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Risk analysis of landslides affecting major transportation corridors in southwestern British Columbia Hazzard, Jennifer 1998

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RISK ANALYSIS OF LANDSLIDES AFFECTING MAJOR TRANSPORTATION CORRIDORS IN SOUTHWESTERN BRITISH COLUMBIA by JENNIFER HAZZARD B.Sc.E., Queen's University, 1996 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Earth and Ocean Sciences We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1998 © Jennifer Hazzard, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of E/zrH-) Osid OclCun SciAnrtS The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT Slope failures on transportation routes can kill or injure motorists, derail trains, damage vehicles, roads and railways, delay traffic, and incur expense to transportation authorities. In southwestern British Columbia, Highways 1 and 99, the British Columbia Railway, the Canadian National Railway, and the Canadian Pacific Railway all traverse mountainous terrain, and as a result are susceptible to a variety of slope hazards. By quantitatively estimating risk at various areas along a transportation route, high-risk areas can be identified, risks can be compared with values accepted by society, remedial programs can be more effectively designed, and their success can be monitored. A database of 3287 slope failure records was compiled for the five routes mentioned above. Of these, 1764 records include volume estimates. The effects of data censoring were reduced by examining spatial and temporal patterns in landslide reporting for failures of different magnitudes on various sections of each route. Magnitude-cumulative frequency relationships were plotted for both rock falls and debris flows on each route. The rock fall relationships each display a power-law distribution for events greater than 1 m3, and are very similar in form over several orders of magnitude. Geological conditions along the routes influence the slope of the magnitude-cumulative frequency slopes. Risk of death due to slope failure on several route segments was calculated using the magnitude-frequency relationships. The estimates of annual probability of death due to rock fall range from 0.008 to 0.10, and are below the upper limits of several risk acceptability criteria. Debris flow risk estimates are less reliable, due to the limited data set. The greatest contribution to risk to life is generally from intermediate rock falls in the Fraser Canyon (1 to 10 m3), and larger rock falls in Howe Sound and the Fraser Lowland (100 to 1000 m3). A C K N O W L E D G E M E N T S The present study was generously supported through a grant from the Terrain Sciences Division of the Geological Survey of Canada (GSC). Dr. S.G.Evans of the GSC took part in steering the progress of this work. Four transportation agencies also supported the study financially and in kind and provided the author with records of landslide occurrence in the study area. They are B.C. Ministry of Transportation and Highways (BCMOTH), CP Rail Systems (CP), C N Rail (CN), and BC Rail (BCR). The project was instigated at the suggestion of Mr. Clive MacKay of CP. The author gives many thanks to Dr. Oldrich Hungr for his guidance and support throughout her time at UBC. Thank you also to Dr. Steve Evans at the GSC, Doug Allen and Brad Follett at BCR, Dave Gerraghty at BC M O T H , Clive MacKay and Chris Bunce at CP, Doug Allen and Tim Keegan at C N for providing vital information and assistance. TABLE OF CONTENTS Abstract . . . . . . . . . ii Acknowledgments . . . . . . . . iii List of Tables . . . . . . . . . vi List of Figures . . . . . . . . . viii CHAPTER 1 OVERVIEW AND SUMMARY 1 1.1 Introduction . . . . . . 1 1.2 Research Objectives . . . . . 3 1.3 Background . . . . . . 4 CHAPTER 2 LITERATURE REVIEW . . . . . 7 2.1 Landslide Hazards . . . . . 7 2.2 Risk Analysis 11 2.3 Risk Analysis for Slope Failures . . . . 12 2.3.1 Hazard Calculations Using Magnitude-Cumulative Frequency Relationships. 16 2.3.2 Vulnerability Calculations . . . 18 2.3.3 Risk Calculations . . . . 19 2.3.4 Acceptability of Slope Failure Risks 20 2.4 Management of Landslide Hazards Along Transportation Routes . . . . . . . 22 2.5 Landslide Hazards on Transportation Routes in British Columbia . . . . . . 26 CHAPTER 3 STUDY AREA 34 3.1 Physiography . . . . . . 34 3.2 Geology . . . . . . 35 3.2.1 Bedrock Geology . . . . 35 3.2.2 Surficial Geology . . . . 36 3.3 Climate. . . . . . . 37 3.3.1 Coast Mountains 37 3.3.2 Fraser Lowland . . . . . 37 3.3.3 Thompson River Valley, Interior Plateau . 38 3.4 Transportation Corridors 39 3.4.1 The Fraser-Thompson Corridor . . . 39 3.4.2 The Howe Sound-Lillooet Corridor 41 CHAPTER 4 LANDSLIDE DATABASE 51 4.1 Data Sources and Collection Procedures . 51 4.2 Event Data . . . . . . 52 4.3 Accident Data . . . . . . 55 iv CHAPTER 5 R O C K F A L L MAGNITUDE-FREQUENCY RELATIONSHIPS 59 5.1 Data Mapping . . . . . . 59 5.2 Elimination of Censoring Effects. . . . 60 5.3 Definition of Sampling Intervals . 66 5.4 Magnitude-Frequency Relationships . . . 70 5.5 Influence of Geology . . . . . 76 5.5.1 Plutonic Rocks . . . . . 77 5.5.2 Sedimentary, Volcanic, and Non-Foliated Metamorphic Rocks 81 5.5.3 Foliated Metamorphic Rocks . . . 85 5.6 Geographic Zones 86 5.7 Influence of Climate 91 5.7.1 Howe Sound-Lillooet Corridor 91 5.7.2 Fraser-Thompson Corridor . . . 93 5.8 Landslide Activity . . . . . 97 CHAPTER 6 DEBRIS FLOW MAGNITUDE-FREQUENCY RELATIONSHIPS 164 6.1 Data Mapping . . . . . . 164 6.2 Sampling Intervals 165 6.3 Magnitude-Frequency Relationships 169 6.4 Influence of Geology 170 6.5 Influence of Climate . . . . . 172 CHAPTER 7 RISK ANALYSIS 184 7.1 Rock fall Risk Calculations for Highway 99 and Highway 1 . . . . . 184 7.2 Debris Flow Risk Calculations for Highway 99 and Highway 1 . . . . . . 192 7.3 Rock fall Risk Calculations for BCR and CPR . 195 7.3.1 Passenger Trains . . . . 195 7.3.2 Freight Trains . 197 7.4 Debris Flow Risk Calculations for BCR . . . 200 CHAPTER 8 CONLCUSIONS 215 Bibliography . . . . . . . . . 222 v L I S T OF T A B L E S 3.1 Mean daily temperatures for various stations within the study area 44 3.2 Days with minimum temperature <0 and maximum temperature >0, for various stations within the study area . . . . . 45 3.3 Rainfall (mm) for various stations within the study area . . . 46 3.4 Snowfall (cm) for various stations within the study area . . . 47 4.1 Recorded damage caused by slope failures on transportation routes in the study area, 1958 to 1996 . . . . . . 57 5.1 Bands within each route, defined based on similar data point density 101 5.2 Sampling intervals used to calculate rock fall frequency per year for each route segment and volume class . 102 5.3 Ages of major rock avalanches crossing the transportation corridors 102 5.4 Magnitude-cumulative frequency slopes for rock falls and slides on each route . . . . . . . . . 103 5.5 Magnitude-cumulative frequency slopes for rock falls in plutonic rocks on each route . . . . . . . . 103 5.6 Magnitude-cumulative frequency slopes for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks on each route 104 5.7 Geographic zones chosen for the Howe Sound-Lillooet Corridor 104 5.8 Geographic zones chosen for the Fraser-Thompson Corridor 105 5.9 Magnitude-cumulative frequency slopes for rock falls in various geographic zones on each route . 105 5.10 Magnitude-cumulative frequency slopes for rock falls in zones of different rock fall activity levels on each route 106 6.1 Sampling intervals used to calculate debris flow frequency per year for each route segment and volume class 174 6.2 Magnitude-cumulative frequency slopes for debris flows on each route . . . . . . . . . 174 7.1 Risk calculations for rock falls/slides on Highway 99, Horseshoe Bay to Squamish . . . . . . . . 202 vi 7.2 Risk calculations for rock falls/slides on Highway 1, Vancouver to Hope . 202 7.3 Risk calculations for rock falls/slides on Highway 1, Hope to Lytton 203 7.4 Risk calculations for debris flows on Highway 99, km 0 to 75 203 7.5 Risk calculations for debris flows on Highway 1, km 125 to 150 . 204 7.6 Risk calculations for rock falls/slides on BCR, Horseshoe Bay to Squamish 204 7.7 Risk calculations for rock falls/slides on BCR, Squamish to Whistler 205 7.8 Risk calculations for rock falls/slides on BCR, Pemberton to Lillooet 205 7.9 Risk calculations for major freight train accidents due to rock falls/slides on BCR, Horseshoe Bay to Squamish . . . . . 206 7.10 Risk calculations for major freight train accidents due to rock falls/slides on BCR, Squamish to Whistler . . . . . . 206 7.11 Risk calculations for major freight train accidents due to rock falls/slides on BCR, Pemberton to Lillooet . . . . . . 207 7.12 Risk calculations for major freight train accidents due to rock falls/slides on CPR, Vancouver to Hope . . . . . . 207 7.13 Risk calculations for major freight train accidents due to rock falls/slides on CPR, Hope to Lytton 208 7.14 Risk calculations for major freight train accidents due to rock falls/slides on CPR, Lytton to Thompson 208 7.15 Risk calculations for major freight train accidents due to rock falls/slides on CPR, Thompson to Kamloops . . . . . . 209 7.16 Risk calculations for debris flows on BCR, Horseshoe Bay to Lillooet 209 7.17 Risk calculations for major freight train accidents caused by debris flows on BCR, Horseshoe Bay to Lillooet. . . . . . 210 vii LIST OF FIGURES Figure 1.1 Study area map . . . . . . . 6 Figure 2.1 Risk acceptability criteria 33 Figure 3.1 Bedrock geology of the study area 48 Figure 3.2 Monthly rain data for various stations in the study area 49 Figure 3.3 Monthly snow data for various stations in the study area . 50 Figure 4.1 BCR Landslide intensity rating system 58 Figure 5.1 Locations, volumes and dates of rock falls on Highway 99 107 Figure 5.2 Locations, volumes and dates of rock falls on Highway 1 . 109 Figure 5.3 Locations, volumes and dates of rock falls on BCR 111 Figure 5.4 Dates of rock falls on CPR 113 Figure 5.5 Locations and dates of rock falls on CNR 114 Figure 5.6 Spatial distribution of rock falls over time, showing bands of similar point density 115 Figure 5.7 Temporal frequency of rock falls in various volume classes; Highway 99, Band A 116 Figure 5.8 Temporal frequency of rock falls in various volume classes; Highway 1, Band D 117 Figure 5.9 Temporal frequency of rock falls in various volume classes; BCR . 118 Figure 5.10 Temporal frequency of rock falls in various volume classes; CPR . 119 Figure 5.11 Temporal rock fall frequency for grouped volume classes; Highway 99, Band A 120 Figure 5.12 Temporal rock fall frequency for grouped volume classes; Highway 99, Band B . . . . . . 121 Figure 5.13 Temporal rock fall frequency for grouped volume classes; Highway 1, Bands A, B, C, D, G 122 Figure 5.14 Temporal rock fall frequency for grouped volume classes; Highway 1, Bands E and F . . . . . 123 viii Figure 5.15 Temporal rock fall frequency for grouped volume classes; BCR 124 Figure 5.16 Temporal rock fall frequency for grouped volume classes; CPR 125 Figure 5.17 Start year of recording interval vs. regression slope; Highway 99 . 126 Figure 5.18 Start year of recording interval vs. regression slope; Highway 1 127 Figure 5.19 Start year of recording interval vs. regression slope; BCR. 128 Figure 5.20 Start year of recording interval vs. regression slope; CPR . 129 Figure 5.21 Magnitude-cumulative frequency plots for each route 130 Figure 5.22 Magnitude-cumulative frequency plot; Highway 99, Bands AandB 132 Figure 5.23 Magnitude-cumulative frequency plot; Highway 1 without Band F . 132 Figure 5.24 Magnitude-cumulative frequency plots for each route; events with unknown volumes distributed from 0.01 to 1 cubic m 133 Figure 5.25 Corrected magnitude-cumulative frequency plots for all routes 137 Figure 5.26 Corrected magnitude-cumulative frequency plots for all routes; 30 million cubic m events not shown . . . . 138 Figure 5.27 Spatial frequency of rock falls within chosen sampling periods; Highway 99 . . . . . . . 139 Figure 5.28 Spatial frequency of rock falls within chosen sampling periods; BCR 141 Figure 5.29 Spatial frequency of rock falls within chosen sampling periods; Highway 1 . . . . . . 143 Figure 5.30 Magnitude-cumulative frequency plot for rock falls in plutonic rocks; Highway 99, Bands A and B 145 Figure 5.31 Magnitude-cumulative frequency plot for rock falls in plutonic rocks; BCR . . . . . . . 145 Figure 5.32 Magnitude-cumulative frequency plot for rock falls in plutonic rocks; Highway 1 without Band F 145 Figure 5.33 Magnitude-cumulative frequency plots for rock falls in plutonic rocks on all routes . . . . . . 146 Figure 5.34 Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; Highway 99 Band A 147 Figure 5.35 Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; BCR 147 Figure 5.36 Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; Highway 1 without Band F . 147 Figure 5.37 Magnitude-cumulative frequency plots for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks on all routes 148 Figure 5.38 Magnitude-cumulative frequency plot for rock falls in foliated metamorphic rocks; Highway 1 . 149 Figure 5.39 Magnitude-cumulative frequency plots for rock falls in different rock types; Highway 99 Bands A and B . 150 Figure 5.40 Magnitude-cumulative frequency plots for rock falls in different rock types; BCR 151 Figure 5.41 Magnitude-cumulative frequency plots for rock falls in different rock types; Highway 1 without Band F 152 Figure 5.42 Magnitude-cumulative frequency plot for rock falls on Highway 99 Zone 1; Horseshoe Bay to Squamish. 153 Figure 5.43 Magnitude-cumulative frequency plots for rock falls on BCR Zones 1, 2 and 4 . . . . . . 154 Figure 5.44 Magnitude-cumulative frequency plots for rock falls on Highway 1 Zones 1 and 2 . . . . . 155 Figure 5.45 Magnitude-cumulative frequency plots for rock falls on CPR Zones 1 to 4 156 Figure 5.46 Monthly frequency and magnitude of rock falls from Horseshoe Bay to Squamish . . . . . . 157 Figure 5.47 Monthly frequency and magnitude of rock falls from Squamish to Whistler . . . . . . . 157 Figure 5.48 Monthly frequency and magnitude of rock falls from Whistler toPemberton . . . . . . . 158 Figure 5.49 Monthly frequency and magnitude of rock falls from Pemberton toLillooet . . . . . . . 158 Figure 5.50 Monthly frequency and magnitude of rock falls from Vancouver to Hope. . . . . . . . 159 Figure 5.51 Monthly frequency and magnitude of rock falls from Hope to Lytton . . . . . . . . 159 Figure 5.52 Monthly frequency and magnitude of rock falls from Lytton to Spences Bridge . 160 Figure 5.53 Monthly frequency and magnitude of rock falls from Spences Bridge to Kamloops 160 Figure 5.54 Magnitude-cumulative frequency plots for rock falls in different activity zones; Highway 99 Bands A and B 161 Figure 5.55 Magnitude-cumulative frequency plots for rock falls in different activity zones; BCR . . . . . . 162 Figure 5.56 Magnitude-cumulative frequency plots for rock falls in different activity zones; Highway 1 without Band F 163 Figure 6.1 Locations, volumes and dates of debris flow events on Highway 99 175 Figure 6.2 Locations, volumes and dates of debris flow events on Highway 1 . . . . . . 176 Figure 6.3 Locations, volumes and dates of debris flow events on BCR 178 Figure 6.4 Magnitude-cumulative frequency plot for debris flows on Highway 99 . . . . . . . 180 Figure 6.5 Magnitude-cumulative frequency plot for debris flows on BCR 181 Figure 6.6 Magnitude-cumulative frequency plot for debris flows on Highway 1 . . . . . . . 182 Figure 6.7 Magnitude-cumulative frequency plots for debris flows on all routes . 183 Figure 7.1 Longitudinal probability of encounter 211 Figure 7.2 Highway rock fall risks according to volume class 212 Figure 7.3 Rock fall risks on BCR according to volume class 213 Figure 7.4 Risks of freight train accidents due to rock falls on CPR, according to volume class . . . . . . . 214 xi CHAPTER 1 - OVERVIEW AND SUMMARY LI - Introduction Slope failure on transportation routes is a common concern in British Columbia. Rock falls, debris flows, and other failures can interrupt traffic, damage roads or railways, cause accidents, damage vehicles or trains, and even cause injury or death. In southwestern British Columbia, Highways 99 and 1, the British Columbia Railway (BCR), the Canadian National Railway (CNR), and the Canadian Pacific Railway (CPR) all travel through mountainous terrain. At least twenty-six deaths due to landslides have been reported on these routes in the past thirty-five years. Economic losses due to road and track damage, traffic delays, train delays and derailments, and damage to property, are a continuing concern to highway and railway authorities in the province. Clearly, the prediction of slope failures in British Columbia is an important topic of study. While the risks due to landslides can not feasibly be reduced to zero at every location on a transportation route, it is desirable to reduce risks to a level acceptable by society. Without quantitative estimates of risk due to slope failure, highway and railway authorities can be susceptible to public outcry and legal consequences in the event of a slope failure which causes damage, delay, injury or death. It is important that the level of risk on transportation routes be known, to compare with other acceptable societal risks, and to effectively assign resources to reduce risks which are unacceptable. Therefore, the calculation of risk is an important step, in that it allows higher-risk areas to be targeted, and resources to be allotted effectively for mitigation. In order to calculate risk, the probability of landslide occurrence must be determined. While this can often be accomplished by detailed field studies combined with inventories of past failure events, the latter can be used alone for estimating slope failure probabilities over very extensive study areas. Slope failure risk on a transportation route includes risks due to small, frequent events as well as large, uncommon events. Decisions regarding the allocation of resources 1 for mitigation of slope failure hazards are better made if the risks from landslides of various magnitude classes can be quantified. Slope failure probabilities for different volume ranges are calculated by establishing frequency-magnitude relationships for each route or part of a route. A significant obstacle in this type of analysis is the censoring of slope failure data due to inconsistent reporting. To determine accurate frequency-magnitude relationships, the effects of data censoring must be removed. Risk calculations also include assessments of the consequences of slope failure. For transportation routes, traffic volumes and velocities must be estimated to determine the probability of a landslide affecting a vehicle at any given time. Geological and climatic conditions can also be taken into account when determining risk levels at various areas of each route. This thesis details the calculation of landslide probabilities and risks on Highways 99 and 1, BCR, CPR, and C N R in southwestern British Columbia. The study area location is shown in Figure 1.1. Risks arising from a variety of slope failure types from both cut and natural slopes are investigated. High-risk areas are identified, and the risk values are compared with other acceptable societal risks. The research is presented in the following stages: 1 - review of research on landslide hazards, risk analysis, the management of landslide hazards on transportation routes, and specifically, landslide hazards on transportation routes in British Columbia; 2 - description of the study area physiography, geology, climate, and of the transportation routes themselves; 3 - description of the landslide database compiled for this study, including information sources, collection procedures, and an overview of the event data and accident data; 4 - development of frequency-magnitude relationships for rock fall events on each route; 2 5 - development of frequency-magnitude relationships for debris flow events on each route; and 6 - estimation of risk for various zones on each route. 1.2 - Research Objectives The primary objectives of this research are: to compile a comprehensive database of all available landslide records for five major transportation routes in southwestern British Columbia; to construct magnitude-frequency relationships for rock falls and debris flows on each route, and for specific high-frequency sections of the routes; to investigate the influence of geology and climate on landslide frequency and magnitude; and to estimate landslide risk values on these routes. The existence of a comprehensive database of landslide records is key in determining hazard and risk values for a transportation route. Even if no quantitative risk values are calculated, having organized records of landslide events on a highway or railway can assist in landslide studies and investigations, and therefore in the mitigation of landslide hazards. While landslide records for past events may be missing or incomplete, the systematic compilation of a slope failure database can highlight these censoring effects, and could possibly encourage future diligence in landslide reporting. Landslide magnitude-frequency relationships are the key to determining landslide hazards and risks in this study. By plotting volume versus cumulative frequency for each of the transportation routes, or for specific sections of each, conditions on each route can be compared. The overall pattern of decreasing frequency with increasing magnitude can be quantified, and used to determine the magnitude range of the highest-risk events. An important objective of this study is to examine any similarities in the shapes of landslide magnitude-frequency curves for different routes, and particularly for sections of the routes which traverse similar geological settings. 3 Investigating the effects of geology and climate on the magnitude-cumulative frequency relationships and overall risk estimates is important for future risk analyses in different areas. If it can be determined that the magnitude-frequency curves are alike for all highway or railway sections traversing similar geologic and climatic conditions, then it may be possible to extend this research to probability and risk analyses for other areas with similar geology and climate. The determination of landslide hazards and risks on transportation routes is valuable to highway and railway authorities, because of economic concerns and legal responsibilities. According to the Canadian Supreme Court, agencies responsible for maintaining highways may be liable for compensating rock fall victims (Cory and Sopinka, 1989). Therefore, the determination and reduction of rock fall risks to users of both highways and railways is important to the Ministry of Transportation and Highways (MOTH), and to the railway companies. Additionally, landslides can damage or destroy road surfaces, rails, vehicles, trains, bridges, retaining walls, and other structures. They can also cause delays or closures of highways and railways. The costs associated with these damages and delays may be effectively reduced by calculating landslide hazards and risks along each route. Further, the effectiveness of remedial programs can be assessed and documented by the calculation of slope failure risks over time. If landslide risk estimates can be made, it is possible to compare the landslide risk for a given area of a transportation route with other societal risks. If landslide risks exceed acceptable levels in certain areas, then action can be taken to assign suitable resources to reduce those risks. 1.3 - Background This research is a joint project of the University of British Columbia and the Geological Survey of Canada, with support from the British Columbia Ministry of Transportation and Highways (MOTH), the British Columbia Railway (BCR), CP Rail Systems Ltd. (CPR), and the 4 Canadian National Railway (CNR). The study was led by Dr. Oldrich Hungr and Dr. Steve Evans. Landslide data and traffic statistics for each of the transportation routes were provided primarily by MOTH and the railway agencies. Further data on large slope failures, including rock avalanches, were provided by GSC files, and the personal files of Dr. O. Hungr and Dr. S.G. Evans. 