Pore water pressure in rock slopes and rockfill slopes subject to dynamic loading

Item Type Thesis-Reproduction (electronic); text

Authors Stevens, W. Richard(William Richard)

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/191872 PORE WATER PRESSURE IN ROCK SLOPES

AND ROCKFILL SLOPES SUBJECT TO DYNAMIC LOADING

by

William Richard Stevens

A Thesis Submitted to the Faculty of the

DEPARTMENT OF MINING AND GEOLOGICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE WITH A MAJOR IN GEOLOGICAL ENGINEERING

In the Graduate College

THE UNIVERSITY OF ARIZONA

1985 STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED: I? vt-PA-;, , .

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

C. E Glass Date ssociate Professor of Mining and Geological Engineering Head of the Department PREFACE

Most dynamic slope stability analyses do not incorporate the

dynamic response of the pore water, especially the water in rock

joints. The purpose of this thesis is to encourage studies in the

dynamic response of water in rock joints and the effects the water has

on rockmass shear strengths. A method is proposed to simulate the pore water pressure in rock slopes under dynamic loading. Hopefully, this

thesis will encourage performance of experimental studies on the

subject.

I would like to thank Dr. C. E. Glass, Dr. J. Daemen and Dr.

Ian Farmer for their advice and counsel. In addition, I would like to

thank my wife, Rose, for spending many long and late hours to complete

the typing and illustrations for this thesis. TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS vi

LIST OF TABLES viii

ABSTRACT ix

1. INTRODUCTION 1

2. SHEAR STRENGTH OF ROCK JOINTS AND ROCKFILLS 3

Roughness Component of Shear Strength (A in Equation 2.4) 4 Joint Roughness Coefficient 4 Equivalent Roughness for Rockf ill 8 Strength Component of Shear Strength (B in Equation 2.4) . 8 Joint Compressive Strength 8 Equivalent Strength for Rockf ill (S in Table 2.1) . . 11 Frictional Component of Shear Strength (C in Equation 2.4) 12 Basic Friction Angle 12 Residual Friction Angle 15 Testing Conditions Versus Field Conditions 15 Rock Block Tilt Test 15 Pull Testing of Rock Blocks 18 Tilt Test for Rockfill 18 Extrapolating JRC from Lab Samples 19 Factors Affecting Shear Strength 19

3. A SIMPLIFIED DYNAMIC SLOPE STABILITY METHOD 22

Constitutive Relation for LADRS-MDF 23 Frictional Model 25 Procedure for Using LADRS-MDF 26 Block Displacement Analysis Used in LADRS-MDF 29

4. DYNAMIC PORE WATER PRESSURE ANALYSIS 31

The Experimental and Theoretical Basis for the Dynamic Pore Pressure Analysis 32 Water Material Parameters Influencing Dynamic Pore Pressure in Unconsolidated Material 33 Material Parameters Influencing Dynamic Water Pressure in a Rockmass 35

iv TABLE OF CONTENTS--Continued

Page

Other Parameters Influencing Dynamic Pore Water Pressure 36 Dynamic Pore Pressure of Very Permeable Rockf ill Slopes 37 Dynamic Pore Pressure of Rockf ill Slopes 40 Dynamic Pore Pressure Prediction for Rock Slopes 42 LADRS-MDF Analysis of the Homestake Pitch Slope Failure 43 Concluding Remarks 57

APPENDIX A: INPUT DATA FOR THE HOMESTAKE PITCH LADRS-MDF ANALYSIS 59 Rock Block Data 60 Variable Input Data 61

APPENDIX B: A COMPARISON OF THE DISPLACEMENTS CALCULATED BY LADRS-MDF WHEN VARYING THE JRC AND WATER TABLE . . 62

APPENDIX C: DISPLACEMENTS CALCULATED BY LADRS-MDF WITH BLAST WAVES 68

REFERENCES 74

SELECTED BIBLIOGRAPHY 77 LIST OF ILLUSTRATIONS

Figure Page

2.1 Joint Roughness Profile Showing the Typical Range of JRC Values Associated with Each One 7

2.2 Method of Estimating Roughness Based on Porosity of Rockf ill, Origin of Materials and Degree of Roundedness and Smoothness of Particles 9

2.3 Method of Estimating Equivalent Strength of Rockf ill Based on Uniaxial Compressive Strength and on d50 Particle Size 13

2.4 Schematic for a) Rock Block Tilt Test, b) Pull Test, and c) Rockfill Tilt Test 16

3.1 Geometry for LADRS-MDF 24

3.2 Freebody Diagram for LADRS-MDF Technique 28

4.1 a) Undrained Triaxial Test on Loose, Saturated Sand; b) Cyclic Triaxial Test for an Anisotropically Consolidated Specimen; and c) Pulsating Load Test on Dense Sand 41

4.2 Experimental and Predicted Data Showing the Size Dependant Dilation that Occurs During Shearing 44

4.3 Dilation Modeling for Shear Tests on Three Different Sample Sizes 45

4.4 Input Ground Motions a) Earthquake Wave, 5 Hertz; b) Blastwave, 50 Hertz 47

4.5 Homestake Pitch Slope Geometry and Water Table Delineation . 52

4.6 Pore Water Response in the Rock Joint of Mass Number 8, with JRC = 6, Earthquake Wave Input and with a Low Water Table 53

4.7 Distribution of Excess Pore Water Pressure Along a 300 foot Long Horizontal Drainage Path 54

vi vii

LIST OF ILLUSTRATIONS--Continued

Figure Page

4.8 Total Displacements of Mass Number 8 with JRC = 6, Earthquake Wave Input and with a Low Water Table . . . . 56

LIST OF TABLES

Table Page

2.1 Shear Strength Estimation for Rock Joints, Rockf ill and Rock Interfaces 5

2.2 Estimating JCS Using Rockmass Density, Joint Wall Density and the Uniaxial Compressive Strength 10

2.3 Basic Friction Angles of Various Unweathered Rocks Obtained From Flat and Residual Surfaces 14

3.1 Suggested Values for the Scaling Factor T 26

4.1 Final Block Displacements for JRC = 6 and a Low Water Table with Variable Input Motions 48

4.2 Final Block Displacements for JRC = 6 and an Earthquake Input Motion 49

4.3 Final Block Displacements for JRC = 15 and an Earthquake Input Motion 50

viii ABSTRACT

A simplified method for simulating the response of rockf ill and rock slopes subject to a dynamic load is presented. A pore pressure analysis is incorporated into a dynamic slope stability computer program, the Linear Acceleration Dynamic Response of Slopes -- Multiple

Degrees of Freedom (LADRS-MDF), developed by Dr. C.E. Glass of the

University of Arizona. LADRS-MDF is based on Barton's empirical shear strength criteria and uses the entire acceleration time history.

The dynamic water pressure analysis depends on the slope conditions. Only the transient water pressure is present in material where the excess pore pressure dissipation exceeds the excess pore pressure generation. When excess pore pressure generation is greater than the dissipation, a water pressure buildup is present along with the transient pore water pressure.

ix CHAPTER 1

INTRODUCTION

Accurate predictions of dynamic slope stability depends upon laboratory and field testing in determining the actual in situ conditions. Many engineering problems have to be solved with a limited amount of data because of economics or other reasons. For these kinds of problems, a few simple and reproducible tests are needed that can be used to approximate the dynamic slope behaviour. Barton's method for determining shear strength and Glass' slope stability analysis are quick and easy procedures for estimating the dynamic stability for slopes.

The pore water response in a slope subject to dynamic forces has been studied for slopes composed of uniform small particles (sands, clays and some rockfill). A literature search reveals, however, that dynamic pore pressures in media with non-uniform particles (i.e., waste dumps) and dynamic water pressure in jointed rock masses has not been investigated. Because of this, a dynamic pore water pressure analysis that can be incorporated into a simplified slope stability method will be developed.

The next chapter will familiarize the reader with Barton's empirical work on the shear strength of rock joints. Chapter 3 will briefly explain the Linear Acceleration Dynamic Response of Slopes -

Multiple Degrees of Freedom (LADRS-MDF) analysis, which uses Barton's

1 2 shear strength criteria. Chapter 4 discusses the processes and parameters critical to dynamic pore water pressure analysis. A dynamic water pressure simulation is then developed and is used to analyse the

Homestake Pitch slope failure.

Throughout this paper, the term "rockfill slope" will denote any slope composed of unconsolidated particles, and "rock slope" defines a massive, jointed rock slope. Pore water pressure, water pressure and pore pressure is used interchangeably and refers to any water pressure that affects the stability of slopes. CHAPTER 2

SHEAR STRENGTH OF ROCK JOINTS AND ROCKFILLS

Many engineering problems have been solved using the Coulomb

criterion,

T = C a'tan* , 2.1 a linear relationship between the shear strength (T) and the effective

stress (0'). If one considers the shear strength of rock joints or

rock fills, the cohesion (c) is most likely equal to zero. The linear

relationship between T and a' may be a good approximation for small

intervals of stress, but is poor for large ranges of stress.

