9 days with MxS = 2 compared to the model (M-P-E) without SK38 which misclassifies only 1 of 9 days with MxS = 2 (Table 9.10). While it is more important for backcountry skiing operations to correctly predict days with class 2 avalanches than days with no avalanches or class 1 avalanches, the classification tree algorithm weights all values of MxS equally. The variables in Model S-P-I can be ranked by increasing the cost-complexity factor from 1 to 10 thereby simplifying the trees and retaining the most important variables at each step (Table 9.9). Using this procedure, the variables in order of decreasing predictive value are SK38, PB, HST, Tmax, HS, MS2, HN and MS2. Notably, Tmax, which did not correlate significantly with MxS, ranked higher than HN or MS2 which did. This highlights

220 the relevance of choosing a forecasting model such as nearest neighbours or classification trees which can include non-monotonic relationships.

Table 9.10 Contingency Table for Daily Maximum Size of Skier-Triggered Persistent Slab in Purcell Mountains, 1992-93 to 1994-95. Observed Size of Slab Avalanche Predicted 012>2 Size of Excl. Incl. Excl. Incl. Excl. Incl. Excl. Incl. Avalanche 1 2 1 2 1 2 1 2 SK38 SK38 SK38 SK38 SK38 SK38 SK38 SK38 0 110 112 5 1 1 4 2 2 1 0 2040000 2 7 3008500 >20 0000000 Total 117 117 5 5 9 9 2 2 Proportion 110/117 112/117 0/5 4/5 8/9 5/9 0/2 0/2 Correct Percent 94% 96% 0% 80% 89% 56% 0% 0% Correct 1 Predictions based on Model S-P-E which excludes SK38 as a forecasting variable. 2 Predictions based on Model S-P-I which includes SK38 as a forecasting variable.

9.6 Summary

Rank correlations, box graphs and multivariate classification trees were used to

assess the merit of shear frame stability indices, SN38 and SK38, for forecasting slab avalanches involving persistent slabs.

For natural avalanches in the Purcell Mountains, SN38 showed promise based on the

correlations and box plots, whereas in the Cariboo and Monashee Mountains, SN38 showed no predictive value. However, these analyses are not conclusive since the data for natural avalanches of persistent slabs are highly unbalanced. Either there are few natural avalanches with persistent failure planes, or difficulty with identifying the failure plane of natural avalanches resulted in too few reports of natural avalanches with persistent failure planes.

221 Fortunately, skier-triggered slabs are not observed from a distance and the reporting of the failure plane is more rigorous. In both the Purcells and in the Cariboo and

Monashee Mountains, correlations and box plots indicate that SK38 is a useful predictor of skier-triggered persistent slabs. Further, including SK38 as a forecasting variable improved the number of days that multivariate classification trees correctly classified the size of the largest skier-triggered persistent slab in both areas. Also, the classification tree algorithm ranked SK38 as the most or the second most important forecasting variable in both areas.

However, the selection of variables was limited to SK38 and meteorological variables from fixed sites that are available most mornings, as well as an index of previous avalanche activity. Although avalanche workers report the results of intermittent snowpack observations and tests from varying locations, such results were excluded from these analyses which were limited to variables available daily from consistent locations. Expert systems under development (e.g. Schweizer and Föhn, 1995) are likely to prove better suited to including roving snowpack observations in a multivariate forecasting model. The multivariate forecasting models presented in Sections 9.3 and 9.5 are of limited value for operational forecasting since they are based on only 94 to 150 days. This is in contrast to a nearest neighbour model that is now used operationally in Switzerland (Buser, 1989) which is based on 20 years of data, and the nearest neighbour model being tested at Kootenay Pass in BC (McClung and Tweedy, 1994) which is based on 10 years of data. Backcountry skiing operations will require many years of data before such models are operational practical, particularly since predictive accuracy is needed for large skier-triggered avalanches which are infrequent. Also, data-based models should be assessed with different data than those used to build the model (e.g. Blattenberger and Fowles, 1995a). The data sets for the various forecasting trees in this chapter were too small to withhold a portion of the data for such an independent assessment. However, the data sets for skier-triggered slabs were sufficient to determine that multivariate forecasting models based on previous avalanche activity and common meteorological variables can be improved by including SK38 in the model. 222 10 CONCLUSIONS 10.1 Field and Finite Element Studies of the Shear Frame Test

Most shear strengths from shear frame tests can be assumed to be normally distributed since only 4 to 8 of 28 sets of 30 or more tests showed evidence of non-normality (Section 4.2).

Coefficients of variation for shear frame tests averaged 0.15 and 0.18 from level study plots and avalanche start zones respectively (Section 4.3). These values are less than the 0.25 reported in previous studies and thus reduce the number of tests required to achieve a specified level of precision. To achieve 10% precision at the 0.10 significance level, 8, 11 and 19 tests are required for shear frame data with coefficients of variation of 0.15, 0.18 and 0.25, respectively.