5 Figure 1.1- Study area 6 C H A P T E R 2 - L I T E R A T U R E R E V I E W 2.1 - Landslide Hazards The terms used in this paper to describe the various types of slope failures will be those presented by Varnes (1978), and adapted by Cruden and Varnes (1996). Slope failures are divided into five categories based on the type of movement and the type of material. These categories are: falls, topples, slides, spreads, and flows. Failures can be further characterized by their state, distribution, style, velocity and water content. For the purposes of this study, only movement type and material type will be considered, due to the very limited descriptions included in most slope failure reports in the study area. The material type involved in a slope failure can be either bedrock or soil. Soil can be further divided into debris and earth (Varnes, 1978). Debris contains a significant proportion of coarse material (20 to 80 percent of particles larger than 2 mm), while earth is a finer soil material (80 percent or more of particles smaller than 2 mm). Again, the landslide reports used in this study often lack detailed descriptions of material type, so labeling the material rock or soil is often the only characterization which can be made. Therefore, the term 'earth' is generally eliminated from failure descriptions in this paper, and any slope movements not involving bedrock are described as debris failures. A fall is a mass movement in which rock or debris detaches from a slope and travels mainly by free-falling or bouncing, with little or no shear displacement (Varnes, 1978). If the material is bedrock, the event is called a rock fall, but if the material consists of soil, talus, or any other overburden material, the event is labeled a debris fall. Falls are very rapid to extremely rapid (typical velocities are greater than 3 m/min). The travel path, velocity, and energy of falling particles depends on slope geometry and material properties (Hungr and Evans, 1988). A topple is the forward rotation of a mass of rock or soil out of a slope, about a pivot point or axis (Cruden and Varnes, 1996). The geometry and spacing of discontinuities in a slope often 7 control toppling susceptibility. For example, joints which dip steeply into a slope, with strike similar to the slope face, contribute significantly to toppling hazards. The presence of water or ice in discontinuities can also increase the likelihood of toppling. Falls or slides may result from initial toppling movement, depending on the geometry of the moving mass, the slope, the rupture surface, and the discontinuities. The rate of toppling can be extremely slow (less than 16 mm/year) to extremely rapid (greater than 5 m/s). Flexural topples, which involve the bending forward of columns which break in flexure, occur most often in slates, phyllites and schists, and are generally slow failures (Goodman and Bray, 1976). Block toppling is a much more rapid mode of failure, and involves the overturning movement of individual columns, separated by widely-spaced joints (Goodman and Bray, 1976). In slope failure reports from highway or railway maintenance workers, toppling is not generally recognized. Therefore, toppling failures, while they may be important in the study area, are generally described as rock falls or rock slides in the database. A slope failure which involves downslope movement of rock or soil mainly along a rupture surface or thin shear zone, during which the material remains in contact with the slope, is a slide. Slides can be rotational (often called slumps), translational, or compound. Rotational slides have concave rupture surfaces, and are generally deep-seated. They occur most often in homogeneous materials, such as fills. Purely rotational slides in natural materials are rare, since rupture surfaces are normally affected by discontinuities or weak horizons. Translational slides have planar or gently undulating rupture surfaces, and are generally shallower than rotational slides (Cruden and Varnes, 1996). The failure surfaces often follow discontinuities in the rock or soil mass, or the contact between bedrock and overburden. Whereas rotational sliding tends to restore equilibrium to a displaced mass, translational sliding will continue as long as the slope remains steep enough. As the slide progresses, the mass may break up, and water content may increase, until the movement becomes flow-like. Slides which have rupture surfaces with steep main scarps which 8 flatten with depth, and are intermediate between rotational and translational slides in depth, are called compound slides. They often indicate the presence of a weak layer in the rock or soil mass. Evans and Hungr (1993) define fragmental rock falls as slope processes at the lower end of the magnitude spectrum (<105 m3), characterized by the independent movement of individual rock particles (p. 620). Rock avalanches and rock fall avalanches are characterized by the disintegration of particles into a rapid movement of unsorted fragments (Evans and Hungr, 1993). While the volume limit is not clearly defined, rock slides, rock avalanches, and rock fall avalanches are generally much larger failures (>106 m3) than fragmental rock falls (Evans and Hungr, 1993). The distinction between a fragmental rock fall and a rock slide or rock avalanche, based on the type of movement, is not always easily made after the failure has occurred. In transportation route maintenance reports, the terms rock fall and rock slide are often used interchangeably, to describe any slope failure event resulting in rocks on or near the road or railway. Therefore, the distinction between rock falls and rock slides in this paper is made based on volume, according to the values suggested by Evans and Hungr (1993). Smaller failures of less than 105 m3 are labeled rock falls, while larger magnitude failures, in which the moving particles act more as a coherent mass, are called rock slides. Extremely large failures in bedrock (> 106 m3) are labeled rock avalanches. Hutchinson (1988) gives a definition of a mudslide, as a complex, composite, retrogressive failure in moist or wet clayey material. However, the term mudslide is generally used in highway and railway maintenance reports to describe failures which Cruden and Varnes (1996) would characterize as debris or earth flows. In this study, the detail of reporting required to characterize a failure as a mudslide was generally not available. As slow earth flows in the study area are restricted to the weak Interior rocks from Cache Creek to Kamloops, it was assumed that any failures outside this area which were described as "mudslides" in failure reports, were actually debris flows. 9 Spreads involve the extension of a cohesive rock or soil mass, and the subsidence of that fractured mass into softer underlying material (Cruden and Varnes, 1996). They may result from the liquefaction or flow of the softer underlying material. Rock spreads do not form identifiable rupture surfaces (Varnes, 1978). Block spreads are extremely slow, typically extremely large failures in rock, overlying softer material which becomes squeezed into fractures in the rock. Liquefaction spreads are very rapid failures in sensitive clays and silts, on very gentle slopes. Neither block spreads nor liquefaction spreads are common risks to transportation routes in the study area, and are generally not a consideration in this paper. Flows are slope movements in which the distribution of velocities resembles that in a viscous liquid (Cruden and Varnes, 1996). There is a complete continuum from sliding to flowing failures, depending on water content, mobility, and the development of the movement. Debris flows involve the flow-like movement of highly saturated debris in a pre-existing channel or gully. They may move in a series of surges or pulses, and can extend for many kilometres before depositing in lower-gradient channels. Channels on steep slopes on which the vegetation has been removed by fire or harvesting are susceptible to debris flows, particularly during heavy rains. Most debris flows in the present study area occur in creeks and rivers which cross or approach the transportation routes. Large boulders, tree stumps and other debris are transported rapidly downslope in a dangerous rush of soil and water. In highway or railway records of mass movements, debris flows may be inaccurately described as mudslides, washouts, or debris floods. The term "debris flood", not discussed by Cruden and Varnes (1996), can be used to describe very rapid, relatively non-destructive, surging flows of heavily debris-charged water in steep channels (Hungr, unpublished 1998). Debris floods have peak discharges comparable to water floods, in contrast to the much higher peak discharges of debris flows. The maximum particle size transported by debris floods is in the order of several tens of centimetres in typical mountain streams, comparable with the peak depth in a major flood. 10 Bedrock flows are extremely slow, creeping movements along many unconnected shear planes, resulting in folding, bending or bulging (Varnes, 1978). Because these failures are so slow, they do not pose any significant short-term threat to transportation routes in this study area, and are therefore not considered in the database. Debris avalanches are larger flows, which often occur on open slopes. These extremely rapid flows are potentially even more hazardous than debris flows because of the difficulty in predicting their locations or flow paths. This difficulty arises from the fact the flow does not follow an existing channel or gully. Lahars are extremely large flows in volcanic rock and debris. Volcanic ash and debris on the volcano's slopes is mobilized and carried downslope with water from crater lakes, streams, water vapour, or melting snow and ice. The events recorded in the database for this study have been divided into two categories based on failure type. The first category encompasses falls, slides and topples, as well as large-scale rock avalanches. While it is recognized that these involve a variety of movement and material types, the term 'rock fall' is useful, for ease of communication, to encompass all failures falling into this category. The second category includes all flow records. In this category, only debris flows are of great importance to transportation routes in the study area. 2.2 - Risk Analysis Risk analysis is defined by the Canadian Standards Association (CAN/CSA, 1991) as a three step process involving scope definition, hazard identification and risk estimation. For any study involving risk analysis, a clear definition of risk is required. In engineering geology, terms such as risk and hazard are not used consistently worldwide. However, they are defined concisely by Varnes (1984), and these definitions form the basis for most contemporary engineering risk analyses. Fell (1994) summarizes Varnes' definitions, with some changes and additions, and these 11 are the definitions used in this study. The following are the general definitions given by Fell (1994) and C A N / C S A (1991), not specifically for slope failures. Danger Hazard Magnitude Vulnerability Risk Elements at Risk - the potentially damaging event in question - the probability of occurrence of the potentially damaging event - also used as a synonym for "danger" - the quantitative size, duration or intensity of the event - the consequence of the event, or degree of loss, expressed as a number from 0 to 1 (no damage to total loss) - the expected losses due to a particular hazard for a given area and time period, or the product of the probability of the event and the degree of loss - the population, structures, etc. potentially affected by the danger Risk = Hazard * Vulnerability Specific Risk Total Risk - the probability times the vulnerability for a given element - the total expected loss over all potential dangers in the study area Total Risk = Specific Risk * Elements at Risk 2.3 - Risk Analysis for Slope Failures For risk analysis problems relating to landslides, the danger is the slope failure itself. Magnitude refers to the volume of material displaced (Fell, 1994). Hazard is determined by assessing the probability of occurrence of a landslide in a given study area, for a given time period. 12 Various means of assessing landslide probability are given by Fell (1994). The first is probabilistic analysis, which involves engineering methods and slope stability analyses. The second, which is to be used in the present study, is the analysis of historic data. Other methods involve relating landslides to precipitation, and the use of geomorphological and geotechnical information. The latter is the most common form of determining landslide probability, but requires detailed field studies, which can be expensive and time consuming. The Resources Inventory Committee, Government of British Columbia (1996), describe the various methods of terrain stability mapping in British Columbia. Terrain stability mapping involves delineating zones of a study area that are stable, and those which are potentially or currently unstable. Probabilities of failure are assigned to these zones, and in some cases, associated risks are assessed. These maps can be used in development planning, land use planning, and the planning of linear projects such as transportation routes or power lines. On terrain stability maps, a given study area is divided into polygons, showing areal terrain stability map units. Each polygon is assigned a terrain stability class. For linear maps or features, linear segments are used instead of polygons. A terrain stability map of landslide initiation zones should include an identification of the potential landslide types, an estimate of potential landslide magnitudes, and an estimate of landslide probabilities. In the runout zone, a terrain stability map should include magnitude-probability relationships for each failure that could enter the runout zone in question, runout analyses, and a summary of elements at risk and their vulnerabilities (Resources Inventory Committee, 1996). Various methods exist for producing terrain stability maps. The study of past events is very useful, and often landslide inventory maps, landslide hazard and/or risk maps, and landslide density maps are used in delineating stability polygons or linear segments (Resources Inventory Committee, 1996). The authors warn that using an inventory of past events is alone often inadequate in determining stability, because this type of study deals only with failures over a given 13 time period, and fails to consider cyclic failures, or the effects of changed conditions. However, if a long sampling period is considered, or if information is gathered over several time periods, this shortcoming can be in part overcome. Field work and analysis of air photographs are therefore useful in establishing critical terrain characteristics which influence stability. The use of the BC Terrain Classification System (Howes and Kenk, 1996) is suggested in delineating polygons of similar terrain characteristics. Methods described by the BC Ministry of Forests (1995) are also widely used to describe terrain attributes and to assess stability. Many landslide hazard and risk studies have involved the analysis of historic data, based On the compilation of event inventories, as part of the hazard assessment. However, studies in which the compilation of historical data and construction of magnitude-frequency relationships are the sole factors in assessing rock fall probability are rare. The benefit of using this kind of statistical approach has been pointed out by Harden and Viberg (1988), in that regional landslide hazards can be assessed without expensive, detailed field studies, which may be impractical for a study of great spatial scale. Most studies which involve gathering historical rock fall data are for the purpose of hazard mapping or zonation. For example, Cascini et al. (1991) collected data on 74 landslides over a 9km2 area in Italy in order to define zones of low, medium and high hazard. They also conducted detailed field mapping, and considered factors such as geomorphology and state of weathering when assessing relative hazard. A hazard assessment of a small area in Northern Ireland involved the collection of historical rock fall data in a single rock type (Douglas, 1980). A frequency-magnitude relationship was established to show that, as expected, high magnitude events were less frequent than low-magnitude events. However, rock and terrain characteristics determined through field studies, not the frequency-magnitude relationship, were used to quantify hazard in the area. Three other studies which involved the compilation of rock fall or debris flow inventories as a small part of a hazard assessment were conducted by Gardner (1977), Culshaw and Bell 14 (1991) and Moon et al. (1991). Gardner (1977) assembled an inventory of high-magnitude slope failure events in Highwood Pass, Alberta. Culshaw and Bell used newspapers and local knowledge to collect data for 18 rock falls in James Valley, St. Helena. Field studies were also conducted to determine current conditions, and probable failure mechanisms, in order to define high hazard areas. The study by Moon et al. involved compiling an inventory of debris flow events in a small area near Melbourne, Australia. This information was used, along with the identification of risk factors by field mapping, to assess the probable magnitude of potential events. From this, a relative hazard ranking was established for the area. Rood (1984) assembled a large inventory of debris slides and debris flows in the Queen Charlotte Islands, to study the effects of deforestation and road construction on landslide frequency and volume. 1337 landslides up to 40 years old were documented over a 350 km2 study area. Landslide data was gathered using measurements from aerial photographs. The purpose of this study is to compare landslide frequency and yield for forested vs. logged terrain, and to assess the effect of logging on landslide debris entering streams. Therefore, while frequencies and magnitudes of landslides are given, future probabilities, hazards and risks are not estimated, and magnitude-frequency relationships are not considered. Hazard maps are commonly compiled as part of hazard or risk studies of areas susceptible to slope failure. Plotting a hazard map involves zoning the area into units which are homogeneous in terms of the probability of occurrence of a certain danger, such as slope failure. Dearman (1991) gives an example of a hazard map for Aspen, Colorado, in which zones of potential occurrence of various geological hazards are shown. Risk maps are similar, but the potential consequences of the given danger are also considered in delineating the zones. Hazard and risk maps are produced by integrating important information from other types of maps and reports. For example, landslide susceptibility maps, in which the area is divided into zones of relative landslide 15 hazard or risk, are compiled based on past slope failure events, current slope conditions, and climatic influences (Dearman, 1991). An example of this type of hazard mapping is the landslide susceptibility maps of the Santa Cruz Mountains in California (USGS, 1976). To produce these maps, data from geological maps, slope maps, and landslide inventory maps were taken into consideration, and synthesized. The ZERMOS landslide susceptibility maps used in France portray the degree of risk for various different types of slope failures. Activity, rate of movement, and potential consequences are considered in defining the zones for these maps. As illustrated by these examples, risk analyses for slope failures are often qualitative, the results presented in terms of risk zones, labeled, for example, 'low', 'moderate', or 'high'. While these results are valuable, it is often desirable to calculate quantitative risk values, to compare landslide risks with acceptability thresholds, or other societal risks. A quantitative value of risk requires the calculation of both hazard and vulnerability. 2.3.1 - Hazard Calculation Using Magnitude-Cumulative Frequency Relationships Calculation of hazard based on the analysis of historical data often involves the construction of magnitude-cumulative frequency relationships. As expected, the frequency of slope failure events generally increases with decreasing volume. If all past events on record are arranged in order of decreasing volume, and the frequencies cumulatively summed, then volume can be plotted against cumulative frequency, or probability of exceedance, on a log-log graph. Directly from the magnitude-cumulative frequency graph, the probability of an event exceeding a given volume can be determined, assuming that past relationships continue into the future. Probability density functions can then be derived from the magnitude-cumulative frequency relationships, if they are required. In the current research, probability density functions were not investigated, as 16 the desired annual frequency values could be read directly from the magnitude-cumulative frequency curves. A study of boulder falls from natural slopes in Hong Kong, by ERM-Hong Kong, Ltd. (1996), outlines the methodology for assessing risk, based in part on magnitude-frequency relationships. Risk of fatality is estimated by determining the frequency of boulder falls, and assessing the consequences of falls in a series of boulder size categories. As part of the study, 74 boulder falls over a 17 year period were ranked in order of decreasing volume. Cumulative frequency per year values were assigned to each event, based on incremental frequency per year values of 1/17 (0.0588). Cumulative frequency per year was then plotted against volume on a log-log scale, resulting in a linear relationship for volumes greater than 1 m3. Cumulative frequency per year was also plotted against vertical travel distance, again yielding a linear relationship on a log-log scale, for travel distances from 2.5 to 50 m. Other factors, such as boulder, slope and climate characteristics are used in the risk analysis, but the frequency-magnitude relationships are an important part of the study. The frequency-size relationship of landslides, which are a natural result of the breaking down of the earth, has a fractal distribution (Turcotte, 1997). Fractal distributions, first introduced by Mandelbrot (1967), are used to describe scale-invariant phenomena such as faults and earthquakes. Turcotte (1997, pp. 1-2) writes that, "A fractal distribution requires that the number of objects larger than a specific size has a power-law dependence on the size." For example, the Gutenberg-Richter law for earthquakes states that the cumulative frequency of events with a seismic moment greater than M 0 is a power-law function of M 0 . This fractal relationship displayed by earthquakes of a certain magnitude range is directly analagous to the frequency-size distribution of landslides (Pelletier et al., 1997). Several studies have shown that when cumulative landslide frequency is plotted against landslide area or volume, the relationship is linear on a log-log scale, for a certain range of magnitudes (e.g. Pelletier et al., 1997; Gardner, 1970). 17 An inventory of small- to medium-scale rock falls was compiled for the Lake Louise area of Alberta by Gardner (1970). A magnitude-cumulative frequency curve was established for these events, showing a power-law relationship between landslide frequency and volume. Pelletier et al. (1997) present cumulative frequency-size distributions, using landslide area as a measure of size, for large landslides in three different areas, with different triggering factors. The three data sets include: 3424 landslides in Japan, triggered by both heavy rainfall and seismic activity; large landslides from two areas in Bolivia, triggered only by heavy rainfall; and more than 11000 landslides triggered by the 1994 Northridge, California earthquake. All of the data sets show power-law cumulative frequency-size distributions, with exponents of-1.6 to -2, for landslides with areas greater than 10"2 km2. From this, the authors suggest that cumulative frequency-size distributions for large landslides are very similar, despite different triggering mechanisms. They also note that the distributions are very similar for each of thirteen different lithologic units in the large data set for Japan. Each of the cumulative frequency-size distributions plotted in this study show a tailing off, or departure from the power-law dependence, for landslides smaller than about 10~2 km2. The authors suggest (p. 262) that this is not a result of an incomplete data set, because the, "roll off is at a scale that is much larger than the resolution scale of the data set." Instead, it is suggested that landslides are fundamentally affected by soil moisture, which also obey power-law statistics above a certain threshold. The authors stress the importance of soil moisture remote-sensing and modeling in landslide hazard assessment. 2.3.2 - Vulnerability Calculations Vulnerability in landslide risk analyses can be assessed in terms of fatalities, injuries, damage to property, or interrupted economic activity (Varnes, 1984). Where vulnerability represents the loss of life, injury, or destruction of property due to impact by a landslide, the probability of that impact, given the occurrence of the slope failure, must be determined. The 18 probability of impact is the product of the probability of spatial impact (that the element at risk is affected by the slope failure, given that it occurs) and the probability of temporal impact (that the element at risk occupies the location of the slope failure at the time that it occurs). This product can then be multiplied by the expected damage cost or probability of injury or loss of life given impact, to give the total vulnerability. Vulnerability can be a very difficult quantity to estimate. For example, the vulnerability of a person driving a vehicle, for a small rock fall, can range from close to zero to one (Cruden, 1997). If the vehicle sustains no damage, the vulnerability value is very low, but if the rock pierces the windshield and impacts the driver, causing death, the vulnerability is one. Therefore, vulnerability is often an estimated value based on previous experience or judgement (IUGS Working Group on Landslides, 1997), and the variability can often be high, contributing to high variability in the calculated risk. In general, vulnerability increases with increasing landslide volume (Cruden, 1997). Because hazard decreases with increasing volume, vulnerability is likely negatively correlated with hazard. In considering landslide risk on transportation routes, there may also be a negative correlation between elements at risk and their vulnerability. This arises from the fact that large, multi-passenger vehicles are generally stronger and sturdier, and more skillfully driven, than smaller vehicles carrying fewer passengers (Cruden, 1997). 2.3.3 - Risk Calculations The product of the hazard and vulnerability calculated by the above methods gives a quantitative measure of risk from a slope failure. For this value to be meaningful, the elements at risk must be clearly defined (Fell, 1994). In a study by Berggren et al. (1991) of landslide susceptibility in clay, the evaluation of consequence involves taking an inventory of threatened 19 objects and assigning a specific score for each. Risk is calculated according to a form of Varnes' equation: Risk = Probability * Consequence. Similarly, rock slopes in Hong Kong were ranked according to a system proposed by Brand (1988). Each slope was assigned a total risk score, which was defined as the product of an instability score and a consequence score. In landslide risk analyses, the specific risk of one specific individual being killed by a slope failure is entirely different from the risk of at least one individual in a given population being killed by a slope failure within a given time period. In general, the latter value is more meaningful. If a quantitative measure can be made of the risk of slope failure fatality to a given population, within a given time period, then this value can be compared with other values of societal risks, to determine its acceptability. 