Influence of ice to the stability of engineering rock slopes and ice securing measures in Cold Regions

Miguel A. Sánchez Moreno

June 2018

MASTER THESIS

Department of Geoscience and Petroleum Norwegian University of Science and Technology

Department of Civil Engineering Technical University of Denmark

Supervisor 1: Charlie Chunlin Li (NTNU) Supervisor 2: Katrine Alling Andreassen (DTU) i

Preface

Engineering Geology and Rock Mechanics, Master’s Thesis (TGB4930) in the Department of Geoscience and Petroleum at NTNU as part of the study program MSc Cold Climate Engineer- ing during the spring semester of 2018.

The basis of this master thesis comes from my interest in Arctic Geoengineering. During the autumn semester of 2017, I worked on a specialization project which was focus on analyzing two rock cuts near Mo i Rana, Norway due to the need to install icenets to prevent icicles for- mation. The field observations revealed frost weathering along the slopes due to high content of moisture and freeze-thawing cycles. This master thesis follows on the influence of ice to the stability of engineering rock slopes.

Trondheim, 07-06-2018

Miguel Angel Sanchez Moreno ii

Acknowledgment

First and foremost I would like to thank my supervisor Charlie Li, who has guided me through- out my thesis with useful comments and remarks as well as introducing me to the topic on the previous specialization project.

I would like to express my thanks to Mikael Bergman from Statens vegvesen who welcomed me during my fieldwork for the specialization course, providing me several reports and driving me around to check how different instabilities have been solved in different projects. I would also like to thank Martin Jungersen from the Qeqqata Municipality for its kind interest on my research and its contribution granting me the possibility to showcase Greenlandic challenges.

Next, my thanks to the all the people involved in the Cold Climate Engineering program giving me the opportunity to study and learn from experts within different international back- grounds in such a challenging environment as is the Arctic. Special thanks to Gunvor Marie Kirkelund for her efforts, guidancee and continuous help and to my colleagues, Ivan Vakulenko and Lorenzo Cicchetti for stimulating discussions, some long sleepless nights working before deadlines and for all the adventures we had in the past two years.

Last but not the least, I would like to thank my family and friends who have always being by my side and who constantly encouraged and motivated me to pursue my interests.

M.A.S.M.

Miguel Angel Sanchez Moreno iii

Abstract

In cold regions, freezing is an important factor for weathering processes in rock slopes. The presence of ice in discontinuities can contribute to maintain the stability of rock slopes. But degrading permafrost and thawing cycles can be considered an important factor for rock slope failures in arctic environments (Michael et al. (2012)). The project aims to the influence of ice and thawing to the stability of a rock cut rock slope or another type of engineering rock slope. The cycle of ice and thawing will periodically change the stress state in the rock mass and grad- ually changes the rock physical and mechanical properties, such as weathering and weakening of the rock mass in the long run.

Davies et al. (2000) showed through direct shear box test that the stiffness and strength of an ice filled joint are a function of normal stress and its temperature. Results revealed that a jointed rock slope that is stable without ice in the joints and is also stable when ice is present at low temperatures will become unstable as the ice thaws. A direct impact of icing to the rock mass is the frost weathering in rock discontinuities which may influence the stability of an engi- neering slope in joint rock masses. Water pressure and volumetric expansion near rock surface influence the rock slope stability due to shear stresses and reducing its resistance.

Preventing measures from literature and commonly used in Norway are presented Norem (1998). Later four case studies are displayed, showcasing different locations in cold regions. The case studies expose the ice problems defined and helps to define the models used. Two simpli- fied cases of possible rock slopes are modeled to account for the ice filled fractures and support the assumptions based on literature. RocPlane 3.0, RocTopple 1.0 and Phase2 9.0 have been used to evaluate a planar sliding failure and a toppling failure in rock slopes. The models aim to show the ice induced forces as destabilizing forces that could compromise the stability of a specific wedge which can lead to an induce failure of the rock slope.

Rock slopes become unstable driven by changes in temperature and precipitation condi- tions. Generally, destabilization on rock slopes tends to occur on thawing periods. Hence, critical slope stability results are expected in warm frozen areas where both ice and water are present. Ice exerts certain force on joint rock slopes and can induce failure in the jointed rock mass. Contents

Preface...... i Acknowledgment...... ii Abstract...... iii

1 Introduction 2 1.1 Background ...... 3 1.2 Objectives ...... 4 1.3 Approach ...... 4 1.4 Outline ...... 5

2 Theory and Analysis of Rock Slope Engineering 6 2.1 Stability of Engineering Rock Slopes ...... 6 2.1.1 Features, Dimensions and Design ...... 6 2.1.2 Bedrock Properties ...... 8 2.1.3 Causes of Slope Failures ...... 10 2.1.4 Modes of Slope Instability ...... 12 2.2 Effect of Ice on Jointed Rock Slopes ...... 15 2.2.1 Water Sources in Rockcuts ...... 16 2.2.2 Frost Weathering ...... 20

3 Preventing Measures to Avoid Ice Presence 22 3.1 Drainage of Surface Water and Groundwater ...... 22 3.2 Streams and Water Flows ...... 23 3.3 Ice Nets ...... 24

4 Case Study 26 4.1 Sarfannguit, Greenland ...... 27 4.2 Roadcuts in E6 near Mo i Rana ...... 29 4.2.1 Roadcut HP8 5447 ...... 30 4.2.2 Roadcut HP9 934 ...... 31 4.3 Nessettunnelen ...... 32

iv CONTENTS v

4.4 Nordmarkstunnelen South Entrance and Sidewall...... 35

5 Numerical Modeling 38 5.1 Single Crack, Planar Failure ...... 40 5.2 Toppling Failure Mode Case ...... 42

6 Conclusions 48 6.1 Summary and Conclusions ...... 48 6.2 Discussion ...... 50 6.3 Recommendations for Further Work ...... 52

Bibliography 53

A RocPlane 3.0 Simulations 55

B RocTopple 1.0 Simulations 65 List of Figures

1.1 Jointed bedrock near the harbor in Sisimut, Greenland. Photo: Ivan Vakulenko.. 3 1.2 Ilustration of frost weathering. Picture A displays some joints and rainfall. Picture B displays ice weathering ...... 4

2.1 Parameters that characterize the discontinuities in rock mass. Figure after Wyllie and Mah (2004) ...... 8 2.2 Geometry of slope exhibiting plane failure: (a) cross-section showing planes form- ing a plane failure;(b) release surfaces at ends of plane failure; (c) unit thickness slide used in stability analysis Wyllie and Mah (2004)...... 12 2.3 Geometric conditions for wedge failure: (a) view of wedge failure; (b) stereoplot showing the orientation of the line of intersection (c); view of slope at right angles to the line of intersection; (d) stereonet showing the range in the trend of the line of intersection Wyllie and Mah (2004) ...... 13 2.4 (a) block toppling of columns of rock containing widely spaced orthogonal joints; (b) flexural toppling of slabs of rock dipping steeply into face; (c) block flexure top- pling characterized by pseudo-continuous flexure of long columns through accu- mulated motions along numerous cross-joints (Wyllie and Mah (2004))...... 14 2.5 Circum-Arctic map of permafrost and ground-ice conditions. Brown, J., O.J. Ferri- ans, Jr., J.A. Heginbottom, and E.S. Melnikov ...... 15 2.6 Runoff water frozen in a rockcut at Sørkilhaugen, Meråkerbanen. Photo: A. Liereng 16 2.7 Rock slope where water is frozen on the rockwall from the mountainside, generat- ing small rockfalls and icicles. Photo: Statens Vegvesen (Jens Tveit) ...... 17 2.8 Rock slope 20km South of Mo i Rana. Streams are present in the area discharging in the fjord and the road has cutted the natural flow of those streams. Photo: Miguel Sanchez ...... 18 2.9 Grounwater causing icicles along the rockwall. Photo: A.Liereng ...... 19 2.10 Grounwater leaking out at the contact between the soil and the bedrock, freezing rapidly and forming large icicles. Photo: A.Liereng ...... 19 2.11 phase diagram of water. Displaying critical pressure around -22degrees ...... 20

vi LIST OF FIGURES vii

2.12 The relationship between peak shear strength and normal stress at three different test temperatures for frozen joint specimens and for an unfrozen joint Davies et al. (2001)...... 21

3.1 Illustration of a blasted pocket in the rockface which allows the water to flow below the road. (Norem (1998)) ...... 23 3.2 The net ends with a wire thrown through the net masks and bolted into the rock. The right picture shows the ice grows from the net so that water can leak behind the ice Photo A. Liereng ...... 24 3.3 Scheme of an icenet mounted by Statens vegvesen...... 25

4.1 Location Of the Settlement of Sarfannguit ...... 27 4.2 Yellow areas mark the zones where the fallen blocks detached. Photo: Martin Jun- gensen ...... 28 4.3 Left picture displays the sliding plane in black and bedrock joints in red. Left pic- ture displays the fallen blocks. Photo: Martin Jungensen ...... 28 4.4 Geological map displaying roadcuts location. Roadcut1 is roadcut HP8 5447 and Roadcut2, HP9 934. Norges Geologiske Undersøkelse ...... 29 4.5 Rock slope E6 at HP8 5447. Photo: Mickael Bergman ...... 30 4.6 Hazards observed during fieldwork, October 2017. Photo: Miguel Sanchez . . . . . 30 4.7 Rock slope E6 at HP9 934 Photo: Mickael Bergman ...... 31 4.8 Hazards observed during fieldwork, October 2017. Photo: Miguel Sanchez . . . . . 31 4.9 The picture shows a rockfall dated from October 2014. From the left picture, the yellow area marks the detachment area and the red area shows several blocks de- posited on the sideroad. The right photo showws that the block presents two joints families forming a wedge dipping to the road. Ice can be observed inside the joints. Photo: Mikael Bergman. Bergman (2016) ...... 32 4.10 Picture also dated from October 2014. The yellow area shows a block in a critical state. The block presents two joints families forming a wedge dipping to the road. Ice can be observed inside the joints. Photo: Mikael Bergman. Bergman (2016) . . 33 4.11 Picture from October 2017. It can be seen that the wedging loose block has been secured with rockbolts. Some additional bolts have been also used on the left side where some minor discontinuities can be observed. Photo: Miguel A. Sanchez . . 34 4.12 Picture from October 2013. Clear discontinuities are observed on the left picture. The discontinuitites are oriented sub-horizontally. The right picture marks the areas were the failure occurred. The red and green areas display hanging sections and the yellow part show borken bolts. Photo: Mikael Bergman ...... 35 viii LIST OF FIGURES