In addition to the stress concentrations associated with the shear frame's rear cross-member and intermediate fins, cutting along the front and back of the frame with a blade notches the weak layer, thereby causing substantial stress concentrations (Section 5.3). However, such cutting is essential to ensure that a specimen of known size is tested.

Finite element studies showed that placing the frame a few mm above the weak layer reduces stress concentrations compared to placing the bottom edges of the frame in the weak layer (Section 5.4). This is consistent with field studies that showed strength increases of 10-20% when the frame was placed 2-5 mm above the weak layer compared to tests with the lower edges of the frame placed in the weak layer (Section 4.8). Although frame placements 2-5 mm above the weak layer are recommended, under certain snowpack conditions frames must be placed in the weak layer or more than 5 mm above the weak layer to obtain planar failures in the weak layer being tested.

For shear frame tests in which the shear frame is placed a few mm above the weak layer, stiffer snow above the weak layer tends to reduce stress concentrations (Section 5.5). 223 Shear frame tests that resulted in divots more than 10 mm deep under the rear compartment of the frame yielded strengths significantly greater than tests with planar fractures (Section 4.4). No significant effect could be detected for 10 other common shapes of non-planar fracture surfaces.

With consistent loading rates and frame placement technique, there was no significant difference in mean strengths obtained by different experienced shear frame operators (Section 4.9).

Faster loading rates tended to reduce the strengths from shear frame tests. However, the effect of loading rate on strength diminished for mean strengths less than 1 kPa and for loading times less than 1 second (Section 4.5).

The first two tests in a set of shear frame tests were significantly more variable than subsequent tests (Section 4.6). Rejecting the first two tests will therefore reduce variability.

Delays of up to 3 minutes between placing the frame and pulling the frame did not affect the resulting shear strengths (Section 4.7).

Shear frames with larger areas resulted in lower mean strengths than smaller frames (Section 4.10), as shown in previous studies. Although strengths obtained with larger frames usually showed reduced variability compared to smaller frames, the reduction was not statistically significant for frames with areas of 0.01, 0.025 and 0.05 m2. Increasing the number of cross-members while keeping the overall dimensions of the frame constant increased the number of stress concentrations (Section 5.6) and reduced the mean shear strength (Section 4.12.1).

Compared to the 0.025 m2 shear frame with three active cross-members used as a standard in the present study, the Swiss shear frame is constructed of thicker metal and consequently is heavier. It resulted in increased shear strengths compared to the standard frame (Section 4.12.3).

Compared to the standard frame, the finger-fin shear frame resulted in decreased shear strengths due to reduced stress concentrations, but operators had difficulty placing the 224 finger-fin frame a certain distance above the weak layer, a practice that is commonly required to obtain planar fractures in certain weak layers (Section 4.12.4).

10.2 Shear Strength of Weak Layers

Regressions for estimating the shear strength of common microstructures from density are presented in Section 6.2. For those weak layers that are too thin for density measurements, Section 6.3 provides a graph for estimating mean strength for common microstructures from classes of hand hardness.

Persistent weak planes consisting of surface hoar or facets showed less strength increase with increased normal load than reported previously (Section 4.11). Since the normal load effect for persistent weak layers was not significant, it was taken to be negligible. This may result in conservative stability indices (lower than otherwise) for thick, dense slabs.

10.3 Shear Frame Stability Indices

Values of shear frame stability index for natural avalanches SN, which differ from S' developed by Föhn (1987a) only in the normal load adjustment, are presented for various slopes that avalanched naturally and those that did not avalanche

(Section 6.5). For each of four slopes that avalanched with high values of SN, warming o or ambient temperatures near 0 C are likely explanations, indicating that SN cannot predict avalanches under such conditions.

SN38 is obtained by calculating SN for a 38° inclination typical of start zones. Most

natural avalanches occurred on surrounding slopes when SN38 was less than 2.8.

However, non-avalanche days were common for a wide range of values of SN38 (Section 6.6). Based on univariate and multivariate analyses of data from three winters

with a limited number of natural avalanches of persistent slabs, SN38 showed promise for forecasting natural avalanches in the Purcell Mountains. A similar relationship

between SN38 and natural avalanche activity was not detected in the Cariboo and 225 Monashee Mountains (Sections 9.2 and 9.3). However, in both forecast areas, identifying the failure plane and occurrence date of natural avalanches was difficult since many natural avalanches were observed from a distance.

The transitional stability of SN and SN38 falls well above 1 suggesting that a critical stress failure criterion is not well suited to predicting natural avalanching.