2.3.4 - Acceptability of Slope Failure Risks The International Union of Geological Sciences (IUGS) Working Group on Landslides (1997, p. 12) define acceptable risk as, "A risk for which, for the purposes of life or work, we are prepared to accept as it is with no regard to its management. Society does not generally consider expenditure in further reducing such risks justifiable." A problem with landslide risk analyses is that there is no published value of acceptable risk specifically for landslides (Fell, 1994). Decisions regarding risk acceptability may vary from project to project, based on the relation to tolerable risk criteria in other engineering industries, familiar risks such as driving a car or drowning, or landslide risks in similar environments (IUGS Working Group on Landslides, 1997). The general principles in establishing tolerable risk criteria, outlined by the IUGS Working Group on Landslides (1997), include the following guidelines: the risk from a given hazard to a 20 person should not be significant compared to other everyday risks, and it should be reduced wherever reasonably practical; the risk o f occurrence of a landslide should be low i f the possible resulting loss o f life is high; higher risks are likely to be tolerated for situations in which the risk cannot be controlled because of financial or other limitations; and higher risks are likely to be tolerated for existing slopes than for planned projects. The I U G S Working Group on Landslides (1997) also indicate that risk tolerance is lower for engineered slopes, including natural slopes under monitoring or risk mitigation measures, than for completely natural slopes. The difference in acceptability of voluntary and involuntary risks is described by Fell (1994). He points out that society is will ing to accept higher risk levels for activities perceived as voluntary. A motorist using Highway 99 for a weekend ski trip to Whistler would be accepting a voluntary risk, whereas a daily commute on the highway to work would be considered involuntary (Bunce, 1994). Both of these types of risks apply to the present study. The prioritization of resources is also important in assessing acceptability of risk. For example, the risk to life from traffic accidents on highways tends to be significantly higher than rock fall risks. Therefore, in some cases, resources may be better allotted to the reduction of risk by other means than rock fall mitigation. Fell (1994) states that most authors give an acceptable annual risk value for landslides o f 10"5 to 10"6, in discussions of other societal risks. Morgan (1991) suggests that society should not accept individual annual landslide risks on highways in excess of IO"4 to2*10" 5 . Sobkowicz, Hungr and Morgan (1995) found that many authors consider 1:10,000, or 10^ to be an important limit for annual landslide hazard. They also indicate that 10"4 can be used as an upper limit for involuntary risk of death from a landslide, or the probability of death of an individual (PDI). In their study of debris flow hazards on the Cheekye Fan, British Columbia, they used acceptability levels for group risks based on data from the European Alps and Japan. These levels are, "based on the premise that if, over a long period of time, communities have knowingly 21 lived with a particular risk in exposed locations, then frequency of death data for that risk constitute an acceptability criterion." (p. 525) Low, moderate, and high risk categories were plotted on a graph of Probability of death of a group of size N (PDGN) vs. Group Size (N). It can be seen in Figure 2.1 that there is a decrease in acceptable risk of one order of magnitude, for every order of magnitude increase in group size. The Japanese landslide frequency levels, about an order of magnitude higher than the European levels, were used as the upper boundary between moderate and high risk, because these data cover a smaller area, and a much shorter time period. It is noted that this upper boundary is identical to the group risk criterion for British Columbia Dams, developed by B.C. Hydro (Salmon and von Hehn, 1993). It is stressed by the IUGS Working Group on Landslides (1997) that estimates of risk are inevitably approximate, and that tolerable risk criteria should not be viewed as absolute boundaries. Tolerance to risk is highly variable, and risk criteria should be seen only as an expression of the assessment of general societal opinion (IUGS Working Group on Landslides, 1997). 2.4 - Management of Landslide Hazards Along Transportation Routes Transportation routes, particularly those traversing mountainous terrain, are susceptible to slope failures from adjacent rock cuts and natural slopes. While complete slope failure inventories for transportation routes are rare, several studies have been conducted in which data on large, damaging failures, and particularly those causing injury are death, are compiled and presented. Culshaw and Bell (1991) documented fatalities due to slope failures on transportation routes on the Island of St. Helena. The role of rock falls in causing accidents and several fatalities on Washington State highways was noted by Badger and Lowell (1992). Litigation regarding slope failure liability on highways is a concern to highways authorities, and cases have been 22 reviewed in British Columbia (Bunce, 1994; Hungr and Evans, 1988 and 1989); California and New York State (Walkinshaw, 1992); and North Carolina (Brawner, 1993). Damage, injury and death due to slope failures is an important concern to highway and railway authorities in many parts of the world. Effectively reducing the risks due to slope failures on transportation routes involves detailed risk analyses, and either risk zonation or quantitative calculations of risk on various parts of the routes. Piteau and Peckover (1978) discuss the prediction and management of landslide risks in designing rock slopes in transportation corridors. Along with detailed studies of the lithological, structural, hydrogeological and climatic conditions, rock slope design should involve consideration of past experience with stable and unstable slopes. Piteau and Peckover (1978, p. 197) state that, "In highway and railway slope problems, the most important factor relating to case history analyses is probably the incidence of failure." By analyzing the characteristics of slopes which have failed most often in the past, future failures can sometimes be predicted and prevented. It is recommended that the proposed cut be analyzed as a series of structural domains, or areas of similar geologic characteristics (Piteau and Peckover, 1978). For each structural domain, the possible modes of failure should be assessed, and slope-stability analyses performed. A detailed record of slope failure frequencies in the Fraser Canyon, British Columbia was prepared by Bell (1980). Rock fall incidence was correlated with various slope attributes such as slope angle, type of material, land use, and presence of gullies. Failure susceptibility was assessed for a series of slope sections, according to these slope attributes. Steep (>41°) bedrock and colluvial slopes were found to be most susceptible to failure, due to jointing and sensitivity to freeze-thaw effects (Bell, 1980). Pierson et al. (1990) presented a landslide hazard zonation method for transportation routes, which is currently used by MOTH in British Columbia (Bunce, 1994) and BCR (Follett 1997, personal communication). The Rock fall Hazard Rating System (RHRS) involves the 23 preliminary rating of all slopes, detailed rating of all slopes deemed hazardous, maintenance design and cost analysis for the most hazardous slopes, identification and implementation of maintenance procedures, and annual reviews. C N R , in conjunction with Bruce Geotechnical Consultants Inc. and Oboni Associates Inc. have developed a system of rock fall risk analysis on C N R (Abbott et al . , 1998). The C N Rockfall Hazard Risk Assessment system ( C N R H R A ) is based on fieldwork and the analysis o f past events, to characterize the relationships between variables such as terrain, train speed, and proximity to population centres, with recorded costs. Field studies are performed to qualitatively assess the probability of failure, based on geological characteristics and mitigation efforts. The probable size o f particles involved in the potential failure is also assessed, in order to estimate the probability o f derailment. Abbott et al. (1998) present a type of magnitude-frequency plot, in the form of landslide frequency vs. derailment hazard. This plot is used to suggest schedules for rock-slope inspections, based on frequency of failure, and potential consequences. A s in other risk analyses of slope failures, quantitative values o f risk may be necessary to compare slope failure risks on transportation routes with risk acceptability levels. To calculate risk, the probability of failure and the expected consequences must be quantified. On transportation routes, the most meaningful consequence is loss of life due to impact from a slope failure. Morgan et al. (1992) presented a method consistent with definitions given by Varnes (1984) and Fell (1994) for calculating risk from rock fall specifically for transportation routes. Risk = Hazard * Vulnerability Vulnerability = P(S:H) * P(T:S) * P(L:T) In the vulnerability equation, P(S:H), the probability o f spatial impact, is the probability that a vehicle wi l l be present in the section of the transportation corridor affected by the failure. P(T:S), the probability o f temporal impact, is the probability that a vehicle wi l l be present in the 24 corridor at the time of the failure. P(L:T) is the probability o f death of at least one person, given impact, or the degree of damage to any impacted vehicles. Therefore, in order to calculate the risk o f death caused by slope failure in a certain area over a certain time period, the probability o f failure must be multiplied by: the probability of a vehicle being in the rock fall impact zone; the probability o f a vehicle being in the area at the time of the rock fal l ; and the probability o f at least one occupant being killed from the impact. I f hazard is expressed as the annual probability o f occurrence of a slope failure within a given magnitude range, then the annual probability o f at least one fatality due to slope failures in that magnitude range is the hazard times the vulnerability. The vulnerability parameters themselves wi l l depend directly on magnitude. For example, the probability o f being killed by a 10000 m 3 rock slide is much greater than the probability of being killed by a 0.1 m 3 rock fall , given that impact occurs. The spatial probability of impact is also greater for the large landslide, because of the wider area it affects. It may be important to consider the increased risk to users of transportation routes when traffic is delayed or stopped. The probability of a stationary vehicle being impacted by falling rock or debris may be greater than that for a moving vehicle (Bunce, 1994). However, the effects o f impact on the operator o f a moving vehicle may also be important. Bunce (1994) identified three different risk scenarios for rock fall on a highway: moving vehicle impacted by falling rock; stationary vehicle impacted by falling rock; and moving vehicle running into fallen rock. For detailed studies at small sites, it may be beneficial to calculate the different risk values for each of these scenarios, and use the highest values for safety studies. For larger areas, over which traffic patterns are highly variable, it may not be practical to calculate the risk for each scenario. Instead, average traffic densities and velocities may be assumed, or for 'worst-case' calculations, the stationary vehicle case may be considered alone. 25 Once the relative risks o f landslides in a given study area have been determined, highways and railways authorities can more effectively distribute resources for prevention and mitigation of slope failures. Mitigation methods can be either active or passive (Einstein, 1988). Passive countermeasures include restrictions on building, installation of warning devices, and the gathering of further information. Methods such as drainage and reinforcement are considered active countermeasures. Also included in the 'active' category is the removal o f rock from the rock face, or scaling. Peckover and Kerr (1977) describe the various methods of mitigation in terms of four categories. The first category is route relocation, which is not a viable option for most major transportation routes. The second category, stabilization, includes scaling, drainage, surface stabilization, support, and restraint. Tools such as wire mesh blankets over the rock slope, ditches, catch nets, fences, rock sheds, and tunnels, fall under the category o f protection. The fourth, most passive, category is warning, which includes railway patrols, warning signs, electric rock fall warning fences, television monitoring, and the use of geophones along the routes to detect movement. 2.5 - Landslide Hazards on Transportation Routes in British Columbia British Columbia is the only province in Canada in which fatalities due to rock fall have been reported (Bunce, 1994). A t least twenty-six people have lost their lives due to slope failures (including debris flows) on transportation routes in southwestern British Columbia in the past thirty-five years. Eighteen of these fatalities occurred along the Howe Sound Corridor between Vancouver and Squamish, a route traversed by B C R and British Columbia Highway 99. Rock falls have been a major problem on all of the transportation routes in the study area, and concentrated mitigation efforts have been made by M O T H and the railways (e.g. Peckover and Kerr , 1977; Theodore, 1986; Hungr and Evans, 1988; Bunce et al . , 1997). Large-scale rock slides 26 have also been reported in rock-cuts at the base of the steep natural slopes lining the transportation routes (Leighton, 1990). Rock avalanches in the Southern Coast Mountains have been documented by Piteau (1977), Ryder (1981) and Evans and Savigny (1994). Naumann and Savigny (1992) give radiocarbon dates o f several major rock avalanches in the Lower Fraser Valley. Large-scale lahars and rock avalanches have also occurred in the Pleistocene volcanic rocks o f the Garibaldi Volcanic Belt. Landslides involving the failure o f the edifice slopes themselves (e.g. Hungr and Rawlings, 1995) and the collapse o f oversteepened lava flow margins (e.g. Moore and Mathews, 1978; Hardy et al. , 1978) have affected the Howe Sound-Lillooet corridor as recently as 1855. Seven debris flows blocking Highway 1 and C P R in Kicking Horse Pass were described by Jackson et al. (1989). The magnitudes o f these events, which occurred between 1925 and 1984, ranged from 5000 to 136000 m 3 . Jokulhlaups from the nearby Cathedral Glacier were blamed for providing the large volume of water necessary to mobilize debris into debris flows. After C P R began pumping meltwater from the glacier in 1985, no further major debris flows were recorded. Eisbacher (1983) assembled a history of large, damaging rock falls, landslides and debris flows along Highway 99, from White Rock to Pemberton. Events described in this survey include a major rock avalanche at Sunset Beach, rock falls at Brunswick Point and Porteau Cove, and a rock avalanche at Mystery Creek. M a n y major debris flows in creeks and rivers along the route are also reviewed, including an event at M Creek which removed eighteen metres o f highway bridge, destroyed a house and several vehicles, and caused the death of nine people. Be l l (1980) conducted a detailed study of slope failure frequencies in the Fraser Canyon, along the C P R and C N R routes. She plotted the number o f rock falls per 0.1 mile of track along C N R and C P R , and compared the total monthly incidence o f rock falls with temperature and precipitation patterns. Bel l described in detail twelve slope attributes including slope angle, surficial material type, the occurrence of gullied slopes, seepage characteristics, and land use. The 27 study area was then divided into terrain units, and slope failure susceptibility was rated according to the above attributes. It was determined that bedrock and/or colluvial units, which often occur as steep cuts, are most susceptible to slope failure, and that slopes greater than 41° fail most often. The susceptibility o f bedrock slopes to failure was credited to the steep and strongly jointed nature o f the bedrock in the area, and the sensitivity to freeze-thaw and groundwater pressure. A number of debris torrents in creeks on Highway 1 and the Coquihalla Highway in southwestern B C were documented in a Thurber Consultants report to B . C . M O T H (Thurber, 1985). A n increase in debris flow frequency in recent years was attributed in part to an increase in long term precipitation totals in southwestern British Columbia, and in particular to three major storm events. Debris flow risks on each creek were assessed in terms of five categories from no risk to very high risk, according to both the existing creek conditions, and past debris torrent activity. A n example of calculation of rock fall risk on a British Columbia highway is given by Bunce (1994) and Bunce et al. (1997). These papers involve a single rock cut near Porteau Cove on Highway 99 in British Columbia. In 1992, a rock fall from this cut struck a vehicle on the highway, kil l ing Janet Yvette Dunn and seriously injuring John Just. The Supreme Court o f Canada ruled that the event was foreseeable, and M O T H was held liable (Cory and Sopinka, 1989). Bunce (1994) and Bunce et al. (1997) present a detailed study of the rock cut, traffic conditions, and previous rock falls at the site, in order to quantify the risks o f rock fall deaths and compare them to other societal risks. A study of previous rock fall events at the site was conducted primarily by analysing impact marks on the highway surface. This was used, along with documented rock fall history at the site, and detailed mapping of the rock face, to calculate rock fall hazard. The hazard value was given as the expected number of rock falls per year greater than 180 c m 3 in volume. The volume restriction was calculated based on the minimum clearance for a small vehicle (15 cm), which 28 represents a volume of 180 c m 3 for a spherical rock. The spatial and temporal probabilities of impact were determined based on traffic statistics such as the average length of a car and the average spacing of cars on the highway. Bunce (1994) calculated the risk o f impact for three scenarios. The annual risk o f a specific stationary vehicle being hit by a falling rock at the study site was calculated to be 1.4* 10"6, or one in 715,000. This assumes that the vehicle is stopped for thirty minutes, and that such a delay in traffic is an annual occurrence. For a moving vehicle struck by a falling rock, the calculated risk was 1.7*10~8, or one in 60 million, per trip across the rock cut. The calculated risk o f a specific moving vehicle striking a fallen rock was 4.5*10"7, or one in 2 million, per trip across the cut. These values were calculated using the binomial theorem, with each rock fall representing one Bernoulli trial, having possible outcomes of impacting or not impacting a vehicle (Bunce et al . , 1997). Assumptions were made that both traffic and rock falls were uniformly distributed over time and space, and were independent of one another. The following expression was derived to represent the probability, P(S), of one or more vehicles being impacted by N r rock falls (Bunce et al . , 1997, p.351): P(S) = 1 - ( l - P ( S : H ) ) N r [2.1] where P(S:H) is the probability that a vehicle occupies the portion of the road affected by a rock fall. The annual probability o f an accident to one or more vehicles was then calculated for each of the three scenarios described above. The only scenario considered in detail in the current research is that of a moving car being impacted by a falling rock. The expression which Bunce et al. (1997, p. 353) used to calculate the annual probability of impact of one or more vehicles, P ( A ) , for this scenario is P(A) = P(T:S) * [1 - (1 - P(S:H)) N r ] [2.2] 29 where P(T:S) is the probability that a vehicle occupies the path of the falling rock at the same time as the rock fall occurs. Based on the assumption of uniformly distributed traffic over time and space, P(T:S) = 1 for the given scenario (Bunce et al., 1997). Therefore, P(A)= 1-(1-P(S:H))N r [2.3] The Poisson approximation to the binomial theorem can be used to simplify this expression (Solomon, 1987). The Poisson approximation states that, for small probability, p and large number of trials, n, ( l -p) n *e- n p [2.4] Therefore, when P(S:H) is small and N r is large, P(A) can be approximated as P(A) * 1 - e ™ S : H » [2.5] Further, because for small values of x, the function e"x can be approximated as (1-x), and it is assumed that (Nr)*(P(S:H)) is small, P(A) * 1 - [1 - (Nr)*(P(S:H))] [2.6] = (Nr)*(P(S:H)) Hungr and Beckie (1998) simplify equation [2.2] in this way by arguing that for small impact probabilities, P(A) can be calculated as P(A) = P(S:H) * P(T:S) * N r [2.7] which, for the given scenario, in which P(T:S) = 1, reduces to P(A) = P(S:H) * N r [2.8] They indicate that for P(S:H) * P(T:S) < 0.001, and N r < 100, the difference in P(A) calculated using this simplified expression, is less than 5% (Hungr and Beckie, 1998). Bunce (1994) estimated values for the probability of death from impact, based on approximations of the fraction of a vehicle affected, and the effect of an impact on driving ability. These values allowed for the calculation of risk values for fatalities at the site. The calculated risk 30 of death for an occupant of a specific vehicle stationary for thirty minutes being impacted by a falling rock was 7.0* 10"7. For a moving vehicle impacted by a falling rock, and a moving vehicle striking a fallen rock, the calculated risks were 1.3*10"8 and 4.8* 10"8 respectively (Bunce, 1994). All of these risk values fall within the range of risks accepted by society, and are below the thresholds suggested by several authors (Fell, 1994). However, when the annual risk of a rock fall incident at the cut is calculated, instead of the risk of any given individual vehicle being impacted, the risk values are higher. Bunce calculated the annual risk of at least one moving vehicle either being impacted by a falling rock or hitting a fallen rock at the site to be 3.1*10~5, or one in 32,000, which exceeds the lower limit of acceptance proposed by Morgan (1991). This result emphasizes the need for a standard acceptable rock fall risk level in British Columbia. The method of calculating risk by multiplying the hazard, or probability of occurrence of a given danger, by the spatial and temporal impact probabilities, and the expected consequences, is used in fields other than rock fall studies (Navin, 1998, personal communication). The use of a source-pathway-receptor model can be useful, in which the probability of impact is the probability that the source, pathway and receptor all coincide. In the current research, the rock fall is the source, the damage corridor is the pathway, and the vehicle is the receptor. Impact occurs when all of the above coincide. Impact probabilities for avalanches, for two separate vehicles, etc. can be considered using the same method. Bunce (1994) and Bunce et al. (1997) give a methodological approach to calculating risk from rock falls on a road cut. However, these studies only deal with a single cut, not the entire highway. The need for a study to assess rock fall risk for other problem areas is apparent. Bunce (1994, p. 97) concludes that, "the decision on how to distribute [remedial] efforts should be based on the risks of the different cuts and the use of relative rating systems such as the RHRS." At present, no large-scale landslide hazard or risk zonation study on major transportation corridors in the Cordillera has been completed (Cruden, 1985). Reconnaissance studies of 31 instability have been conducted in certain areas, including the Intermontaine Belt (Evans, 1984a), the Coast Plutonic Complex (Ryder, 1981) and the southern Cordillera (Evans, 19846). These studies generally only deal with damaging, high magnitude events. Similarly, MOTH conducts studies of extensive hazards in developing areas (Cruden, 1985), but no program of systematic hazard or risk analysis involving landslides of all magnitudes on transportation routes exists in British Columbia. 32 Figure 2.1 - Risk acceptability criteria (from Sobkowicz et al., 1995) Curves reduced by a factor of 500 to account for number of exposed sites Source of information: Morgan (1991). after Schuster &. Flemming (1986) Events with N | or more Deaths: A l l occurrences I Events with N or more Deaths: Single Landslide Events with N Deaths: Single Landslide 1E0 1E1 1E2 # OF DEATHS (N) 1E3 1E4 33 CHAPTER 3 - STUDY AREA 3.1 - Physiography The study area is bounded by the Pacific Coast on the west, and extends north to Cache Creek and east to Kamloops (Figure 1.1). The Coast Ranges traverse most of the study area, reaching altitudes of up to 2944 m. The mountain ridges are oriented north-west south-east, and are separated by deep glacial valleys, many of which are occupied by lakes or inlets at or near sea level. The main valleys are cut by some perpendicular valleys which appear to follow prominent joint sets (Monger and Journeay, 1994). The fault-controlled Fraser valley bounds the Coast Mountains on the east. The Fraser Lowland, south of the Coast Mountains, is a relatively flat, triangular area covered with Quaternary sediments. The Lowland occupies a section of the study area east of Vancouver, and is bounded on the east by the Cascade Mountains, west of Hope. The Fraser River traverses this part of the study area, occupying a late glacial and post-glacial valley up to 5 km wide (Armstrong, 1984). East of the Coast Mountains is the southwestern Interior Plateau, an area of rolling uplands, deeply incised by north-south oriented, steep-sided valleys and many long, deep lakes. (Bostock, 1948). Near Kamloops, the uplands have elevations of about 1500 to 2000 m, with valley floors about 800 to 1600 m below the plateaux (Fulton, 1975). The major river valleys, Fraser, Thompson and Nicola, have semi-arid environments, contrasting strongly with the surrounding mountains and plateaux (Ryder, 1981). The Interior Plateau extends east to the Rocky Mountains, but the city of Kamloops marks the eastern boundary of the present study area. 34 3.2 - Geology 3.2.1 - Bedrock Geology Figure 3.1 shows the bedrock geology of the study area, from Monger and Journeay (1994). The Late Jurassic to early Tertiary quartz-diorites and granodiorites of the Coast Plutonic Complex dominate the geology of the Coast Mountains (Monger and Journeay, 1994). Stress relief, or sheeting, joints formed parallel to topographic surfaces are common throughout these plutonic rocks. These joints are susceptible to sliding or toppling when daylighted in cut slopes due to undercutting by erosion or human activity. Northwest-southeast running faults and shear zones, such as the Downtown Creek Fault, and the Brittania Shear Zone, are common. Various metamorphic rocks such as the Gambier Group, and thin units of fault-bounded sedimentary rocks such as the Jackass Mountain Group and the Dewdney Creek Formation, are also important at all levels within the valley slopes of the study area. These rocks are most significant in the Fraser River Fault System between Hope and Boston Bar. This major, Eocene fault system trends north-south, across the regional grain (Monger and Journeay, 1994). The rocks in this area are generally highly altered and/or fractured, often leading to significant slope hazards. East of the Downtown Creek Fault, into Lillooet, the bedrock consists of the Carboniferous to Middle Jurassic undifferentiated cherts, pelites, and mafic volcanic rocks of the Bridge River Complex. The Downtown Creek Fault is a southwest-directed contractional fault which marks the boundary between the coherent western Bridge River assemblage and the sheared melange of the eastern Bridge River assemblage (Monger and Journeay, 1994). Gambier Group argillites also outcrop in the southwestern part of the study area, north of Horseshoe Bay. At the north end of Howe Sound, in the western part of the study area, a string of Quaternary volcanic centres comprising the Garibaldi Volcanic Belt runs north-south across the Coast Mountains. This belt, which is made up of andesite, basalt and dacite flows, and pyroclastic rocks, is an extension of the Cascade Volcanic Belt of the northwest United States. 