Nicholas R. Barton (1973), developed an empirical shear

strength equation for weathered or unweathered rock joints:

T = tan[(JRC)log(JCS/a ) + •r ] 2.2 n n

The equation has a zero T intercept (c 0) and is nonlinear. This

relationship is used for rock on rock contacts without infilling material. JRC is the Joint Roughness Coefficient, JCS is the Joint

Compressive Strength and *r is the residual friction angle.

A similar expression for rockfill (Barton, et al., 1979) is:

S' Rlog(S/an ) + *b 2.3

3 4 where $' arctan(Ths ) is the peak drained angle of friction, R is n the equivalent roughness, S is the equivalent strength and Sb is the basic friction angle.

For both rock joints and rock fill, S' depends on (i) sample size, (ii) stress level, (iii) surface roughness, and (iv) the uniaxial compressive strength (oc ) of the rock. The shear strength equations

(2.2 and 2.3) can be used in three ways:

(1) curve fitting of experimental peak shear strength data;

(2) extrapolation of experimental peak shear strength data; and

(3) prediction of peak shear strength.

Depending on the rock conditions (see Table 2.1 for example), the following general equation:

S' arctan(T/o ) Alog(B/a ) + C, 2.4 n n can be solved using the values for A (roughness), B (strength) and C

(friction angle) given in Table 2.1.

Roughness Component of Shear Strength (A in Equation 2.4)

Joint Roughness Coefficient

The JRC is approximately equal to the ratio of asperity height to the testing sample length. Five ways of estimating JRC are:

(1) Crude visual inspection of the joints and assigning JRC

values as listed below: 5

Table 2.1. Shear Strength Estimation for Rock Joints, Rockf ill and Rock Interfaces. (Barton, 1982)

CONDITION A B C

Rockj oint

JRC JCS weathered *r unweathered JRC o c .b

Rockf ill

R S weathered .b R S unweathered 4)b

Rock-rockf ill

JRC(

A roughness

B strength

C friction angle 6

(a) rough, undulating joints, tension joints, rough

sheeting, rough bedding -- JRC 20

(b) smooth undulating joints, smooth sheeting,

non-planar foliation, undulating bedding -- JRC = 10

(c) smooth, nearly planar joints, planar shear joints,

planar foliation, planar bedding -- JRC = 5

(2) Estimate JRC by a crude visual inspection and comparing

the profiles of the joints with Figure 2.1;

(3) Use the approximations:

JRC 400a/L for L = 0.1m

JRC 450a/L for L lm

JRC 500a/L for L 10m

where a is the asperity height and L is the joint length

tested.

(4) Back analyze JRC from shear tests using

-1 JRC [tan (Tha ) - Plog(JCS/a ) 2.5 n b n

If the rock is fresh and unweathered, o replaces JCS c for unweathered rocks. The procedure is to:

(a) Measure a for the unweathered rock c (b) Using the upperbound peak shear strength, T

envelope, substitute the measured Tia values into n Equation 2.5 with ac (if the rock is badly

weathered, use JCS). 7

TYPICAL ROUGHNESS PROFILES forJRC mile:

1 F 0-2

2 f -I 2-4

3 4-6

4f — — ---I 6-11

5 —I 11 - to

6 1------I to - 12

7 1------,---' --.1 12 - 14

8 1------_ .-----....,---1 14 - 16

9 16 - 111

10 111-20

6 s 16 I ...... 1 cm SCALE

Figure 2.1. Joint Roughness Profile Showing the Typical Range of JRC Values Associated with Each One. (Barton, 1977) 8

(c) Obtain the mean JRC for the upper bound test results.

(d) Assume a /4 for JCS, for the weathered condition. c

(e) Using the lower bound T envelope, substitute the

measured T/a values into Equation 2.5 with n JCS /4. c (f) Obtain the mean JRC for the lower bound test results.

(g) Take the mean of the two.

(5) Estimate JRC by tilt tests or push/pull tests, which is

the preferred method and is explained later.

Equivalent Roughness for Rockf ill

The equivalent Roughness (R) is dependent on the porosity (n) of the rockf ill and the angularity of the rock particles. There are three methods for determining R.

(1) from Figure 2.2, using the known porosity in conjunction

with the origin, roundedness or smoothness of the

material;

(2) extrapolating from available triaxial strength (or plane

strain) data; and

(3) from tilt tests, which will be discussed later.

Strength Component of Shear Strength (B in Equation 2.4)

Joint Compressive Strength

The degree of weathering of the rock joint determines whether a or JCS is used. There are four methods proposed to determine the c strength component for rock joints: 9

MANIPLES SNOWING DEGREE OF R OLOODE OWE SS

CILIA" le 0 TALUS NORAMFE °LAC' FLUVIAL FLUVIAL ROE* MATERIAL MATERIAL

/1041IP Illdlot 110•110 O4HIO 41wigsn11P ra sin M ::: Oa.* 4114110 n A—.M. 41 4400110 Ffl =

Figure 2.2. Method of Estimating Roughness Based on Porosity of Rockfill, Origin of Materials and Degree of Roundedness and Smoothness of Particles. (Barton and Kjaernsli, 1981)

10

(1) B = a if the joint is unweathered; c (2) If no test results are available and the rock joint is

weathered, use B = (1/4)a;

(3) If the density of the rock mass, density of the joint

walls and a are known, Table 2.2 can be used to c estimate the JCS.

Table 2.2 Estimating JCS Using Rockmass Density, Joint Wall Density and the Uniaxial Compressive Strength. (Barton & Choubey, 1977)

Percentage of Change in Joint Density C Ratio from Rockmass Density

1-2 0% 2-3 -TL 3-4 -10% 4-10 -20%

(4) Use the Schmidt Hammer Index Test (SHT) on the joint

wall. The practical range of this is for JCS values

between 20 MN/m2 to 300 MN/m2 (Miller, 1965). The

equation for JCS is:

log(JCS) = 0.00088yr + 1.01 2.6

where r is the rebound number and y is the dry rock

density (kM/m). The SHT cannot be used for "drummy" or

weak rock or for rocks with closely spaced and loose

joints (as in phyllite). The procedure is to take ten

SHT readings, ignore the lowest 5 and average the highest

5. The presence of moisture reduces the JCS values by

5%-8%, with granite reduced the least and gneiss reduced 11

the most. The reader should note that some researchers

(Daemen, 1985) found inconsistencies in the Schmidt

Hammer readings. For in situ testing, it was found that

test of arbitrary surfaces gave inconsistent results.

Smaller samples had to be properly secured to obtain

consistent SHT data. However, Carter and Sneddon (1977)

performed a study comparing the SHT and the uniaxial

compressive strength. They found that for small core

testing, the core diameter had to be at least 75 mm and

had to have a curved jaw vice mounted on concrete blocks

to obtain an accurate correlation with measured uniaxial

compressive strengths. For the in situ SHT, the walls

were washed down and subsequently rubbed with an abrasive

disk for accurate correlations.

Equivalent Strength for Rockf ill (S in Table 2.1)

The equivalent strength (S) of rockf ill is strongly dependent on the particle sizes. The following factors were observed by Marachi et al. (1969, 1972) to increase the amount of particle crushing:

(1) increased water content;

(2) increased uniformity of the rockfill;

(3) increased particle angularity;

(4) increased effective confining pressure;

(5) increased shear stress under a given confining pressure;

(6) triaxial cell testing as compared to plain strain testing; 12

(7) reduced particle strength; and

(8) increased particle size.

Two methods for calculating S involve the use of Figure 2.3.

Depending on the type of tests run, triaxial or plain strain, the d50 particle size of the rockf ill and o of the rock, Figure 2.3 will give c the corresponding S from the S/oc ratio.. A third method uses either laboratory test data or large scale tilt test data. The equivalent strength is then back calculated from Equation 2.3 using the test data.

Frictional Component of Shear Strength (C in Equation 2.4)

Basic Friction Angle

The basic friction angle is used when the rock on rock contact is not weathered. If the contact is even slightly weathered, the compressive strength of the thin weathered layer is significantly less than the competent rock mass compressive strength. If the rock on rock contact has a thin layer of weathered rock, the basic friction angle is used instead of the residual friction angle for high levels of normal

0 stress. The basic friction angle is usually 25 0 - 35 for most rocks,

procedures to evaluate • are: but the four b

(1) Assume cpb = 30 0 if no data are available;

(2) Use Table 2.3 (Barton, 1977);

(3) Estimate .13 from residual tilt tests on flat, dry,

nondilatent, sawn rock surfaces;

(4) Estimate etb from tilt tests on three drill core sticks. 13

TRIAX I AL TEST

11=101111h.."1411 1•1111111•1111MMWM11111111 MIIIIIIIIIMPAN..— 11111•11=511MNIIMMOIN " maismumnim....L.weasiimmuma 0.5 Mi.' I-" gUINVAIIIIIMIIMIENIMIUM1111111111111111111MIM1111 M1011117-4111111111MIMMIIIIIIIINNIMIUMMIIIIIIIII 111=11111111109111111NMMIIIIIIIIIIIIIIIIIIIMIMMI OE4 11111•1111111111111MMIMINIIIIIIIULME 02 immiunnummommmium--raz., 2 3 4 S 11 4 SIO 20 10 £0 50 100 200 ILO 00 S

dia particle is (wan)

Figure 2.3. Method of Estimating Equivalent Strength of Rockf ill Based on Uniaxial Compressive Strength and on d50 Particle Size. (Barton and Kjaernsli, 1981) 14