An empirical formula for estimating ski penetration from slab density and thickness was incorporated into a formula derived by Föhn (1987a) resulting in a stability index for skier-triggering, SK, which has a reduced number of false stable predictions for skier-tested avalanche slopes (Section 6.8).

SK38 is obtained by calculating SK for a 38° inclination typical of start zones. In

Section 6.9, SK38 is shown to be better predictor of skier-triggered avalanches in surrounding terrain than is SN38 for natural avalanches. Also, values of SK and SK38 between 1 and 1.5 correspond to transitional stability for both test slopes and surrounding terrain, indicating that the critical stress failure criterion upon which SK and SK38 are based is effective for skier-triggered avalanches. Univariate and multivariate analyses for three winters at both forecast areas showed

SK38 to be a better predictor for skier-triggered slabs than common meteorological observations (Sections 9.4 and 9.5). Including SK38 as a forecasting variable improved the number of days that multivariate forecasting models correctly classified the size of the largest skier-triggered persistent slab in both areas. However, the selection of variables excluded roving snowpack observations and tests such as profiles, shovel tests, compression tests, and rutschblock tests normally done only when deemed necessary.

Differences in the initial size of surface hoar crystals between two study sites affect stability. If surface hoar crystals at a particular site are substantially larger than at a second site, then stability will tend to be lower at the first site and remain that way for a period of weeks. 226 10.4 Rutschblock Results

Closely spaced rutschblock tests on nine avalanche slopes illustrate snowpack and terrain factors that affect rutschblock scores (Section 7.2). Sites near the top of slopes, near trees, over rocks and at pillows of wind-deposited snow sometimes exhibited rutschblock scores and/or failure planes quite different from the remainder of the slope. Even when avoiding such sites, rutschblock scores two steps above the slope median occurred occasionally, indicating the merit of using other sources of information such as profiles to confirm or question the results of one or two rutschblock tests.

The percentage of skier-triggered persistent slabs on skier-tested avalanche slopes decreased from over 80% to 33% as median rutschblock scores increased from 2 to 5 (Section 7.3). Three of nine skier-tested slopes with median scores of 7 for persistent slabs were skier-triggered, indicating that the median rutschblock score is, by itself, not a completely reliable indicator of stability. For non-persistent weak layers, no slabs were skier-triggered on 10 slopes with median rutschblock scores above 3.

The frequency of avalanching for non-persistent slabs with rutschblock scores of 2, 3 and 4 was approximately the same as for persistent slabs with rutschblock scores of 4, 5 and 6, respectively. Consequently, the interpretation of rutschblock scores should depend on whether the weak layer is persistent or not.

An empirical relationship between skier-stability index, SK, and median rutschblock scores was determined (Section 7.4). However, this relationship does not apply on

slopes of less than 20° where SK usually predicts higher stability than the rutschblock

test. Since SK is based on shear failure, it is argued that the primary fractures sometimes initiated by skiers on slopes of less than 20° are compressive.

Rutschblocks on safe study slopes are shown to have predictive value for skier-triggering of particular persistent layers on surrounding slopes (Section 7.6). However, as for rutschblock tests on avalanche slopes, the particular persistent weak 227 layer is sometimes skier-triggered when the rutschblock score for that layer on the study slope indicates stability.

10.5 False Stable Predictions

Case studies illustrated that stability tests where snowpack conditions are judged typical of start zone are occasionally misleading and cannot predict avalanches triggered at localized weaknesses or remotely from sites with a less stable snowpack than the start zone (Chapter 8). These case studies confirm the advice of other authors that the results of such tests should be interpreted together with knowledge of terrain, snow distribution and mesoscale stability trends based on regular weather, study site and avalanche observations, rather than on a stand-alone basis. 228 11 RECOMMENDATIONS FOR FURTHER RESEARCH

The relationship of observable microstructural properties of buried surface hoar layers such as mean grain size and change in mean grain size to the strength of these layers should be studied through a combination of microphotography and strength tests. The changes of particular layers over time on slopes and at level sites would be helpful since creep on steeper slopes may increase the number of bonds per crystal over time by inclining the crystals. An increase in the number of bonds per crystal and consequently an increase in strength on steeper slopes may explain why avalanches are sometimes triggered remotely from level areas or shallow slopes, sometimes after the steeper slopes have apparently stabilized. The strength tests in the level areas should not be restricted to shear tests since the primary fractures at such sites probably involve compression.