35 In the eastern part of the study area, the Coast Mountains are bordered by the Interior Plateau. Here, the bedrock consists of the andesite, basalt, limestone and argillite of the Triassic Nicola Group, the andesite and basalt flows and pyroclastic rocks of the Tertiary Kamloops Group, the limestone of the Paleozoic Cache Creek Group, and some middle Jurassic sediments. 3.2.2 - Surficial Geology Glaciation has significantly affected the topography of the Coast Mountains, producing steep valley slopes of bedrock, coarse colluvial fans, and terraces of fluvial or glacio-fluvial sands and gravels. The glacial deposits in this area are the products of the Fraser Glaciation, the ice sheets of which receded from the area approximately 12000 years ago. The most recent glacial period of continental ice sheet proportions produced the Vashon Drift. Valley ice remained in the mountains after this period, depositing the sediments of the Sumas Drift (Armstrong, 1960). Surficial deposits are thin on the mountain slopes, and bedrock is commonly exposed over widespread areas, with only a very thin covering layer of glacial drift (Armstrong, 1960). The narrow valley floors, commonly occupied by streams, lakes or inlets, contain glacial deposits up to about one hundred metres thick (Armstrong, 1960). The Fraser Lowland, a relatively flat zone of thick Quaternary drift, alluvium, glacio-fluvial and lacustrine deposits, covers a triangular area starting south of Vancouver, at the Pacific coast, and tapering out near Agassiz. The surficial deposits are extremely varied, and have thicknesses up to at least 350 m. Overlying the Fraser Glaciation sediments in this area are the Salish post-glacial sediments, which are still in the process of formation. These deposits include the Fraser River Sediments, and sediments from smaller streams, peat bogs and lakes (Armstrong, 1960). In the Fraser Lowland, slumping, liquefaction failures, and debris flows are the main geotechnical concerns, particularly during episodes of heavy rain. Rock falls and rock slides are not important hazards in this part of the study area. 36 In the Interior Plateau, some post-glacial sediments overly the Kamloops Lake Drift. The non-glacial Bessette Sediments underlie these glacial deposits (Fulton, 1975). Glacio-lacustrine silt is the dominant surficial material. These white silts are widely distributed in the valleys of the Interior, in places reaching thicknesses of over one hundred metres (Barton et al., 1964). Throughout the Interior, other local surficial deposits include glacio-fluvial sands and gravels, eskers, kames, and glacio-fluvial deltas from ice-contact lakes (Barton et al., 1964). 3.3 - Climate 3.3.1 - Coast Mountains The maritime climate of the Coast Mountains is characterized by mildness, humidity, and heavy precipitation (Kendrew and Kerr, 1955) Rain dominates in the lower areas, falling mostly in the winter months. Frost is usually slight, and temperatures do not often dip below zero. Snow falls for only a few days each winter. July and August comprise the area's dry season, during which temperatures are warm, but kept moderate by marine winds. In the winter months, temperatures tend to be lower with increasing distance north of Vancouver. This can lead to a greater possibility of freeze-thaw cycles affecting slope stability. Snowfall is also heavier with increasing distance north from Vancouver. Rainfall tends to increase northward from Vancouver to Squamish, but decreases inland, towards Pemberton. In the mountains, even on the lower slopes, many feet of snow cover the ground from November to March (Kendrew and Kerr, 1955) Again, summers are generally comparatively dry. 3.3.2 - Fraser Lowland The inshore maritime climate of the Fraser Lowland is heavily influenced by the mountains that surround it (Armstrong, 1984). Precipitation, which varies greatly from year to year, increases strongly from south to north, and west to east. The mean annual precipitation values in 37 the Fraser Lowland generally range from 1000 to 1700 mm (Armstrong, 1984). About 7 5 % of this ample precipitation occurs from October to M a r c h inclusive. Most of it falls as rain, but episodes o f snow and freezing rain occasionally occur in the winter months. Snowfall generally increases east o f Vancouver. Winters are mild, and the summer climate is generally warm and dry. Frost-free periods in the Fraser Lowland are long, generally ranging from 150 to 300 days at Vancouver City H a l l (Environment Canada, 1994). 3.3.3 - Thompson River Valley. Interior Plateau The uplands of the Interior Plateau have a continental climate, featuring fairly low humidity, and precipitation levels much lower than on the Pacific Coast. Temperatures in summer are hot, but summer nights are generally cool or occasionally cold. Winters are much colder than on the coast, and the ground is usually snow-covered for most of December and January. Precipitation is well-distributed throughout the plateau uplands, with most of the rain falling in the summer, often as thunderstorms, and the winter. In spring, precipitation is lowest, and frosts occasionally occur. This area is famous for its orchards, which are almost exclusively irrigated, due to the low precipitation. The deep river valleys in the Interior are very dry, especially in the area surrounding Ashcroft. In the Fraser valley between Lillooet and Lytton, the lower Thompson valley between Kamloops and Lytton, and the N i c o l a valley, mean annual precipitation values are the lowest in the province, reaching only about 18 cm (Kendrew and Kerr, 1955) Snow is not as common in the valleys as on the uplands, but winters are colder and much drier than in the coastal areas. Sage-brush and dwarf cacti are common, and trees are few. Climate data for various stations throughout the study area are given in Tables 3.1 to 3.4. (Environment Canada, 1994). Entries marked with a dash indicate that no data was available for 38 that particular parameter, station and year. Figures 3.2 and 3.3 display rain and snow data graphically for various locations. 3.4 - Transportation Corridors The study area comprises two main transportation corridors in southwestern British Columbia. The Trans-Canada Highway (B.C. Highway 1), C P R and C N R travel 420 km through the Fraser-Thompson corridor from Vancouver to Kamloops, via Hope and Lytton. B C R and B . C . Highway 99 occupy the Howe Sound-Lillooet corridor for a distance o f 250 km. 3.4.1 - The Fraser-Thompson Corridor From Vancouver, the Fraser-Thompson corridor crosses the wide floodplain and glacial lowlands o f the Lower Mainland and the Lower Fraser Valley, through Abbottsford and Chilliwack. The climate in this area is characterized by mild winters, temperate summers, and plentiful rainfall. A t Hope, the corridor turns north to continue through the narrow, steep-sided Fraser Canyon, which is associated with the Fraser River Fault System. Slope failure hazards are important in this area, due to the highly altered and fractured nature o f the rocks in the fault zone. Rainfall levels and winter temperatures are significantly lower than those in the Fraser Valley. Between Lytton and Spences Bridge, the corridor follows the Thompson River through the Mount Lytton Complex, a transition zone between the Coast Mountains and the Interior Plateau. This part o f the corridor runs along the northern edge of the Cascade Mountains and along the southern edge of the Fraser and Nicoamen Plateaux. The river is deeply incised into the highly fractured flows and pyroclastic rocks of the Spences Bridge Group. Railway lines in this area are protected by numerous rock sheds. A t Spences Bridge, exposures of the Interior Plateau's typical glacio-lacustrine silts begin to dominate along the corridor. Towards Ashcroft, the Thompson River is incised into the volcanic 39 rocks o f the Triassic N i c o l a Group, the Tertiary Kamloops Group, the Paleozoic Cache Creek Group, and the middle Jurassic sediments o f the Ashcroft Formation. The Fraser-Thompson corridor ends at the thick Quaternary deposits surrounding Kamloops. Here, the climate is semi-arid, with rainfall levels being much lower than any other area along the transportation corridor. However, due to the cold winter temperatures, freeze-thaw effects in this part o f the corridor are more important than in areas farther south. The Canadian Pacific Railway, Canada's first cross-country railroad, was constructed in the late 1800s, soon after British Columbia joined the Dominion of Canada in 1871 ( M i k a et al . , 1986). Construction began in the Fraser Canyon, near Yale, in 1880. This area, from Yale to Savona, is one of the most rugged sections o f the railway, featuring many steep rock walls, and 15 tunnels. The section of railway from Yale to the sea at Port Moody was completed in 1884, one year before the ceremonial final C P R spike was driven at Craigellachie, in Eagle Pass, to celebrate the completion of the cross-country route ( M i k a et al. , 1986). A n extension from Port Moody to Vancouver was added in 1887. The Canadian National Railways did not build in this area for another thirty years, having previously elected to end its cross-country route at Prince Rupert (Stevens, 1973). The southern extension, built with the purpose of accessing Vancouver Island, was built in the 1910s. From Kamloops to the sea, C N was restricted by physiography to the Thompson and Fraser canyons. Because the C P tracks were already built through this rugged section, construction for C N was even more challenging. In some areas, there was no option but the blast out a niche in the canyon wall for miles, resulting in costs of up to $300,000 per mile at the time (Stevens, 1973). A particularly hazardous section, where many labourers were injured and killed during the construction of both C P R and C N R , was Hel l ' s Gate, where the Fraser River is confined to a steep, narrow canyon (Stevens, 1973). 40 Before either railway began construction, trails and wagon roads were built in the Fraser and Thompson Canyons, to support gold mining, agricultural settlement, and the haulage of timber (BC MOTH, 1986). The first proper trails were built from Spuzzum to Yale from 1856 to 1861. Soon after this, the Caribou Wagon Road, wide enough to accommodate two wagons, was built from Yale through the Fraser Canyon. Another wagon road from Cache Creek to Savona was built in 1866 to provide access to the goldfields above Revelstoke (BC MOTH, 1986). Trunk roads from Kamloops to Nicola and Nicola to Spences Bridge were built in the 1870s. Some sections of the Caribou Road in the Fraser Canyon were destroyed when CPR and CNR built through the area. As a result, future highway construction was very difficult in places, due to the presence of the two railways in such a restricted area. Near Lytton, the highway was built out into the Fraser River, behind a retaining wall, because of the railway above (BC MOTH, 1986). The Fraser Canyon section of the road was re-opened in 1926 as the Fraser Canyon Highway (BC MOTH, 1986). In the 1950s and 1960s, highway improvements, expansion, and paving were undertaken as part of the construction of the Trans-Canada Highway, which was completed at Rogers Pass in 1962. 3.4.2 - The Howe Sound-Lillooet Corridor From North Vancouver, the Howe Sound-Lillooet corridor follows a fjord and valleys scoured by glaciers in the granodiorites and quartz-diorites of the Coast Plutonic Complex. Highway 99 and BCR cross steep bedrock slopes, coarse talus aprons and alluvial and debris flow fans. Rainfall in this southern part of the corridor is abundant. Snowfall levels are minimal south of Squamish, but increase northward along the corridor. Slope hazards include rock falls, rock slides and debris flows (e.g. Evans and Savigny, 1994). South of Porteau Cove, there is a steep cut in the argillites of the Lower Cretaceous Gambier Group, known as the Argillite Cut. A short distance north, the routes cross the contact into granodioritic rocks, and another steep cut known as 41 the Porteau Bluffs borders the highway. Both the Argillite Cut and the Porteau Bluffs have caused particular concern regarding rockfall hazards on Highway 99 and B C R . Consequences of rock fall in this area over the past thirty years include six rock fall-related deaths, damage to numerous vehicles, and highway and railway closures and delays. North o f Squamish, the transportation routes approach the Garibaldi Volcanic Centre, dominated by Mount Garibaldi (2678 m), an extinct Pleistocene volcano with a record of large scale slope instability. However, few volcanic rock outcrops appear in the immediate vicinity of the highway and railway. Farther north, the corridor ascends the Lower Squamish Valley to Cheakamus Canyon near the core o f the Coast Plutonic Complex, and proceeds over a low pass near Whistler to join the Lillooet River valley at Pemberton. It then cuts northeast across the Coast Mountains again, and crosses the Downtown Creek Fault west of Lillooet. Winter temperatures here are significantly lower than farther south. Precipitation levels are also generally lower than along the coastal section of the corridor. Rock falls have been frequent in this area, possibly due to the sheared nature o f the eastern Bridge Creek tectonic melange. Past the Downtown Creek Fault, the highway and railway continue east along the north shore of Seton Lake, to end at Lillooet on the Fraser River. In 1912, the British Columbia Railway, at the time known as Pacific Great Eastern, began plans to build a railway north from Vancouver, to link the Pacific coast with the province's interior ( M i k a et a l . , 1986). B y 1915, sections of the route were built from North Vancouver to Whytecliff, and Squamish to Clinton. However, construction through the Coast Mountains proved more difficult than expected, involving many steel bridges and tunnels. Due to high costs, the project was abandoned in 1917, until the province completed the line between Squamish and Quesnel in 1921 ( M i k a et al . , 1986). The completed route from North Vancouver to Squamish was not complete until the mid-1950s (Brad Follett, 1998, personal communication). 42 , The Sea to Sky Highway (Highway 99) from Vancouver to Squamish was built in the late 1950s and early 1960s ( B C M O T H , 1986). The section of highway from Squamish to Pemberton was built and paved in the 1970s. Also in the 1970s, the existing Duffey Lake Road from Pemberton to Lillooet was upgraded to a hard surface highway. Since the completion of Highway 99, extensive improvements have been made, particularly along the route from Horseshoe Bay to Whistler. 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S 5 u a to E & § I e  c3 -2 8 3 2 ^ 3 : ^ cr 5 -3 >, ca ca © Ov Ov 47 Figure 3 . 1 - Bedrock geology of the study area L E G E N D S T R A T I F I E D R O C K S Pleistocene and Recent Q Quaternary Sediments PRCJ Garibaldi Group Early and Late Cretaceous K G Gambier Group eKJ Jackass Mountain Group Lower Jurassic to Lower Cretaceous £ 1 Cayoosh Assemblage Early and Middle Jurassic Harrison Lake Formation JH J L Ladner Group Late Triassic and Early Jurassic T C Ted Cultus Formation Cadwaller Group Carboniferous to Middle Jurassic CJB | Bridge River Complex HI Hozameen Complex CJCJ Cache Creek Complex P L U T O N I C R O C K S p | Late Tertiary to Late Triassic granodiorite, quartz diorite, and other plutonic rocks M E T A M O R P H I C A S S E M B L A G E S jjaga Custer Gneiss Mst Settler Schist 48 Figure 3.2 - Monthly rain data for various stations in the study area E e CO cr: 800 400 (a) Vancouver, 1990 J F M A M J J A S O N D Month E E CO or 800 400 (e) Cilliwack, 1990 I I I I I I T I I I I I J F M A M J J A S O N D Month co or (b) Squamish, 1990 800 E r 400 J F M A M J J A S O N D Month (f) Lytton, 1990 800 E E — 400 'co or T I I ITI I I I I J F M A M J J A S O N D Month E E, c CO or 800 400 (c) Pemberton, 1990 I T T f i l l T T J F M A M J J A S O N D Month E E, c co or 800 400 (d) Lillooet, 1990 T T W -I I I I I I I J F M A M J J A S O N D Month 800 f- 400 ro or (g) Cache Creek, 1989 I I T I T I T I T I T I J F M A M J J A S O N D Month 800 f- 400 'ro or 0 (h) Kamloops, 1990 I I I "TT T I I I I I I J F M A M J J A S O N D Month 49 Figure 3.3 - Monthly snow data for various stations in the study area E IT o c w 150 100 50 0 (a) Vancouver, 1990 T I I I I I I I I J F M A M J J A S O N D Month E o c co 150 100 50 0 (e) Cilliwack, 1990 I I I T I I I I I I IT J F M A M J J A S O N D Month E o tz CO 150 100 50 0 (b) Squamish, 1990 I I N I I I I I I J F M A M J J A S O N D Month E o c CO 150 100 50 0 (f) Lytton, 1990 I T I I I I I I I I T I J F M A M J J A S O N D Month E o c CO 150 100 50 0 (c) Pemberton, 1990 I I I I I I I I J F M A M J J A S O N D Month E o c CO 150 100 50 0 (g) Cache Creek, 1989 I T I I I I I I I I i I I J F M A M J J A S O N D Month (d) Lillooet, 1990 E IT o c CO 150 100 50 0 I I I I I I I I I I I I I J F M A M J J A S O N D Month E IT o tz CO 150 100 50 0 (h) Kamloops, 1990 liilssi I T I I I I I I I I I J F M A M J J A S O N D Month 50 CHAPTER 4 - LANDSLIDE DATABASE 4.1 - Data Sources and Collection Procedures Landslide data for Highway 1 and Highway 99 were collected from paper fdes during two visits to the British Columbia Ministry of Transportation and Highways (MOTH), Geotechnical and Materials Engineering offices in Burnaby. A large number of landslide events were recorded in MOTH rock fall, rock slide, or rock-on-road reports, and some were written up in police accident reports. Both of these types of reports generally include some estimate of volume, and some contain other information, but many are simply reports that rock has reached the road, including the location, date and occasionally the time of the event. Many of the more recent slope failure events affecting the highways were recorded by maintenance contractors. These reports of rock fall or rock-on-road events were synthesized into database files by MOTH and provided for use in this project. Most of the maintenance contractor reports include an estimate of volume, and some other information such as precipitation or freeze-thaw prior to the event, and number of injuries, if any. A disk containing the British Columbia Railway (BCR) MS Access database of slope failure events from 1985 to early 1997 was provided by BCR in North Vancouver. These reports include the location, date and often time of the event, usually an estimate of the volume, the BCR intensity classification, the number of deaths or injuries, if any, the weather at the time of the event, the damage to trains or tracks, if any, the length of track affected, and the delay in train traffic, if any. Not all records are complete, but most have at least some of the above information. To clarify the type of failure for some of the events, written landslide reports were also reviewed. Slope failures in creeks adjacent to the railway, described as mudslides and/or washouts, were classified as debris flows in the database. An Excel file of rock fall events from 1974 onward was provided by the Canadian Pacific Railway (CPR). Exact locations of the events are not given in this spreadsheet, but instead relative 51 locations are assigned within specified geologic zones. These records also include the date of the event and usually an estimate of the volume. Canadian National Railway (CNR) slide detector fence records for 1994 and 1995 were provided by CNR. These records show the date and time at which the slide detector fence was set off, but give no estimate of volume, and are not definite indicators of slope failure. Very few events were recorded based on paper files and reports at CNR in Edmonton, but no further files or landslide reports were available. Data on high-magnitude failures on all transportation routes were provided by Dr. Steve Evans of the Geological Survey of Canada. The personal files of Dr. Evans and Dr. Hungr were also used to supplement the landslide information collected from the above sources. 4.2 - Event Data All data were compiled into an MS Access database called Slide Inventory. A table of events was created for each highway and railway. The slope failure events for each route were then subdivided into two categories: one for rock falls, rock slides and topples; and one for debris flows. Four failures were described as sags or spreads, but these failure types were rare, and volumes were difficult to quantify, so they were excluded from further analysis. The first, much larger category contains mainly rock fall events, with some large scale rock or debris slides, and very few rock avalanches. The second category is dominated by debris flow events, as sags and spreads are not common problems for the transportation routes in the study area. The CPR data were not separated into these two categories, because only rock fall data were available. For ease of communication, because the events in the former category are dominantly rock falls, this term is used in reference to all events in the fall/slide/topple category in this paper. The event tables for Highway 99 and Highway 1 include the following fields: Segment (MOTH classification); km; Date; Time; Material Type; Movement Type; Volume Displaced (m3); Number o f Fragments; Volume on Road (m 3); Source Height (m); Cut Slope Angle; Cut Slope Height (m); Natural Slope Angle; Natural Slope Height (m); Width o f Highway Affected (m); Hwy/lane Closures; Deaths/Injuries; Precipitation in Last 48 hours; and Description, Causal Factors, Consequences, Comments. M a n y of these fields remain empty, due to the very brief incident descriptions given in most records. A significant number o f event reports contain data regarding the location, date, volume displaced, and deaths or injuries resulting from the event, but more detailed descriptions o f the slope geometry, source height, and even material and movement type are often lacking. A total of 885 slope failure events were recorded on Highway 99, from November, 1964 to July, 1996. O f these, 616 events have magnitude estimates. A n y events with unknown locations were discarded and are not included in this total. M a n y of the event records for each route do not include any information about the type of failure. Because falls and slides are the most common failure types along most of these routes, and most o f the slope failure reports include notes about rocks or boulders on the road or in the ditch, it was assumed that events without failure type information fell into the fall/slide category. Events reported as mudslides, washouts, flows, floods, etc. were assigned to the debris flow category. In the Highway 99 data table, 880 of the 885 slope failures recorded are rock fall events, 611 (69%) of which have known magnitudes. Four events are debris flows, all o f which have known magnitudes. The remaining event is described as a rock slump. A total of 417 failures were recorded on Highway 1, from January, 1967 to A p r i l , 1996. O f these, 310 records (74%) include volume estimates. 395 failures are classified as rock fall events, o f which 297 have known volumes. Debris flows make up the other 22 events, o f which 13 have known volumes. The B C R event table includes mostly the same information as the highway tables. Instead of Segment and km fields, there is a single M i l e field. There are also extra fields for: B C R Class, 53 a rock fall intensity rating assigned by B C R (Fig. 4.1); Train Delay (instead of the Hwy/lane Closures field); and Track or Train Damage. There is no field for Deaths/Injuries. 442 failures, 209 (47%) with known volumes, were recorded on B C R from January, 1976 to October, 1996. Fall/slide events comprise 407 of these, of which 183 have known volumes. The other 34 events are debris flows, 26 of which have known volumes. The C N R table has a field for Subdivision as well as M i l e , a Deaths/Injuries field, and a Temperature field. It does not include an intensity rating field, but is otherwise the same as the B C R table. A total o f 625 events were recorded for C N R , of which only 6 had known volumes. These six failures seem to have been reported as rock-on-track events. Almost all of the remaining events were reported as slide detector fence signals in 1995 and 1996, and the type o f failure for these events remains unknown. The events signaled by the slide detector fence were classified, where possible, according to the type of material in the railway cut. For example, failures in rock cuts were classified as rock falls or rock slides, but these classifications were merely estimates, as the records did hot include data on failure types. Seven events from M a r c h , 1946 to February, 1971 were also recorded, likely due to the destructive nature of these events. A l l except one of these failures led to some kind of damage, and four were responsible for a total o f eight fatalities. The descriptions o f these events included material and failure types, but did not include volume estimates. O f the 625 events recorded in total, 620 were classified as falls/slides, three as earth slumps, and one as a debris flow. The C P R table includes fields only for Zone, km, Date, and Volume Displaced. The kilometre values provided by C P R do not represent the exact location of rock fall events. Instead, within defined geographic zones, the locations are scrambled. These zones are: Vancouver to Agassiz; Agassiz to Hope; Hope to Lytton; Lytton to Thompson; Thompson to Ashcroft; and Ashcroft to Kamloops. A l l o f the events recorded on C P R were slide/fall events. In total, 918 54 events were recorded, from March, 1974 to February, 1997. Of these, 623 (68%) have magnitude estimates. 