4.13 Pictures from October 2013. Details from thebroken bolts that were holding the blocks Photo: Mikael Bergman...... 35 4.14 Picture from October 2013. Yellow area marks a clear discontinuity block. Some ice has been observed from inflow water trhough the joint. The red circle marks a bolted area which is also displayed in figure 4.15. Photo: Mikael Bergman . . . . . 36 4.15 Picture from October 2017. THe main discontinuity is mark by the difference in color. The lower section of the slope presents a more weathered color due to the water flowing from the discontinuity. The red circle marks the same area observed in figure 4.14 from 2013. It can be observed an increase in the number of joints. Photo: Miguel A. Sanchez ...... 37 4.16 Picture from October 2013.Details of the east rockwall from the South entrance of the tunnel. Left picutre displays a block in contact with the top soil layer and a wide discontinuity. The right picture shows the water flowing through the joints. Photo: Mikael Bergman ...... 37

5.1 Sketches of two failure modes studied. The left sketch displays a planar sliding failure. The right sketch shows a weathered rock slope with a set of joints making the blocks to topple down...... 38 5.2 Slope near Mosjøen. The vertical face displays some discontinuities where water is flowing out. Photos: Miguel Sanchez ...... 39 5.3 Picture shows a slope were some blocks fell in 2014. The sketch shows the orien- tation of the foliation causing the hazard. Photo: Statens Vegvesen Bergman (2014) 39 5.4 RocPlane planar wedge stability analysis in dry conditions.Factor of safety of 2.77 . 40 5.5 RocPlane planar wedge stability analysis in saturated conditions.Factor of safety of 2.37 ...... 41 5.6 RocPlane planar wedge stability analysis with ice stresses. Factor of safety of 0.97 for an ice pressure of 0.8 MPa ...... 41 5.7 Roctopple failure case in dry conditions ...... 42 5.8 Roctopple failure case in saturated conditions ...... 42 5.9 Roctopple imported geometry to phase2 analysis in saturated conditions. Display- ing mean stress ...... 43 5.10 Roctopple imported geometry to phase2 analysis in saturated conditions. Display- ing shear stress ...... 44 5.11 Roctopple imported geometry to phase2 analysis in saturated conditions. Display- ing total displacement ...... 44 5.12 Roctopple imported geometry to phase2 analysis with a single joint containing ice. Displaying shear stress ...... 45 LIST OF FIGURES 1

5.13 Roctopple imported geometry to phase2 analysis with a single joint containing ice. Displaying total displacement ...... 45 5.14 Roctopple imported geometry to phase2 analysis with three joints containing ice. Displaying shear stresst ...... 46 5.15 Roctopple imported geometry to phase2 analysis with three joints containing ice. Displaying total displacement ...... 46 5.16 Roctopple imported geometry to phase2 analysis with all joints containing ice. Displaying shear stress ...... 47 5.17 Roctopple imported geometry to phase2 analysis with all joints containing ice. Displaying total displacement ...... 47

6.1 Road in Sisimiut, next to the harbor. In both pictures it can be observed how some blocks have fallen in a plane paralel to the slope orientation. Photos: Miguel Sanchez 49 6.2 Factor contributing to the gap between current and long-term rates of rockwall erosion in cold mountains. Matsuoka and Murton (2008) ...... 52 Chapter 1

Introduction

When building new roads or widen existing ones, part of a hillside might need to be removed. In road construction, a cut slope is defined as a soil or rock surface that remains above the road after the material has been removed. The design of a rock slope can be defined by the engineer- ing requirements of the cut and by the geologic conditions of the site.

In general, the geology and the orientation and condition of the discontinuities present in a rock mass are the most significant factors determining the stability od a rock slope. In practice, the design process is a balance between stability and other elements such as its constructibility, economics, and the accepted level of risk. Steeper cut slope angles result in lower construction costs due to smaller volume of rock excavations. But rock cuts steeper than its controlling geo- logic structure may require expensive maintenance and wider fallout areas.

Another important condition to take into account is the geographic location, specially in cold regions. Depth and degree of weathering vary with climate. The number of cycles of freez- ing and thawing per year are also tied to the climate. The topographic location affects the depth and degree of weathering and the movement of ground water. The orientation of the cut slope fixes the exposure of the slope to the sun and therefore affects the number of cycles of freezing and thawing, and wetting and drying per year. Additionally, the length of time that ice would form on the slope during the winter can be measured.

2 1.1. BACKGROUND 3

1.1 Background

In cold regions, freezing is an important factor for weathering processes in rock slopes. The presence of ice in discontinuities can contribute to maintain the stability of rock slopes. Dur- ing winter, the bare bedrock in rock cuts makes very favorable conditions for ice to form. The surface of the rock is cooled down easier than surrounding soils or vegetation due to its thermal properties. Early winter, the bedrock will therefore reach sub-zero temperatures while still being fed with water from uphill soil cover. This water will freeze progressively faster as the outside air temperature gets colder.

Although is accepted that the presence of ice in discontinuities contributes to maintain the stability of rock slopes Bjerrum and Jørstad(1968), there has been also studies showing that melting ice in joints is an important factor for rock slope failures in Arctic environments. The cycle of ice and thawing will periodically change the stress state in the rock mass and gradually changes the rock physical and mechanical properties, such as weathering and weakening of the rock mass in the long run. Davies Davies et al. (2000) showed through direct shear box test that the stiffness and strength of an ice filled joint are a function of normal stress and its tempera- ture. Results revealed that a jointed rock slope that is stable without ice in the joints and is also stable when ice is present at low temperatures will become unstable as the ice thaws.Figure 1.1 shows a block which an open joint that is being opened. Melting of ice could induce its failure

Figure 1.1: Jointed bedrock near the harbor in Sisimut, Greenland. Photo: Ivan Vakulenko 4 CHAPTER 1. INTRODUCTION

1.2 Objectives

The main objectives of this Master’s project are

1. Literature review of frost weathering applied to engineering rock slopes in cold region in order to give an outline of the current state of the art and future directions.

2. Define how ice influences the stability of engineering rock slopes. In particular, the effects of volumetric expansion as liquid water turns into ice.

1.3 Approach

Water pressure and volumetric expansion near rock surface influence the rock slope stability due to shear stresses and reducing its resistance. Analysis of field observations and literature re- view gives an understanding on how frost weathering (figure 1.2) affects the rock slope stability and achieves the first objective.

Based on the knowledge obtained, two simplified geometry models are proposed and tested: A planar sliding failure and a toppling failure. Ice properties have been taken into account in or- der to use ice-induced pressure into the jointed bedrock. As a result, volumetric expansion as liquid water turns into ice is assessed as a hazard that may provoke slope failure.

Figure 1.2: Ilustration of frost weathering. Picture A displays some joints and rainfall. Picture B displays ice weathering 1.4. OUTLINE 5

1.4 Outline

Overview of the structure of the report:

• Preface

• Acknowledgments

• Abstract

• Chapter 1. Introduction: Structure already discussed in this chapter.

• Chapter 2. Theoretical background: Analysis of Rock slope engineering. First an intro- duction to rock slope stability and its design is given. Later a basic bedrock description, causes of slope failure and its mode are presented. Finally, the ice on jointed bedrock are described.

• Chapter 3. Preventing measures to avoid ice presence. A description of currently used measures in Norway is given.

• Chapter 4. Case studies: Four different cases are presented. Two cases with the prob- lem description and proposed solutions and two cases that instabilities have been already reinforced.

• Chapter 5. Numerical modeling. Two simplified models are presented based on literature and field observations.

• Chapter 6. Conclusions, discussion, and recommendations for further work.

• Bibliography

• Appendix A: RocPlane 3.0 Simulations.

• Appendix B: RocTopple 1.0 Simulations. Chapter 2

Theory and Analysis of Rock Slope Engineering

2.1 Stability of Engineering Rock Slopes

The required stability conditions of rock slopes will vary depending on the type of project and the consequence of failure. For example, for cuts above a highway carrying high traffic volumes it will be important that the overall slope be stable, and that there be few if any rock falls that reach the traffic lanes. This will often require both careful blasting during construction, and the installation of stabilization measures such as rock anchors. Because the useful life of such sta- bilization measures may only be 10–30 years, depending on the climate and rate of rock degra- dation, periodic maintenance may be required for long-term safety (Wyllie and Mah (2004)).

2.1.1 Features, Dimensions and Design

In the design of cut slopes, there is usually little flexibility to adjust the orientation of the slope to suit the geological conditions encountered in the excavation. For example, in the design of a highway, the alignment is primarily governed by such factors as available right-of-way, grades and vertical and horizontal curvature. Therefore, the slope design must accommodate the par- ticular geological conditions that are encountered along the highway. Circumstances where ge- ological conditions may dictate modifications to the slope design include the need for relocation where the alignment intersects a major landslide that could be activated by construction(Wyllie and Mah (2004)).

The common design requirement for rock cuts is to determine the maximum safe cut face angle compatible with the planned maximum height. The design process is a trade-off between stability and economics. That is, steep cuts are usually less expensive to construct than flat

6 2.1. STABILITY OF ENGINEERING ROCK SLOPES 7 cuts because there is less volume of excavated rock, less acquisition of right-of-way and smaller cut face areas. However, with steep slopes it may be necessary to install extensive stabilization measures such as rock bolts and shotcrete in order to minimize both the risk of overall slope instability and rock falls during the operational life of the project.

The design of rock cuts involves the collection of geotechnical data, the use of appropriate design methods, and the implementation of excavation methods and stabilization/protection measures suitable for the particular site conditions 8 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

2.1.2 Bedrock Properties

An important factor to take into account is the geometry of the bedrock. When defining a rock- cut, the orientation and dipping of discontinuities should be accounted since the joints will determine wheter the bedrock can slide or topple. Figure 2.1 shows the different parameters affecting the stability and rock strength. These features describe the geological structure of the bedrock and will provide a useful tool to asses the performance of the bedrock. A full description of each feature can be found in the chapter of "Site investigation and geological data collection" from Rock Slope Engineering. 4th Edition by Wyllie and Mah (2004)

Figure 2.1: Parameters that characterize the discontinuities in rock mass. Figure after Wyllie and Mah (2004) 2.1. STABILITY OF ENGINEERING ROCK SLOPES 9

For the design of a rock slope, the determination of a reliable shear strength vaule is impor- tant. To decide the selection of a proper shear strength, the overall state of the bedrock has to be accounted. In this project the focus in set on complex jointed rock masses which are made up of discontinuities and fractures trough the bedrock. Two strengths are then characterize based on Wyllie and Mah (2004):

• Discontinuities that account for single bedding planes, joints or fault. Properties influ- encing the shear strength include the shape and roughness of the surfaces, the rock on the surface which may be weathered, and infillings that may be low strength or cohesive.