Table 2.3. Basic Friction Angles of Various Unweathered Rocks Obtained from Flat and Residual Surfaces. (Barton, 1977)

Moisture Basic friction Rock Type Condition Angle Reference

A. Sedimentary Rocks

Sandstone Dry 26-35 Patton, 1966 Sandstone Wet 25-33 Patton, 1966 Sandstone Wet 29 Ripley & Lee, 1962 Sandstone Dry 31-33 Krsmanovic, 1967 Sandstone Dry 32-34 Coulson, 1972 Sandstone Wet 31-34 Coulson, 1972 Sandstone Wet 33 Richards, 1975 Shale Wet 27 Ripley & Lee, 1962 Siltstone Wet 31 Ripley & Lee, 1962 Siltstone Dry 31-33 Coulson, 1972 Siltstone Wet 27-31 Coulson, 1972 Conglomerate Dry 35 Krsmanovic, 1967 Chalk Wet 30 Hutchinson, 1972 Limestone Dry 31-37 Coulson, 1972 Limestone Wet 27-35 Coulson, 1972

B. Igneous Rocks

Basalt Dry 35-38 Coulson, 1972 Basalt Wet 31-36 Coulson, 1972 Fine-grained granite Dry 31-35 Coulson, 1972 Fine-grained granite Wet 29-31 Coulson, 1972 Coarse-grained granite Dry 31-35 Coulson, 1972 Coarse-grained granite Wet 31-33 Coulson, 1972 Porphyry Dry 31 Barton, 1971b Porphyry Wet 31 Barton, 1971b Dolente Dry 36 Richards, 1975 Dolente Wet 32 Richards, 1975

C. Metamorphic Rocks

Amphibolite Dry 32 Wallace, et al., 1970 Gneiss Dry 26-29 Coulson, 1972 Gneiss Wet 23-26 Coulson, 1972 Slate Dry 25-30 Barton, 1971b Slate Dry 30 Richards, 1975 Slate Wet 21 Richards, 1975 15

Residual Friction Angle

The residual friction angle (cpr ) is the friction angle of the weathered rock on rock contacts after large shear displacements have worn down the asperities. Depending on the degree of weathering and the mineralogy of the rock, 4, is approximately 15-300 . The residual friction angle can be calculated from the following equation:

(.1) - 20 0 ) + 20(rw/rf ) 2.7

where r is the Schmidt rebound number on dry, unweathered surfaces and f r is the rebound number on wet, weathered surfaces. w

Testing Conditions Versus Field Conditions

Extrapolating small scale tests to the in situ field conditions is one of the most uncertain aspects of geotechnical engineering.

Engineers know that the actual field conditions are different from the controlled laboratory tests, but quantifying this difference is difficult. Barton, et al., have developed simple large scale tests to determine the shear strength of rock joints and rockf ills, and extrapolated lab data to in situ conditions.

Rock Block Tilt Test

The Rock Block Tilt Test is an in situ test involving very low normal stress and is shown schematically in Figure 2.4(a).

The blocks are slowly tilted until the top block starts

sliding. The angle at which the block starts sliding, a, has the

following relationship: 16

(a) (b)

,-..v

. . 11-•' '4..?1 ;'''', 4•::•,..,.....,. èr. ,.,,,„...1!"1 . . 1....i

PI.. Tut 6011 ON 11,11 •OC•111.1. . -...... '

111001, 1 loota• •1•141 IT urrINIII ANS Slam 44444 NO

• 0011 CON•IICT Situ NIE?

COOCINAT1

Mi £11111 tilt ••n • n 11 if% • n vf Non* •Anyibl OcCollt

(e)

Figure 2.4. Schematic for a) Rock Block Tilt Test, b) Pull Test, and c) Rockfill Tilt Test. (Barton, 1979 and 1982) 17

a = arctan(i / a ) 2.8 o no

where the normal stress is

2 = yhcos a 2.9 0

The thickness of the top block, h, is in meters and the rock density, 3 y is in fl/m . The cosine factor is squared to compensate for the low normal stress and tipping of the top block at high tilt angles.

The JRC can then be calculated by substituting Equation 2.8 into Equation 2.4 and rearranging:

(a - .)/log(JCS/ar ) 2.10 JRC = no

The tilt test is limited to low JRC values because blocks with high JRC values topple instead of slide. Laboratory tilt tests are only accurate for JRC up to 8, and field tilt tests for JRC up to 10. The push/pull test is used for estimating higher JRC.

If the slope encountered is unsaturated, the tilt tests should be run on dry surfaces with corresponding JCS values calculated from

the Schmidt Hammer Index Test performed on dry surfaces. If moisture

is expected, the tilt test and SHT should be performed on saturated

surfaces. The tilt test is preferred over shear box testing to

calculate JRC because shear testing produces nonuniform strain and progressive failure, whereas gravity-induced loads give a more uniform

nature of loading over the contact area. 18

Equation 2.10 has a compensating effect for estimates of JRC.

If the residual friction angle and/or JCS is overestimated, the JRC will be underestimated and visa versa.

Pull Testing of Rock Blocks

If the JRC value is too high (i.e., too rough of a joint), the pull test may be performed. Laboratory pull tests can be conducted for

JRC values up to 12, and field tests can be performed for JRC values up

to 20, as illustrated in Figure 2.4(b).

The equation for calculating the JRC from the pull test is:

JRC (arctan((T1 + T2 )/N) - •rylog[(JCS)(a)/N] 2.11

where T is the tangentional component of the weight of the block for 1 inclined surfaces, T2 is the applied force and N is the normal

weight (W). a is the joint area and a = N/a. To component of the n avoid moments, apply T2 close to the joint plane.

Tilt Test for Rockf ill

Tilt Testing for rockfill or waste dumps can be accomplished

easily, as shown in Figure 2.4(c). The box length should be at least

30 x or 5 x d of the rock particles, whichever is largest. d50 max 0 Since the stresses are very low, a is 55 to 65 ° , which is equivalent

to The strength of the rockf ill can be extrapolated to design

stresses by:

(1) estimation of S and $1) from index tests;

(2) calculating R from rearrangement of Equation 2.4, using

the results from the tilt test, 19

R (a - •11 )/log(S/an ) 2.12

(3) and then using Equation 2.4 to calculate V.

The tilt test is also used to estimate the porosity, n, of the fill. This is accomplished by measuring the force required to lift one end of the box before and after filling.

Extrapolating JRC from Lab Samples

If large scale tilt tests or pull tests cannot be performed, small scale tilt test results can be used. The small scale JRC calculated can be extrapolated to the field JRC (Barton, 1977) by using the following expression:

(JRC natural block)/(JRC lab) (a natural block)/(a lab) 2.13

(JRC lab) is from the small scale tilt tests; (a lab) is the mean inclination angle of asperities of the lab block, equal to 2% of specimen length; (a natural block) is the mean inclination angle of asperities of the natural block, equal to 2% of specimen length; and

(JRC natural block) is the unknown.

Factors Affecting Shear Strength

Shear strength of natural slopes is usually lower than the shear strength measured in the lab. Large samples mobilize the larger asperities, but only a few of these large asperities control the shear strength. Smaller samples mobilize smaller asperities, but the relative number of contact areas is larger. As sample sizes are

increased incrementally, the incremental reduction in shear strength 20 between increments becomes smaller, until a critical sample size is

reached. If the sample size is increased beyond the critical sample

size, the reduction in shear strength becomes negligible. The

saturation state, preconsolidation and the stress level also affects

the shear strength.

As the length of the joint increases, the JRC decreases because

smaller blocks rotate more than the stiffer, longer joints, thus producing larger contact areas. The amount of reduction in JRC as joint length increases is a function of the JRC. For planar joints

(low JRC), the maximum reduction in JRC as the sample size is

increased, is 1.3. For rough joints (high JRC), the maximum reduction

in JRC is 11.2, as reported by Bandis, et al., (1981).

There is a corresponding scale affect on the JCS. Increasing

the sample size reduces JCS by a factor of 2.5 for dense rock and 10

for porous rock (Bandis, et al., 1981). If JCS is extrapolated from

dry lab tests to in situ saturated conditions, the uniaxial compressive

strength and JCS can be reduced by 25%.

The shear strength for rock joints and rockf ill developed by

Barton is for use in low to medium stress conditions. The peak shear

strength is most often reached after the shear displacement (6) is 1%

of the joint length. The slip magnitude (Barton, 1982) to mobilize

peak T or to remobilize is:

6 = EL/500)(JRC/L)0.33 2.14

where L is the joint length and R can replace JRC for rockf ill. At 21 peak shear strength, a /a = 0 /JCS, where a is the maximum 1 0 n 0 possible area of joint contact and a is the area of actual contact. 1 If = JCS, then the asperities are crushed and the entire contact n area helps mobilize the peak shear strength.