4.3 - Accident Data Accident and damage data were available for both of the highways, BCR and CNR, but were unavailable for CPR because of the nature of the event records for that railway. While damage was not included systematically in many of the slope failure reports, any significant damage was normally noted in the reports, and injuries or fatalities were always recorded. A total of nineteen deaths and five injuries due to slope failures were reported on Highway 99 in the past thirty-five years, all within 25 km north of Horseshoe Bay. Twelve of these fatalities were attributed to debris flow events. A debris flow at M Creek in 1981, resulted in the deaths of nine people on Highway 99. Debris flow events at Charles Creek in 1981, and Alberta Creek in 1982, caused the deaths of three more people, including a pedestrian near the highway, and two people in a house which was destroyed by the debris flow. Five fatalities due to rock falls on Highway 99 have also been recorded. It remains unclear whether the remaining fatality was actually related to slope failure. MOTH records for this incident indicate that a vehicle accident was responsible for the death of one person, but the accident may or may not have been caused by fallen rock on the road. Many landslide reports noted lane or highway closures, or indicated that rock or debris blocked at least one lane of the highway. Several reports noted damage to vehicles, but very few indicated that the road surface had been damaged. Only one fatality, in January, 1993, has been recorded on Highway 1. This accident involved an ambulance which collided with the highway rock cut, but it is again unclear whether a slope failure was to blame for the accident. A number of slope failure records included information about damage to vehicles on the highway, but very few noted delays to traffic or closure of the highway. 55 N o slope failure fatalities have been recorded on B C R . Although two of the debris flows which led to fatalities on Highway 99 also affected B C R , no railway users were killed in these events. The standard B C R slope failure report form includes sections for notation of track damage, train damage, train derailment, and train delays. Damage to other structures such as bridges and retaining walls is sometimes recorded in a 'Comments' section. Eight people have been killed by slope failures on C N R since 1958. In February, 1996, the operator o f a cleaning machine was injured when a falling rock struck the machine. Most o f the C N R slope failure records are in the form of slide detector fence signal reports, and do not contain written descriptions of damage. However, many refer to broken slide fence sidewall or overhead wires. Train delays, and damage to the track, trains and equipment, are noted in some reports. Table 4.1 summarizes the death, injury and damage statistics for each of these four transportation routes. The numbers presented here are minimum values, as many other incidences of damage may have gone unreported. 56 Table 4.1 - Recorded damage caused by slope failures on transportation routes in the study area, 1958 to 1996 Type of Damage Hwv99 H w v l B C R CNR Deaths 19 1 0 8 Injuries 5 5 0 1 Hwy. blocked/closed 69 9 n/a n/a Train delayed n/a n/a 102 4 Bridge(s) damaged/destroyed 4 0 3 0 House(s) damaged/destroyed 2 1 0 0 Vehicle(s) damaged/destroyed 21 22 n/a n/a Train/speeder damaged n/a n/a 9 7 Train derailed n/a n/a 4 2 Road damaged 3 0 n/a ri/a Track damaged n/a n/a 70 2 Retaining wall damaged/destroyed 0 0 2 0 Retaining mesh damaged 2 0 1 0 Hydro tower damaged 0 0 1 0 Power line down 0 1 0 0 Sidewall wires broken n/a n/a n/a 71 Overhead wires broken n/a n/a n/a 14 57 Figure 4.1 - B C R Landslide intensity rating system Few rocks between rails. N o delays to patrols or trains. B Rocks above rails. Can be cleared by one or two men or knocked clear by passing unit. M a y inflict some minor damage to unit. Rock covering or blocking rails. M a y result in minor train delay. Requires several men to clear track. Track damage very minor, i f any. D Track buried. Results in significant train delay. Additional men and equipment required to clear track. Some track damage likely / . (i.e. rails displaced or broken). E Major rock slide. Results in major train delay and/or lengthy track closure. Heavy equipment required to clear track - possibly drilling & blasting. Serious track damage. 58 CHAPTER 5 - R O C K F A L L MAGNITUDE-FREQUENCY RELATIONSHIPS 5.1 - Data Mapping Several plots of rock fall data were created for each transportation route, to show the distribution of events in space and time, and to highlight any patterns in the magnitudes of events, where magnitudes were known. These graphs were plotted as a preliminary investigation into spatial and temporal rock fall patterns on each route. From the rock fall data table for each highway and railway, another table was created to show the number of events to occur at each location (broken into 0.1 km segments) along the length of the route. The Grapher program was used to plot number of events vs. location. Another similar table was made to show the frequency of events with known magnitudes, at each location. This table also included a field for the sum of the magnitudes of the events to occur at each 0.1 km segment. The frequency of these events vs. location, and the magnitude vs. location, were again plotted using Grapher. A log scale was used for the magnitude axis on each graph due to the large variation in magnitudes. No plots involving magnitudes were made for CNR, due to the very small number of event records which included magnitude estimates. Another table was created for each route to give the dates of all events vs. location. A scatter plot for each highway and railway shows the distribution of events over time and space. A second date graph was plotted for each route to show only the dates of events for which the event magnitudes were known. These plots give an initial impression of any particular areas on each route which may be more susceptible to rock fall than others. For example, the scatter plot for Highway 99 shows a high density of points over a wide range of dates in the first thirty kilometres of the route. This shows that Highway 99 between Horseshoe Bay and just north of Porteau Cove may be a particularly hazardous area in terms of rock fall. Figures 5.1 to 5.5 show the resultant frequency vs. location and magnitude vs. location plots for each of the five transportation routes. Because exact locations of rock falls were not available from CPR, plots of frequency vs. location, 59 and magnitude vs. location could not be produced. However, the dates o f events were plotted, using the scrambled locations given, to show temporal rock fall patterns between the defined zones. Figure 5.4 shows that the pattern of rock fall recording appears to be consistent for all zones. 5.2 - Elimination of Censoring Effects A major obstacle in calculating slope failure risk on all o f the transportation routes is the effect o f censored data due to inconsistent landslide recording over the years. Recently, slope failures are recorded fairly diligently in many areas. However, in past years, many landslides were not recorded i f they did not lead to major damage, injury or death. It can be seen on the Highway 99 date vs. location plot (Figure 5. Id) that there is a cluster o f data points between km 203 and 240. According to landslide records, no events in this area occurred before about 1993, but a great number occurred in the next few years. It is unlikely that no slope failures actually took place in this area prior to 1993, but instead, it is probable that events were small and did not cause major damage, so went unreported. In contrast, the record of slope failures along the first thirty kilometres o f the highway is fairly consistent after about 1980, indicating that reporting in this area has been fairly diligent since that time. This is likely due to the hazardous nature o f the area, and the high volume of traffic. In order to establish a cumulative frequency-magnitude relationship for an area or transportation route, annual frequency values for landslides o f various magnitudes must be defined. To do this, a sampling interval must be chosen, over which slope failure recording has been diligent and consistent. Once this sampling interval has been chosen, each event in the record can be assigned an incremental annual frequency value, which is simply the reciprocal o f the sampling interval, in years. The events can then be arranged in descending order according to magnitude, and the annual frequency values summed cumulatively, to give the cumulative frequency-magnitude relationship. 60 It can be seen from the above examples that landslide reporting consistency varies from place to place along the transportation routes. Therefore, the sampling interval will not be the same over the entire length of each route. Instead, bands with similar patterns of landslide reporting must be defined, and the sampling interval determined for each of these bands. For each date vs. location scatter plot (all events), bands of reasonably constant point density were chosen visually. For example, as stated above, the Highway 99 scatter plot shows a high density of points from km 0 to 26, but there the density decreases for all dates. Thus, km 26 was chosen as the dividing point between two bands on Highway 99. Bands were defined in this manner, by visually determining the changes in data point density, for both of the highways (Figure 5.6). Because the pattern of recording frequency appeared to be consistent throughout the BCR and CPR routes, bands were not defined for the two railway lines. Table 5.1 shows the chosen bands for Highway 99 and Highway 1. Once these bands had been defined, it was necessary to determine the pattern of data censoring for each band, in order to choose appropriate sampling intervals. This was done by plotting the number of recorded landslide events vs. year, to visually note the increase in events over time. Because data censoring not only varies according to location, but also according to magnitude, frequency vs. year plots were constructed for a series of magnitude ranges. This procedure was repeated only for a small number of bands, instead of every one, to determine censoring patterns for different magnitude ranges. From this analysis, it was possible to group several magnitude classes together, reducing the large number of plots necessary to determine censoring patterns for all of the bands. Bands with a moderate to high density of data points over a wide range of dates were chosen for this analysis. For each of these bands, database tables were made to show year versus frequency for a series of different magnitude classes. For example, the number of events with magnitudes from 0.1 to 1 m3, 1 to 10 m3, 10 to 100 m3, etc. to occur in each year were calculated. 61 This information was plotted as a series o f frequency vs. year histograms, one for each magnitude class. Histograms for events with unknown magnitudes, and for all events together were also plotted. The purpose o f preparing these plots, as discussed above, was to show how reporting consistency could censor the data. For example, i f rock fall reporting and recording became more diligent over time for a given area, the number of rock falls in the database would increase, but not necessarily because events were more frequent. This effect was expected to be more significant in smaller magnitude events, since large events are generally considered to be more important in terms of highway economics and safety, and so were likely recorded fairly diligently for a lengthy time period. B y plotting the number o f events versus year, the censoring effect could be seen for each magnitude class, and an appropriate starting date for consistent rock fall reporting could be chosen. Figures 5.7 to 5.10 show the frequency vs. year histograms, for each magnitude class, for Highway 99 Band A , Highway 1 Band D , the entire B C R line, and the entire C P R line. B y visually inspecting these histograms, groups of volume ranges with similar histogram shapes and trends were chosen. For example, i f the 1 to 10 m 3 , 10 to 100 m 3 , and 100 to 1000 m 3 histograms al l displayed a similar pattern, these classes were grouped together for ease of further analysis. Since it would not be effective to repeat the same procedure for bands with much lower point densities, the chosen magnitude classes for each band studied in detail were considered appropriate for use in analyzing the entire routes. The following summarizes those magnitude classes chosen to be grouped together due to similarities in the frequency vs. year plots. Highway 99. Band A : 1) Unknown magnitudes, 0 to 0.1 m3, and 0.1 to 1 m3. The histograms for 0 to 0.1 m 3 and 0.1 to 1 m 3 each show a few scattered events from 1982 to 1993, with a significant jump in frequency in 1994. It was assumed that detailed recording of events of this size started in 1994, and hence, these two magnitude classes were grouped together. Events with unknown magnitudes were also grouped into this category, because it was assumed that detailed 62 reporting, including magnitude estimates, would be more likely for large events. Combining the unknown magnitude events with the events smaller than 1 m3 resulted in a more uniform histogram from 1992 to 1996. This supports the assumption that most of the events with unknown magnitudes were small, and suggests that more quantitative volume observations were introduced during the given years. 2) 1 to 10 m3,10 to 100 m3, and 100 to 1000 m3. The histograms for all three of these magnitude classes show a small number of events between 1969 and 1971. After 1971, no events are recorded until the early 1980s, at which point all three histograms show a rise in frequency, with the number of events remaining variable, but without a distinct skew, up until the mid 1990s. The 100 to 1000 m 3 histogram does not show any events occurring after 1989, but this could be due to the natural variability in occurrences of events this size, and not due to a decrease in reporting consistency. 3) 1000 to 10000 m3. The first record of an event greater than 1000 m3 is in 1964. After 1964, the frequency of occurrence of these events is low, and no skew is apparent on the histogram. This indicates that from 1964 on, the reporting of these large scale events was fairly consistent, and did not increase or improve in later years. Events greater than 10,000 m3 will be considered separately, as there were no such events in this band of Highway 99. Highway 1. Band D: 1) Unknown magnitudes, 0 to 0.1 m3, 0.1 to 1 m3, and 1 to 10 m3. For the three histograms showing events from 0 to 10 m3, very few (if any) events are recorded before 1993. After 1993, a jump in frequency of events is observed in all three histograms. Hence, it was assumed that the starting date for consistent recording of events of these three magnitude classes was be similar, at around 1993, and they were grouped together. As for Highway 99, Band A, events with unknown magnitudes were also included in this group, because it was assumed that since the magnitudes were not recorded, the events were likely to be small-scale. Again, this 63 assumption is supported by the increased uniformity of the histogram by the addition of the unknown magnitude events. 2) 10 to 100 m 3 and 100 to 1000 m 3 . Both of these histograms show no recorded events before 1988, and fairly consistent occurrences o f events after 1988. Only two events are recorded in the 100 to 1000 m 3 class, but again, this is likely due to the low frequency o f events of this size, and not due to inconsistent reporting. Again, events greater than 10,000 m 3 w i l l be considered separately. B C R . Entire Line. 1) Unknown magnitudes, 0 to 6.1 m 3 , 0.1 to 1 m 3 , 1 to 10 m 3 , 10 to 100 m 3 ,100 to 1000 m 3 , and 1000 to 10,000 m 3 . A l l of these histograms show very few or no recorded events before 1985, and random, non-skewed occurrences after 1985. Thus, all o f the magnitude classes were grouped together, assuming that consistent reporting for all events began in about 1985. Events over 10,000 m 3 w i l l be considered separately. C P R , Entire Line: 1) Unknown magnitudes, 0 to 0.1 m 3 , 0.1 to 1 m 3 , 1 to 10 m 3 , 1 0 to 100 m 3 ,100 to 1000 m 3 , and 1000 to 10,000 m 3 . A l l o f these histograms show very few or no recorded events before 1975, and random, non-skewed occurrences after 1975. A s above, all o f the magnitude classes were grouped together, assuming an approximate starting date for consistent reporting o f 1975. Events over 10,000 m 3 w i l l be considered separately. Once these grouped magnitude classes had been chosen, frequency vs. year for each class could be plotted in a similar manner for all bands on all routes. However, to reduce the large number of plots to be generated, the bands were also grouped. B y looking again at the date vs. location scatter plots, it could be seen that some bands had similar dates for which events began to 64 occur. Assuming that the starting date for unbiased reporting would be approximately the same for these bands, they were grouped together. The following describes how the Highway 99 and Highway 1 bands were grouped together, and why those groups were defined as such. Highway 99: 1) Band A . The high density of data points in Band A begin shortly after 1980. Throughout to the late 1990's, the density o f points remains high, but it is difficult to see in the scatter plot whether the density varies or displays any skew to later dates. However, it is known from the frequency vs. year histograms plotted for Band A that the number of events per year does begin to increase in the mid to late 1980s, and stays fairly high through to 1996. 2) Band B. The light scatter o f data points in Band B begins in the mid 1980s. Therefore, Band B was considered separately from Band A for further analysis. 3) Band D. A l l except one data point in Band D are found in either 1993 or 1994. 4) Bands E , F , G , H , I, J . The density of data points in these bands is highly variable, but the date at which data points first begin to appear (or at which there is a distinctive jump in density o f data points) is similar for al l , at around 1994. Data points are found in 1994 and 1995, but are not common in 1996. Highway 1: 1) Bands A , B, C , D, G . Data points in all of these bands are scattered at relatively low density for earlier dates, but the first occurrence of points, apart from one early event in band B , is between 1984 and 1988 for all bands. This is distinctively different from the starting date for data points in the other two bands. 2) Bands E and F. Both of these bands show data points concentrated much later 65 than those for the other bands on highway 1. Except for one early event in band E, data points begin at around 1993 for both bands. For each grouped band, frequency vs. year histograms were plotted for each grouped magnitude class. Again, the purpose of these histograms was to show the increase in frequency over time, and to allow an appropriate starting date for unbiased reporting to be chosen for each band and magnitude class. Histograms were not plotted for Highway 99, Band D, because virtually all of the events in this band were recorded in 1993 and 1994. Therefore, frequency vs. year histograms were not necessary to see patterns in event frequency over the years. Similarly, no histograms were plotted for Highway 99, Bands E to J, because events were only recorded in 1995 and 1996. Although all magnitudes up to 10000 m3 were grouped together for BCR and CPR, histograms were plotted for the three magnitude classes defined for the highways, to ensure that the intervals of consistent rock fall recording were the same for all magnitudes. Figures 5.11 to 5.16 show the frequency vs. year histograms for each magnitude class in each grouped band. The histograms for medium to large events on Highway 99, Band A, have a negative skewness within the sampling interval. This is likely caused by the effects of major rock slope stabilization in this area during the 1980s and 1990s. More recent stabilization work, including extensive meshing, was applied after 1995. This would probably also affect the temporal frequency trends, but is not covered by data available for this study. 5.3 - Definition of Sampling Intervals For each frequency vs. year histogram, an end date for consistent recording frequency was chosen based on the shape of the graph. Once the end date had been chosen, it was necessary to 66 choose a start date for the time interval of consistent recording. To do this for each grouped band and magnitude class, a series of linear regressions were performed on the histogram data, to determine the average slope of the curve. An initial estimate of the start date was chosen visually, and a linear regression was performed on the data from this start date to the chosen end date. The start date was then varied over several years in either direction from the initial value, and a linear regression was performed for each start date. The purpose of performing these linear regressions was to determine which start date yielded a regression slope closest to zero, and to observe systematic changes in data trends, as shown by distinct changes in the regression slope. The slope of the regression curve was taken as an indication of the skewness of the histogram data, so a slope close to zero would indicate little or no skew to later dates. Distinct changes in the slope may also indicate changes in rock fall recording frequency. The start dates were then chosen using the regression slope data, while continuing to consider the histogram data. Initial end dates for each magnitude class, in each grouped band, were chosen by visually examining the frequency vs. year histograms. If the frequency values remained high, or within the same general pattern, up to 1996, then 12/31/96 was chosen as the end date. If the histogram showed a significant decrease in frequency for 1996, then 12/31/95 was chosen as the end date. For these examples, the actual dates of occurrence of those events recorded in 1996 were also investigated. If it was found that very few events were recorded for the later part of the year, but many were recorded earlier in 1996, then a specific date during 1996 could be chosen as the end date. However, no such patterns were found, so all end dates were chosen as either 12/31/95 or 12/31/96. For Highway 99, Band A, the number of events in the record with magnitudes less than 1 m3 or unknown decreased slightly from 1995 to 1996. For events with magnitudes from 1 to 1000 m3, the frequency dropped more dramatically in 1996. It was assumed from this pattern that the record for 1996 was not complete for these larger events, from 1 to 1000 m3. Because it is likely that the diligence o f recording was less for smaller events than larger ones, it was also assumed that the record was incomplete for events less than 1 m 3 and with unknown magnitudes. Inspecting the dates of events in 1996 revealed that even though the events in 1996 were fewer, they were distributed throughout the year, and there was no absence o f events recorded near the end of the year. Therefore, the end dates for all magnitudes for Highway 99, Band A , were chosen as 12/31/95, assuming that the record was incomplete for 1996. The event record for Highway 99, Band B , appeared to be complete through 1996 for all events, so the end date was chosen as 12/31/96. A n initial start date was also chosen for each magnitude class, in each grouped band. This was done again by visually examining the frequency vs. year histograms. The year at which there was a significant rise in frequency, after which the frequencies remained random, without showing any significant skew, was chosen as the start date. Figures 5.17 to 5.20 show the slope vs. sampling period start date plots for each magnitude class in each grouped band, with the chosen start date marked on each graph. Once the start date for each data set was determined, it could be subtracted from the end date to give the number of years in the recording interval. This value represents an estimate o f the number o f years for which recording of events was consistent, for each magnitude class, and in each grouped band. It was required to calculate the frequency per year values needed for plotting cumulative frequency per year vs. magnitude. Several bands and magnitude classes had very few recorded events, or had events recorded over only a very short time period. For these data sets, it was not considered useful to perform linear regressions to choose start dates for intervals o f consistent recording frequency. These data sets are: Highway 99, Band B (1 to 1000 m 3 ); Highway 99, Band D (all events); Highway 99, Bands E to J (all events); Highway 1, Bands A to D, G (1000 to 10,000 m 3 ) ; and Highway 1, Bands E and F (under 1 m 3 or unknown). 