• Rock mass. Factors that influence the shear strength of a jointed rock mass include the compressive strength and friction angle of the intact rock, and the spacing of the discon- tinuities and the condition of their surface.

When determining the shear strength of a jointed bedrock, the critical shear strength is asso- ciated to its discontinuities. There are different procedures for determining the strength proper- ties. In rock slope design, rock is assumed to be a Coulomb material in which the shear strength of the sliding surface is expressed in terms of the cohesion (c) and the friction angle (Φ)(Wyllie and Mah (2004))

Characteristics that affect the shear strength of discontinuities are: continuous length, sur- face roughness, thickness and infillings. For the influence of ice on the stability of rock slopes, its important to determine the influence of water on shear strength of the discontinuities and how its phase change into ice is gonna affec the shear strength. 10 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

2.1.3 Causes of Slope Failures

Is rare to attribute slope failure to any single cause. Usually a number of causes exist simultane- ously to eventually trigger the slope failure Kliche (1999). Varnes classifies these factors into the two major categories Varnes (1978): Firstly, factors that contribute to increased shear stress and secondly, factors that contribute to low or reduced shear strength.

Increased Shear Stress

Factors that contribute to increased shear stress are:

• The removal of lateral support. This is a very common cause of slope instability and may be the result of any of a number of actions, such as erosion by streams or rivers; wave action on lakes and glaciers; previous rockfall, slide, subsidence, or large-scale faulting that creates new slopes; or the work of humans, as in the creation of mines or quarries, the construction of cuts in rock, the removal of retaining structures, or the alteration of water elevation in lakes and reservoirs.

• The addition of surcharge to the slope. Surcharge may be added to a slope by natural ac- tions, such as the weight of rain, hail, snow, or water; by the accumulation of talus material on top of a landslide; by the collapse of accumulated volcanic material; and by vegetation. Surcharge may also be added to a slope by the action of humans, as in the construction of a fill; the construction of mine waste dumps, ore stockpiles, or leach piles; the weight of buildings, other constructed structures, or trains; and the weight of water from leaking pipelines, sewers, canals, and reservoirs

• Transitory earth stresses, which include vibrations from earthquakes, blasting, heavy ma- chinery, traffic, pile driving, vibratory compactors, etc.

• A slow increase in the overall slope of a region as a result of tectonic uplift stresses, stress relief, or other natural mechanisms (i.e., regional tilt).

• The removal of underlying support of the slope. The support underlying a slope may be decreased or removed by undercutting of banks by rivers, streams, or wave actions; sub- aerial weathering, wetting and drying, and frost action; subterranean erosion in which soluble material (such as gypsum) is removed and overlying material collapses; mining, quarrying, road construction, and similar actions; loss of strength or failure in underlying material, such as in clays; and the squeezing out of underlying plastic material.

• Lateral pressure, most commonly from water in pore spaces, cracks, caverns, or cavities. Other sources of lateral pressure include the freezing of water in cracks, swelling of soils as a result of hydration of clay or anhydrite, and the mobilization of residual stresses 2.1. STABILITY OF ENGINEERING ROCK SLOPES 11

• Volcanic processes, such as swelling or shrinking of magma chambers

• Tectonic activities, which may alter the stress fields on a very large scale, causing an in- crease or shift in the direction of geostatic stresses.

• Processes that created the slope. These may include creep on the slope or creep in weak strata below the foot of the slope.

Low or reduced Shear Strength

Factors that contribute to low or reduced shear strength are:

• Factors stemming from the initial state or inherent characteristics of the material. These factors include material composition; texture; and gross structure and slope geometry, i.e., the presence and orientation of discontinuities, slope orientation, the existence of massive beds over weak or plastic materials, and the alternation of permeable beds and weak impermeable beds.

• Changes in shear strength due to weathering and other physicochemical reactions. These changes can include softening of fissured clays; physical disintegration of granular rocks due to the action of frost or by thermal expansion and contraction; hydration or dehydra- tion of clay materials (including the absorption of water by clay minerals, which may de- crease the cohesion; the swelling—and thus loss of cohesion— by montmorillonitic clays; and the consolidation of loess upon saturation); base exchange in clays; migration of wa- ter due to electrical potential; drying of clays, which results in cracks; drying of shales, which creates cracks on bedding and shear planes; and removal of cement within discon- tinuities by solution.

• Changes in intergranular forces due to water content and pressure in pores and fractures, which may result from(1) rapid drawdown of a lake or reservoir, (2) rapid changes in the elevation of the water table, (3) rise of the water table in a distant aquifer, and (4) seepage from an artificial source of water.

• Changes in structure, which can be caused by remolding clays or clay-like materials upon disturbance, by the fissuring of shales and preconsolidated clays, and by the fracturing and loosening of rock slopes due to the release of vertical or lateral restraints upon exca- vation.

• Miscellaneous causes, which can include weakening of a slope due to progressive creep or due to the actions of roots and burrowing animals. 12 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

2.1.4 Modes of Slope Instability

In soil slopes the failure will occur along the line of maximum stress. However, rock slopes failures planes can be predetermined studying the orientation and spacing of the discontinuities of the slope. Types of failure can be classified in: Planar, wedge and toppling failures.

Planar Failure

Planar failure (figure 2.2) the block moves down through a planar surface. The failure surface is commonly a structural discontinuity plane such as a fault or a surface between weathered rock and underlying bedrock. Planar failure occurs along a single discontinuity. For a planar failure, some conditions are necessary: The strike of the failure plane and the strike of the slope face must be within 20º; the dip angle of the failure plane should be less than the dip of the angle of the slope face and the dip of the failure plane must be greather than the friction angle.

Figure 2.2: Geometry of slope exhibiting plane failure: (a) cross-section showing planes form- ing a plane failure;(b) release surfaces at ends of plane failure; (c) unit thickness slide used in stability analysis Wyllie and Mah (2004). 2.1. STABILITY OF ENGINEERING ROCK SLOPES 13

Wedge Failure

Wedge failure (figure 2.3) causes a rock mass to slide along two intersecting discontinuity planes. Wedge failure needs one of the joints intersection to be greater than the friction angle of the joint surface. Wedge failure is is prone in lithology with foliation or cleavages such as shales or limestones.

Figure 2.3: Geometric conditions for wedge failure: (a) view of wedge failure; (b) stereoplot showing the orientation of the line of intersection (c); view of slope at right angles to the line of intersection; (d) stereonet showing the range in the trend of the line of intersection Wyllie and Mah (2004) 14 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

Toppling Failure oppling failure (figure 2.4) occurs due to steep discontinuities in the rock mass and the blocks fall outside the base of the block. Toppling failures develop on closely spaced discontinuities and undercutted beds

Figure 2.4: (a) block toppling of columns of rock containing widely spaced orthogonal joints; (b) flexural toppling of slabs of rock dipping steeply into face; (c) block flexure toppling char- acterized by pseudo-continuous flexure of long columns through accumulated motions along numerous cross-joints (Wyllie and Mah (2004)). 2.2. EFFECT OF ICE ON JOINTED ROCK SLOPES 15

2.2 Effect of Ice on Jointed Rock Slopes

Ground-ice related problems are natural phenomenon that can occur in arctic and subarctic re- gions. The main conditions for ice related problems are enough water supply and sufficient frost conditions. To characterize ice hazards, the risk has to be consider and defined. Risk assessment defines the basis for decision-making and hazard mitigation. The risk is typically defined as the expected value of consequence and to calculate risk quantitatively the following equation is used:

R C p (2.1) = × f where R risk; C = consequence of the hazard, and p = probability of the hazard. Eq. (2.1) = f is applicable when the consequence of a hazard is a deterministic value and when the conse- quence and the failure probability can be evaluated separately Zhang and Huang(2016).

Infrastructure and/or buildings present in areas with icy rock slopes will generate risk and hence, the interest on analyzing possible slope instabilities. Therefore, the infrastructure of countries in arctic and subarctic regions affected by ice hazards related problems are: Norway, Sweden, Finland, Russia, Alaska (USA), Canada, Greenland (Denmark), Mongolia and North China. The map in (figure 2.5) below gives an overview of the areas where permafrost and ground-ice conditions are present.

Figure 2.5: Circum-Arctic map of permafrost and ground-ice conditions. Brown, J., O.J. Ferrians, Jr., J.A. Heginbottom, and E.S. Melnikov 16 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

2.2.1 Water Sources in Rockcuts

Andrea Liereng (Liereng (2016)) describes and classifies in her thesis project the different types of ice formations along roads and railroads. Liereng describes how human intervention in na- ture affects the regular water and groundwater paths and amplify the problems generated by ice, being the infrastructures often the problem. Therefore, these problems are present in rock- cuts when a source of water is found neaarby, saturating the road slopes. The main sources of water are classified as (1) Runoff water streams: (2) Surface water in the upper soil layer; (3) Groundwater streams and (4) distributed groundwater.

Runoff Water Streams

Surface water can drain down into cuttings in larger and smaller streams. Characteristic of This water source is that the water flows channeled to the surface throughout the year. Water access will often be stable throughout the winter due to larger water reservoir above the cut. Therefore, larger ice can be formed from those water streams. Figure 2.6 shows a typical example of ice- cooling in a stream that flows out over a cut.

Figure 2.6: Runoff water frozen in a rockcut at Sørkilhaugen, Meråkerbanen. Photo: A. Liereng 2.2. EFFECT OF ICE ON JOINTED ROCK SLOPES 17

Surface Water in Top Layer

Surface water can also drain into cuttings from the upper layers. Often the water flows between a loose soil layer and the bedrock Norem (1998). The water flows spread along the terrain, and the amount of water is largely dependent on rainfall. The presence of streams, ponds, marshes or other water reservoirs above the rockcut can add surface water to the rockcut. Figure 5.2 shows an example of a rockslope where ice is formed due to the frozen water coming from the top soil. In comparison with other source of water, the icicles do not achive large dimensions, but it can still cause instabilities while melting.