Residual shear strength is used in high stress stability analyses and the residual friction angle replaces the basic friction angle and o' - 0 replaces JCS (or c ) in Equation 2.4. 0 . is 1 3 c 1 the effective maximum principal stress and c' 3 is the effective minimum principal stress. The maximum shear strength occurs when

0 = o' - a' which would be when a' = 30' cp' = 30 and a = n 1 3' 1 3' 1 a (Barton, et al., 1977). is the normal effective stress. 0 4 'n Preconsolidation of joints gives higher shear strength than normally consolidated joints. Collecting samples for testing disturbs the sample, and the preconsolidation is lost. If preconsolidation testing is desired, it would be impossible to calculate the preconsolidation force that should be applied to the sample. Barton

(1973) experimented with preconsolidation ratios of 1:4 and 1:8, and

0 0 the dilatation angle was found to increase 5 to 10 respectively.

This increase in the dilatation angle increases CHAPTER 3

A SIMPLIFIED DYNAMIC SLOPE STABILITY METHOD

The trend in slope stability analysis is towards predicting probability of failure, instead of using factors of safety. This is

especially true for dynamic slope stability analyses. Pseudostatic

slope stability techniques have numerous limitations when used to solve

dynamic slope stability problems:

(1) The ground motion forces are set as a constant, usually

equal to the maximum ground motion force;

(2) Frequency effects are not taken into account;

(3) Most do not account for the roughness of the failure

plane;

(4) Output is usually in the form, "failure" or "safe";

(5) Failure is instantaneous and simultaneous along the

failure plane.

Pseuodostatic techniques are simple to do, but they are not accurate

for dynamic driving forces.

Finite Element (FE) or Finite Difference (FD) methods have been

developed to analyze dynamic slope stability. These methods require

the accurate input of soil and/or rock strength properties. The

results from FE or FD analysis are only as good as the input, and

acquiring accurate intrinsic strength properties for geologic media is

22 23 expensive and time consuming. These methods may develop stresses and strains which are difficult to relate to a dislocated surface.

A Dynamic slope stability analysis has been developed by Glass

(1982) that is simple to run and requires minimal soil/rock strength parameters. The Linear Acceleration Dynamic Response of Slopes -

Multiple Degrees of Freedom (LADRS-MDF) program is ideal for checking initial stability conditions, for mining applications and other non life-threatening slope problems. Some of the advantages of the

LADRS-MDF technique over the simplified pseuodostatic and numerical techniques are:

(1) The program is not complicated;

(2) Failure is progressive, not simultaneous;

(3) Blast vibration propagation can be studied;

(4) Failure plane roughness is considered in the stability

analysis;

(5) Output is a slope displacement time history;

(6) Ground motion time history is incorporated, which

includes all characteristics of ground motion.

Constitutive Relation for LADRS-MDF

The slope is idealized as a spring-mass-dashpot system, as seen

in Figure 3.1. The masses are discretized along joint planes and rock

type variations for rock slopes. For rockf ill slopes or waste dumps,

the discretization is accomplished by the knowledge of the

stratification (lifts or dumped) and the assumed failure surface. 24

(a)

(b)

(c )

Figure 3.1. Geometry for LADRS-MDF. (a) is an idealized slope, (b) is a MDF analog for slope stability with masses (Mi), stiffnesses (Ki) and damping (Ci) and (c) is a MDF analog for embankment response with masses (Mi) and shear moduli (Gi). (Glass, 1981) 25

The dynamic equation of motion for the blocks is:

Mx + Cx + Kx = A(t) + F(t) 3.1 where x is the block acceleration, x is the velocity, x is the displacement, M is the block mass, C is the damping, K is the interblock stiffness, A(t) is the input ground motion force and F(t) is the frictional force. LADRS-MDF assumes a linearly varying acceleration between timesteps, At.

The input to the LADRS calculation is a digitized accelerogram

[a(t)] representing the ground motion. This enables accurate inclusion of all ground motion parameters, including frequency and duration of ground motion. The stiffness decreases to zero as blocks separate and

damping is set to zero because once block movement begins, the effect

of stiffness and damping is small compared to the frictional component.

Frictional Model

The friction model used in LADRS-MDF uses Barton's empirical

model. The equation for the friction [f(t)] is,

= tan[(T)(A)log(B/J) + C] 3.20 f = Th5n

A, B and C are defined in the previous chapter (roughness, strength and

friction angle), T is a scaling factor defined by Table 3.1 (suggested

by Barton, 1980), and J represents the dynamic normal force and will be

discussed later. 26

Table 3.1. Suggested Values for the Scaling Factor T.

Ratio = 6/6

1.0 < Ratio > 2.5 (1/6)(7.0 - Ratio)

2.5 < Ratio > 10.0 (1/30)(25.0 - Ratio)

10.0 < Ratio > 100.0 (1/80)(100.0 - Ratio)

> 100.0 0.0

6 is the block displacement and 6 is the block displacement distance to peak shear strength, usually I% of the joint length up to a limiting joint length. 6 can be up to 5m for undulating joints and up to 3m for planar surfaces.

Procedure for Using LADRS-MDF

By definition, angular frequency, w = (KIM) 1"2 and critical damping occurs when C/2M = w, i.e., C 2Mw. The fraction of critical damping is 0, and 0 = C/Ccr C/204, i.e., C = 2Mw0. Using

Equation 3.1, the above definitions and some calculus, the method for using LADRS-MDF proceeds as follows, with 0 and w set to zero (Glass,

1981):

(1) Compute xo from

x = a(t ) + f(t 3.2 0 0 0 ) (2) Compute Bo from

B = 3x /At + 2x + (1/2)x At 3.3 0 0 0 0 (3) Compute 81 from 2 B = 6x /At + 6x /At + 2x 3.4 1 0 0 0 (4) Compute xl from 2 X1 = (At /6)(a(t ) + f(t ) + B ] 3.5 1 1 I 27

(5) Compute xl from

x = 3x /At - B 3.6 1 1 0 (6) Compute xl from

X1 = a(t ) + f(t 3.7 1 1 ) The subscripts 0 and 1 refer to timesteps, where 0 is the known and 1 is the value for the next timestep. The procedure outlined above can be repeated for as many iterations as are needed.

The free body diagram, as seen in Figure 3.2, shows that slope stability depends on the friction coefficient, slope angle and forcing function. The forcing function is the accelerogram with a displacement vector in the plane of the rock slope. The resultant vector is decomposed into two orthogonal vectors normal and parallel to the rock slope. The static acceleration on the rock block due to gravity is

D = gsina 3.8 s

R = g(cosa)f 3.9 s

where:

D = driving acceleration (driving force/mass)

R = resisting acceleration (resisting force/mass)

f = friction coefficient

When the resultant acceleration vector moves the slope toward the block, the normal force increases, resulting in an increase in resisting acceleration and a decrease in the driving acceleration: 28

Figure 3.2. Freebody Diagram for LADRS-MDF Technique. (Glass, 1980) 29

D = D - a(t)cosa 3.10 d s

R = R + a(t)(sina)f d s = [g cosa + a(t)sina]f 3.11 = (J)(f)

When the acceleration vector moves the slope away from the block, the normal force decreases, so the driving force increases and the resisting force decreases:

D = D + a(t)cosa 3.12 d s

R = R - a(t)(sina)f 3.13 d s

The resultant block acceleration is then:

xl = Dd ± Rd 3.14

where the sign of Rd is opposite the sign of the block velocity.

Block Displacement Analysis used in LADRS-MDF

The failure of each block is checked progressively from the top of the slope down. If an upslope block is unstable, the resultant driving force of the upslope block is added to the driving force of the downslope block and another stability check is made. This procedure continues downslope. The entire slope is determined to be unstable if all blocks are unstable or if the lowest (key) block is unstable.

If the upslope block displacement exceeds that of the immediate downslope block, a collision occurs. The collision is considered perfectly elastic if the ratio, EP = oc /F, is greater than 1, where 30

is the unconfined compressive strength of the material and F is the c collision force. If EP < 1, an inelastic collision occurs, and the final velocity, Vf is

V = V (1 - EP) + V(EP) 3.15 f p where VP is the plastic-collision velocity and V is the e elastic-collision velocity.

The failure surface is abitrary and handled using a look-up table approach to determine the failure slope angle under each block as it displaces down the slope. CHAPTER 4

DYNAMIC PORE WATER PRESSURE ANALYSIS

Dynamic pore pressure experimental data and analyses are extensive for sands and cohesive soils. Rockf ill slopes have been studied, but not to the extent that soils have. Dynamic pore pressure research of well graded cohesionless soil slopes and rock slopes has not been undertaken. The author will attempt to quantify the pore pressure response of slopes subject to earthquake or blasting ground motions. The pore pressure hypothesis developed will serve two purposes: i) to insert into a dynamic slope analysis (LADRS-MDF) which does not take pore pressure into account and ii) to encourage further research in this area. Experimental data for this paper could not be obtained because the problem is very complicated and would require sophisticated field and laboratory tests to obtain the data.

LADRS-MDF requires as input only the ground motion time history, a roughness coefficient, a compressive strength parameter and a frictional component. These input parameters are relatively simple and inexpensive to obtain. The pore pressure analysis should also be simple, and not require any more input data than is already used.

The extent of the pore water pressure buildup of a rock fill

(Sadigh, et al., 1978) depends upon (i) rate of pore pressure generation; (ii) rate of pore pressure dissipation; (iii) duration of

31 32 strong shaking; and (iv) location on the drainage path. The dynamic pore water pressure prediction in this thesis is classified according to the following three conditions:

(1) Very permeable rock fill slopes in which the pore

pressure dissipation is faster than the excess pore

pressure generation. The pore pressure would include the

in situ static pore pressure and the transient pore water

pressures induced by a dynamic load.