68 The recording intervals for the data sets for which no regressions were performed were chosen either by visual assessment of the frequency data, or by using the same interval as for another data set. For Highway 99, Band B (1 to 1000 m 3 ) , the interval was chosen as 1980 to 1996. Because o f the low frequency of events, particularly o f large magnitudes, in Band B , a recording interval was difficult to determine using linear regressions. While the first event in the record was in 1984, the number of events was so few that it could be considered that rock fall recording was diligent before this time, but no events o f this magnitude occurred. Therefore, 1980, the same start date as for Highway 99, Band A (1 to 1000 m 3 ) was used, assuming that diligent recording of rock falls o f this magnitude may have started at approximately the same time for this entire section of the highway. A n end date of 1996 was used because the record for smaller events in this section of Highway 99 appeared to be complete for 1996, so it was assumed that the record of larger events in 1996 was also complete. For Highway 99, Band D (all events), all recorded events except one occurred in 1993 or 1994. Therefore, these two years were chosen as the time interval for this section. Similarly, 1994 to 1995 was chosen as the interval for Highway 99, Bands E to J (all events), as they were the only two years with recorded events in this section. O n Highway 1, Bands A to D , G (1000 to 10000 m 3 ) , only one event, in 1991, was recorded, so the start date was chosen as 1957, the same as the start date for H w y . 99, band A . It was assumed that the recording consistency for large events would be approximately the same for al l major highways in B C , so choosing the same start date as for H w y . 99 would be reasonable. 1996 was still used as the end date for these events, under the assumption that the record for 1996 was complete for events o f all magnitudes in this section of Highway 1. For Highway 1, Bands E and F (events less than 1 m 3 or unknown), no regressions were necessary, because virtually all of the recorded events occurred only in 1994 and 1995. Due to the 6 9 significant increase in recorded events from 1994 to 1995, it was assumed that the record for 1994 was incomplete, and the only year considered for these events was 1995. Table 5.2 summarizes the start dates and recording intervals chosen for each data set. Two events with magnitudes greater than 10000 m3 were recorded in the rock fall database. The Cheakamus Canyon Rock Slide, which had a magnitude of 65000 m3, occurred on Highway 99, Band B, in 1996. The other event was a 15000 m3 rock fall which occurred on BCR in 1986. The time intervals of consistent recording for events of this size were assumed to be the same as the intervals assigned to events 1000 to 10000 m3 in the same railway or highway sections. Because any slope failure over 1000 m3 is a major event, it is reasonable to assume that recording diligence of all events greater than 1000 m3 would be consistent for a particular area. Therefore, the interval assigned for the event on Highway 99 was 40 years, from 1957 to 1996 (using the same start date as for Highway 99, Band A), giving that event a frequency per year value of 0.025. The interval assigned for the BCR event was 12 years, from 1985 to 1996, giving it a frequency per year value of 0.083. Major rock avalanches were treated separately in constructing magnitude-frequency relationships. Approximately four major rock avalanches are known to have taken place in each of the corridors in the 10,000 years of post-glacial time, as summarized in Table 5.3. Therefore, the annual frequency value for each corridor is 0.0004. The volume of these major rock avalanches averages approximately 30 million cubic metres. 5.4 - Magnitude-Frequency Relationships Once the start and end dates had been chosen, a new table was made for each highway and railway, including only those events falling within the intervals of consistent recording. Each event was assigned a frequency per year value, equal to the reciprocal of the interval value. For example, every event on Highway 99, Band A, between 1 and 1000 m3, was assigned a frequency 70 per year value o f 1/16, or 0.0625, because the chosen recording interval for that data set was 16 years. The data was then sorted in descending order of magnitude, and a new column was constructed, in which these incremental annual frequencies were summed cumulatively. Events with unknown magnitudes were assumed to be small-scale events, and assigned magnitudes of 0.01 m 3 for the purpose of plotting magnitude-frequency curves. This assumption was made based on the idea that larger events are generally recorded more diligently than smaller ones, and volume estimates are generally given in the reports. Therefore, records with no magnitude estimates are most likely for smaller, less significant events. Using Grapher, a plot of cumulative frequency per year vs. magnitude was constructed for each highway and railway, on a log-log scale. Figure 5.21 shows the magnitude-frequency relationships for each transportation route. On Highway 99, Bands A and B were markedly different from the rest of the highway in terms of point density and starting dates for uncensored recording. While consistent rock fall reporting appears to have begun on this southern section of the highway in the mid to late 1980s, reporting in other areas o f Highway 99 seems to have only taken place on a wide scale very recently. The short sampling interval in Bands C to J would likely result in the under-representation of large events, when constructing magnitude-frequency relationships. Also, there were a large number o f mostly small-scale events recorded for Band H in February, October, and November of 1995. M a n y of these events were recorded in the same kilometre, on the same day. This suggests that many small events in the same area, which may in some places be considered to be one large event, have been recorded as separate events. This could be due to the division in the highway maintenance contract between Pemberton and Lillooet (Geraghty, 1998, personal communication). The diligence and format o f recording small rock falls was apparently different for the two maintenance zones, due to the difference in personnel. The result is the under-representation of large events in the area mentioned, and possible over-representation of smaller 71 events, caused by the short sampling interval. This contrasts strongly with the steady, consistent recording of rock fall events over a number o f years in Bands A and B. Therefore, a separate magnitude-frequency plot was constructed for Bands A and B alone (Figure 5.22). Because this represents only about one quarter o f the corridor length, the annual frequency value for major rock avalanche events (30 x 10 6 m 3 ) was reduced from 0.0004 to 0.0001. Similarly, a plot for Highway 1, without Band F, was constructed, because the temporal rock fall patterns for Band F were quite distinct from the rest of the highway (Figure 5.23). Again, a very large number o f small events were recorded in this area, mostly in 1995, while no events were recorded before 1994. This contrasts with the rest of the highway, for which there is an apparently steady pattern of rock fall recording over several years. N o reduction in the rock avalanche frequency value was necessary, as eliminating Band F reduces the length of sampling in the corridor by only 15 km (less than 4%). It can be seen that each of the magnitude-cumulative frequency curves has a linear section across several orders o f magnitude, but that there is generally strong curvature for magnitudes less than 1 m 3 . Therefore, the events with unknown magnitudes were assigned new magnitude values, ranging from 0.01 to 1 m 3 . These events were distributed linearly along the log-log plots, leading to a straightening of the magnitude-cumulative frequency curves in the upper ranges. Figure 5.24 shows the magnitude-cumulative frequency relationships for each route, with the events o f unknown volumes distributed from 0.01 to 1 m 3 . The thin line in the upper ranges o f each graph represents the curve for which all events with unknown magnitudes were assigned volumes of 0.01 m 3 . The magnitude-cumulative frequency curves span more than six orders o f magnitude. The Highway 99 curve is linear over more than four orders o f magnitude without the correction for unknown volumes, and more than five with it. Each of the other curves has a linear segment over at least three orders of magnitude. 72 Viewing all four of the corrected curves on the same set of axes (Figure 5.25), it can be seen that, with the exception of BCR, the slopes of the curves at magnitudes above 1 m3 are similar. The addition of the major rock avalanche data to the relationships shows that linear extensions of the curves continue over eight to ten orders of magnitude. There is a conspicuous lack of data for large failures, from 100,000 and 3 x 107 m3, possibly a result of non-recognition, due to failures from the high mountain slopes not actually reaching the transportation routes. However, it should be considered that events in this magnitude range are anomalous to the plotted magnitude-frequency relationships. For example, the possibility of a multi-fractal distribution should be considered. While the distribution for certain magnitudes is linear, there must be an upper and lower limit to this fractal relationship. Because of the gap in data for large events, it is not clear whether the historical events form this upper limit. Figure 5.26 shows the four magnitude-cumulative frequency curves without the avalanche data, to better examine the main parts of the curves. Curvature of the relationships at magnitudes below 1 m3, with the exception of Highway 99, is probably due to systemic censoring. It is possible, however, that some residual non-systemic censoring effects may also contribute to the curvature of the graphs. The linear ranges of the magnitude-cumulative frequency plots can be represented by a power law relationship between magnitude (M) and cumulative frequency (F). The form of the equation is: logF = b x logM + a [5.1] The slopes of the power relationship within the linear segments of the curves were calculated by linear regressions. For Highway 99, the range of magnitudes included in the slope calculation was 0.01 to 100000 m3, encompassing all events except the major rock avalanches. For the other 73 routes, only the events from 1.0 to 100000 m3 were used to calculate the slope, due to remaining curvature in the small-magnitude ranges. Table 5.4 summarizes the regression data, including the slopes of the linear segments of each curve. Highway 99, Bands A and B, appears to be the most robust data set, linear over more than six orders of magnitude. It has the greatest number of data points in the linear section of the curve and the longest sampling period for large events. It also appears to be least affected by censoring of small-magnitude events. The two Fraser-Thompson data sets (Highway 1 and CPR) are linear only at magnitudes greater than 1 m3, and it is assumed that the data at lower magnitudes are still distorted by censoring. It is probable that systemic censoring exists in this corridor as a result of the effectiveness of ditches along the highway and railway tracks, which intercept many of the smaller events. The BCR relationship is highly curved, and suggests censoring effects. This is the smallest data sample, and has the shortest sampling period. It is also the data set with the most events of unknown magnitudes (over 50%). These factors have likely affected the quality of the curve. The BCR track north of Pemberton was affected by a cluster of medium scale rock slides in the nineteen-eighties (Leighton, 1990). It is possible that the frequency of the larger events is exaggerated by the occurrence of this cluster within the short sampling period. It is also possible that small events which do not affect the operation of railway equipment are not generally recorded by BCR. The magnitude-cumulative frequency curves within each of the two corridors are fairly consistent, despite the fact that each corridor contains both highway and railway data, and despite the presence of residual censoring. The Howe Sound-Lillooet corridor is best represented by the Highway 99 curve, which has a slope of-0.43. Although the quality of the BCR curve is somewhat lower, it yields a slope of -0.40 for magnitudes above 1 m3. The slightly flatter slope 74 may reflect the fact that most o f the rock falls on B C R occurred in the core o f the Coast Plutonic Complex, in the north part o f the corridor, while all of the Highway 99 events occurred near the coast. The characteristic slope for the Fraser-Thompson corridor is -0.65 to -0.70 for magnitudes above 1 m 3 , and -0.18 to -0.25 for smaller events. These slope values indicate that the Highway 99 and B C R experience a relatively higher frequency of larger events, while smaller events are more dominant on Highway 1 and C P R . This may be due to the different geological settings o f the two corridors, with the Howe Sound-Lillooet corridor being closer to the core of the Coast Plutonic Complex, and the Fraser-Thompson corridor traversing structurally and lithologically complex, faulted rocks. The influence o f geology on the shape of the magnitude-cumulative frequency curves w i l l be investigated further in the following section. The distinct break in slope on both the Highway 1 and C P R curves, at about 1.0 m 3 , highlights the apparent systemic censoring of the Fraser-Thompson corridor data. This suggests that ditches and roadside barriers have been more effective in this area, preventing small-magnitude rock falls from reaching the transportation route. The lines extending the curves from the largest events in the database to the 30 mill ion cubic metre points represented by the rock avalanche records have an average slope of -0.64. This value is similar to the Fraser-Thompson data. However, these extensions must be viewed with caution, due to the very small sample represented by the large rock avalanche events. Nevertheless, the curves including the rock avalanche data do suggest that the linear sections o f the magnitude-cumulative frequency relationships for these corridors may extend over many higher degrees o f magnitude, although sampling is difficult. The magnitude-cumulative frequency relationships established for these two transportation corridors can be compared with those determined by Gardner (1970) in the Lake Louise area, Rocky Mountains, Alberta. Here, data representing direct observation o f 409 mostly small-magnitude rock fall events from natural calcareous and quartzitic cliffs were compiled over two 75 summers. The resulting magnitude-cumulative frequency relationships again have curvature in the lower-magnitude regions, but the curves are nearly linear between 0.1 and 10 m 3 . These linear sections are characterized by a slope of -0.72, which is remarkably similar to the slopes o f the Fraser-Thompson curves (above the censoring limit) calculated above. In summary, the results of this study indicate that a slope of about -0.43 is characteristic o f the magnitude-cumulative frequency relationships for the Howe Sound-Lillooet transportation corridor o f southwestern British Columbia. For the Fraser-Thompson corridor, a slope of about -0.7 appears to be suitable. Comparison with Gardner's (1970) data indicated that the slope of the relationship is independent of whether the slopes are natural, or constructed road cuts. 5.5 - Influence o f Geology The difference in magnitude-cumulative frequency slopes for the two transportation , corridors in the study area is likely a result of the different geological and physiographical settings. To further investigate the influence of geology on rock fall magnitude-frequency relationships in this area, the corridors were divided into zones o f roughly homogeneous lithologic types (see Figure 3.1). For each transportation route, magnitude-cumulative frequency relationships were then plotted for the separate geologic zones. The same methods and sampling intervals as those described in the previous sections were used in constructing these curves. Figures 5.27 to 5.29 show the spatial frequency of rock falls on each route, with bedrock geology marked on. A graph was not plotted for C P R , due to the unavailability of exact rock fall locations. The divisions in bedrock type are fairly broad, but serve to divide the routes into generally different lithologies. Information used to plot these zones was taken from Monger and Journeay (1994) and Armstrong (1984). 76 5.5.1 - Plutonic Rocks At the southern limit of the study area on Highway 99, there are two small zones of Jurassic and Cretaceous plutonic rocks. 10 rock fall events were recorded within the sampling intervals from km 0 (Horseshoe Bay) to 0.8. 14 events were recorded from km 4.3 to 6.3. Apart from these two small areas, there are two major zones of plutonic rocks on Highway 99 within which rock fall events were recorded during the defined sampling intervals. From the Porteau Bluffs (km 24.6) to the Cheakamus River Bridge (km 77), 61 events were recorded. Along the southern part of this section, to Squamish, are many road cuts into the massive, well jointed Middle Cretaceous granodiorite and quartz diorite of the Howe Sound Batholith. The only exception is a small sliver of deformed volcanic Gambier Group rocks, known as the Brittania Shear Zone, from km 30.1 to 32. No rock fall events were recorded in this zone, as there are few highway rock cuts. North of Squamish to the Cheakamus River, the highway again traverses plutonic rocks, namely the Jurassic Cloudburst quartz diorite. Jurassic plutonic rocks line the highway from about km 86 to 96, but no events within the sampling periods were recorded in this area. The next plutonic zone in which events were recorded is the area earlier defined as Highway 99, Band D. There are seven rock fall events in the record from km 107.5 (Green Lake) to 155 (Owl Creek Fault), which is about 15 km northeast of Pemberton. In this zone, the rocks are Jurassic quartz diorites and Early to Middle Cretaceous diorites and quartz diorites. Beyond Pemberton, the geology becomes more complex, involving various volcanic and sedimentary rocks, phyllites and some schists, as well as plutonic rocks. In any of the plutonic zones between the Owl Creek Fault and Lillooet, no rock fall events were recorded in the defined sampling periods. Upon plotting a preliminary magnitude-cumulative frequency curve, it was noted that the short sampling interval of the events in Band D caused the curve to take distinct jumps in . 77 frequency. The frequency of these events may have been distorted due to the sampling interval of only two years. Therefore, as for the curve representing all rock types on Highway 99, the events from Band D were discarded, and only the 85 events from Bands A and B were used to plot the magnitude-frequency relationship. O f these 85 events, 45 had magnitude estimates, ranging from 0.01 to 65000 m 3 . The magnitude-cumulative frequency relationship for these events was plotted as above, using Grapher, and is shown in the Figure 5.30. Again, the events with unknown magnitudes were originally assigned volumes of 0.01 m 3 , then were distributed linearly along the log-log plot, from 0.01 to 1 m 3 , to straighten the curve and reduce the effects of data censoring. The thin line represents the curve before this correction for events with unknown magnitudes was made. The relationship appears to be linear for magnitudes of 0.01 to 1000 m 3 . It then curves upward slightly to the large event, the frequency of which is possibly exaggerated due to a too short sampling interval. The slope of the linear section of the curve from 0.01 to 1000 m 3 is -0.42, calculated by linear regression. I f the 65000 m 3 event is included, the slope becomes -0.41. Both of these slope values are quite similar to the overall slope values calculated for Highway 99 Bands A and B , and B C R . Along B C R , the following rock fall events were recorded in plutonic rock during the defined sampling periods: • 96 events in Middle Cretaceous granodiorite and Jurassic quartz diorite, from mile 15.3 (Porteau) to 59.6 (Daisy Lake); • 3 events in Jurassic quartz diorite, from mile 64.6 to 68.4 (south of Whistler); • 65 events in the quartz diorite and granodiorite Mount Rohr and Spetch Creek Plutons, from mile 73.3 (near Whistler) to 105.0 (near Gramsdns); • 3 events in Late Cretaceous quartz diorite, from mile 112.8 to 114.6 (near Birken); 78 • 22 events in the Late Cretaceous granodiorite Scuzzy Pluton, from mile 127.4 to 130.5 (about 4 miles south of Downtown Creek). The total number of events in this record is 189, of which 84 have magnitude estimates, ranging from 0.03 to 4600 m3. As for Highway 99, the magnitude-cumulative frequency relationship was plotted for this data set, and the events without magnitude estimates were distributed linearly from 0.01 to 1 m3 (Fig. 5.31) The curve can be approximated as linear from 0.01 to 4600 m3. Calculated by linear regression, the slope of the curve is -0.31. This slope values is lower than that calculated for plutonic rock falls along Highway 99, and may be affected by residual censoring as discussed in Section 5.4.. It should also be considered that the majority of events in the BCR plutonic rock data set are from the north-east area of the corridor, north of Pemberton, while the Highway 99 plutonic rock data set comprises only events in the southern section of the corridor. Therefore, the BCR magnitude-cumulative frequency curve may be representative of rock falls in the massive core of the Coast Plutonic Complex, while the Highway 99 curve describes the magnitude-frequency relationship of rock falls along the coast. Highway 1 traverses fewer areas of plutonic rock than Highway 99 or BCR. However, there are several plutonic areas along its route, and various rock fall events were recorded in these sections, during the appropriate sampling periods. It should be noted that the intrusive rocks encountered in this corridor tend to be more fractured, faulted and sheared than the generally massive, well jointed plutonic rocks in the Howe Sound-Lillooet corridor. The plutonic rock fall events recorded on Highway 1 are summarized below: • 5 events in Late Tertiary granodiorite, from km 133.2 to 137.9 (east of Agassiz); • 7 events in Middle Cretaceous quartz diorite of the Spuzzum Pluton, from km 145.5 to 153 (Hope Faul); 79 • 2 events in Early Tertiary granodiorite, from km 155.5 to 162 (surrounding Hope); • 80 events in faulted, variably fractured, locally schistose Middle Cretaceous quartz diorite and pegmatite, from km 205 (1 km west of Alexandra Tunnel) to 219.5 (Kwoleck Creek Fault); • 7 events in Permian/Triassic complex, massive granodiorite, cut by pegmatite, from km 266 (Lytton) to 283.5 (Nicoamen River). Of these 101 events, 56 have magnitude estimates, ranging from 0.02 to 300 m 3 . Figure 5.32 shows the magnitude-cumulative frequency relationship for this data set, before and after corrections were made for events with unknown magnitudes. There is a break in the curve at a magnitude value of 3 m 3, above which the curve is steeper than for the smaller events. The curve for Highway 1 is somewhat different from those for the other two routes, in that the slope for events greater than 1 m 3 is -0.69. This steeper slope for larger events indicates that smaller events are more frequent along this route, which could be attributed to the faulted, fractured nature of many of the rock cuts. The majority of the events in this data set occurred in the marginal areas of the Spuzzum Pluton, from km 205 to 220. The rocks here are described by Monger and Journeay (1994, p. 31) as, "variably fractured, but generally more massive than the country rocks they intrude." Faulting is abundant. This contrasts with the massive plutonic rocks with widely spaced joints found along the Howe Sound-Lillooet corridor. Figure 5.33 shows the similarity of the magnitude-cumulative frequency relationships for plutonic rocks along the three transportation routes. The linear regression data from these curves is summarized in Table 5.5. The Highway 1 curve is distinctively steeper than the others at magnitudes greater than about 1 m 3. This suggests that, while it may be possible to define characteristic slopes of magnitude-cumulative frequency curves for given rock types, the structural 80 setting must also be considered. The sheared and faulted nature of the rocks in the Fraser-Thompson corridor may be responsible for the steeper slope, due to a higher frequency of smaller scale rock fall events. For rock falls in the massive, jointed plutonic rocks in the Howe Sound-Lillooet corridor, the results indicate that a typical magnitude-cumulative frequency slope in the order of-0.3 to -0.4 is appropriate. A slope of about -0.6 to -0.7 seems suitable for rock fall events in the fractured plutonic rocks in the Fraser-Thompson corridor. 5.5.2 - Sedimentary. Volcanic, and Non-Foliated Metamorphic Rocks A similar approach was taken to plotting rock fall events in sedimentary and volcanic rocks along the three transportation routes with geological information. Highway 99 traverses several areas of pyroclastic rocks, flows, and metamorphosed sedimentary rocks, particularly in the area between Cayoosh Creek (km 167.5) and Lillooet (km 232.6). However, as discussed in the previous section, the sampling interval for events beyond km 75 is too short to give reliable magnitude-frequency relationships. Therefore, only the areas of meta-sedimentary and volcanic rocks from Horseshoe Bay to km 75 (Cheakamus River Bridge) were considered in this analysis. Rock fall events within the defined sampling intervals for Highway 99 were recorded in a single zone of volcanic and meta-sedimentary rocks, from km 6.3 to 24.6 (Porteau). Outcrops along this part of Highway 99 are of the Lower Cretaceous Gambier Group. The northern 5 km section features thinly bedded silicified tuff and argillite, while massive, altered volcaniclastics dominate farther south (Monger and Journeay, 1994). 