Figure 2.7: Rock slope where water is frozen on the rockwall from the mountainside, generating small rockfalls and icicles. Photo: Statens Vegvesen (Jens Tveit)

Groundwater Streams

Groundwater can sometimes flow out through the rock slope. This may occur naturally due to local geology and topography and its usually found at the bottom of the slopes. The sources can also be created by human intervention, for example in earthquakes or mountain cuts that cut through the water table. Ice-cooling from groundwater sources can achieve very large di- mensions, since water access often is stable throughout the winter. It is important to map such sources and take action to avoid ice formation. Figure 2.8 shows an example of water flowing through a base joint. 18 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

Figure 2.8: Rock slope 20km South of Mo i Rana. Streams are present in the area discharging in the fjord and the road has cutted the natural flow of those streams. Photo: Miguel Sanchez

Distributed Groundwater

Groundwater is mostly found in between the top soil layer and the bedrock. Under undisturbed conditions the water usually stays frost free throughout the winter. Ice formation from ground- water is therefore most frequent caused by human intervention. Rockuts are particularly vulner- able to this type of icing since the insulating earth layers have been removed. While distributed groundwater do not often creates large icicles as a strem where the water flow is constant, the water can still freeze and form long stretches of ice along the rock slopes as seen in figure 2.9 (Liereng (2016)). 2.2. EFFECT OF ICE ON JOINTED ROCK SLOPES 19

Figure 2.9: Grounwater causing icicles along the rockwall. Photo: A.Liereng

Depending on the topography and the geology distribbution of the area, groundwater can also leak out on the contact between the top soil and the bedrock as seen in figure 2.10. Ground- water does not freeze inside the soil layer, but when it reaches the rockcut, the cold surface makes the water freeze rapidly forming icicles that can be a hazard to traffic (Liereng (2016)).

Figure 2.10: Grounwater leaking out at the contact between the soil and the bedrock, freezing rapidly and forming large icicles. Photo: A.Liereng 20 CHAPTER 2. THEORY AND ANALYSIS OF ROCK SLOPE ENGINEERING

2.2.2 Frost Weathering

Frost wedging is a type of mechanical weathering. Water present in the rock mass will period- ically freeze and thaw. In areas where the temperature fluctuates about the freezing point. As freezing occurs, additional water tends to be attracted to the ice. When water freezes to form ice, its volume increases by about 9%, leading to high stresses in the rock and causing mechanical disruption. Figure 2.11 shows the point where ice can induce its maximum pressure. Theo- retically, at 22°C the ice can generate a maximum pressure of 207MPa (Matsuoka and Murton (2008), Tharp(1987)) This ice stress is enough to fracture any rock but this will be with the per- fect conditions (bedrock saturated and frozen fast to generate confined pressure) and is not realistic to find them in real conditions.

Figure 2.11: phase diagram of water. Displaying critical pressure around -22degrees 2.2. EFFECT OF ICE ON JOINTED ROCK SLOPES 21

It is accepted that where ice is present in discontinuities it contributes to maintaining the stability of rock slopes (Bjerrum and Jørstad(1968)) The reduction in rock slope stability with increase in ambient temperature - resulting in both toppling and deep seated failure - has been attributed to the loss of the stabilizing influence of ice in joints when it melts.

The phase change from ice to water has two effects. The first is a loss of joint bonding, which is provided by ice/rock interlocking and ’adhesion’ of the ice to the rock. The second is the release of water, which if it cannot drain away, results in elevated water pressures in the joint, leasing to a reduction in the effective pressure normal to the joint and thus lowering of its shear strength (Davies et al. (2001)).

Studies of the mechanical properties of ice have revealed that its strength and stiffness are a function of temperature. Some studies have shown that with decrease in temperature there is an increase in both stiffness and strength of ice. Hence, as the temperature of ice in a frozen joints increases, its stiffness and strength properties will decrease has confirmed by direct shear laboratory test by (Davies et al. (2000)). In result, the stability of such slopes is more sensitive to changes in the thermal regime and specially when the ice in the joint is close to the pressure melting point (Davies et al. (2001)) Is it then important to fully understand the trigger failure mechamisns in order to improve the slope stability and determine which stabilizing measure can be performed.

Figure 2.12: The relationship between peak shear strength and normal stress at three different test temperatures for frozen joint specimens and for an unfrozen joint Davies et al.(2001) Chapter 3

Preventing Measures to Avoid Ice Presence

Measures to prevent icing in cuts should reduce the problems the ice creates for the infrastruc- ture and road users. The measures have different strategies to achieve this goal. The preventa- tive measures Anti-icing in cuts has been divided into:

• rain surface water and / or groundwater

• channeling of water streams

• Ice nets

3.1 Drainage of Surface Water and Groundwater

The safest way of dealing with ice formation is stopping the problem at its source and that is by cutting off the water supply. Ice-cutting in rock cuts and ditches can be avoided by cutting off groundwater and surface water before It is exposed along the roadcut. This is done by collecting the water in open or closed ditches above the road. Depending on where the water comes from, there are different types of ditches that can be used (Liereng (2016)). As these solutions aim at preventing icicle formation, they are bound to provide better safety than barriers or ice nets.

22 3.2. STREAMS AND WATER FLOWS 23

3.2 Streams and Water Flows

Streams and groundwater from concentrated sources often carry water to the rock slopes con- tinuously throughout the winter. Experience indicates that channeling the water is the best solution. (Norem(1998)). Surface water should be diverted from the top of the rockcut. Often, some ice is formed on the channels while running down in cold periods, but then much of the water can drain on the back of the ice.

Channels are a simple, affordable measure with a good effect. As long as the slopes are nar- row and deep, the flow of water will most likely remain concentrated and frost free (figure 3.1). The challenge with downruns is to make them narrow and deep enough, at the same time as the capacity is retained. Difficulties can arise if the flows surpasses the designed measure since its difficult to design considering winter and summer conditions.

Figure 3.1: Illustration of a blasted pocket in the rockface which allows the water to flow below the road. (Norem (1998)) 24 CHAPTER 3. PREVENTING MEASURES TO AVOID ICE PRESENCE

3.3 Ice Nets

Where preventing water to flow over the top of the rock cut proves to be unfavorable, measures for preventing the fall of icicles into the roads has been used. This includes ice nets, ice pins and wide trenches at the bottom of the rock cut. These procedures aim at making water freeze at controlled places. A hexagonal mesh of steel is used. The wires are galvanized and covered with a plastic coating (PVC) to prevent corrosion. The nets are mounted to the rock slope with spaced bolts. The distance between the rock face and the icenet should be about 20 to 30cm (see figure 3.2 and figure 3.3 ). The length of the bolts must adapted to the rock slope so the grid is set up evenly. The bolts are placed in a pattern with about 3m between each but needs to be adapted to local conditions (Norem (1998)).

Figure 3.2: The net ends with a wire thrown through the net masks and bolted into the rock. The right picture shows the ice grows from the net so that water can leak behind the ice Photo A. Liereng 3.3. ICE NETS 25

Figure 3.3: Scheme of an icenet mounted by Statens vegvesen.

This method has proven to have good results against ice fall. It does, however, not reduce the amount of ice which is formed over the winter period. Therefore the risk of ice fall is reduced but not eliminated.

In high rock cuts with big risk of ice formation, the weight of the ice load accelerates the need for maintenance. Any maintenance is likely to cause the road to be closed for traffic in at least, one direction. The runoff from the ice net will include zinc from the galvanized iron in the ice net. If the galvanization is covered with PVC the zinc content will be minimized. It is important that all lose rock on the face of the rock cut is removed before the net is set up as falling rock will cause damage to the net and increase maintenance (Norem (1998)). Chapter 4

Case Study

Four study cases are presented. The first scenario is located in Greenland, while the next three are located in Norway. All cases have in common that the presence of water is difficult to avoid. Hence, problems associated with ice described in the previous chapter that, while it may not be the only cause of failure, plays and important role and allows to showcase ice problems in real locations. In order to display the problems and how are they being approach, the cases could be divided in two groups:

• Cases that are currently being observed and a solution for probable instabilities has to be performed:

– Sarfannguit Settlement, Greenland.

– Two roadcuts in the Road E6, 20km south of Mo i Rana, Norway.

• Cases that presented instabilities from 2013-2015 with partial failures and rockfalls. The slopes have being currently been reinforced.

– Rockfalls and open joints with icicles present on the sidewall of the Nessett Tunnel, Norway.

– Rockfalls on the southern entrance and sidewall of Nordmarks Tunnel, Norway.

26 4.1. SARFANNGUIT, GREENLAND 27

4.1 Sarfannguit, Greenland

Saarfannguit is a settlemment in the Qeqqata minucipality in central-western Greenland (Figure 4.1). Saarfannguit is situated approximately 35km east of Sisimiut, the closest town. Saarfann- guit has a population of 111 inhabitants in 2018 Statbank Greenland

Figure 4.1: Location Of the Settlement of Sarfannguit

This case study bears some complexity due to its dipping orientation and the jointed bedrock. Figure 4.2 shows the slope. The detachment area, marked in yellow, shows how to slope is loos- ing its foot. This entails that further blocks, initially supported by the fallen blocks in the foot, will hay a higher exposure, incrising its liability. Left picture on figure 4.3 shows the present dis- continuities in the bedrock. A clear sliding plane in is observed and seems to be the cause of the falling blocks observed in the right picture in figure 4.3. The approach to reinforce this slope has to take into account the families of joint present in the bedrock which will require a set of different bolting attaching the blocks through the sliding plane but also, they need to be secured trough each other to fasten the blocks together. Another possible solution could to remove the exposed blocks, eliminating the falling hazard, albeit that removing the blocks could also have negative effects on the households above the slope and furthermore, its a solution that may only solve the problem temporarily and since the hazard will be moved to the bedrock layer below, that displays the same discontinuities. 28 CHAPTER 4. CASE STUDY

Figure 4.2: Yellow areas mark the zones where the fallen blocks detached. Photo: Martin Jun- gensen

Figure 4.3: Left picture displays the sliding plane in black and bedrock joints in red. Left picture displays the fallen blocks. Photo: Martin Jungensen 4.2. ROADCUTS IN E6 NEAR MO I RANA 29

4.2 Roadcuts in E6 near Mo i Rana

This study case is based on the report TGB4500, Engineering Geology and rock mechanics spe- cialization project at Norwegian University of Science and Technology during autumn 2017 (Sanchez (2017)). The roadcuts studied are situated around 20km south of Mo i Rana follow- ing the road E6 (figure 4.2). The map also shows the geological conditions in both roadcuts.

Figure 4.4: Geological map displaying roadcuts location. Roadcut1 is roadcut HP8 5447 and Roadcut2, HP9 934. Norges Geologiske Undersøkelse

The problems observed on the roadcuts have been reported by local stakeholders to Statens Vegvesen. Both roadcuts are situated following the fjord which causes that water flowing from the mountainside ends on the roadcuts. During winter the water is freezing on the bedrock, generating icicles that may fall down into the road. In spring, the melting causes weathering on the surface and some rockfalls have been observed. 30 CHAPTER 4. CASE STUDY

4.2.1 Roadcut HP8 5447

Roadcut HP8 5447 has a height of approximately 20m and the gneiss joint surfaces surveyed dip to the North. Figure 4.2.1 shows the slope from the road.