(2) Rock fill slopes in which the excess pore pressure

generation is faster than the pore pressure dissipation.

The pore pressure would have three components: static,

transient and excess.

(3) Jointed rock mass slope with three components of water

pressure: static, transient and excess.

The Experimental and Theoretical Basis for the Dynamic Pore Pressure Analysis

Most theoretical dynamic pore water pressure analyses are too complicated to be used in most engineering applications. The reader is referred to the References and the Bibliography for further literature regarding dynamic pore pressure analyses, especially the papers on soil liquefaction.

The dynamic pore pressure response in geologic media is dependant upon numerous factors. Unconsolidated materials are affected by the (i) grain size distribution, (ii) grain shape, (iii) void ratio,

(iv) compactiveness, (v) structural arrangement of the particles, (vi) 33 chemical cementing, (vii) age of the deposit, (viii) drainage path location, (ix) duration of strong shaking, (x) frequency of strong motion, and (xi) depth below the surface (Ishibashi, et al., 1982 and

Garga and McKay, 1984). The pore pressure response in rock joints depends upon (i) joint wall compressive strength, (ii) fracture characteristics, (iii) asperity characteristics, (iv) duration of shaking, (v) frequency of motion, (vi) chemical composition of the rock, and (vii) shear strength.

Material Parameters Influencing Dynamic Pore Water Pressure in Unconsolidated Material

The pore water analysis of unconsolidated geologic media subject to a dynamic load is mainly dependent upon the permeability of the deposit. More permeable material will have less excess pore pressure buildup. The permeability is controlled by the physical and chemical state of the material.

The chemical properties of the particles determine the degree

of interparticle "welding, - the ground water reactivity, particle shape and deposit age. As the degree of cementation between particles increases, the permeability decreases. If the matrix material dissolves readily in the ground water, the viscosity will increase, thus decreasing the permeability. The infrastructure of the particle depends upon the chemical bonding, which affects the way a mineral weathers. If particles are more round (usually older and more weathered minerals), the permeability is higher (given a constant void ratio) than if particles are angular. 34

The physical properties of the mineral particles, such as the compressive strength, gradation, compactiveness, void ratio and uniformity, also control the deposit's permeability. The permeability is higher for particles of high compressive strength. Minerals with higher compressive strength will not crush as readily as those of lower compressive strength. If particles are crushed, the smaller "broken" pieces fit in the interstices of the matrix, thus reducing the permeability of the deposit as a whole.

The media's particular arrangement, i.e., compactiveness, void ratio and gradation, affects permeability. Highly compacted material has less pore space (lower void ratio) than uncompacted media (higher void ratio) and the former case will usually have a lower permeability than the latter. If the particles are well graded, (particles of different sizes) the smaller particles will fill the interstices left by the larger particles, thus reducing the void ratio and permeability. Uniformly graded materials would have a correspondingly higher permeability.

The engineer should be aware of the possibilities of soil

liquefaction, which occurs most often in sandy soils with uniform

gradation, high void ratio and rounded particles. The reader is

referred to the Bibliography and References concerning this topic which

are contained herein. 35

Material Parameters Influencing Dynamic Water Pressure in a Rockmass

Rock slope stability is usually controlled by the

discontinuities, such as joints, fractures and faults, hence, the

dynamic water pressure in the discontinuities is more critical than the pressures within the rock matrix. The dynamic pore pressure (pore pressure developed due to a dynamic load) response of the joint is dependent on several factors: (i) aperture width, (ii) asperity height or roughness, (iii) normal load on the joint, (iv) joint compressive

strength, and (v) shear strength.

Discontinuities with wide apertures transmit water pressures

"instantaneously" when a dynamic load is applied, hence, these large

apertures do not permit a build up of water pressures as readily as do

smaller apertures. Smaller aperture discontinuities have transient and excess dynamic water pressure components, whereas larger aperture joints have the only transient pressure pulse.

Asperity size, distribution and geometry plays an important role in the dynamic water pressure response in discontinuities.

According to Kopf (1982), the undulatory walls of faults create chambers and bottlenecks. Shear displacements cause the chambers to expand and contract, thus acting as a bellows pump. Rock slopes could exhibit the same "bellows" affect during slope movement, especially if mineral particles block the bottlenecks further.

Adding a normal load or increasing the existing normal load

(static or dynamic) on discontinuities decreases the aperture width.

The reduced volume in the joint transmits this load to the entrapped 36 water, thus increasing the pore pressure. Removing the normal load should have the opposite affect.

The joint wall compressive strength can also increase or decrease the water pressure in the joint. If the applied normal stress exceeds the compressive strength of the asperities in contact on opposite walls, the asperities are crushed. The crushed contacts reduce the aperture opening and confine the water in the joint, thus increasing the water pressure. Crushing also reduces the volume occupied by the rock, so the volume available for the water is increased, thus decreasing the water pressure. Intuitively, the decreased volume due to aperture width reduction should exceed the increased volume due to crushing, causing a net increase in water pressure.

When a dynamic load is applied to a jointed rockmass, shearing forces may exceed the shear strength of the rock joint at local contact asperities. Shearing the asperities decreases the volume available for the water in the discontinuities because of aperture closure. Thus, when the peak shear displacement is exceeded, there will be a water pressure buildup. Prior to peak shear displacements, dilation may induce a pore pressure drop, as will be shown later.

Other Parameters Affecting Dynamic Pore Water Pressure

The time-motion history of the input dynamic load influences the water pressure behavior. Soil liquefaction research has shown that liquefaction occurs after a critical number of input motion cycles. 37

The chances of building excess pore water pressure increase as the

duration of shaking increases.

Water is usually assumed to transmit loads instantaneously.

When high frequency dynamic loads are applied to the media "holding"

the water, this may not be true. Earthquakes create relatively low

frequency ground motion, so the instantaneous transmission assumption

is not violated. Blast waves usually have higher frequencies,

depending on the size of the explosion and the rock characteristics.

The most critical frequency to consider is the resonant frequency of

the mineral-water-air system.

The strength of the input motion, or amplitude, affects the pore water pressure response. A higher amplitude motion would

obviously increase water pressures more than lower amplitudes.

Slopes impounding a body of water will "feel" a hydrodynamic

force caused by the body of water (Ghaboussi and Hendron, 1984). The water only transmits the compressional wave, however, not the shear wave.

Fluid properties in the pore spaces affect the water's dynamic

response. Temperatures do not vary substantially below the ground

surface, so the temperature effects on the fluid can usually be neglected. Earthquakes have relatively low frequencies, so the viscous

affects of the flowing fluid can also be neglected.

Dynamic Pore Pressure of Very Permeable Rock Fill Slopes

Harp, et al. (1984) derived an expression for transient pore

pressures measured during the 1980 Mammoth Lake, California 38 earthquake. Transducer piezometers were installed 1.3 m deep in a

lakeshore deposit to record the pore pressure variations during an earthquake. The equation reproduces the compressional wave of the earthquake, and it has the form:

U = (a /g)S 4.1 where U is the pore pressure, av is the vertical acceleration of the

P-waves, g is gravity and Sv is the total vertical stress.

Excess pore pressure was not recorded by Harp et al. because

the piezometer was not deep enough and the soil was able to dissipate

any excess pore pressure build up. Equation 4.1 simulates the

transient pore pressures produced by the earthquake load cycles.

A rockf ill slope that dissipates the dynamic pore water pressure as it is generated is considered very permeable. Highly permeable material (Terzaghi, 1967) include soils with a permeability

greater than 0.1 cm/sec. Clean gravels and sand and gravel mixtures

fall into this range. The increase and decrease of pore pressures

coincides with the ground motion history, i.e., when acceleration is at

a maximum, so is the pore pressure, and when acceleration is at a

minimum, the pore pressure is reduced. This cyclic pore pressure

response is instantaneous. The pore water pressure response for very

permeable rockf ill slopes is then:

U = U + U = U + U (a/g) 4.2 d s t s s 39

is the static pore water pressure prior to ground vibrations, where Us U is the transient pore water pressure, a is the vertical acceleration t of the ground movement and g is gravity.

Equation 4.1 is a special case for the general equation simulating transient pore water pressure, U. Equation 4.1 was developed using limited data that was collected near the ground surface and close to the phreatic surface. The total vertical stress is equal to the effective stress, and Harp's equation would predict a transient

if the media were unsaturated (S equals the pore water pressure even v overburden minus the pore pressure). Equation 4.1 is unsuitable for

conditions where the overburden stress is many times greater than the pore pressure (high Sv ), i.e., a basin, as in Tucson, with a very deep water table wherein the dynamic pore pressure would be measured close

to the phreatic surface.