Based on shear frame tests in well chosen study sites, the skier-stability index, SK38, is an effective predictor of skier-triggered persistent slabs in surrounding terrain. However, because of the costs associated with skilled avalanche technicians and transportation to study sites to do shear frame tests, there are economic advantages to reducing the frequency of the tests. Although interpolating SK38 between test days proved useful for assessing the merit of SK38 for predicting past skier-triggered avalanche activity, operational use of SK38 will require either that shear frame tests in study sites be conducted frequently, perhaps every third day, which is expensive, or that SK38 be estimated based on last measured value and on easily measured field parameters since the last test day. Since SK38 is based on shear strength of the persistent weak layer, load (slab weight per unit area) and slab thickness based on snowfall and settlement, predicting SK38 will require estimates of 1. changes in shear strength of the persistent weak layer based on easily measured parameters such as temperature of the weak layer, temperature gradient across the weak layer, load and microstructure, 2. increases in load based on daily measurements of snowfall or precipitation from a easily accessible study site or automatic weather station, and 229 3. settlement based on snowfall, load, slab density, microstructure and, perhaps, temperature (e.g. Navarre, 1975; Armstrong, 1980; Brun and others, 1989). While the load and settlement can be estimated from easily measured field parameters, predictive models for changes in shear strength of thin persistent weak layers are needed. Such models will permit less frequent visits to study sites to test persistent weak layers with the shear frame and may prove cost-effective for backcountry avalanche forecasting operations. Forecasting models based on data, knowledge or both should be developed for backcountry forecasting programs. The skier-stability index, SK38, and/or rutschblock tests at regular intervals on study slopes should be incorporated into such models. However, data-based models will require additional years of systematic snowpack tests and weather observations. Various snowpack tests such as rutschblock tests, compression tests, shovel tests and profiles done at sites in and near avalanche start zones may prove useful for expert systems particularly when coupled with past, present and forecast weather (Schweizer and Föhn, 1995). 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Proceedings of a Workshop on the Properties of Snow, Snowbird, Utah, U.S. Army, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, Special Report 82-18, 1-19. Salway, A.A. 1976. Statistical Estimation and Prediction of Avalanche Activity from Meteorological Data for the Rogers Pass Area of BC. PhD Dissertation, University of British Columbia, Vancouver, BC. 114 pp. Schaerer, P.A., 1987. Avalanche Accidents in Canada III. A Selection of Case Histories 1978-1984, National Research Council of Canada, Institute for Research in Construction, Paper No. 1468, 138 pp. Schaerer, P.A. 1981. Avalanches. Handbook of Snow: Principles, Processes, Management and Use, Edited by D.M. Gray and D.H. Male, Pergamon, 475-516. Schaerer, P.A. 1989. Evaluation of the shovel shear test. Proceedings of the 1988 International Snow Science Workshop at Whistler, BC, 274-276. Schaerer, P.A. 1991. Investigations of in-situ tests for shear strength of snow. Unpublished, 29 pp. Schleiss, V.G. and W.E. Schleiss. 1970. Avalanche hazard evaluation and forecast, Rogers Pass, Glacier National Park. Ice Engineering and Avalanche Hazard Forecasting and Control, National Research Council of Canada, Technical Memorandum 98, 115-121. 242 Schweizer, J. 1991. Dry slab avalanches triggered by skiers. Proceedings of the International Snow Science Workshop in Bigfork, Montana, 1990. ISSW '90 Committee, P.O. Box 372, Bigfork, Montana 59911, 307-309. Schweizer, J. 1993. The influence of the layered character of snow cover on the triggering of slab avalanches. Annals of Glaciology 18, 193-198. Schweizer, J., M. Schneebeli, C. Fierz and P.M.B. Föhn. In press. Snow mechanics and avalanche formation: Field experiments onto the dynamic response of the snow cover. Surveys in Geophysics, 1-13. Schweizer, J and P.M.B. Föhn. 1995. Two expert systems to forecast the avalanche hazard for a given region. Proceedings of the 1994 International Snow Science Workshop in Snowbird, Utah. ISSW '94, P.O. Box 49, Snowbird, Utah, USA, 295-309. Schweizer, J., C. Camponovo, C. Fierz and P.M.B. Föhn. 1995. Skier-triggered slab avalanche release - some practical implications. Proceedings of the International Symposium at Chamonix, 30 May - 3 June 1995: The Contribution of Scientific Research to Snow, Ice and Avalanche Safety. Association Nationale pour l'Etude de la Neige et des Avalanches. Grenoble. Schweizer, M. P.M.B. Föhn and J. Schweizer. 1994. Integrating neural networks and rule based systems to build an avalanche forecasting system. Proceedings of the IASTED International Conference: Artificial Intelligence, Expert Systems and Neuronal Networks, Zurich, Switzerland. Seligman, G.,1936. Snow Structure and Ski Fields. International Glaciological Society, Cambridge, 555 pp. Shapiro, S.S, M.B. Wilk and H.J. Chen. 1968. A comparative study of various tests for normality. American Statistical Association Journal, 1343-1372. Singh, H, 1980. A Finite Element Model for the Prediction of Dry Slab Avalanches, Ph.D. Thesis, Colorado State University, Fort Collins, Colorado, 183 pp. Smith, F.W. and J.O. Curtis, 1975. Stress analysis and failure prediction in avalanche snowpacks, Snow Mechanics Symposium, Proceedings of the Grindewald Symposium, 243 International Association of Hydrological Sciences, Washington, D.C., Publication No. 114, 332-340. Sommerfeld, R.A., 1973. Statistical problems in snow mechanics. U.S. Dept. of Agriculture, Forest Service, General Technical Report RM-3, 29-36. Sommerfeld, R.A., 1974. A weibull prediction of the tensile strength-volume relationship of snow, Journal of Geophysical Research, 79(23), 3353-3356. Sommerfeld, R.A. 1979. Accelerating strain preceding an avalanche. Journal of Glaciology, 22(87), 402-404. Sommerfeld, R.A., 1980. Statistical models of snow strength, Journal of Glaciology, 26(94), 217-223. Sommerfeld, R.A. 1984. Instructions for using the 250 cm2 shear frame to evaluate the strength of a buried snow surface. USDA Forest Service Research Note RM-446, 1-6. Sommerfeld, R.A. and R.M. King, 1979. A Recommendation for the application of the Roch Index for slab avalanche release, Journal of Glaciology, 22(87), 402-404. Statsoft, 1994. Statistica for Windows: General Conventions and Statistics I. Statsoft Inc, Tulsa, OK. 1718 pp. Stethem, C. and R. Perla. 1980. Snow-slab studies at Whistler Mountain, British Columbia, Canada. Journal of Glaciology 26(94), 85-91. Stethem, C.J. and J.W. Tweedy, 1981. Field tests of snow stability. Proceedings of the Avalanche Workshop in Vancouver, November 3-5, 1980, Edited by Canadian Avalanche Committee, National Research Council of Canada, Technical Memorandum No. 133, 52-60. Stevens, J. E. Adams, X. Huo, J. Dent, J. Hicks and D. McCarty. 1995. Use of neural networks in avalanche hazard forecasting. Proceedings of the 1994 International Snow Science Workshop in Snowbird, Utah. ISSW '94, P.O. Box 49, Snowbird, Utah, USA, 327-340. Topping, J. 1955. Errors of Observation and their Treatment. Chapman and Hall Ltd, London. 119 pp. 244 Witmore, D, S.A. Burak, J. Malone and R.E. Davis. 1987. The Swiss rutschblock snow stability evaluation test. Proceedings of International Snow Science Workshop at Lake Tahoe, ISSW Workshop Committee, Homewood, California, 207-209. Williams, K. and B. Armstrong. 1984. The Snowy Torrents: Avalanche Accidents in the United States, 1972-79. Teton Bookshop, Box 1903, Jackson, Wyoming, 221 pp. 245 A ESTIMATING DENSITY FROM MICROSTRUCTURE AND RESISTANCE