Figure 4.5: Rock slope E6 at HP8 5447. Photo: Mickael Bergman

Figure 4.2.1 shows the problems on the roadcut. The left picture shows a water stream in a section of the slope. On the right picture some fallen blocks of around 10cm fell into the verge of the road. (Sanchez (2017)). The flowing water from the stream and some runoff water from the topsoil requires an ice net to be installed on the rockwall.

Figure 4.6: Hazards observed during fieldwork, October 2017. Photo: Miguel Sanchez 4.2. ROADCUTS IN E6 NEAR MO I RANA 31

4.2.2 Roadcut HP9 934

Roadcut HP9 934 (figure 4.7) has an height of approximately 7m with a verge of 2m and 0.5m depth. As the previous location, this cut slope also dips to the North (Sanchez(2017 )).

Figure 4.7: Rock slope E6 at HP9 934 Photo: Mickael Bergman

At the time of the field study, the slope seemed to be dryer than the first road cut studied. However, some runoff water was observed on the rock face. Figure 4.8 shows in the left picture how the joints present a subhorizontal orientation which is making some blocks to fail. The right picutre displays the other family of joints observed and some of them where opened and weathered. Again, the ice is causing problems during winter and the emplacement of an ice net is being planned (Sanchez(2017)).

Figure 4.8: Hazards observed during fieldwork, October 2017. Photo: Miguel Sanchez 32 CHAPTER 4. CASE STUDY

4.3 Nessettunnelen

The Nessett tunnel was built in 1996. The main inspection of the tunnel was carried out in 2008, but while the inspection was carried out, time the tunnel was covered with water and icicles, which caused the mountain wall to not be properly investigated.

The rock slope has had two failures in 2014 and 2015. In October 2014 several small blocks ended up on the road and sideroad. Figure 4.9 Left. The slope presented also a wider disconti- nuity in a larger block Figure 4.9 Right.

Figure 4.9: The picture shows a rockfall dated from October 2014. From the left picture, the yellow area marks the detachment area and the red area shows several blocks deposited on the sideroad. The right photo showws that the block presents two joints families forming a wedge dipping to the road. Ice can be observed inside the joints. Photo: Mikael Bergman. Bergman (2016)

On November 2015 a new inpection was carried out by statens vegvesen for the purpose con- trolling the boreholes that were supposed to hold the bigger block. These holes were completely empty. It was suggested that the construction speeded up the work to complete the tunnel and forgot to secure the rock slope 4.3. NESSETTUNNELEN 33

Figure 4.10: Picture also dated from October 2014. The yellow area shows a block in a critical state. The block presents two joints families forming a wedge dipping to the road. Ice can be observed inside the joints. Photo: Mikael Bergman. Bergman(2016)

The rock wall is characterized by several unfavorable cracks and exposed to frost blasting each years when water flows through the cracks. The terrain and the mountain’s tight ripple make it It is difficult to establish water scrubs above the difference. 34 CHAPTER 4. CASE STUDY

The Block was finally secured thorugh the uses of rock bolts. Figure 4.11 shows the distri- bution of bolts trhough the rock slope. The extent of the bolts must allow to anchor them to the mountains below. This is especially important for the bigger block since the discontinuity is dipping to the road.

Figure 4.11: Picture from October 2017. It can be seen that the wedging loose block has been secured with rockbolts. Some additional bolts have been also used on the left side where some minor discontinuities can be observed. Photo: Miguel A. Sanchez 4.4. NORDMARKSTUNNELEN SOUTH ENTRANCE AND SIDEWALL 35

4.4 Nordmarkstunnelen South Entrance and Sidewall

On the E6-hp08 in the southern part of Nordmarkstunnelen in Hemnes kommune, precipita- tions on October 2013 provoked a 15-20 m3 rockfall that came down and ended up mostly in the ditch next to entrance of the tunnel but also, a smaller part of the rock ended up on the road Bergman(2013) . Figure 4.12 and figure 4.13 shows the failure.

Figure 4.12: Picture from October 2013. Clear discontinuities are observed on the left picture. The discontinuitites are oriented sub-horizontally. The right picture marks the areas were the failure occurred. The red and green areas display hanging sections and the yellow part show borken bolts. Photo: Mikael Bergman

Figure 4.13: Pictures from October 2013. Details from thebroken bolts that were holding the blocks Photo: Mikael Bergman 36 CHAPTER 4. CASE STUDY

South entrance of Nordmarkstunnelen was inspected in 2008 by Multiconsult and hanging rock blocks on the roof were bolted. This bolts are the ones displayed in figure 4.13 that broke after the rainfall in October 2013. The report mentions a constant flow of water next to the hang- ing rock blocks and it was stated that the overhang blocks may be a future cause of fallout. It is also mentioned that the loosened blocks are associated to frost cycles Bergman (2013).

But the entrance of the tunnel is not the only section that may fail in this area. The right and east sub-vertical rock slope also presents some loose blocks. Figure 4.14 shows a clear disconti- nuity on the top and it has been covered by an ice net. Still, the rock slope presents some loose blocks and some bolts have failed Bergman (2013). The inspection realized by Mikael Bergman suggest mounting closer net bolts to support loose blocks.

Figure 4.14: Picture from October 2013. Yellow area marks a clear discontinuity block. Some ice has been observed from inflow water trhough the joint. The red circle marks a bolted area which is also displayed in figure 4.15. Photo: Mikael Bergman 4.4. NORDMARKSTUNNELEN SOUTH ENTRANCE AND SIDEWALL 37

Figure 4.15: Picture from October 2017. THe main discontinuity is mark by the difference in color. The lower section of the slope presents a more weathered color due to the water flowing from the discontinuity. The red circle marks the same area observed in figure 4.14 from 2013. It can be observed an increase in the number of joints. Photo: Miguel A. Sanchez

Figure 4.16: Picture from October 2013.Details of the east rockwall from the South entrance of the tunnel. Left picutre displays a block in contact with the top soil layer and a wide discontinu- ity. The right picture shows the water flowing through the joints. Photo: Mikael Bergman Chapter 5

Numerical Modeling

Ice-induced pressure is simulated in order to support the statements made in the theory. Figure 5.1 shows sketches of the two cases modeled. The choice to work with this models is because they represent failures that occur often (Kliche (1999)) and its geometry has been use regularly in cold regions such as Norway (Braathen et al. (2004)). This is supported by the case studies presented in the previous chapter. Figures 5.2 and 5.3 are other examples where this failures are present. For the modeling, RocPlane, RocTopple and Phase2, programs from the Rocscience suite have been used. All simulations have been characterized by Mohr-Coulomb criteria and maintaining friction angle and cohesion constant. A full review of the simulation results is at- tached as annexes.

Figure 5.1: Sketches of two failure modes studied. The left sketch displays a planar sliding fail- ure. The right sketch shows a weathered rock slope with a set of joints making the blocks to topple down.

38 39

Figure 5.2: Slope near Mosjøen. The vertical face displays some discontinuities where water is flowing out. Photos: Miguel Sanchez

Figure 5.3: Picture shows a slope were some blocks fell in 2014. The sketch shows the orientation of the foliation causing the hazard. Photo: Statens Vegvesen Bergman (2014) 40 CHAPTER 5. NUMERICAL MODELING

5.1 Single Crack, Planar Failure

The planar failure has been modeled with RocPlane, a software tool for performing planar rock slope stability analysis and design. The stability has been assesed using a deterministic analysis which resulted in a safety factor value. the models follow the shear strength model of Mohr- Coulomb criteria.

Figures 5.4, 5.5 and 5.6 show the rock slope in dry, wet and icy conditions respectively. In dry conditions a safety factor of 2.77 is obtained. The friction angle and the cohesion are kept constant. The factor of safety for saturated conditions is 2.37 and for icy conditions 0.97. The last simulation has been carried out with a pressure of 0.8Pa to simulate the effect of ice just below a safety factor of 1.

Figure 5.4: RocPlane planar wedge stability analysis in dry conditions.Factor of safety of 2.77 5.1. SINGLE CRACK, PLANAR FAILURE 41

Figure 5.5: RocPlane planar wedge stability analysis in saturated conditions.Factor of safety of 2.37

Figure 5.6: RocPlane planar wedge stability analysis with ice stresses. Factor of safety of 0.97 for an ice pressure of 0.8 MPa 42 CHAPTER 5. NUMERICAL MODELING

5.2 Toppling Failure Mode Case

The toppling failure follows the same structure as the previous model. First, RocTopple has been used. RocTopple is a simple analysis tool for evaluating block toppling in rock slopes which produces a preliminary analysis based on Mohr-Coulomb. Dry (figure 5.7) and fully saturated (figure 5.8) conditions have been run in RocTopple, obtaining 0.567 and 0.564 safety values re- spectively. A factor of safety below 1 is used to display the block failures.

Figure 5.7: Roctopple failure case in dry conditions

Figure 5.8: Roctopple failure case in saturated conditions 5.2. TOPPLING FAILURE MODE CASE 43

RocTopple did not allow to apply an external force to simulate ice- induced pressure. For this purpose, the RocTopple model has been exported to Phase2, which uses a finite element slope stability analysis using the shear strength reduction method together with Mohr-Coulomb strength parameters. Figure 5.9 shows the model obtained once imported in Phase2.

Figure 5.9: Roctopple imported geometry to phase2 analysis in saturated conditions. Displaying mean stress

The model imported starts with fully satured conditions and two types of joints have been determined. Base joints and toppling joints. Later a ice-filled joint is generated and an addi- tional pressure of 0.8MPa is set to maintain same conditons as given in the sliding failure. The ice-filled joints are added gradually resulting in four cases:

• Saturated conditions

• Single ice-filled joint

• Three ice-filled joints

• All joints ice-filled.

Figures 5.10 to 5.17 show the results obtained for total displacements and Maximum shear stress. Results do not show big differences from single ice-filled joints to full ice-filled joints. 44 CHAPTER 5. NUMERICAL MODELING

Case a): water

Figure 5.10: Roctopple imported geometry to phase2 analysis in saturated conditions. Display- ing shear stress

Figure 5.11: Roctopple imported geometry to phase2 analysis in saturated conditions. Display- ing total displacement 5.2. TOPPLING FAILURE MODE CASE 45

Case b): single joint ice filled

Figure 5.12: Roctopple imported geometry to phase2 analysis with a single joint containing ice. Displaying shear stress

Figure 5.13: Roctopple imported geometry to phase2 analysis with a single joint containing ice. Displaying total displacement 46 CHAPTER 5. NUMERICAL MODELING

Case c): Three joints ice filled

Figure 5.14: Roctopple imported geometry to phase2 analysis with three joints containing ice. Displaying shear stresst

Figure 5.15: Roctopple imported geometry to phase2 analysis with three joints containing ice. Displaying total displacement 5.2. TOPPLING FAILURE MODE CASE 47

Case d): All joints ice filled

Figure 5.16: Roctopple imported geometry to phase2 analysis with all joints containing ice. Dis- playing shear stress

Figure 5.17: Roctopple imported geometry to phase2 analysis with all joints containing ice. Dis- playing total displacement Chapter 6

Conclusions, Discussion, and Recommendations for Further Work

6.1 Summary and Conclusions

Several papers study and review frost-weathering and new techniques have allowed to monitor moisture content and crack movements in near-surface hard jointed bedrocks (Matsuoka and Murton(2008)). But most of this studies are focused on rockfall activities in high mountains. Hence, a lack of information regarding how frost weathering affects rockcuts and rock slopes is yet to be answered. To understand the influence of ice on engineering rock slopes, the project describes what is a rock slope, rock slope stability and goes through the different types of failure that may occur.