Earthquakes affect large areas, and if the slope was impounding

a body of water, the slope would "feel" a hydrodynamic force from the

body of water. This hydrodynamic force is assumed not to affect the

pore pressures in the interior of the slope. The hydrodynamic force is

cyclic and instantaneous, and should only only affect the slope

surface. The hydrodynamic force reduces the stability of the slope

surface, but it may increase the stability of a deep seated sliding

mass by increasing the frictional resistance on the failure plane due

to the increased normal force. 40

Dynamic Pore Pressure of Rockf ill Slopes

In this section rockf ill slopes can be characterized as having medium to low permeability, such as waste dumps, tailing ponds and other slopes composed of sands, gravels and fines. The pore water pressure generated exceeds the pore pressure being dissipated. The cyclic pore water behavior is still present, but there is a gradual buildup of excess pore pressure as shown in Figure 4.1.

The data for Figure 4.1 were obtained from undrained tests.

The behavior of rockf ill slopes lies between drained and undrained conditions, so the pore pressures depicted in Figure 4.1 are too conservative. The slope of the linear buildup of pore water pressure from Figure 4.1 is 0.05 for a) and b) and 0.0375 for c). Since no data are available for rockf ills, the slope of the linear buildup in excess pore pressure has been chosen as 0.04. The proposed dynamic pore water response would then be:

2 U U + U + U U + U (a/g) + 0.04N(kg/cm ) 4.3 d s t bf s s

U is the excess pore pressure buildup and N is the number of cycles. bf Material with low to medium permeability (Terzaghi, 1967) are clean sands, very fine sands and sand and silt mixtures. The corresponding permeability is in the range between about 0.1 to 0.0004 cm/sec.

Seed, et al. (1976) pointed out that the increase in pore water pressure in saturated undrained sands occurrs on the unloading portion of the load cycle. This means that the maximum pore pressure would not 41

(a)

SINGLE - CYCLONED TAILINGS SAND D503 0.27 mm ro • 1526.7 kg/m 5 (b) Or • 40.9% o• c • 2 kg/cm2 Kc • 1.5

1 0 5 10 15 20 25 30 Number of Cycles

(111) Can.0.8 Lie a Pin MOW P.040% 100MYI 0 C/00

Mal Ofes... .1....1 it. ---". \ 0.7.7.1...... , i .., .-,-...... li • 040••0 n 119ft ..or wt...... — — 0... .--. — 0 •n•••0 70 .p ve Sp ‘- no n , ...... , ...... • .. 0 04. w on 60.n MAY.. A 0 ft.. kg A iiiii -0 n pi , +a c. Y T / ! ' lir Y Y

• 0 00 *maw C”fte

Figure 4.1. a) Undrained Triaxial Test on Loose, Saturated Sand (Terzaghi and Peck, 1967); b) Cyclic Triaxial Test for an Anisotropically Consolidated Specimen (Finn, et al., 1978); and c) Pulsating Load Test on Dense Sand . 42 coincide with the maximum cyclic load amplitude. Equation 4.3 predicts

that the increase in pore water pressure will coincide with the maximum point in the load cycle. When the maximum dynamic load is "felt," the pore pressure will be at a maximum. The opposite is true when the minimum cyclic load is applied, the pore pressure would be minimum.

Dynamic Pore Pressure Prediction for Rock Slopes

The pore pressure response to a dynamic load in rock joints has yet to be investigated. It is not known if the dynamic loads imposed

on a rock slope, such as an earthquake or a blast, would be strong

enough to cause crushing of the rock contacts in joints. Crushing of

the joint contacts would reduce joint aperture, causing a pore pressure

increase.

The lack of research data in the dynamic water pressure

behavior in rock joints has led the author to propose an equation

similar to equation 4.3:

2 U =U+U+U. =U+U(a/g) + 0.06N(kg/cm ) 4.4 d s t bj s s

The excess pore pressure term, Ubj , was chosen to be 1.5 times

U because the drainage characteristics in a rock joint are different bf from those of a rock fill. In a rockf ill, the excess water pressure

can be dissipated in all directions. Excess pore pressure dissipation

in a joint can only flow along the joints and are more confined; hence,

rock joints should build up water pressure more readily than a rockf ill. 43

Barton (1982) shows in Figure 4.2 and 4.3 that dilation of rock joints occurs when the ratio 6/6 reaches 0.3, where 6 is the shear displacement and 6 is the shear displacement at peak shear strength, which is approximately 1% of the joint length. Figures 4.2 and 4.3 show this to be the case, where the ratio 6/6 falls between 1/2 to

1/3, and which was supported by Bandis et al. (1981).

Equation 4.4 is used to calculate the dynamic pore-water pressure up to a limiting shear displacement. When the limiting displacement is reached, the dilation in the joint causes a drop in pore pressure due to drainage. After the limiting shear displacement of 6 0.36 occurs, the pore pressure in the joint can be assumed to equal the original static pore water pressure. When the peak shear strength displacement is reached, the pore water pressure generation would then continue.

LADRS-MDF Analysis of the Homestake Pitch Slope Failure

The dynamic pore water pressure simulation presented in this paper was incorporated into LADRS-MDF. A stability analysis of the

Homestake Pitch slope failure was then performed to see if the results of Lhe analysis seemed reasonable.

The geology of the Homestake Pitch area is composed of

competent igneous and metamorphic rocks. The location of the slope

failure, however, is a shear zone (Savely, 1985). JRC values of 15

(for Lhe competent rocks) and 6 (for the shear zones) were used to

analyze the stability of the Homestake Pitch slope. 44

PHYSICAL MODEL NUMOUCAL MODEL

RESIDUAL

10

1 1 1 I 1 1 1 1st 1st I 1 1 3 4 5 6 7 1 2 3 4 5 6 7

SHEAR DISPLACEMENT. dh ( wn) SHEAR DISPLACEMENT (wn)

0 10 20 30 s I Cm

PRO1U OF MODEL JOINT SURFACE

Figure 4.2. Experimental and Predicted Data Showing the Size Dependent Dilation that Occurs During Shearing. (Barton, 1982) 45

LAB IN SITU NATURAL TEST TEST BLOCKS JRC 15 7.5 6.6 JCS 150 50 40 LIPa SPEAK 1.0 4.0 6.1 mm 0 9r 30 30° 30°

IN SITU BLOCK TEST

LABORATORY TEST Ira L=0.1m ASSUMED NATURAL BLOCK SIZE 2 METERS

01 3 4 5 6 7 3 9 10 11 12 13 14 15 SHEAR DISPLACEMENT (mm)

Figure 4.3. Dilation Modeling for Shear Tests on Three Different Sample Sizes. (Barton, 1982) 46

Three different dynamic loads were studied. A sine wave with a maximum amplitude of 0.75g, frequency of 5 hertz and an 8 second duration simulated an earthquake (Figure 4.4a). Figure 4.4b illustrates a 50 hertz sine wave simulating a blast wave. The 0.4 sec duration blast wave (maximum amplitude of 0.75g) was propagated upslope and downslope. The amplitudes of the blast and earthquake waves are similar, so comparisons between the two outputs are simpler.

The input motions, an earthquake, a blastwave propagating upslope and a blastwave propagating downslope, were varied with JRC equal to 6 and with a low water table. Table 4.1 shows the final block displacements corresponding to the three different input dynamic

loads. The earthquake (low frequency) caused larger displacements than

the higher frequency blastwaves. The block displacements were

insensitive to the direction of blastwave propagation.

JRC values of 6 and 15 were chosen for comparison. A value of

15 was thought to simulate joint conditions before shearing of the

asperities occurred. The lower JRC value is thought to simulate the

joint asperities at the time of failure, when the asperities had

already been worn down.

Tables 4.2 and 4.3 illustrate the effects the JRC has on

dynamic slope stability. Doubling the JRC value for a slope reduces

the block displacements by one half when the slopes are unsaturated or

the water table is low (low static pore pressure). However, the JRC 47

▪ P•••• • 1.••• I..., •

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Lr)

co

=OW

n•n•n ▪ .1111, Cd =NED c:r 4-) cd 41.n cx.1 .•••. - un •"1

••=1. ••n cd ••••••n1.1

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Table 4.1 Final Block Displacements for JRC = 6 and a Low Water Table with Variable Input Motions.

Mass Input Displacements Mass Input Displacements No. Motion (m) No. Motion (m)

1 Earth- 0.40 6 Blast- 0.008 quake wave 2 0.53 7 Propa- 0.009 gating 3 0.53 8* Upslope 0.220

4 0.53 9* 0.221

5 0.53 10 0.221

6 0.78 1 Blast- 0.004 wave 7 0.89 2 Propa- 0.005 gating 8* 1.18 3 Down- 0.005 slope 9* 1.20 4 0.005

10 1.20 5 0.005

1 Blast 0.004 6 0.008 wave 2 Propa- 0.005 7 0.009 gating 3 Upslope 0.005 8* 0.220

4 0.005 9* 0.220

5 0.005 10 0.221

*Water Present in the Joints. 49

Table 4.2 , Final Block Displacements for JRC . 6 and an Earthquake Input Motion.

_ Mass Water Displacements Mass Water Displacements No. Table (m) No. Table (m)

1 Below 0.40 6 Low 0.78 Failure 2 Plane 0.53 7 0.89

3 0.53 8* 1.18

4 0.53 9* 1.20

5 0.53 10 1.20

6 0.61 1 High 0.40

7 0.61 2 0.53

8 0.61 3 0.53

9 0.62 4 0.53

10 0.62 5 0.53

1 Low 0.40 6* 1.22

2 0.53 7* 5.59

3 0.53 8* 73.69

4 0.53 9* 99.83

5 0.53 10* 100.32

*Water Present in the Joints. 50

Table 4.3. Final Block Displacements for JRC = 15 and an Earthquake Input Motion.