260 events were recorded in this zone, of which 139 had magnitude estimates, from 0.01 to 7000 m3. Another small zone of Cretaceous volcanic and sedimentary rocks forms the Brittania Shear Zone from km 30.1 to 32, but no events were recorded in this area during the sampling period. Figure 5.34 shows the magnitude-cumulative frequency curve for this data set, the events with unknown magnitudes distributed from 0.01 to 1 m3. The curve has a linear section from 0.01 81 to about 1500 m3, then drops off slightly to the largest events. The slope of the curve from 0.01 to 1500 m3 is -0.42. If the larger events are added, up to 7000 m3, the slope becomes -0.43. Interestingly, these slopes are comparable with those calculated for rock falls in plutonic rocks, for the same section of Highway 99. Along BCR, the following rock fall events in meta-sedimentary and volcanic rock were recorded within the defined sampling periods: • 6 events in Cretaceous Gambier Group tuffs, argillites, and altered volcanic rocks, from mile 3.9 to 15.2 (Porteau); • 1 event in Pleistocene Cheakamus Valley basaltic flows and pyroclastic rocks, from mile 59.5 to 60.8 (Daisy Lake); • 10 events in Gambier Group meta-sedimentary and meta-volcanic rocks, schists and phyllites, from mile 119 to 128 (surrounding Whistler); • 2 events in Jurassic flows and pyroclastics, with minor sedimentary rocks, from mile 104.8 to 112.5 (Birken); • 32 events in Cretaceous and Lower Jurassic sedimentary rocks and phyllites, and Triassic sedimentary rocks, from mile 114.4 to 127.1 (about 7 miles southwest of Downtown Creek) - no events were recorded in the zone of Permian ophiolites from mile 120.9 to 122.8; • and 89 events in Bridge River Complex rocks, from mile 130.2 to 149.2. West of the Downtown Creek Fault, these rocks consist of coherent layers of greenstone, chert and argillite. East of the fault is a sheared melange of interlayered greenstone, greenschist, chert, and siliceous siltstone (Monger and Journeay, 1994). Of these 140 events, 62 had magnitude estimates, ranging from 0.08 to 15000 m3. The magnitude-cumulative frequency curve was plotted as described previously (Figure 5.35). The 82 curve has a linear section from about 10 m3 to the largest event, at 15000 m3. The slope of this section of the curve is -0.44. Some residual censoring of the smaller events appears to have affected the data set, leading to the curvature of the relationship below about 10m3. The slope value calculated for this data set is remarkable close to the slope of the Highway 99 curve for rock falls in metamorphosed sedimentary and volcanic rocks. It is slightly steeper than the slope of the magnitude-cumulative frequency curve for rock falls in plutonic rocks along BGR. This indicates that smaller events are more prominent than the larger events in this rock type on BCR. It also could be a product of the cluster of medium-scale events north of Pemberton, mentioned above. Highway 1 crosses several zones of metamorphosed sedimentary and volcanic rocks, some highly faulted and sheared. The following summarizes the rock fall events which have been recorded in these zones, within the sampling intervals defined above: • 2 events in Carboniferous/Jurassic chert and volcanics, from km 162 to 165.5 (east of Hope); • 41 events in a faulted mix of Jurassic and Cretaceous meta-sedimentary rocks, phyllites, slates, tuffaceous shales, flows, and pyroclastic rocks of the Boston Bar Formation, Dewdney Creek Formation, and Jackass Mountain Group, from km 219.5 (Kwoleck Creek Fault) to 266 (Lytton); • 3 events in Cretaceous flows, pyroclastics and sedimentary rocks, from km 283.5 (Nicoamen River) to 298.4 (south of Spences Bridge); • and 19 events in Jurassic sedimentary rocks and argillite, Paleocene/Eocene and Triassic flows, pyroclastics and sedimentary rocks, from km 356.5 (east of Cache Creek) to 423.5 (Kamloops). Another 144 events were recorded in the Cretaceous and Triassic flows, pyroclastics, volcanic and sedimentary rocks from km 315 to 330. However, the sampling period for this area, 83 which has previously been defined as Highway 1, Band F, is only one year, which is not useful for establishing a magnitude-frequency relationship. Therefore, these events were not used in plotting the magnitude-cumulative frequency relationship for rock falls in metamorphosed sedimentary and volcanic rocks for Highway 1 (Figure 5.36). The plot was constructed using the 66 events listed above, of which 52 had magnitude estimates, ranging from 0.03 to 200 m3. Because there were so few events with unknown magnitudes, they were all assigned volumes of 0.01 m3, and no correction was made to straighten the curve in the upper section. The curve again shows strong curvature for the smaller magnitudes, possibly as a result of censoring due to the effectiveness of highway ditches. It does have a linear section from about 0.02 to 200 m3. The slope of this section is -0.56. This is slightly steeper than the slopes calculated for rock falls in metamorphosed sedimentary and volcanic rocks on Highway 99 and BCR. However, it is lower than the overall slope for all events on Highway 1. The fact that the slope is steeper than those calculated for the Howe Sound-Lillooet routes indicates that smaller events are more dominant along Highway 1. Again, this could be a result of the highly faulted and sheared nature of these rocks, in comparison to those along Highway 99 and BCR. Figure 5.37 shows the magnitude-frequency relationships for rock falls in metamorphosed sedimentary and volcanic rocks along all three routes. Table 5.6 summarizes the linear regression data for the four curves. Again, it is noted that the shapes of the curves are fairly similar, suggesting that the slope may be dependent more on geological setting than particular location. However, the difference between the Howe Sound-Lillooet curves and the Highway 1 curve indicates again that the structural setting as well as the lithology must be considered in attempting to define a characteristic slope for a rock fall magnitude-cumulative frequency relationship. The data from Highway 99 and BCR suggest that the characteristic slope of magnitude-cumulative frequency curves for rock falls in fairly coherent sedimentary and volcanic rocks in the study area 84 is about -0.4 to -0.45. A slope of about -0.5 to -0.6 seems appropriate for rock falls in the sheared, fractured meta-sedimentary and volcanic rocks of the Fraser River fault zone. 5.5.3 - Foliated Metamorphic Rocks While the BCR and Highway 99 routes are almost entirely through plutonic, sedimentary, volcanic, and non-foliated metamorphic rocks, Highway 1 traverses some foliated metamorphic rock areas as well, and a zone of tectonic melange. The following summarizes the events recorded in metamorphic rocks, within the sampling intervals defined for Highway 1: • 13 events in Cretaceous greenschist grade meta-sandstone, siltstone and pelites of the Settler Schist, from km 137.9 (east of Agassiz) to 145.5; • 1 events in Cretaceous/Tertiary highly fractured, variably mylonitic granitic Custer Gneiss, from km 153 (Hope Fault) to 155.5; • and 35 events in Custer Gneiss, from km 165.5 (about 10 km north of Hope) to 205 (5 km north of Spuzzum). Of these 49 events, only 13 had magnitude estimates, ranging from 0.01 to 2500 m3. Because so few of the events in the record had known magnitudes, it was not possible to establish an accurate magnitude-cumulative frequency curve. Figure 5.38 shows the rough curve which was plotted with the available data, the events with unknown magnitudes distributed from 0.01 to 1 m3. The slope of the approximately linear section of this curve, from 0.01 to 100 m3 is -0.32, and the slope of the entire curve is -0.38. These slope values are similar to those calculated for rock fall events in plutonic rock on all routes. However, as stated above, the data set is too poor to give an accurate representation of the magnitude-cumulative frequency relationship. Including the granitic gneissic rocks with the plutonic rocks on Highway 1 in constructing magnitude-cumulative frequency relationships does not significantly alter the slope of the curve. 85 The resultant frequencies of events are slightly higher throughout, but the overall shape of the curve remains virtually the same. From km 333 to 356.5 (5 km east of Cache Creek), Highway 1 traverses a Middle Jurassic tectonic melange, with a chert and argillite matrix. Within the appropriate sampling periods, only one rock fall event, with a magnitude of 10 m3, was recorded. Figures 5.39 to 5.41 summarize the magnitude-cumulative frequency relationships for rock falls in different rock types on the three transportation routes. It is clear that the shapes of the curves are very similar for different rock types within a single transportation route. This indicates that the relationship of geology to magnitude-frequency is complex, and it may not be possible to define a characteristic slope based on lithology. Structure, climate, slope geometry, and many other factors likely also contribute to the magnitude-frequency relationships for rock falls in a given transportation corridor. It does seem clear that the degree of faulting and fracturing of rocks on the transportation routes has a significant effect on rock fall frequency. Even within similar lithological zones, the magnitude-cumulative frequency curves for routes through faulted, fractured rocks are steeper than those for routes through massive rocks, indicating a relative dominance of smaller scale events. 5.6 - Geographic Zones Lithology is evidently not the only factor influencing the shapes of magnitude-cumulative frequency curves for slope failures in the study area. Changes in geology and physiography along each route are broad, and likely influence the landslide magnitude-frequency relationships. Therefore, in addition to separate curves based on lithology, curves were plotted for a series of geographic zones. These curves were then analyzed to determine any patterns in slope based on the geographic location. 86 Tables 5.7 and 5.8 describe the zones within each corridor, which were defined broadly based on lithology, structure, and physiography. On Highway 99, only data from Zones 1 and 2 were used, due to censoring of data in the other zones, as outlined above. In Zone 1, 379 failures were recorded, of which 206 had known volumes. The resulting magnitude-cumulative frequency curve (Figure 5.42) is approximately linear for magnitudes up to about 1000 m 3, and can be approximated as linear for all recorded magnitudes. The slope of the curve for magnitudes from 0.01 to 1000 m 3 is -0.43. This corresponds with the slope values of the magnitude-cumulative frequency curves representing slope failures on Highway 99 in both plutonic rocks and sedimentary-volcanic rocks. No curve was plotted for Highway 99, Zone 2, because only one event with a known magnitude value was recorded in this area. Magnitude-cumulative frequency curves were plotted for slope failures within Zones 1, 2 and 4 on B C R (Figure 5.43). 206 of the 379 events recorded in Zone 1 had known volumes, ranging from 0.01 to 7000 m3. The magnitude-cumulative frequency curve is fairly linear throughout, with a slope of -0.29. Again, this value is similar to the slope of the curve representing failures in plutonic rocks on BCR. It is also similar to the average slope for all events in sedimentary and volcanic rocks on BCR, but is flatter than the part of that curve for magnitudes greater than 10 m3. In B C R Zone 2, 48 failures were recorded, of which 26 had known volumes, from 0.08 to 612 m 3. The curve representing these failures is approximately linear for magnitudes of 0.01 to about 1000 m3. The slope of this section of the curve is -0.24, which is very close to the value for Zone 1. In Zone 3 only 9 of the 27 events recorded in this area had known volumes, resulting in an inadequate curve. Of the 256 events recorded in Zone 4, 107 had known volumes, ranging from 0.03 to 15000 m 3. Two distinct sections of the Zone 4 curve can be defined. For magnitudes less 87 than about 100 m3, the slope is -0.24, which compares with the values for Zones 1 and 2. For events larger than 100 m3, the slope is -0.67, which is much steeper than any of the curves plotted for BCR based on lithology alone. It is possible that this is a result of data censoring due to inadequate sampling periods for large events, over a small area. However, it should also be considered that the relatively steep curve may be a result of the faulted, sheared nature of the rocks in Zone 4. The flatter section of the curve for small volumes may be a result of censoring of smaller events. This would indicate that the structural setting may be of greater importance than lithology alone, with a steeper slope being appropriate for more faulted, fractured rocks. Highway 1 data were used to plot magnitude-cumulative frequency curves for slope failures in Zones 1 and 2 (Figure 5.44). The Zone 3 data were insufficient for producing a useful curve, as only 7 events were recorded. The Zone 4 data were discarded due to the inadequate sampling periods in this area, as discussed above. Within Zone 1, 35 events were recorded, of which only 13 had volume estimates. Therefore, the resulting magnitude-cumulative frequency curve is of limited quality. The slope of the Zone 1 curve within the approximately linear section from 0.01 to 1000 m3, is -0.33. This is somewhat shallower than the slope of the curves representing failures in both plutonic and sedimentary/volcanic rocks on Highway 1. This may be a result of the relatively massive, coherent nature of the rocks in this area, again indicating that the degree of faulting and shearing of rocks along the highway is a greater influence on the slope of the curve than lithology alone. However, the relative flatness of the slope may also be a result of the poor quality of the data set. 158 failures were recorded in Zone 2 of Highway 1, of which 87 had known volumes, ranging from 0.01 to 200 m3. The Zone 2 curve has a slope of -0.61 for events greater than 1 m3. For events from 0.01 to 1 m3, the slope is -0.28, which may reflect censoring of small event records. The slope value for larger events is comparable with the slope values of the curves representing failures in both plutonic and sedimentary/volcanic rocks on Highway 1. It is steeper 88 than the curves representing failures in Zones 1 and 2 of the Howe Sound-Lillooet corridor, but is similar to the slope of the BCR Zone 4 curve. This again suggests that the faulted and sheared nature of the rocks in this area is an important influence on the slope of the magnitude-cumulative frequency curve. On CPR, magnitude-cumulative frequency curves were plotted for each of the four geographic zones (Figure 5.45). 116 events were recorded in Zone 1, 88 of which had volume estimates ranging from 0.04 to 170 m3. The resultant magnitude-cumulative frequency curve has a linear section from about 1.0 tol70 m3, with a slope of -0.64. This slope is considerably steeper than that for Highway 1, Zone 1. However, the Highway 1 curve in this area is likely unreliable, as discussed above, due to the small data set. Zone 2 on CPR travels along the Fraser River fault zone, from Hope to Lytton, through sheared and fractured sedimentary and volcanic rocks, and some variably fractured plutonic rocks. 75 events were recorded on this section of CPR, of which 54 had known magnitudes, ranging from 0.08 to 270 m3. The curve is linear for volumes of about 1.0 to 270 m3. The slope of this section is -0.54, which is slightly steeper than the slopes calculated for rock falls in sedimentary and volcanic rocks in the Howe Sound-Lillooet corridor, but is very similar to that calculated for Highway 1. This suggests that the fractured nature of the rocks along the Fraser Canyon may influence the shape of the magnitude-cumulative frequency curve, resulting in a steeper slope than for more massive rocks of similar lithology in the Howe Sound-Lillooet corridor. CPR Zone 3, from Lytton to Thompson, again traverses faulted, fractured granodiorite. Here, 687 events were recorded, of which 454 had magnitude estimates, from 0.02 to 3060 m3. The slope of the linear section of the magnitude-cumulative frequency curve, from 1.0 to 3060 m3 is -0.63, which is remarkably similar to the slope calculated for rock falls in Zone 1. No comparison curve was available for Highway 1 data in the same area, due to the small data set in that zone. 89 CPR Zone 4, from Thompson to Kamloops, also traverse mainly volcanic, pyroclastic, and sedimentary rocks, with some local diorite and granodiorite intrusives. Only 39 events were recorded in this zone, of which 27 had known magnitudes, from 0.08 to 77 m3. The magnitude-cumulative frequency curve plotted for this data is of fairly poor quality. A linear section can be approximated for magnitudes of about 1.0 to 12 m3, the slope of which is -0.44. This slope is somewhat flatter than the slope of the curve through rocks of similar lithology in the Fraser River fault zone, which again likely reflects the structural differences in these rocks. The curves for Zones 1, 2 and 3 are steeper than the curve for the more massive, coherent rocks in Zone 4, indicating a relative abundance of smaller failures. Table 5.9 summarizes the linear regression data for the magnitude-cumulative frequency curves in each of the geographic zones described above. The conclusion that can be drawn from the comparison of magnitude-cumulative frequency curves for routes through a series of geographic zones is that lithology is certainly not the only influence on the shapes of the curves. Conversely, it appears that the structural and physiographical setting may have a greater influence on the slope of the magnitude-frequency curve for a given area than the lithology. Steeper slopes seem appropriate for highly faulted, sheared and fractured rocks, while shallower slopes dominate in routes through more massive rocks. Therefore, in calculating risk for different sections of the routes, it is likely more suitable to divide the routes based on broad geographic zones, defined based on geology, structure, and physiography, rather than lithology alone. Characteristic slopes of magnitude-cumulative frequency curves can be roughly defined for this study area, based on the nature of the rocks in the geologic zones. For areas of fairly massive, coherent rocks with widely-spaced joints, a slope value of about -0.20 to -0.45 seems appropriate. For more faulted, sheared and fractured rocks, the characteristic slope is about -0.55 to -0.70. 90 5.7 - Influence of Climate Figures 5. la, 5.2a, 5.3a, and 5.5a show the spatial frequency of rock fall events along each route except CPR. Climatalogical information throughout the study area is discussed in Section 3.3, and Tables 3.1 to 3.4. 5.7.1 - Howe Sound-Lillooet Corridor On Highway 99, 80 of the rock fall records in the database contain information about whether or not any precipitation fell in the 48 hours preceding the event. Of these, precipitation was recorded in 68 (85%). The magnitudes of these events range from 0.01 to 65000 m3. The magnitudes of the 12 events not preceded by precipitation range from 0.01 to 2 m3. These results imply that precipitation strongly influences both the frequency and magnitude of rock falls on this route. 58 event records on BCR note precipitation in the preceding 48 hours, and only one specifies that no precipitation preceded the event. Obviously, this also implies that rock fall frequency is positively influenced by precipitation. The maximum magnitude for both categories is 15000 m3, so no conclusions can be drawn about the influence of precipitation on rock fall magnitude for BCR. It should be considered that it may be more likely for a record of precipitation prior to an event to be made if there was indeed measurable precipitation. For example, many event records read, "heavy rain prior to event," but very few contain comments about dry weather prior to events, possibly because dry weather is not as notable as heavy rain. Along the Howe Sound-Lillooet corridor, the rainiest segment is the southernmost area, from Vancouver to about Squamish. On Highway 99, and BCR, this section can be represented using the Zones defined above, as Zone 1. 91 The rainiest month in this area is generally November. Freeze-thaw is of greatest concern in January and February, followed by December, and March for areas north of Vancouver. Snow is heaviest generally in February, but sometimes in January. Therefore, the combined effects of freeze-thaw and precipitation are strongest in the winter months of November, December, January and February. On Highway 99, Zone 1, 45% of all rock falls in the record occurred in the one third of the year represented by these three months. The driest three months of the year, in which freeze-thaw is not a concern, are normally June, July, August and September. 30% of all events in the record occurred in these four months. On BCR, 49% of rock fall events in Zone 1 occurred in the months of November, December, January and February, while only 20% occurred in June, July, August and September. Figure 5.46 summarizes the monthly frequencies and volumes of rock falls affecting Highway 99 and BCR, Horseshoe Bay to Squamish. These results suggest that precipitation and freeze-thaw do have some influence on rock fall frequency. While only a rough estimate, it appears that rock fall events in this area are between 1.5 and 2.5 times more likely to occur between November and February than between June and September. Precipitation and freeze-thaw may also affect rock fall magnitudes in this area, as both maximum and median rock fall magnitudes tend to be higher in the winter months than in summer (Figure 5.46c). Figures 5.47 to 5.49 show monthly rock fall frequencies and magnitudes from Squamish to Whistler, Whistler to Pemberton, and Pemberton to Lillooet. Only BCR data was used in plotting Figures 5.48 and 5.49, because of the unreliability of the Highway 99 data set in this area. These figures again show that rock falls are more frequent in the winter months. The total magnitudes tend to be higher in winter. The large volume shown for the month of May, Squamish to Whistler (Figure 5.47c) is the result of one event, the 65,000 m3 Cheakamus Canyon Rock Slide. This was a rare event, and does not represent normal rock fall volumes for the month of May in this area. 92 Because of the great discrepancy in the time intervals of diligent rock fall recording on Highway 99, the frequency of events in this southern, rainy section cannot be compared with the frequency of events farther north. It is noted that the record shows a large cluster of events in the 40 km south of Lillooet (Figure 5.1a). While freeze-thaw may be a slightly greater influence in this area than nearer Vancouver, Lillooet is generally dry, and does not receive heavy snowfall. Therefore, it is unlikely that this cluster of events can be related to climate, unless they were the result of a large storm or series of storms. On BCR, only 13% of the 402 events in the record occur in the rainy area along the first 50 miles of track (Figure 5.3a). This zone represents 31% of the length of the studied section of BCR, so the number of events is proportionately low. 195 events (48%) in the record occurred along the last 40 miles of track (25%). Again, this area is generally drier and receives less snow than the Vancouver-Squamish section, so it is unlikely that climate is the cause of the large number of events in this northeastern part of the study area. 5.7.2 - Fraser-Thompson Corridor On Highway 1, 85 event records contain information about precipitation in the preceding 48 hours. 81 of these records do note measurable precipitation prior to the rock fall, and four do not. Again, this implies that rock falls preceded by precipitation are far more frequent than those in dry weather. However, the above-mentioned caution about climate data censoring also applies here. The maximum volumes of events in both wet and dry conditions is 25 m3. The rainiest section of the Fraser-Thompson corridor is in the Fraser Lowlands, between Vancouver and Hope. Chilliwack receives more rain than Vancouver, but both cities are very wet. The winter months from October to February are generally wettest, and July, August and September the driest. Snow is not abundant in this area, particularly in Vancouver. The only months with significant snowfall in the Fraser Lowland are December, January, and February, with 93 areas east of Vancouver receiving some snow in November and March. The number of days with maximum temperature above zero, and minimum below zero, is generally greatest in December, January and February for this area. On Highway 1, between Vancouver and Hope, 35 rock fall events were recorded in the assigned sampling periods. More than half of these have unknown magnitudes, and the maximum magnitude recorded was 2500 m3. 37% of all events in this area were recorded from November to February, and 26% from June to September. This indicates that rain, snow and freeze thaw may have some positive influence on rock fall frequency. 116 events were recorded between Vancouver and Hope on CPR. 56% of all events occurred between November and February, and 21% occurred between June and September. Figure 5.50 summarizes the monthly frequency and magnitude of rock falls affecting Highway 1 and CPR in this area. On CNR, 425 rock fall events were recorded between Vancouver and Hope (mile 0 to 100). 397 of these occurred between mile 80 and 100. 39% of all events in this area were recorded from November to February, and 28% from June to September. This again implies that rain, snow, and freeze-thaw effects may serve to increase rock fall frequencies. However, it should be noted that the CNR record in particular is very short, and may not be representative of climate effects over a long term. The above data for Highway 1, CNR, and CPR suggest that between Vancouver and Hope, roughly 1.4 to 4.6 times more rock fall events can be expected to occur in the winter months than in the summer. From Hope to Spences Bridge, rainfall is much lighter than on the Fraser Lowland. The wettest months are generally October or November, but rain is generally well distributed, without clear-cut rainy and dry seasons. Snowfall is heaviest from December to February, with small amounts in November and March. Freeze-thaw days are more frequent than on the lowland, the number of days each month being variable between November and March. 94 169 rock fall events were recorded in this zone, on Highway 1, with magnitudes from unknown to 200 m3. 64% of all events occurred from November to February, and 12% from June to September. It is interesting that this large difference in rock fall frequency between summer and winter is found in an area without distinct wet and dry seasons. This suggests that snow and freeze-thaw may have a greater effect on rock fall frequency here than in the Fraser Lowland. The faulted nature of the rocks in this area may make them more susceptible to the effects of freeze-thaw than more massive rocks, due to the many cracks and fractures for water to seep into. The rock fall record for CPR, Hope to Spences Bridge, contains 762 events. 