Frost Weathering occurs when the temperature fluctuates across the freezing point and mois- ture is present in the jointed bedrock. When ice is formed, it may generate and propagate cracks in rocks and the cyclical freeze-thawing will weaken the rock strength generating rock debris or rockfalls causing safety hazards to the infrastructure. Problems reported and showcased proves two marked hazards:(1) Frozen streams and runoff water on vertical to sub-vertical rock slope faces forming icicles that break down and fall into the road during winter and (2) Ice affecting the rock mass stability due to the wedging effect in rock discontinuities, weakening the rock, propagating cracks and endangering the stability of the slope through its joints during warming periods. Nevertheless, conditions all cases display the same main issue: avoiding the presence of moisture. The cases in Norway are focused on transportation infrastructure. The complex topography of the country has entailed that most roads and railroads have been build parallel to the system of fjords. Therefore, the natural water-flow from the mountains to the fjords ends into the infrastructure, which have to deal with constant rainfall and melt water. On the other hand, Greenland has its problems inside their towns and settlements. Traditionally, households

48 6.1. SUMMARY AND CONCLUSIONS 49 have been build upon outcropping bedrock to avoid permafrost issues. however the roads are at lower height and build uppon permafrost. Therefore, it is common to find subvertical slopes around the town as seen in figure 6.1. The harsh climate conditions make the slopes to be frozen most of the year, but there are still some warm periods. Moreover, towns and settlements are spread mostly along Greenland west coast, having huge variations from North to South. In the cases from figure 6.1 in Sisimiut the temperatures fluctuate across the freezing point around May-June and the town is snow free up to September.

Figure 6.1: Road in Sisimiut, next to the harbor. In both pictures it can be observed how some blocks have fallen in a plane paralel to the slope orientation. Photos: Miguel Sanchez

In order to prevent these problems, different securing measures are used to stabilize the slopes. Two main approaches are currently in use depending on the situation: When building a new road or repairing an old road layout, designing natural ditches to avoid having water leaking through the slope and building wider verges are the best long term and cost efficient solution. However, these solutions require to be planned ahead and to have suitable areas to enlarge and build the ditches. The second and most common solution is to use a net to reinforce the rock face and bind and break the ice to contain it outside the driving areas. The ice net has been proved a solid and effective solution which, however, comes with a but: Ice nets require main- tenance. The metallic net can be exposed to severe weathering conditions due to harsh winters (oxidation, ice loads, loose rocks...) and must be monitored to ensure a proper performance Sanchez (2017).

As mentioned before, Frost weathering results from freezing and thawing of water within the rock joints which involves two processes: Volumetric expansion and ice segregation. The processes are described from a theoretical point of view in the second chapter, focusing later on the volumetric expansion which is analyzed through two simple idealized models: A verti- 50 CHAPTER 6. CONCLUSIONS cal tension crack on a sliding plane following some of the wedged failures observed in the field and a toppling jointed bedrock. In both cases the models are computed in dry, saturated and simulating ice pressure conditions. This pressure is assumed as the pressure that ice may exert due to volumetric expansion. When liquid water turns into ice, a volumetric expansion of nine per cent takes place. If the water completely fills all spaces in the bedrock and freezes in situ, then, theoretically, at 22°C the ice can generate a maximum pressure of 207MPa (Matsuoka and Murton(2008), Tharp (1987)) This ice stress is enough to fracture any rock but this will be with the perfect conditions (bedrock saturated and frozen fast to generate confined pressure) and is not realistic to find them in real conditions. The results obtained in both models (planar sliding and toppling) show that even with a smaller ice induced pressure(0.8MPa), the ice pressure will already generate instabilities on jointed bedrocks where deterioration of the bedrock has not taken into account. Hence, the importance of monitoring rock slopes where ice is present and the surface rock has been weathered.

6.2 Discussion

Recent studies (Matsuoka and Murton (2008), Tharp (1987), Michael et al. (2012)) show that vol- umetric expansion does not play the main role in frost weathering. But this results are proposed for rockfalls and slope failure in high mountains. The size and conditions of those slopes are not the same as artifical rockcuts slopes on the side-road. On the other hand, Matsuoka and Murton (2008) suggests volumetric expansion could play a relevant role on the surface of the bedrock, which is relevant in this study. While in high alpine terrain rock blocks of several centimeters may not activate any major rockfalls or landslides, this small block failures are an issue if they land in the infrastructure and potentially causing casualties. Detachment areas often modify the strength of the jointed rock mass, causing further instabilities on adjacent blocks as observed in the case study in Sarfannguit, Greenland. The cases along the roads in Norway could also be affected by volumetric expansion due to its moisture content during melting periods, together with daily variations in temperature could generate near surface confined conditions.

There are also other issues that need to be considered when considering ice hazards. The models run for the planar sliding failure show that with a 0.8MPa the safety factor drops below 1 from an initial value in dry conditions of 2.77. Ice-induced pressure is a variable to consider, but other negative effects on the slope stability are also observed. The ice pressure can also lift blocks or open joints. During winter the ice behaves like a cement and glues the blocks together, but when the ice melts, the expansion generated by the ice reduces the contact points and the friction which in the end results in a lose of bedrock strength. 6.2. DISCUSSION 51

On the cases for toppling failure the simplified solution from RocTopple gives a factor of safety of 0.564 while with Phase2 with the same parameters and using the shear strength reduc- tion method the factor of safety obtained is of 0.36. When some of the joints are characterized as ice filled joints, adding an extra pressure of 0.8MPa, the factor of safety drops to 0.31.Gradu- ally increasing the number of ice filled joints the factor of safety goes up to 0.34 and 0.36 again. While the safety factor doest not seems to be vary , the shear stress and displacements show a gradual increase as expected.

It is accepted that where ice is present in discontinuities it contributes to maintaining the stability of rock slopes (Bjerrum and Jørstad(1968)) The reduction in rock slope stability with increase in ambient temperature has been attributed to the loss of the stabilizing influence of ice in joints when it melts.

Results obtained are consistent with the theoretical approach. Conditions met in cold re- gions change the stress state in jointed bedrocks and gradually changes its physical and me- chanical properties. Rock slopes become unstable driven by changes in temperature and pre- cipitation conditions. Generally, destabilization on rock slopes tends to occur on thawing pe- riods. Hence, critical slope stability results are expected in warm frozen areas where both ice and water are present. Ice exerts certain force on joint rock slopes and can induce failure in the jointed rock mass. 52 CHAPTER 6. CONCLUSIONS

6.3 Recommendations for Further Work

Looking at the figure 6.2 from Matsuoka and Murton (2008) and focusing on the 1 to 10 years time scale, freeze-thaw frequency, moisture content, freeze-thaw depth and joints spacing and rock mass strength will determine the stability of an engineering rock slope. Joints and rock mass strength are used as design parameters when building an infrastructure. But special con- siderations should be taken into account in cold regions. Small scale features that are affected by freeze-thaw cycles and its depth needs to be studied. Furthermore, cold regions are experi- encing warming climates which results in changes in mountain sides (e.g. more runoff water from mountains) and longer melting periods increasing failure hazards. Hence, the importance of assessing securing measures to avoid water and ice on the rock slopes.

Figure 6.2: Factor contributing to the gap between current and long-term rates of rockwall ero- sion in cold mountains. Matsuoka and Murton (2008) Bibliography

Bergman, M. (2013). Stabilitetsvurdring e6-hp08 søndre på hugg nordmarkstunnelen etter ned- fall fra påhuggsflate i hemnes kommune.

Bergman, M. (2014). Tro fergekai -rødøya. rasfarevurdering av bergskjæring bak fendervegg.

Bergman, M. (2016). Bergsikring forskjæring nesset nord.

Bjerrum, L. and Jørstad, F.(1968). Stability of Rock Slopes in Norway. Norges Geotekniske Insti- tutt. Norges Geotekniske Institutt.

Braathen, A., Blikra, L., Berg, S., and Karlsen, F. (2004). Rock slope failures of norway: type, geometry, deformation mechanisms and stability. 84:67–88.

Brown, J., O.J. Ferrians, Jr., J.A. Heginbottom, and E.S. Melnikov. Circum-arctic map of per- mafrost and ground-ice conditions.circum-pacific map series cp-45, scale 1:10,000,000, 1 sheet.

Davies, M. C. R., Hamza, O., and Harris, C. (2001). The effect of rise in mean annual temperature on the stability of rock slopes containing ice-filled discontinuities. Permafrost and Periglacial Processes, 12(1):137–144.

Davies, M. C. R., Hamza, O., Lumsden, B. W., and Harris, C. (2000). Laboratory measurement of the shear strength of ice-filled rock joints. Annals of Glaciology, 31:463–467.

Jens Tveit, R. D. Rv 5, hp 3, km 8.630-8.940. fodnes fergekai. vurdering av skredfare mot kaian- legget.

Kliche, C. (1999). Rock Slope Stability. Rock Slope Stability. Society for Mining, Metallurgy, and Exploration.

Liereng, A. (2016). Iskjøving i grøfter og skjæringer langs veg og jernbane. prosesser, årsaker og forebyggende tiltak.

Matsuoka, N. and Murton, J. (2008). Frost weathering: recent advances and future directions. Permafrost and Periglacial Processes, 19(2):195–210.

53 54 BIBLIOGRAPHY

Michael, K., Daniel, F.,and K., G. F.(2012). Why permafrost rocks become unstable: a rock–ice- mechanical model in time and space. Earth Surface Processes and Landforms, 38(8):876–887.

Norem, H. (1998). Sikring av vegar mot isras : årsaker til isras, samling a erfaringer, utføring av sikringstiltak. Statens vegvesen. Sogn og Fjordane .

Norges Geologiske Undersøkelse. Berggrunn - Nasjonal berggrunnsdatabase. http://geo. ngu.no/kart/berggrunn_mobil/. Accessed: 2017-08-20.