A.1 Introduction Estimated densities may be useful when densities have not been measured, sometimes because the layer was too thin for the density sampler or the measurement was omitted, possibly due to time constraints. This appendix outlines a method for estimating density from observed microstructure and resistance.

A.2 Hand Hardness The most widely used measure of resistance in Canada and internationally is “hand hardness”. A fist, four finger tips, one finger tip, the blunt end of a pencil or a knife tip is pushed horizontally into a snow layer while wearing gloves. The hand hardness is simply the bluntest object that can be pushed into the snow with 10-15 N in Canada (CAA, 1989, 1995) or 50 N internationally (Colbeck and others, 1990). The levels of hard hardness are abbreviated as F, 4F, 1F, P and K. Snow layers with resistance between the five major levels of hand hardness can be qualified with a “+” or “-” sign, giving 15 levels: F-, F, F+, 4F-, 4F, 4F+, 1F-, 1F, 1F+, P-, P, P+, K-, K and K+ (CAA, 1995). Ice layers harder than “knife” are labelled I for ice. Since the area of the objects being pushed into the snow does not decrease proportionally from fist to knife, the hand hardness is an ordinal and not an interval measure. However, to give a numeric scale suitable for graphing, the five major levels are scaled geometrically based on doubling (NRCC/CAA, 1989; CAA, 1995). Using 1 for F, this results in a scale from 1 to 16 for the five major levels or 0.7 to 26.7 for the 15 major and minor levels as shown in Table A.1.