Mass Water Displacements Mass Water Displacements No. Table (m) No. Table (m)

1 Below 0.07 6 Low 0.45 Failure 2 Plane 0.24 7 0.45

3 0.24 8* 0.45

4 0.24 9* 0.45

5 0.24 10 0.45

6 0.25 1 High 0.06

7 0.25 2 0.25

8 0.25 3 0.25

9 0.25 4 0.25

10 0.25 5* 0.25

1 Low 0.06 6* 0.57

2 0.25 7* 1.96

3 0.26 8* 56.33

4 0.26 9* 94.84

5 0.26 10* 96.71

*Water Present in the Joints. 51 has a negligible affect on the block displacements when the static pore pressure is very high, as with an elevated water table.

Three different phrentic surfaces (Figure 4.5) were invesLigated. The LADRS-MDF analysis clearly demonstrates the destabilizing affects of a high water table (Tables 4.2 and 4.3).

The joint pore water time history of mass Number 8 under an earthquake load is shown in Figure 4.6. The transient pore pressure response is very similar to the input ground motion, Figure 4.4a).

When the amplitude of the earthquake acceleration is maximum, the transient pore pressure is maximum. The transient pore pressure is minimum when the input acceleration is a minimum.

The region between A and C in Figure 4.6 has an excess pore pressure buildup. This is when the joint displacement is less than

3/10 of the displacement needed to reach peak shear strength (around 1% of the joint length). Once 0.36 is reached, the joint starts to dilate.

Intuitively, the transition from pt. C to C' should be gradual, and not abrupt as in Figure 4.6, i.e., the excess pore pressure should dissipate, not disappear. Sadigh (1978) studied the drainage effects on the excess pore pressure generation and dissipation for rockf ill dams. Figure 4.7a and b combined can be assumed to simulate the water force in Figure 4.6, pts. A-B-C-C'. Sadigh assumes unidirectional drainage away from the impermeable core, which would resemble the flow of water in a rock joint. Figure 4.7b is compatible with a rock joint model that generates and dissipates pore pressure before joint

•

52

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r..•••n1111,

nn•111n

(ÛI x suovi)N) aplod ialrm oTumuSa 8 54

I.)-- Drained Upstream Slope Impermeable Core 100 \ Assumed Distribution of Excess Pore (a) Dissipation allowed 80 Pressure U t = 3 seconds between 3 and 5 seconds in.fsec 60

40

20 ea o o 50 100 150 200 300 z

1 100 80 (b) Allowing for generation o and dissipation during 3 seconds c 60

— 40

20 4-, o o 50 100 150 200 250 300

o a. E loo U1 80 (c) Allowing for generation and dissipation during 5 seconds 60

40

20

O o 50 100 150 200 250 300 Distance from Upstream Slope - feet

Figure 4.7 Distribution of Excess Pore Water Pressure Along a 300-Ft Long Horizontal Drainage Path. (Sadigh, 1978) 55 dilation occurs (pt. A-B-C in Figure 4.6). Point C can be thought to be equal to the point on Figure 4.7b where the K = 10 in/sec curve plots the maximum excess pore pressure percent, around 40%. The transition from C to C' is simulated by Figure 4.7a, and the corresponding maximum pore pressure percent would be around 60%. Point

C' would then be 40% of 60% of the maximum excess pore pressure, or 24% of the maximum. Hence, one could assume that the dynamic water force in Figure 4.6 should be 25% higher at pt. C' than is shown.

When 0.3d is reached, joint dilation occurs and excess pore pressure generation is absent. The dynamic water force response at this point is shown as C'-D-E-F in Figure 4.6. When peak shear strength is achieved, joint dilation ends and the dynamic excess pore pressure buildup begins anew (point F).

Figure 4.8 graphs the total displacement of Mass Number 8 versus time, as calculated by LADRS-MDF. Figure 4.6 is the corresponding dynamic pore pressure for Mass Number 8. The displacements in the range A-B-C reflect the transient as well as the excess water pressure in the joint. When the excess water pressure is dissipated, as in points C-D-E-F, the slope of the displacement versus time curve decreases. When the excess pore pressure begins to build, point F, the slope of the curve in Figure 4.8 increases.

These two figures illustrate the dependance of the block displacements to the transient and excess pore water pressure. At relatively low water pressures, the transient water pressure affects block displacement more than the excess pore pressure. At relatively 56

(Rialnv ) 57 moderate water pressures, points B-C and F-G, both the excess and transient water pressures affect block displacements. When the excess pore pressure reaches a critical point, as in point G in this example, the excess pore pressure affects the block displacements much more than the transient water pressure.

Concluding Remarks

Barton's shear strength criteria requires only three input parameters, a roughness, compressive and friction component. These parameters are easy and inexpensive to estimate or measure.

Glass' LADRS-MDF uses the whole time history of ground motion as input, thus using all the dynamic characteristics of motion, such as frequency, duration and magnitude. LADRS-MDF uses easily obtainable parameters (Barton's) for analyzing the slope stability. In many engineering problems, LADRS-MDF could be used to evaluate the dynamic stability of slopes.

Pseudo-static techniques can be an oversimplification because the time history of ground motion is not taken into account. Inserting pore pressures into the analysis may further reduce the validity of using pseudo-static techniques because the pore pressure response to dynamic loads is also time-dependent.

Most of the published dynamic pore pressure analyses necessitates input parameters that are complicated and expensive to define accurately. The simplified dynamic pore pressure equations proposed by the author take into account the generation and dissipation of pore pressure and ties the cyclic response of the pore pressures to 58 the input ground motion. Equations 4.2, 4.3 and 4.4 can be used in conjunction with LADRS-MDF to analyze dynamic slope stability problems.

Research in the prediction of dynamic pore water pressure response of rock slopes is needed. The proposed analysis in this paper needs laboratory and field experiments for verification. APPENDIX A

INPUT DATA FOR THE HOMESTAKE PITCH

LADRS-MDF ANALYSIS

59 60

Table A-1. Rock Block Data.

Failure Residual Plane Mass Friction Joint Joint JCS Slope Mass (x106) Angle Length Area (x103) Angle No. (kg) (Degrees) (m) (m2) (N/m2) (Degrees)

1 0.532 25.5 28.9 843 100.1 20

2 1.34 25.5 22.95 580 100.1 20

3 4.28 25.5 37.88 1431 100.1 20

4 11.2 25.5 68.02 4714 100.1 20

5 21.1 25.5 98.60 9813 100.1 20

6 12.0 23.4 51.08 2672 100.1 20

7 5.77 23.4 28.93 795 100.1 20

8 12.0 23.4 68.09 4564 100.1 20

9 12.4 23.4 89.30 8093 100.1 20

10 8.53 23.4 138.24 19,180 100.1 20 61

Table A-2. Variable Input Data.

Wavetype, 1 = Earthquake Static Water 2 = Blastwave Propagating Upslope Pressure 3 = Blastwave Propagating Downslope JRC Along Joint

1 6 None

1 6 Low Water Table

1 6 High Water Table

1 15 None

1 15 Low Water Table

1 15 High Water Table

2 6 Low Water Table

3 6 Low Water Table APPENDIX B

A COMPARISON OF THE DISPLACEMENTS CALCULATED BY

LADRS-MDF WHEN VARYING THE JRC AND WATER TABLE

62 63

Table B. Displacements for the Rock Blocks Using an Earthquake Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope.

DISPLACEMENTS

Water Absent Low Water Table High Water Table Mass Time JRC = 6 JRC = 15 JRC = 6 JRC = 15 JRC = 6 JRC = 15 # (sec) (m) (m) (m) (m) (m) (m)

1 1 0.011 0.006 0.011 0.003 0.009 -0.001

2 0.100 0.030 0.100 0.019 0.097 0.020

3 0.177 0.052 0.177 0.041 0.174 0.042

4 0.285 0.092 0.285 0.081 0.283 0.083

5 0.338 0.094 0.338 0.083 0.335 0.084

6 0.387 0.096 0.386 0.085 0.384 0.087

7 0.406 0.089 0.406 0.078 0.403 0.080

8 0.401 0.074 0.401 0.063 0.398 0.064

2 1 0.014 0.011 0.014 -0.003 0.018 0.005

2 0.129 0.064 0.128 0.058 0.131 0.061

3 0.228 0.115 0.228 0.115 0.229 0.119

4 0.367 0.192 0.367 0.200 0.368 0.196

5 0.434 0.221 0.434 0.230 0.435 0.227

6 0.494 0.246 0.493 0.257 0.494 0.247

7 0.523 0.250 0.523 0.260 0.523 0.254

8 0.526 0.243 0.525 0.253 0.525 0.247 64

Table B. Displacements for the Rock Blocks Using an Earthquake Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

DISPLACEMENTS

Water Absent Low Water Table High Water Table Mass Time JRC = 6 JRC = 15 JRC = 6 JRC = 15 JRC = 6 JRC = 15 # (sec) (m) (m) (m) (m) (m) (m)