Sanchez, M. (2017). Influence of ice to the stability of engineering rock slopes. TGB4500 - Engi- neering Geology and Rock Mechanics, Specialization Project.

Statbank Greenland. Population in locatilities January 1st. 1977-2018. http://bank. stat.gl/pxweb/en/Greenland/Greenland__BE__BE01__BE0120/BEXST4.PX/table/ tableViewLayout1/?rxid=d586902d-6091-4e27-96dc-c2a33f443374. Accessed: 2018- 05-20.

Tharp, T. M. (1987). Conditions for crack propagation by frost wedging. GSA Bulletin, 99(1):94.

Varnes, D. J. (1978). Slope Movement Types and Processes In Landslides, Analysis and Control. Edited by R.L. Schuster and R.L. Krizek. Special Report 176. Washington, D.C. Transporta- tion Research Board, Commission on Sociotechnical Systems, National Research Council, Na- tional Academy of Sciences.s.

Wyllie, D. and Mah, C. (2004). Rock Slope Engineering, Fourth Edition. Taylor & Francis.

Zhang, J. and Huang, H. (2016). Risk assessment of slope failure considering multiple slip sur- faces. Computers and Geotechnics, 74:188 – 195. Appendix A

RocPlane 3.0 Simulations

55 

   !""

  


#  $

G69`458 F95G('&4 a G('&'6 b4Ic4 d8'e1(18) %&'()010

%&'()010 3405617819&

36'B& C) @9A7'&)

3'84 QRSTQSQTRUV QQWXYWTR D1(4 E'A4 F95G('&4HI6)P7(& Ff@Gg%Eh XPTTY ) ! 0


12$%34 8  ! !

12$%  00' 12$%7#9 "##$%&

 "##$%&7#(9 '()0

  @#2%0 )ABC

 
7#'!9

2$56$#7#89 

B$2%'0ABC I

2$%D
$DE  I @#2% 0 )ABC F#2% 8'ABC 343  (!ABC 34G5 8))0H8C

I8
$
# 08A6$
$F$#% 8'ABC B$2% '0ABC 6$#3$@# 9 I0 I I    8 0 ! rad Y`c qd`rSRQY9†9rSRQRa9‡YtˆY9‰cRVSVcT9PQRSTUVU

PQRSTUVU9XYU`aVbcVdQ

XaRgQ9hT edfbRQT

XRcY vwxyvxvyw€9vv‚ƒ„‚yw iVSY9pRfY qd`rSRQYstaTubSQ q‘er’Pp“9ƒuyy„ rs“tmuvbwxyyz ‘’“”•–—b™b“”•–•dbe—fg—bhi•jk”kilbm–•”lnknob“•g—bpb‘qbp

 


 !"# 

 
%"&

 AB14C2D4 '()0123456789@13 07(S4)ITBI14 '()01234E012327F46G4HI2PB1BI8Q3218RBR d2I4e742I46 UVWXUWUXVY`UUabcaXV  &

Q3218RBRT8@4Ed4I47DB3BRIB)

C(7D21A(7)4 Y9UfVghiCWD d7BqB3GA(7)4 f9pcYciCWD '4RBRIB3GA(7)4 Vb9VYfUiCWD A2)I(7(rH2r4I8 U9ppXhh  s


H1(@4t4BGuI UXD F46G4F4BGuI g9cVpiCWD F46G4w(1xD4 bhh9XbYDvbWD F46G4t4BGuI UXD y3BIF4BGuI X9XUhiCWDb H1(@4Q3G14 Yc€ A2B1x7401234Q3G14 bX€ y@@47A2)4Q3G14 VX€ 43)uFB6Iu C(I074R43I F2qB34RR X€ „3I47R4)IB(30(B3I‚ƒ(rR1(@4236x@@47r2)4 ‚V9pfgpp`UXƒ „3I47R4)IB(3@(B3I‚eƒ(rI43RB(3)72) 236x@@47r2)4 ‚Uh9pfgY`Uf9fXYUƒ „3I47R4)IB(3@(B3I‚dƒ(rr2B1x74@1234236I43RB(3)72) ‚Uh9pfgY`Vc9fffƒ H1(@4143GIu‚†7BGB3EE‡ƒ UX9XpUYD T43RB(3e72) ˆ43GIu‚eEE‡dƒ Y9ghfVgD A2B1x7401234143GIu‚†7BGB3EE‡dƒ bX9YYYD T43RB(3e72) 074R43I T43RB(3e72) Q3G14 gX€ dBRI23)4A7(De74RI UcD T43RB(3e72) ˆ43GIu Y9ghfVgD  "!‰

Hu427HI743GIui(641i(u7Ee(x1(DP A7B)IB(3Q3G14 bc€ e(u4RB(3 X9UfiCWDU Hu427HI743GIu X9fUhYbgiCWDU Hu427'4RBRI23)4 Vb9VYfUiCWD 

‘’“”•–—{fdlx|”– bbb}p~y}~}yp€b}}owzoyp $% 5617! 9 &'(# "(#

561 ! 44# )00%180 2@ 56180 &@ )00%1

" 234#


 


 ! $A0 61(&BC# & "#

61DDE "9' 80 (@ $A0 61 (&BC# F0 61 &"&BC# 6 
080 9@ 7  ! 2("BC# 7 G # 9334#H9C#  B#61332BC# !0 ! 92
 !F01 &"&BC# B#61 332BC#
0A0 @ 6106 
0 &93BC# 610)00%1 92BC# I& I" I&  & " 9 4 ( rad„Y`c qd`rSRQY9 9rSRQRa9†Y‡ˆY9‰cRVSVcT9PQRSTUVU

PQRS TU V U 9 XYU ` a V bc V dQ

XaRgQ9hT edfbRQT

XRcY uvwxuwuxvy€9uu‚ƒxv iVSY9pRfY qd`rSRQYsgRcYatbSQ q‘er’Pp“9‚txxƒ st“umvwbxyzz{ ‘’“”•–—b™b“”•–•dbe—fg—bhi•jk”kilbm–•”lnknob“•g—bpb‘qbr

 


 !"# 

 
%"&

 AB14C2D4 '()0123456789@13 07(S4)ITBI14 '()01234E012327F46G4HI2PB1BI8Q3218RBR d2I4e742I46 UVWXUWUXVY`UUabcaXV  &

Q3218RBRT8@4Ed4I47DB3BRIB)

C(7D21A(7)4 f9fYfgfhCWD d7BqB3GA(7)4 c9XiiYphCWD '4RBRIB3GA(7)4 VU9XicUhCWD A2)I(7(rH2r4I8 U9bgVfi  s


H1(@4t4BGuI UXD F46G4F4BGuI i9cVghCWD F46G4w(1xD4 bff9XbYDvbWD F46G4t4BGuI UXD y3BIF4BGuI X9XUfhCWDb H1(@4Q3G14 Yc€ A2B1x7401234Q3G14 bX€ y@@47A2)4Q3G14 VX€ 43)uFB6Iu C(I074R43I F2qB34RR X€ „3I47R4)IB(30(B3I‚ƒ(rR1(@4236x@@47r2)4 ‚V9gpigg`UXƒ „3I47R4)IB(3@(B3I‚eƒ(rI43RB(3)72) 236x@@47r2)4 ‚Uf9gpiY`Up9pXYUƒ „3I47R4)IB(3@(B3I‚dƒ(rr2B1x74@1234236I43RB(3)72) ‚Uf9gpiY`Vc9pppƒ H1(@4143GIu‚†7BGB3EE‡ƒ UX9XgUYD T43RB(3e72) ˆ43GIu‚eEE‡dƒ Y9ifpViD A2B1x7401234143GIu‚†7BGB3EE‡dƒ bX9YYYD T43RB(3e72) 074R43I T43RB(3e72) Q3G14 iX€ dBRI23)4A7(De74RI UcD T43RB(3e72) ˆ43GIu Y9ifpViD  "!‰

Hu427HI743GIuh(641h(u7Ee(x1(DP A7B)IB(3Q3G14 bc€ e(u4RB(3 X9UphCWDU Hu427HI743GIu X9biVcYphCWDU Hu427'4RBRI23)4 VU9XicUhCWD 

‘’“”•–—|}•i—dy~”– bbbrpzrrzp€brrox{ozp IstRuhvw9xy€€ IPQRSTUV9X9RSTUTY9`VabV9cdTefSfdg9hUTSgifip9RTbV9q9Pr9q


!"#$%&'" #'()"   4$#335$#6'3"$'75"'8&89#@ 012!3# 4#$A#&"B'@@#901  D(&8$#B!'@5$#4@!&#4$#335$# C !"#$B8$A#8&B!'@5$#4@!&# EF !"#$B8$A#8&0#&3'8&1$!AH4@!&# GG 

IPQRSTUV‚ƒTdVYy„SU 999q †€q†q€ ‡ˆ9qqpxp€ $% 5617! 9 &'(# "(#

561 ! 44# )00%180 2@ 56180 &@ )00%1

" 234#


 


 ! $A0 61&2'BC# & "#

61DDE 2' 80 (@ $A0 61 &2'BC# F0 61 &3'BC# 6 
080 9@ 7  ! 2("BC# 7 G # 9334#H9C# 

 
 B#61433BC# !0 ! 9(
 !F01 &3'BC# B#61 433BC#
0A0 @ 6106 
0 BC# 610)00%1 '&'BC# I& I" I&  & " 9 4 ( rad„Y`c qd`rSRQY9 9rSRQRa9†Y‡ˆY9‰cRVSVcT9PQRSTUVU

PQRS TU V U 9 XYU ` a V bc V dQ

XaRgQ9hT edfbRQT

XRcY uvwxuwuxvy€9uu‚ƒxv iVSY9pRfY qd`rSRQYsV`YtbSQ q‘er’Pp“9‚txxƒ st“umvwbxyzz{ ‘’“”•–—b™b“”•–•dbe—fg—bhi•jk”kilbm–•”lnknob“•g—bpb‘qbr

 


 !"# 

 
%"&

 9614@2A4 '()0123456)47813 0C(S4)HT6H14 '()01234B01232CD4EF4GH2I616HPQ321PR6R d2H4eC42H4E UVWXUWUXVY`UUabcaXV  &

Q321PR6RTP84Bd4H4CA636RH6)

@(CA219(C)4 f7gcgUhi@WA dC6p63F9(C)4 VX7hghVi@WA '4R6RH63F9(C)4 VX7gqbci@WA 92)H(C(rG2r4HP X7hqbXcb  s