A.3 Mean Densities by Microstructure and Hand Hardness Based on snow profiles done during the winters of 1993-95, density and hand hardness were measured and microstructure observed for over 900 layers as summarized in Table A.1. (Since substantial metamorphic and mechanical changes of snow often occur within a day, the same level in the snowpack at the same location on different days is 246

Table A.1 Density of Layers Grouped by Hand Hardness and Microstructure Hand Scaled Precip. Decomp./ Rounded Faceted Depth Crusts Hardness Hand Particles1 Fragmented Grains Crystals Hoar Hardness N Mean N Mean N Mean N Mean N Mean N Mean RH ±SD ±SD ±SD ±SD ±SD ±SD F- 0.67 4 58 255------±40 0 F 1 46 86 70 112 9 179 11 167 5 212 -- ±31 ±29 ±45 ±49 ±44 F+ 1.33 8 116 12 131 1 170 1 179 - - - - ±32 ±35 4F- 1.7 - - 3 139 ------±28 4F 2 4 133 69 136 31 193 48 216 1 234 -- ±14 ±34 ±38 ±40 1 ±28 4F+ 2.7 - - 14 156 7 196 4 222 2 305 1 148 ±32 ±30 ±14 ±7 1F- 3.3 - - 9 160 8 211 6 265 1 240 - - ±21 ±23 ±38 1F 4 - - 40 164 95 207 83 262 1 260 -- ±34 ±37 ±36 4 ±59 1F+ 5.3 - - 11 164 16 214 4 239 --- - ±29 ±35 ±48 P- 6.7 - - 6 212 35 248 3 272 --- - ±29 ±37 ±16 P 8 - - 5 217 12 271 50 294 3 290 3 222 ±58 2 ±42 ±43 ±36 ±28 P+ 10.7 - - 1 254 38 285 7 323 --- - ±48 ±25 K- 13.3 - - - - 1 302 ------K 16 - - - - 4 308 4 317 1 270 1 259 ±57 ±52 6 ±54 K+ 26.7 ------1 276 1 excludes graupel and hail 247 considered to be a different layer.) Although the microstructure subclass (Colbeck and others, 1990) was often recorded, the microstructure of layers is tabulated only by the major class. Layers of graupel or hail are omitted from Table A.1 since there were only six layers for which density and hand hardness were recorded and because the strength and hence hardness of these layers are quite different from other subclasses of precipitation particles (Section 6.2). The class of “wet grains” (which can include some types of dry snow such as rounded polycrystals) is omitted since there were only two such layers for which density and hand hardness were recorded. Although surface hoar is very important to snow stability, it must be omitted because the layers were almost always thinner than the diameter of the density sampler. The mean densities based on three or more measurements for the remaining six classes of microstructures are plotted against the scaled hand hardness in Figure A.1. For these microstructures, there is a general increase in mean density with increasing hand hardness. For most microstructures, the sample size is large enough that the density is increased between minor levels of hand hardness. Precipitation particles show a rapid increase in density with increasing hand hardness and a smooth transition to decomposed and fragmented precipitation particles which is consistent with the common metamorphic transition. The mean density of faceted crystals is close to that of depth hoar for particular levels of hand hardness. The mean density of faceted crystals and depth hoar exceeds that of rounded grains for most levels of hand hardness implying that, for a given density, layers of rounded grains are generally harder than layers of faceted crystals and depth hoar. Similarly for a given density, crusts are harder than layers of rounded grains, faceted crystals and depth hoar which is indicative of the extensive bonding that is characteristic of crusts. It is surprising that for densities between 175 and 220 kg/m3, layers of decomposed and fragmented grains are harder than layers of rounded grains. Linear equations of the form ρ = A + B RH (A.1) and logarithmic equations of the form 248 ρ = A + B ln RH (A.2) where RH is the scaled hand hardness from Table A.1 and A and B are empirical constants are fitted to the individual points for each major microstructure class. The empirical constants along with the coefficient of determination, R2, and the standard error of estimation, s, are given in Table A.2. Standard errors of estimation range between 32 and 49 kg/m3. Such high variability is not surprising since the regressions are based on a ordinal measure of hardness.

Figure A.1 Density by hand hardness for six common classes of microstructure.

Using R2 as a measure of fit, the linear equation (Eq. A.1) fits the data for layers of rounded grains best and the logarithmic equation (Eq. A.2) best fits the data for the other five microstructures. Since the linear equation only fits the data for rounded grains slightly better than the logarithmic equation, Eq. A.2 is shown in Figure A.1 for the six microstructures. Since Equation A.2, which is based on a logarithm of a geometric sequence, best fits the data for five of the six microstructures, the merit of the geometric scaling of hand hardness for estimating density is questionable. Nevertheless, the empirical 249 equations from Table A.2 offer a means of estimating density from hand hardness for six common classes of microstructure.