3 1 0.017 0.012 0.017 -0.001 0.019 0.005

2 0.134 0.066 0.133 0.070 0.134 0.068

3 0.229 0.121 0.229 0.124 0.229 0.120

4 0.369 0.196 0.368 0.206 0.369 0.199

5 0.437 0.223 0.436 0.236 0.436 0.228

6 0.494 0.246 0.494 0.258 0.495 0.251

7 0.523 0.251 0.523 0.263 0.523 0.255

8 0.526 0.243 0.525 0.256 0.525 0.247

4 1 0.017 0.011 0.017 0.006 0.019 0.006

2 0.134 0.067 0.134 0.070 0.134 0.068

3 0.233 0.121 0.232 0.124 0.234 0.121

4 0.372 0.196 0.372 0.207 0.374 0.200

5 0.438 0.224 0.438 0.236 0.440 0.229

6 0.494 0.247 0.494 0.258 0.495 0.251

7 0.524 0.251 0.523 0.263 0.523 0.255

8 0.526 0.243 0.525 0.256 0.526 0.247 65

Table B. Displacements for the Rock Blocks Using an Earthquake Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

DISPLACEMENTS _ Water Absent Low Water Table High Water Table Mass Time JRC = 6 JRC = 15 JRC = 6 JRC = 15 JRC = 6 JRC = 15 # (sec) (m) (m) (m) (m) (m) (m)

5 1 0.020 0.011 0.020 0.010 0.019 0.006

2 0.136 0.067 0.136 0.073 0.136 0.068

3 0.233 0.122 0.233 0.127 0.234 0.121

4 0.372 0.197 0.372 0.210 0.374 0.202

5 0.438 0.225 0.438 0.236 0.440 0.230

6 0.495 0.247 0.495 0.258 0.496 0.251

7 0.524 0.251 0.523 0.263 0.524 0.255

8 0.526 0.243 0.525 0.256 0.527 0.247

6 1 0.022 0.011 0.037 0.012 0.045 0.023

2 0.150 0.072 0.185 0.106 0.223 0.159

3 0.260 0.123 0.320 0.204 0.362 0.258

4 0.403 0.202 0.495 0.342 0.543 0.393

5 0.487 0.233 0.601 0.402 0.664 0.458

6 0.563 0.257 0.697 0.443 0.794 0.515

7 0.605 0.262 0.758 0.460 0.972 0.553

8 0.614 0.252 0.781 0.453 1.217 0.569 66

Table B. Displacements for the Rock Blocks Using an Earthquake Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

DISPLACEMENTS

Water Absent Low Water Table High Water Table Mass Time JRC = 6 JRC = 15 JRC = 6 JRC = 15 JRC = 6 JRC = 15 # (sec) (m) (m) (m) (m) (m) (m)

7 1 0.024 0.011 0.044 0.013 0.070 0.053

2 0.151 0.070 0.214 0.214 0.286 0.233

3 0.260 0.123 0.361 0.245 0.464 0.383

4 0.404 0.204 0.553 0.363 0.701 0.586

5 0.487 0.231 0.675 0.403 1.177 0.778

6 0.563 0.255 0.780 0.444 2.000 0.936

7 0.605 0.262 0.855 0.460 3.416 1.274

8 0.614 0.252 0.888 0.453 5.589 1.957

8 1 0.023 0.011 0.049 0.014 0.662 0.351

2 0.151 0.070 0.255 0.125 2.795 1.351

3 0.260 0.124 0.391 0.247 7.008 3.562

4 0.405 0.203 0.567 0.365 13.848 7.876

5 0.488 0.231 0.675 0.403 23.83 15.070

6 0.563 0.255 0.785 0.444 37.13 25.500

7 0.605 0.262 0.953 0.461 53.83 39.320

8 0.614 0.252 1.181 0.453 73.69 56.330 67

Table B. Displacements for the Rock Blocks Using an Earthquake Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

DISPLACEMENTS

Water Absent Low Water Table High Water Table Mass Time JRC = 6 JRC = 15 JRC = 6 JRC = 15 JRC = 6 JRC = 15 it (sec) (m) (m) (m) (m) (m) (m)

9 1 0.023 0.012 0.049 0.015 1.372 1.187

2 0.150 0.071 0.329 0.126 5.446 4.651

3 0.260 0.125 0.504 0.285 12.789 11.300

4 0.404 0.203 0.680 0.366 23.460 21.260

5 0.487 0.232 0.795 0.404 37.550 34.660

6 0.564 0.256 0.893 0.445 55.000 51.410

7 0.606 0.262 0.996 0.461 75.85 71.560

8 0.615 0.251 1.202 0.453 99.830 94.840

10 1 0.024 0.012 0.052 0.016 1.378 1.240

2 0.151 0.073 0.339 0.126 5.514 4.890

3 0.261 0.127 0.506 0.286 12.930 11.800

4 0.404 0.205 0.681 0.366 23.670 22.050

5 0.488 0.233 0.797 0.405 37.830 35.700

6 0.564 0.258 0.895 0.445 55.350 52.740

7 0.606 0.262 0.997 0.461 76.280 73.160

8 0.615 0.251 1.202 0.453 100.320 96.710 APPENDIX C

DISPLACEMENTS CALCULATED BY LADRS-MDF WITH BLAST WAVES

68 69

Table C. Displacements for the Rock Blocks Using Blastwave Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope.

Displacements for JRC . 6, Low Water Table, and a Blastwave Traveling

Mass Time Down Slope Up Slope No. (sec) (m) (m)

1 0.1 0.0007 0.0008

0.2 0.0018 0.0019

0.3 0.0026 0.0027

0.4 0.0031 0.0032

0.5 0.0035 0.0037

0.6 0.0038 0.0040

0.7 0.0038 0.0040

0.8 0.0037 0.0039

2 0.1 0.0009 0.0010

0.2 0.0023 0.0023

0.3 0.0033 0.0034

0.4 0.0038 0.0039

0.5 0.0044 0.0045

0.6 0.0048 0.0049

0.7 0.0048 0.0050

0.8 0.0048 0.0050 70

Table C. Displacements for the Rock Blocks Using Blastwave Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

Displacements for JRC = 6, Low Water Table, and a Blastwave Traveling

Mass Time Down Slope Up Slope No. (sec) (m) (m)

3 0.1 0.0009 0.0010

0.2 0.0023 0.0024

0.3 0.0033 0.0035

0.4 0.0039 0.0041

0.5 0.0045 0.0046

0.6 0.0049 0.0050

0.7 0.0050 0.0051

0.8 0.0050 0.0051

4 0.1 0.0009 0.0010

0.2 0.0023 0.0024

0.3 0.0034 0.0035

0.4 0.0039 0.0041

0.5 0.0045 0.0046

0.6 0.0049 0.0051

0.7 0.0050 0.0051

0.8 0.0050 0.0051 71

Table C. Displacements for the Rock Blocks Using Blastwave Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

Displacements for JRC . 6, Low Water Table, and a Blastwave Traveling

Mass Time Down Slope Up Slope No. (sec) (m) (m)

5 , 0.1 0.0010 0.0011

0.2 0.0024 0.0025

0.3 0.0034 0.0035

0.4 0.0040 0.0041

0.5 0.0045 0.0046

0.6 0.0050 0.0051

0.7 0.0050 0.0051

0.8 0.0050 0.0051

6 0.1 0.0012 0.0014

0.2 0.0030 0.0031

0.3 0.0044 0.0046

0.4 0.0054 0.0055

0.5 0.0063 0.0065

0.6 0.0071 0.0073

0.7 0.0075 0.0076

0.8 0.0077 0.0079 72

Table C. Displacements for the Rock Blocks Using Blastwave Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

Displacements for JRC = 6, Low Water Table, and a Blastwave Traveling

Mass Time Down Slope Up Slope No. (sec) (m) (m)

7 0.1 0.0015 0.0015

0.2 0.0034 0.0034

0.3 0.0050 0.0050

0.4 0.0061 0.0061

0.5 0.0071 0.0071

0.6 0.0081 0.0080

0.7 0.0085 0.0085

0.8 0.0088 0.0088

8 0.1 0.0016 0.0016

0.2 0.0037 0.0038

0.3 0.0076 0.0078

0.4 0.0177 0.0018

0.5 0.0394 0.0408

0.6 0.0787 0.0812

0.7 0.1422 0.1461

0.8 0.2197 0.2200 73

Table C. Displacements for the Rock Blocks Using Blastwave Input Motion Calculated by LADRS-MDF for the Homestake Pitch Slope (Continued).

Displacements for JRC . 6, Low Water Table, and a Blastwave Traveling

Mass Time Down Slope Up Slope No. (sec) (m) (m)

9 0.1 0.0019 0.0016

0.2 0.0052 0.0043

0.3 0.0137 0.0124

0.4 0.0322 0.0303

0.5 0.0611 0.0589

0.6 0.1005 0.0978

0.7 0.1509 0.1481

0.8 0.2206 0.2204

10 0.1 0.0019 0.0017

0.2 0.0052 0.0043

0.3 0.0140 0.0124

0.4 0.0326 0.0308

0.5 0.0614 0.0591

0.6 0.1009 0.0983

0.7 0.1513 0.1483

0.8 0.2207 0.2207 REFERENCES

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