G1(84t46FuH UXA D4EF4D46FuH h7cVqi@WA D4EF4w(1xA4 bgg7XbYAvbWA D4EF4t46FuH UXA y36HD46FuH X7XUgi@WAb G1(84Q3F14 Yc€ 9261xC401234Q3F14 bX€ y884C92)4Q3F14 VX€ 43)uD6EHu @(H0C4R43H D2p634RR X€ „3H4CR4)H6(30(63H‚ƒ(rR1(8423Ex884Cr2)4 ‚V7qfhqq`UXƒ „3H4CR4)H6(38(63H‚eƒ(rH43R6(3)C2) 23Ex884Cr2)4 ‚Ug7qfhY`Uf7fXYUƒ „3H4CR4)H6(38(63H‚dƒ(rr261xC48123423EH43R6(3)C2) ‚Ug7qfhY`Vc7fffƒ G1(84143FHu‚†C6F63BB‡ƒ UX7XqUYA T43R6(3eC2) ˆ43FHu‚eBB‡dƒ Y7hgfVhA 9261xC401234143FHu‚†C6F63BB‡dƒ bX7YYYA T43R6(3eC2) 0C4R43H T43R6(3eC2) Q3F14 hX€ d6RH23)49C(AeC4RH UcA T43R6(3eC2) ˆ43FHu Y7hgfVhA  "!‰

Gu42CGHC43FHui(E41i(uCBe(x1(AI 9C6)H6(3Q3F14 bc€ e(u4R6(3 X7Ufi@WAU Gu42CGHC43FHu X7bfcccci@WAU Gu42C'4R6RH23)4 VX7gqbci@WA 

‘’“”•–—|k’—y}”– bbbrp~zr~rzp€brrox{ozp FpqIrest6uvwwx FGHIPQRS6U6IPQRQV6WSXYS6`aQbcPcad6eRQPdfcfg6IQYS6h6Gi6h


!"#$%&'" #'()"   4$#221$#5'2"$'61"'3&37#8 012"34$#221$# !"#$4$#221$#3&@!'81$#48!&# 9 !"#$4$#221$#3&A#&2'3&0$!BC48!&# 9 !"#$@3$B#3&@!'81$#48!&#  !"#$@3$B#3&A#&2'3&0$!BC48!&# DDE 

FGHIPQRSycHSv€PR 666h‚wh‚hwƒ„6hhguxgw Appendix B

RocTopple 1.0 Simulations

65 Factor of Safety: 0.567 30

Stable Toppling Sliding

Base in Tension Upper Slope Angle 2 ° 20

Slope Angle 89 °

2.5 m

Slope Height 20 m 10

Block Base Angle 30 °

Overall Base Inclination 35 ° 0 -10

0 10 20 30 Project ROCTOPPLE - Rock Toppling Analysis

Analysis Description

Drawn By Miguel A Sanchez Company NTNU Date File Name ROCTOPPLE 1.005 30/02/2018, 21:59:37 roctopple_dry.rtop ROCTOPPLE 1.005 Page 1 of 3

RocTopple Analysis Information ROCTOPPLE - Rock Toppling Analysis

Project Summary

File Name roctopple_water.rtop File Version 1.005

Project Title ROCTOPPLE - Rock Toppling Analysis Author Miguel A Sanchez Company NTNU Date Created 30/02/2018, 21:59:37

General Settings

Units Metric, stress as kPa Unit Weight of Water (kN/m3) 9.81 Analysis Type Deterministic

Analysis Results

Factor of Safety Factor of Safety 0.567

Block Details

roctopple_water.rtop NTNU 30/02/2018, 21:59:37 ROCTOPPLE 1.005 Page 2 of 3

Height Weight Base Pn-1,t Pn-1,s Pn-1 Pn,s Index Yn/x Type Pn,t (kN) Pn (kN) Qn (kN (m) (kN) Tension (kN) (kN) (kN) (kN) 15 0.287 19.388 0.115 Group No -68.224 -13.238 0.000 0.000 0.000 0.000 0.000 14 1.835 123.878 0.734 Group No -42.101 -72.704 0.000 0.000 0.000 0.000 0.000 - 13 3.383 228.368 1.353 Group No -15.979 0.000 0.000 0.000 0.000 0.000 132.170 - 12 4.931 332.857 1.972 Group No 10.143 10.143 0.000 0.000 0.000 0.000 191.636 - - 11 6.479 437.347 2.592 Group No 41.111 41.111 10.143 10.143 8.339 251.253 191.636 - - 10 8.027 541.837 3.211 Group No 86.165 86.165 41.111 41.111 33.798 311.181 251.253 - - 9 9.575 646.326 3.830 Group No 144.219 144.219 86.165 86.165 70.838 371.319 311.181 - - 8 11.123 750.816 4.449 Group No 214.969 214.969 144.219 144.219 118.566 431.651 371.319 - - 7 12.671 855.306 5.068 Group No 298.304 298.304 214.969 214.969 176.731 492.172 431.651 - - 6 14.219 959.795 5.688 Group No 394.177 394.177 298.304 298.304 245.243 552.881 492.172 - - 5 15.767 1064.285 6.307 Group No 578.921 578.921 394.177 394.177 324.062 613.777 552.881 - - 4 13.906 938.674 5.563 Group No 934.577 934.577 578.921 578.921 475.945 545.045 613.777 - - 3 9.964 672.590 3.986 Group No 1436.854 1436.854 934.577 934.577 768.338 398.919 545.045 - - 2 6.022 406.507 2.409 Group Yes 3154.228 3154.228 1436.854 1436.854 1181.272 254.979 398.919 - - 1 2.080 140.424 0.832 Toe No -0.000 -0.000 3154.228 3154.228 2593.166 129.159 254.979

Note: Index 1 is the toe of the slope.

Slope Geometry

Property Value Slope Angle (°) 89 Slope Height (m) 20 Upper Slope Angle (°) 2 Toppling Joint Spacing (m) 2.5 Toppling Joint Dip (°) 60 Overall Base Inclination (°) 35

Rock Properties

roctopple_water.rtop NTNU 30/02/2018, 21:59:37 ROCTOPPLE 1.005 Page 3 of 3

Property Value Rock Unit Weight (kN/m3) 27 Base Shear Strength Model Mohr-Coulomb Base Cohesion (kN/m2) 0.5 Base Friction Angle (°) 35 Base Tensile Strength (kN/m2) 0 Toppling Joint Shear Strength Model Mohr-Coulomb Toppling Joint Cohesion (kN/m2) 0 Toppling Joint Friction Angle (°) 25 Toppling Joint Tensile Strength (kN/m2) 0

roctopple_water.rtop NTNU 30/02/2018, 21:59:37 40 Factor of Safety: 0.564

Stable Toppling 30 Sliding 100% Base in Tension

Upper Slope Angle 2 ° 20

Slope Angle 89 °

2.5 m

Slope Height 20 m 10

Block Base Angle 30 °

Overall Base Inclination 35 ° 0 -10

-10 0 10 20 30 40 Project ROCTOPPLE - Rock Toppling Analysis

Analysis Description

Drawn By Miguel A Sanchez Company NTNU Date File Name ROCTOPPLE 1.005 30/02/2018, 21:59:37 roctopple_water.rtop ROCTOPPLE 1.005 Page 1 of 2

RocTopple Analysis Information ROCTOPPLE - Rock Toppling Analysis

Project Summary

File Name roctopple_water.rtop File Version 1.005

Project Title ROCTOPPLE - Rock Toppling Analysis Author Miguel A Sanchez Company NTNU Date Created 30/02/2018, 21:59:37

General Settings

Units Metric, stress as kPa Unit Weight of Water (kN/m3) 9.81 Analysis Type Deterministic

Analysis Results

Factor of Safety Factor of Safety 0.564

Block Details

Height Weight Base Pn-1,t Pn-1,s Pn-1 Index Yn/x Type Pn,t (kN) Pn,s (kN) Pn (kN) Qn (kN (m) (kN) Tension (kN) (kN) (kN) 15 0.287 19.388 0.115 Group No -59.491 -9.915 0.000 0.000 0.000 0.000 0. 14 1.835 123.878 0.734 Group No -33.041 -55.734 0.000 0.000 0.000 0.000 0. 13 3.383 228.368 1.353 Group No -8.965 -92.437 0.000 0.000 0.000 0.000 0. 12 4.931 332.857 1.972 Group No 10.908 -129.141 10.908 0.000 0.000 0.000 0. 11 6.479 437.347 2.592 Group No 34.784 -166.114 34.784 10.908 -129.141 10.908 9. 10 8.027 541.837 3.211 Group No 67.847 -203.409 67.847 34.784 -166.114 34.784 28. 9 9.575 646.326 3.830 Group No 109.488 -240.931 109.488 67.847 -203.409 67.847 56. 8 11.123 750.816 4.449 Group No 159.541 -278.666 159.541 109.488 -240.931 109.488 90. 7 12.671 855.306 5.068 Group No 217.944 -316.608 217.944 159.541 -278.666 159.541 131. 6 14.219 959.795 5.688 Group No 284.669 -354.758 284.669 217.944 -316.608 217.944 180. 5 15.767 1064.285 6.307 Group No 553.229 -160.307 553.229 284.669 -354.758 284.669 235.

4 13.906 938.674 5.563 Group Yes 1193.121 1440.590 1440.590 553.229 -160.307 553.229 457.

3 9.964 672.590 3.986 Group Yes 1088.428 2055.568 2055.568 1193.121 1440.590 1440.590 1190.

2 6.022 406.507 2.409 Group No 1948.262 -43.354 1948.262 1088.428 2055.568 2055.568 1698. 1 2.080 140.424 0.832 Toe No 0.000 -85.301 0.000 1948.262 -43.354 1948.262 1609.

Note: Index 1 is the toe of the slope. roctopple_water.rtop NTNU 30/02/2018, 21:59:37 ROCTOPPLE 1.005 Page 2 of 2

Slope Geometry

Property Value Slope Angle (°) 89 Slope Height (m) 20 Upper Slope Angle (°) 2 Toppling Joint Spacing (m) 2.5 Toppling Joint Dip (°) 60 Overall Base Inclination (°) 35

Rock Properties

Property Value Rock Unit Weight (kN/m3) 27 Base Shear Strength Model Mohr-Coulomb Base Cohesion (kN/m2) 0.5 Base Friction Angle (°) 35 Base Tensile Strength (kN/m2) 0 Toppling Joint Shear Strength Model Mohr-Coulomb Toppling Joint Cohesion (kN/m2) 0 Toppling Joint Friction Angle (°) 25 Toppling Joint Tensile Strength (kN/m2) 0

External Loads

Water Pressure in Joints

Percent Fill (%) 100 Unit Weight of Water (kN/m3) 9.81

roctopple_water.rtop NTNU 30/02/2018, 21:59:37