Table A.2 Regression Parameters for Estimating Density from Resistance and Microstructure ρ ρ Microstructure No. of Regression = A + B RH Regression = A +B ln(RH) (Colbeck and Layers others, 1990) ABR2 p s ABR2 p s Precipitation 62 48 39 0.15 0.002 32 87 60 0.19 <10-3 32 Particles1 (1) Decomposed & 243 102 15 0.39 <10-6 33 109 43 0.40 <10-6 33 Fragmented (2) Rounded 367 167 12 0.41 <10-6 41 141 58 0.38 <10-6 42 Grains (3) Faceted 220 204 11 0.37 <10-6 42 177 58 0.46 <10-6 39 Crystals (4) Depth Hoar (5) 37 231 5 0.10 0.06 46 217 31 0.17 0.01 45 Crusts (9) 7 200 3 0.27 0.23 36 123 48 0.30 0.21 35 1 excludes graupel and hail 250 B ERROR ANALYSIS FOR STABILITY INDICES

B.1 Sources of Variability

Stability indices SN and SK depend on Daniels strength measured with the shear frame, Σ∞, on slab density, ρ, on slab thickness in the start zone, h, and on slope Ψ inclination, . In addition, SK depends on the estimate of penetration during skiing, PK. In avalanche start zones, at least seven shear frame tests were usually made of the failure plane, and coefficients of variation averaged 18% (Section 4.3), implying a standard error of 7% of the mean strength. Mean slab density was either measured once with a vertical density profile or one or more times with a core sampler (Section 3.4). Coefficients of variation for mean slab densities based on density profiles at a given site are typically 2-4% (Jamieson, 1989, p. 67). Mean slab thickness was usually measured to the nearest cm at two or more places along the crown that appeared to be of average thickness. Since these measurements rarely vary by more than 5% from the mean, the coefficient of variation is assumed to be 3%. The slope inclination, Ψ, was usually measured at two or more locations that appeared typical of the start zone. Since these typical values rarely vary by more than 2o, the standard deviation of Ψ is approximately 1o and the coefficient of variation of cos Ψ or sin Ψ is typically 1-2%. ρ The variability in PK depends on the regression on 30 in Section 6.8. For a given ρ value of 30, the standard deviation for PK is given by ρ 2 ½ s(PK| 30) = s(PK)(1-R ) (B.1) 2 ρ From the data in Figure 6.21, R = 0.50 and s(PK) = 0.11 m, giving s(PK| 30) = 0.08 m which is 28% of the mean value of PK. 251

B.2 Variability for Index SN

The stability index SN is given by Σ∞ +σ φ(σ , Σ∞) S = zz zz (B.2) N ρgh sin Ψ cos Ψ However, φ ≅ 0 for the persistent layers that are central to this study, and the variability in Ψ Σ ρ cos is only 1-2%, so the main sources of variability are ∞, and h. Using the standard formula for error propagation for uncorrelated measurements (Clifford, 1973), the standard deviation for SN is 1/2  ∂  2  ∂  2  ∂  2  ( )= SN 2(Σ )+ SN 2(ρ) + SN 2( ) s SN   s ∞ s   s h  (B.3)  ∂Σ∞  ∂ρ  ∂h 

Although Σ∞, ρ and h are likely correlated between sites since weak layers are generally stronger under thicker, denser slabs, measurement variability probably obscures any correlation for repeated measurements in a particular snow pit. Assuming that the Σ ρ standard deviations of ∞, and h are proportional to their means, Equation B.3 simplifies to 2 2 2 1/2 s(SN)=SN[v(Σ∞) + v(ρ) + v(h) ] (B.4) where v(u) represents the coefficient of variation of a variable u and SN is the mean value Σ ρ of SN. Using the coefficients of variation for ∞, and h from the previous section, the coefficient of variation for SN is approximately 9% of its mean value.

The band of transitional stability 1 < SN < 1.5 used by Föhn (1987a) and Jamieson and Johnston (1995a) can be interpreted as a one-sided confidence band above the critical value of 1. Using SN = 1.5 and s(SN) = 0.09 for the standard error in the formula for the confidence band S − 1 N = t (B.5) s(SN) gives t = 5.6. Since SN is usually based on at least seven shear frame tests, it has at least -3 six degrees of freedom, resulting in a 10 probability of a measured value of SN exceeding 1.5 when its true value is 1. Shear frame data with higher variability would result in lower confidence attached to the safety margin 1 < SN < 1.5. 252 However, this approach to the safety margin is based on variability of measurements such as shear strength within a snow pit and does not take into account the greater variability within a start zone. The merit of SN and its safety margin really depends on the proportion of prediction errors. However, such an approach requires more data than presented in Section 6.5.

B.3 Variability for Index SK Since the variability in slab density, ρ, and slab height, h, have a limited effect on the variability of SN, the main sources of variability for stability index SK, are the measurement Σ Σ of shear strength, ∞, and the estimate of skiing penetration, PK. Assuming ∞ and PK are uncorrelated, the standard deviation for SK is 1/2  ∂  2  ∂  2  ( )= SK 2(Σ )+ SK 2( ) s SK   s ∞   s PK  (B.6)  ∂Σ∞ ∂PK  where the partial derivatives of SK are ∂S K = 1 (B.7) ∂Σ∞ σxz +∆σ xz and 2 ∂S −2LΣ∞cos αmaxsin αmaxsin(Ψ + αmax) K = (B.8) ∂ 2 2 PK π(σxz +∆σ xz) (h − PK) cos Ψ using the symbols introduced in Sections 2.4 and 6.8.

2 The variability of SK depends strongly on the term (h-PK) in the denominator of

Equation B.8. As the skiing penetration, PK, approaches the slab thickness, h, the term 2 (h-PK) approaches zero causing potentially unlimited variability for low values of SK.

However, such unlimited variability for low values of SK can, at worst, cause some false unstable results that do not have serious consequences (Section 6.7). For h-PK > 0.8 m, σ ∆σ the stress due to the slab, xz dominates the stress due to the skier, 'xz (Figure 6.19), causing SK to approach SN, the variability of which is discussed in Section B.2. Since the merit of SK depends on its ability to discriminate between stable and unstable slabs, the variability of SK is most important near its critical value which is expected to fall between ∂ ∂Σ ∂ ∂ 1 and 1.5. Since the partial derivatives SK/ ∞ and SK/ PK are not simple functions of 253 Σ ρ, , Ψ ∞, h PK and , the standard deviation of SK is estimated for the critical range.

However, there are only eight persistent skier-tested slabs for which 1 < SK < 1.5 in

Figure 6.22 whereas there are 36 persistent skier-tested slabs in the range 0.5 < SK < 2. Using the larger set of 36 persistent skier-tested slabs, the mean values of the independent Σ = , ρ 3 Ψ o variables are ∞ 1.27 kPa = 203 kg/m , h = 0.64 m, PK = 0.24 m, = 38 , and α o ∂ ∂Σ ∂ ∂ max = 46 (Föhn, 1987a) and the corresponding partial derivatives SK/ ∞ and SK/ PK are approximately 1.03 kPa-1 and 1.20 m-1 resulting in an estimated standard deviation for

SK of 0.13 (Eq. B.5). Thus the regression estimate of PK causes the standard deviation of

SK to be approximately 50% greater than that of SN.

As was done with SN in Section B.2, the safety margin 1 < SK < 1.5 can be interpreted as a one-sided confidence band above SK = 1. Replacing SN in Equation B.5 by

SK and using s(SK) = 0.13 for the standard error gives t = 3.85 implying a probability of

0.004 of a measured value of SK exceeding 1.5 when its true value is 1. However, this approach to the safety margin is based on variability of measurements such as shear strength within a snow pit and does not take into account the greater variability within a start zone. The merit of SK and its safety margin really depends on the proportion of prediction errors (Section 6.8). 254 C EXAMPLE OF FIELD NOTES

An example of two facing pages of field notes are shown in Figure C.1. Field notes are made on specially prepared field books with pages of water resistant paper. In the heading at the top of the pages, the weather, location, equipment and weak layer are described in lines 1-4, respectively. Symbols for weather (CAA, 1995) show the sky was overcast and snow was falling at less than 1 cm per hour when observations started at 1055. The profile is recorded on the left page. Layer boundaries, in cm, are recorded in the column headed H. In this example, boundaries are measured vertically upwards from the ground. Hand hardness for the layers are recorded in the column headed R. These show the hardest layers between 100 and 144 cm above the ground. The weak layer that failed consisted of 2 mm faceted crystals (
) and 2-3 mm surface hoar (V). To save time because of deteriorating weather, grain form (F) and size (D) were only recorded for the substratum (called the bed surface), the weak layer that failed, and the surface hoar layer buried on 10 February that did not fail. The right page shows notes of a density profile (for calculating slab weight per unit area), shear frame tests and rutschblock tests. In subsequent winters, densities were measured layer-by-layer as described in Section 3.4. Eight shear frame tests were done with a 0.025 m2 frame. Pull forces at failure ranged from 6.8 to 8.0 kg-force. Fracture surfaces were all planar (marked "C" for "clean"). Only one rutschblock test was done because of deteriorating weather. Ski penetration after gently stepping onto previously undisturbed snow (SP) was 25 cm, and 36 cm after two jumps in the same place (JPx2). After the skier moved onto the rutschblock column, the top 55 cm of the column slid on loading step 6. The remaining 45 cm (down to 100 cm from the surface) did not displace after repeated jumps, resulting in a score of 7. Although redrafted, these are the field notes for the observations at the one-day-old slab avalanche on Mt. Albreda described in Section 8.2. 255