70% of events were recorded from November to February, and only 9% from June to September. The maximum rock fall volume recorded in the winter was 3058 m3, much greater than the summer maximum of 268m3. The winter median volume (0.38m3) is also higher than that for the summer (0.08 m3). These results again suggest that rain may not be the major influence in this area, but snow and freeze-thaw strongly influence rock fall frequency, and possibly magnitude. Figures 5.51 and 5.52 show the monthly rock fall statistics for Highway 1 and CPR, from Hope to Lytton, and Lytton to Spences Bridge. On CNR, 188 events were recorded between Hope and Spences Bridge. 65% of all events occurred from November to February, and 13% from June to September. This again suggests that snow and freeze-thaw have a fairly strong positive influence on rock fall frequency. Again, the short sampling period should be noted. Based on the above data for three transportation routes between Hope and Spences Bridge, rock falls in winter are at least five times more frequent than in summer in this area. There may also be a tendency for rock fall magnitudes to be greater in winter than summer (Figures 5.51c and 5.52c), but no conclusions can be drawn regarding magnitude, based on available data. As mentioned above, a possible reason for the strong seasonal difference in frequency in this area is the fact that the routes follow a major fault zone. Rocks which are highly sheared and fractured 9 5 are very susceptible to weathering due to rain, snow and freeze-thaw action, due to the great number of spaces into which water can enter. The section of the Fraser-Thompson corridor from Spences Bridge to Kamloops is the driest part of the study area. From 1988 to 1990, rainfall in Vancouver was 4.5 times higher than in Kamloops, and 3.8 times higher than in Cache Creek. Rainfall is again more variable in this area than on the Fraser Lowland. The wettest months are generally from May to August, and the driest months from November to February. Snow is also fairly light, and falls mostly from December to February. There are significantly more freeze-thaw days in this area than farther south. The important months in terms of freeze-thaw are normally November to March. The rock fall data for this area of Highway 1 is fairly poor, in that it only spans one year. All but one of the 164 events recorded between Spences Bridge and Kamloops fall into Highway 1 Band F. In this record, rock fall events are much more common in the winter than in summer. 51% of the 164 events were recorded from November to February, and .15% from May to August. This suggests again that freeze-thaw and snow may have more of an effect on rock fall frequency than rain, since events are more common in the drier season. However, these results are unreliable due to the nature of the rock fall record in this zone. 39 rock falls were recorded on CPR from Spences Bridge to Kamloops. Rock falls in the winter months of November to February make up 64% of all records, while summer events comprise 20. These results support the Highway 1 data, suggesting that snow, and primarily freeze-thaw are the important climatic influences on rock fall frequency in this zone. Figure 5.53 shows the monthly frequencies and magnitudes of rock falls affecting CPR from Spences Bridge to Kamloops. Assuming that the CPR data set gives a more accurate picture of climatic effects on rock fall frequency than the Highway 1 data, it can be said that roughly three times more rock fall events occur in the winter months than the summer in this area of the Fraser-Thompson Corridor. 96 It is difficult to summarize the spatial frequency of rock fall events on Highway 1, because of the poor quality of records in the northeastern part of the study area. It is unclear whether rock falls are more frequent in this colder, drier area of the Highway, or if the frequency levels are distorted by the short sampling periods. The rock fall record for CNR is also very short, covering only two years in most areas. However, the consistency of this recording period throughout the length of the route makes it possible to roughly compare rock fall frequencies in different areas. Almost all of the recorded events on CNR occurred from about Agassiz to Mowhokam Creek, which is about equidistant from Boston Bar and Lytton. Very few events were recorded west of Agassiz, and virtually none were recorded from Lytton to Kamloops, indicating that rock falls are less frequent in the drier areas to the northeast of the study area (Figure 5.5a). This is supported by the results throughout the study area, which suggest that rain, snow and freeze-thaw have some significant positive effect on rock fall frequency. The spatial frequency of rock falls on CPR is similar to CNR, in that 83% of all events were recorded between Hope and Spences Bridge, and only 4% from Spences Bridge to Kamloops. This again shows that rock falls are relatively uncommon in the arid part of the study area, east of the Fraser River fault zone. While snow, rain, and particularly freeze-thaw do seem to have a positive influence on rock fall frequency, the effects of climate cannot be considered alone. The high frequency of rock falls in the corridor from Hope to Spences Bridge compared with areas farther east is likely a combined result of climatic effects, geological conditions, and various other factors. 5.8 - Landslide Activity It was considered that different levels of landslide activity in various areas along the transportation routes may affect the shapes of the magnitude-cumulative frequency curves. To 97 determine the effect of landslide activity, separate curves were plotted for zones labeled 'active', 'moderate', and 'inactive', depending on the number and distribution of landslides in the area. All landslides were used in this analysis, including those without volume estimates. Each route was divided into one kilometre sections, each of which was given an activity rating. Sections with landslide records for at least 5 locations, or with a total of 10 or more records, were considered active zones. For example, if failures were recorded at km 3.1, 3.3, 3.4, 3.7, and 3.8, or if ten failures were recorded at km 3.2, the zone from km 3 to 4 would be labeled active. Zones with failure records for two to four locations, or with at least five records at one location, were labeled moderately active. Zones with no records within the one kilometre section, or no more than four records for one location, were considered inactive. On Highway 99, Bands A and B, 339 slope failure events were recorded in active zones. Of these, 197 had known volumes, ranging from 0.01 to 7000 m3. The magnitude-cumulative frequency curve of these events (Figure 5.54) has a fairly linear section from 0.01 to 1500 m3. The slope of this section is -0.42, which is very similar to the slope of the Highway 99 curve for all events. Within the moderately active zones, 39 failures were recorded, 19 of which had known magnitudes. The slope of the magnitude-cumulative frequency curve for all events (Figure 5.54), from 0.01 to 1000 m3, is -0.44, which is again similar to the curve plotted for all events. Only 11 events were recorded in inactive zones of Highway 99, Bands A and B. Of these, only one had a known magnitude value (65000 m3), so no magnitude-cumulative frequency curve could be plotted. 220 events on BCR were recorded in active landslide zones. Of these, 105 had known magnitudes, ranging from 0.08 to 15000 m3. The slope of the magnitude-cumulative frequency curve (Figure 5.55) for events up to 100 m3 is -0.21. For events greater than 100 m3, the slope is -0.63, which is steeper than that for all events on BCR. Within the moderately active zones, 150 landslides were recorded. Of these, 62 had known magnitudes, from 0.03 to 4600 m3. The magnitude-cumulative frequency curve (Figure 5.55) again shows a distinct break in slope at about 98 100 m3. For events smaller than 100 m3, the slope is -0.31, and for larger events, the slope is -0.47, similar to the overall BCR curve. A total of 32 slope failures were recorded in inactive zones on BCR. 13 of these had known volumes, ranging from 0.08 to 1530 m3. The magnitude-cumulative frequency curve for these events is fairly linear throughout (Figure 5.55), without a break in slope as seen for the active and moderately active curves. The slope of the curve, for all events, is -0.28. This slope is similar to the slope of the upper section of the curve (events smaller than 1 m3) for all areas of BCR. On Highway 1, 51 events were recorded in active landslide zones. Volumes were known for 32 of these events, ranging from 0.03 to 2500 m3. The magnitude-cumulative frequency curve representing these events (Figure 5.56) again shows a strong break in slope, becoming much steeper for magnitudes greater than about 2 m3. The slope for events from 0.01 to 2 m3 is -0.26, and for events greater than 2 m3, the slope is -0.65. This slope of this steeper section of the curve is similar to the slope of the curve representing all landslides on Highway 1. In moderately active zones on Highway 1, 129 slope failures were recorded. 65 of these had known magnitudes, from 0.01 to 300 m3. Two separate slopes could again be defined for the resulting magnitude-cumulative frequency curve (Figure 5.56). The slope for events smaller than 2 m3 is -0.28, and the slope for events greater than 2 m3 is -0.55. This slope is slightly flatter than that of the curve representing all events on Highway 1. A total of 44 landslide events were recorded in inactive zones on Highway 1. Magnitudes were known for 32 of these, ranging from 0.03 to 100 m3. A break in slope could again be defined at about 2 m3 (Fig. 5.56). For events smaller than 2 m3, the slope is -0.15. For events greater than 2 m3, the slope is -0.81. Again, this slope is similar to that for the curve representing all events on Highway 1, but is slightly steeper. Table 5.10 shows the linear regression data for magnitude-cumulative frequency curves in active, moderately active, and inactive zones on each route. 9 9 In examining the slopes of the magnitude-cumulative frequency curves for different activity levels on all routes, no consistent pattern becomes apparent. On BCR, the slope becomes flatter with decreasing activity, but this pattern is not evident for Highway 99 or Highway 1. One pattern which is consistent except for inactive zones on Highway 1 is that any break in slope of the magnitude-cumulative frequency curve becomes less distinct with decreasing activity. For example, the difference in slope for the two sections of the 'active' curve on BCR is much greater than that for the 'moderately active' curve. The 'inactive' curve does not show a break in slope at all. This may indicate that censoring of small events is more important in active zones than in inactive zones. However, the break in slope for inactive zones on Highway 1 is quite distinct. Based on this research, no conclusions regarding characteristic patterns in magnitude-cumulative frequency curves can be drawn based on differences in landslide activity. 100 Table 5.1 - Bands within each route, defined based on similar data point density Route Band km Range Description Highway 99 A 0<=km<26 High density of data points B 26<=km<75 Low-moderate density C 75<=km<106 No data points D 106<=km<130 Low-moderate density E 130<=km<170 No data points F 170<=km<186 Low density G 186<=km<203 No data points H 203<=km<240 High density I 240<=km<284 Low density J 284<=km<300 High density Highway 1 A 0<=km<132 Low density B 132<=km<155 Moderate density C 155<=km<180 Low density D 180<=km<260 High density E 260<=km<315 Low-moderate density F 315 <=km<3 3 0 Extremely high density G 330<=km<400 Low density Table 5.2 - Sampling intervals used to calculate rock fall frequency per year for each route segment and volume class Band Magnitude (m3) Start Year End Year Inf Hwy. 99 - A <1, unknown 1990 1995 6 Hwy. 99 - A 1 to 1000 1980 1995 16 Hwy. 99 - A 1000 to 10000 1957 1995 39 Hwy. 99 - B <1, unknown 1989 1996 8 Hwy. 99 - B 1 to 1000 1980 1996 17 Hwy. 99 - D <1, unknown 1993 1994 2 Hwy. 99 - D 1 to 1000 1993 1994 2 Hwy. 99 - E-J <1, unknown 1994 1995 2 Hwy. 99 - E-J 1 to 1000 1994 1995 2 Hwy. 1 - A-D, G <1, unknown 1993 1996 4 Hwy. 1 - A-D, G 1 to 1000 1993 1996 4 Hwy. 1 - A-D, G 1000 to 10000 1957 1996 40 Hwy. 1 - E, F <1, unknown 1995 1995 1 Hwy. 1 - E, F 1 to 1000 1993 1995 3 BCR <1, unknown 1985 1996 12 BCR 1 to 1000 1985 1996 12 BCR 1000 to 10000 1985 1996 12 CPR <1, unknown 1975 1996 22 CPR 1 to 1000 1975 1996 22 CPR 1000 to 10000 1975 1996 22 Table 5.3 - Ages of major rock avalanches crossing the transportation corridors Corridor Rock Avalanche Aee (v B.P.) Dating Method Source H-L Mystery Creek 880±100 C-14 Evans (unpublished) . H-L Rubble Creek 1855 A.D. Dendrochronology Moore and Mathews (1978) F-T Katz 3260+70 C-14 Naumann and Savigny (1992) F-T Lake of the Woods 8260+70 C-14 Naumann and 8430+60 C-14 Savigny (1992) F-T Cheam 5010+70 C-14 Naumann and 4690+80 Savigny (1992) 4350+70 102 Table 5.4 - Magnitude-cumulative frequency slopes for rock falls and slides on each route Correlation Route Corridor # of records Intercept (a) Slope (b) Coefficient Hwy. 99 (Bands A, B) H-L 389 0.772 -0.434 0.99 BCR H-L 123 1.121 -0.402 0.94 Hwy. 1 (excluding F) F-T 64 1.359 -0.704 0.95 CPR F-T 295 1.133 -0.646 0.99 Table 5.5 - Magnitude-cumulative frequency slopes for rock falls in plutonic rocks on each route Route Magnitude Range (m3) Slope Intercept Number of Observations Correlation Coefficient Highway 99 0.01 to 1000 -0.42 0.116 84 0.98 (Bands A,B) 0.01 to 65000 -0.41 0.128 85 0.98 BCR 0.01 to 76.5 -0.28 0.595 178 0.99 0.01 to 4600 -0.31 0.567 189 0.98 Highway 1 1.0 to 300 -0.69 1.042 29 0.96 0.01 to 1.0 -0.25 0.883 74 0.98 . 103 Table 5.6 - Magnitude-cumulative frequency slopes for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks on each route Route Magnitude Range (m3) Slope Intercept Number of Observations Correlation Coefficient Highway 99 0.01 to 1500 -0.42 0.624 256 0.99 (A and B) 0.01 to 7000 -0.43 0.613 260 0.99 B C R 10 to 15000 -0.44 0.936 32 0.95 0.01 to 15000 -0.26 0.577 140 0.94 Highway 1 0.2 to 200 -0.56 0.717 40 0.96 (excluding F) 0.01 to 0.2 -0.15 0.882 26 0.86 Table 5.7 - Geographic zones chosen for the Howe Sound-Lillooet corridor Zone Location Description 1 Horseshoe Bay to Squamish - Coast Mountains - Mountain ridges and deep glacial valleys - Mainly plutonic rocks and Gambier Group metamorphosed sedimentary and volcanic rocks - Fairly massive or with widely-spaced joints - some Gambier rocks more heavily jointed - Coast Mountains - Mainly massive plutonic rocks, some meta-sedimentary and volcanic rocks - Massive or with widely-spaced joints - Mainly Gambier group rocks, some plutonic rocks - Gambier rocks faulted and foliated in places - Plutonic rocks generally massive - Volcanic and sedimentary rocks, sheared tectonic melange of the Bridge River Complex - Faulted, sheared and fractured 2 Squamish to Whistler 3 Whistler to Pemberton 4 Pemberton to Lillooet 104 Table 5.8 - Geographic zones chosen for the Fraser-Thompson corridor Zone Location Description 1 Vancouver to Hope Hope to Lytton Lytton to Thompson Thompson to Kamloops - Fraser Lowland - Broad river valley - Thick Quaternary sediments - Some plutonic and metamorphic rocks near Hope - Fraser Canyon - Varying lithology, including: Custer Gneiss, marginal plutonic rocks, phyllites, slates, etc. - highly faulted, sheared, altered and fractured - Thompson River Valley - Traversing a fault zone - Marginal plutonic rocks cut by pegmatite, some volcanic and sedimentary rocks - Highly faulted, sheared and fractured - Interior Plateau - Uplands and deeply incised, semi-arid river valleys - Thick deposits of glacio-lacustrine silt Table 5.9 - Magnitude-cumulative frequency slopes for rock falls in various geographic zones on each route Route Zone Magnitude Ranee (m3) Slope Intercept Number of Observations Correlation Coefficient Highway 99 1 1 to 1000 -0.43 0.796 375 0.99 BCR 1 0.01 to 612 -0.29 0.051 48 0.95 BCR 2 0.01 to 1000 -0.24 0.260 71 0.96 BCR 4 100 to 15000 -0.67 1.63 26 0.98 Highway 1 1 0.01 to 1000 -0.33 0.244 34 0.99 Highway 1 2 1 to 200 -0.61 1.10 35 0.96 CPR 1 1 to 170 -0.64 0.266 42 0.98 CPR 2 1 to 270 -0.54 0.644 23 0.96 CPR •3 1 to 3060 -0.63 0.976 207 0.99 CPR 4 1 to 12 -0.44 0.0297 16 0.98 105 Table 5.10- Magnitude-cumulative frequency slopes for rock falls in zones of different rock fall activity levels on each route Rte. Activity Level Volume Range (m3) Slope 99 Active 0.01-1500 -0.42 99 Moderate 0.01-1000 -0.44 BCR Active 0.01-100 -0.21 BCR Active 100-1500 -0.63 BCR Moderate 0.01-100 -0.31 BCR Moderate 100-4600 -0.47 BCR Inactive 0.01-1530 -0.28 1 Active 0.01-2 -0.26 1 Active 2-2500 -0.65 1 Moderate 0.01-2 -0.28 1 Moderate 2-300 -0.55 1 Inactive 0.01-2 -0.15 1 Inactive 2-100 -0.81 106 Figure 5.1 - Locations, volumes and dates of rock falls on Highway 99 (a) spatial frequency of all events Lll4 f I J , , I T n i | •rr i i | i n i | i i I I 11 T f | I I I 0 50 100 150 200 250 300 km (b) Spatial frequency of events with known volumes 100 50 f r n i i i i i i i i n i i i i i i it 50 100 150 km 200 250 300 (c) Rock fall volume vs. location 00 00 TTTT I I I I I I I 0 50 100 150 200 250 300 km Figure 5.1 - Locations, volumes and dates of rock falls on Highway 99 (d) Dates of all events ro 2000 1990 1980 1970 1960 OS o O <3> i i i i i i i i i i i i i i i i i i i i i i 50 100 150 km 200 250 300 (e) Dates of events with known volumes 2000 1990 $ 1980 1970 1960 O «» I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 50 100 150 km 200 250 300 108 in -*-» c CD > 111 E u Figure 5.2 - Locations, volumes and dates of rock falls on Highway 1 80 60 40 20 0 (a) Spatial frequency of all events J k * . » , ill , i.. I, 100 200 I , n '[ ' 1 "| 300 400 500 km 2 c CD > 111 CD E 3 (b) Spatial frequency of events with known volumes 80 60 40 20 0 100 200 300 km 400 500 E o 3 CD E 10000.00 1000.00 100.00 10.00 1 0 0 0.10 0.01 0.00 o <*> m o oo (c) Rock fall volume vs. location o o 0 o o o % % \ <& o o o o o ° T 100 200 300 400 km 500 109 Figure 5.2 - Locations, volumes and dates of rock falls on Highway 1 (d) Dates of events vs. location 2000 1995 1990 1985 1980 <P o o o o ^ - f t - ^ 0 o % o 0 o oo o o o o 9 o -O—o o 0 100 200 300 400 500 km (e) Dates of events with known volumes co >-2000 1995 1990 1985 1980 t o <f> o 0 ° o o $<*o* o -9 4»<&°* O^CO><^' o<*% oo o *> oo o oo o o T 100 200 300 km 1 p 1 1 400 500 110 Figure 5.3 - Locations, volumes and dates of rock falls on BCR (a) Spatial frequency of all events 20 c CD Lt3 E 3 10 !• UMI I HI I 11 40 ^ijl l l^ t i l l . J ILJ 80 Mile 120 160 (b) Spatial frequency of events with known volumes c > 111 CD XI E 10 40 80 Mile II 120 160 (c) Rock fall volume vs. location 100000.00 -s 10000.00 „ 1000.00 100.00 o o o o 10.00 °o o%<> <r o o o $ Z <*> 1.00 o#>o 0.10 o o o oo o o % 0.01 I I I I I I I o%> &o <5 <$>o o 40 80 Mile 1 — T - T 120 160 2000 Figure 5.3 - Locations, volumes and dates of rock falls on BCR (d) Dates of all events ro a> >-1995 1990 1985 o # o o o — ° s o <« V w o o. 3tt o o v8t 8 o o 00 o — o >^<a> o o o oo o «3*> o o o ° o — o « O o o o^o o o oo°o —o o o -00-% o <^ >ooo o ° o o § C9J.° O O #><POc> •<>o o ° ft #<^>o <xX>$ — o & : Q Q O O O 1980 i — i — r i — r 40 80 Mile 120 160 2000 (e) Dates of events with known volumes ro tu >-1995 1990 1985 0$ <3> ~0" o <s><° .—jg-o o o o o o o 0>O<§ o -00-o o o o o o o o<x> o*^ > o 0§"> ooo Ov§!> ooo 1980 i — i — r 1 — r 40 80 Mile 120 160 112 Figure 5.4 - Dates of rock falls on CPR (a) Dates of all events 2000 1990 1980 1970 14400 14500 14600 14700 14800 km 2000 (b) Dates of events with known volumes 1990 CD 1980 o<w>c> o o < » o o o<y o o o% o o * o* ° ° f O O O X> of, • » ^ o * - ° •%% oof 1970 i—r i—i—r i—r 14400 14500 14600 km 14700 14800 113 Figure 5.5 - Locations and dates of rock falls on CNR (a) Spatial frequency of all events 100 50 _ J J—i I—JL T 50 100 150 Mile 200 250 1997 (b) Dates of all events 1996 O O 1995 o o o o o o 1994 50 100 150 Mile 200 250 Figure 5.6 - Spatial distribution of rock falls over time, showing bands of similar point density ca CD 2000 1990 1980 1970 1960 A B (a) Highway 99 C D E F G H I J ^4 T # O 50 100 150 k m I I I I I I I M I I I 200 250 300 CO cu >-2000 1995 1990 1985 1980 1975 (b) Highway 1 B C D E F G 100 200 k m 300 400 115 Figure 5.7 - Temporal frequency of rock falls in various volume classes; Highway 99, Band A c > 111 E 80 40 (a) All events 60 70 80 90 Year | 20 cu > LU 10 cu E (e) 1 to 10 cubic m r l f 60 70 80 Year 90 (b) Unknown volumes (f) 10 to 100 cubic m 60 70 80 90 60 70 80 90 Year Year (c) 0 to 0.1 cubic m (g) 100 to 1000 cubic m Year Year (e) 0.1 to 1 cubic m (h) 1000 to 10,000 cubic m Year Year 116 Figure 5.8 - Temporal frequency of rock falls in various volume classes; Highway 1, Band D £ 80 CD > LU ° 40 E 3 80 (a) All events I T I T T T T T I n n 85 90 Year 95 20 10 (b) Unknown volumes — " - I -n r 1 80 85 90 Year 95 £ 10 E 3 80 (e) 1 to 10 cubic m w in , . . I | III I I I I I III 85 90 Year 95 20 10 (c) 0 to 0.1 cubic m i i i i i l l i i i i i l l 80 85 90 95 Year c CD > UJ CO 3 (f) 10 to 100 cubic m I I II I I I 80 85 90 Year 95 10 (d) 0.1 to 1 cubic m T T T I I I I I I n 80 85 90 Year 95 v> 2 0) > UJ cu E z (g) 100 to 1000 cubic m 80 I | I Ml | I I II | I I 85 90 95 Year 117 Figure 5.9 - Temporal frequency of rock falls in various volume classes; BCR (a) All events (e) 1 to 10 cubic m £ 80 > cu E 40 T T T n TTT £ c cu > LU CU x 10 T T T r r TTT 80 85 90 Year 95 80 85 90 Year 95 (b) Unknown volumes (f) 10 to 100 cubic m £ 40 cu > LU CU X E 20 £ c CO > LU CU X I E 3 20 10 T T 1 I I I I I I I 80 85 90 Year 95 80 85 90 Year 95 £ 2 cu > LU CU X I E •3 z (c) 0 to 0.1 cubic m T T n T T n £ 8 c cu > LU 0) X I (g) 100 to 1000 cubic m TT CL 80 85 90 Year 95 80 85 90 Year 95 £ 10 cu X E 3 (d) 0.1 to 1 cubic m TTT n n n £ 2 c cu > LU CU X E 3 (h) 1000 to 10000 cubic m TTTT n TT n 80 85 90 Year. 95 80 85 90 Year 95 118 Figure 5.10 - Temporal frequency of rock falls in various volume classes; C P R (a) All events j i 70 ( ri'l'l'l'ITIT|TITITI 80 90 Year £ 30 CO L U 20 CO - O E 10 0 (e) 1 to 10 cubic m n r •tr n- ' u LI... . 70 80 90 Year (b) Unknown volumes l k l U _ _ r IIIIIIII111IIIII M l 11IIIII 70 80 90 Year £ 8 CO > L U CO (f) 10 to 100 cubic m 111111111 70 80 90 Year (c) 0 to 0.1 cubic m (g) 100 to 1000 cubic m n rrr " 'I IrIL 70 80 90 Year U) o C CO > L U CO E 13 70 80 90 Year (d) 0.1 to 1 cubic m nf mrOrffr i -| i i i i i i n i | 70 80 90 Year £ 2 CO X I E 3 (h) 1000 to 10000 cubic m 70 80 90 Year 119 Figure 5.11 - Temporal rock fall frequency for grouped volume classes; Highway 99, Band A (a) Under 1 cubic m or unknown volumes 60 40 20 TI I I I I I I I I I I I I I I I I I I I I I II I 60 65 70 75 80 85 90 Y e a r 95 (b) 1 to 1000 cubic m 20 10 60 65 70 75 80 Y e a r 85 90 95 (c) 1000 to 10,000 cubic m 0 I I I I I I IT I II I I I I I I 55 60 65 70 75 80 Y e a r 85 90 95 Figure 5.12 - Temporal rock fall frequency for grouped volume classes; Highway 99, Band B (a) Under 1 cubic m and unknown volumes 76 80 84 88 92 96 Y e a r (b) 1 to 1000 cubic m 76 80 84 88 92 96 Y e a r Figure 5.13 - Temporal rock fall frequency for grouped volume classes; Highway 1, Bands A, B, C, D, G * c a> > LU JO E zs Z 80 40 (a) Under 1 cubic m or unknown volumes 75 80 85 Y e a r 90 95 CO -•—* c > UJ 0> JO E z 20 10 (b) 1 to 1000 cubic m T T T 75 80 m.i.h 85 Y e a r I I I I I I 90 95 (c) 1000 to 10000 cubic m c UJ 0 JO E 3 75 80 85 90 Y e a r 95 122 w c cu > UJ CD E 3 CO -•—* c cu > LU cu .Q E 3 Figure 5.14 - Temporal rock fall frequency for grouped volume classes; Highway 1, Bands E and F (a) Under 1 cubic m or unknown volumes 150 100 50 10 80 i — i — r 85 i — i — i — r Y e a r 90 i r i 1 | T 95 (b) 1 to 1000 cubic m i — r i — i — r i—i 80 85 90 Y e a r 95 123 Figure 5.15 - Temporal rock fall frequency for grouped volume classes; BCR (a) Under 1 cubic m or unknown volumes w c cu > UJ CD -Q E =J z 60 40 20 l—I—i i i " i—i—i—r 80 85 90 Y e a r i i i . | — r n 95 (b) 1 to 1000 cubic m CD > UJ cu _Q E ro 30 20 10 I I I I | I I I I | I I I I | I 80 85 90 95 Y e a r (c) 1000 to 10000 cubic m w c CD > LU CD JO E z 124 Figure 5.16 - Temporal rock fall frequency for grouped volume classes; C P R (a) Under 1 cubic m or unknown volumes 100 c CD > UJ o 50 \ CD . Q E 3 70 75 80 85 Y e a r 90 95 to c 0 > UJ E 3 (b) 1 to 1000 cubic m 30 20 10 I I I I T T I I I I TT TTT I I I I" I I 70 75 80 85 Y e a r 90 95 (c) 1000 to 10000 cubic m co -*—» c • % UJ vt— O 1 i_ <D J Q E 3 I I I I I I I I I I I I I I I I I I I I I I I I I I 70 75 80 85 Y e a r 90 95 125 Figure 5.17 - Start year of recording interval vs. regression slope; Highway 99 (a) Band A; Under 1 cubic m or unknown volumes 84 86 88 90 92 Start Year (b) Band A; 1 to 1000 cubic m 76 80 84 88 92 Start Year (c) Band A; 1000 to 10,000 cubic m S. 0.005 o co c 0.000 o I -0.005 D) SL -0.010 54 56 58 60 62 Start Year (d) Band B; under 1 cubic m or unknown volumes 80 84 88 92 Start Year 126 Figure 5.18 - Start year of recording interval vs. regression slope; Highway 1 (a) Bands A, B, C, D, G; under 1 cubic m or unknown volumes 4.0 — 0.0 -4.0 — 88 90 92 94 Start Year (b) Bands A, B, C, D, G; 1 to 1000 cubic m 10.0 — i l 88 90 92 94 Start Year (a) Bands E and F; 1 to 1000 cubic m 4.0 — i 0.0 -4.0 90 92 94 Start Year Figure 5.19 - Start year of recording interval vs. regression slope; BCR (a) Under 1 cubic m or unknown volumes 2.0 — , 82 84 86 88 90 Start Year (b) 1 to 1000 cubic m 1.0—, . , 80 82 84 86 88 Start Year (c) 1000 to 10000 cubic m 0.5 — | CD J 82 84 86 88 90 92 Start Year 128 Figure 5.20 - Start year of recording interval vs. regression slope; CPR (a) Under 1 cubic m or unkown volumes 0.8 0.0 -0.8 70 72 74 Start Year 76 0.6 — i 0.4 — 0.2 0.0 (b) 1 to 1000 cubic m 70 72 74 76 Start Year 78 80 0.01 — i 0.00 -0.01 72 (c) 1000 to 10000 cubic m 74 76 Start Year 78 80 Figure 5.21 - Magnitude-cumulative frequency plots for each route (a) Highway 99 1 0 0 0 . 0 0 - s 1 0 0 . 0 0 -1 0 . 0 0 -1 . 0 0 - J 0 . 1 0 -0 . 0 1 - -0 . 0 0 1 — 0 . 0 0 0 4 J 0 . 0 0 0 9 4 0 . 0 0 1 1000.00 100.00 -Z 10.00 -1.00 -0.10 - d 0.01 -0.001 -0.0004J 0.00094 llllllj llllllllj llllllllj llllllllj llllllll| lll!llll| Mil 0.10 10.0 1000 100000 Volume (cu m) (b) B C R 11 llllllj II llllllj llllllllj 11 llllllj 11 llllllj llllllllj llllllllj llllllllj Mil 0.001 0.10 10.0 1000 100000 Volume (cu m) ll l l l l III 100M lllllllll III 100M 130 Figure 5.21 - Magnitude-cumulative frequency plots for each route (c) Highway 1 1000.00 - g 0.001 0.10 10.0 1000 100000 100M Volume (cu m) (d) CPR 1000.00 - = 0.001 0.10 10.0 1000 100000 100M Volume (cu m) 131 Figure 5.22 - Magnitude-cumulative frequency plot; Highway 99, Bands A and B 1000.00 - s 100.00 -10.00 -1.00 - d 0.10 -0.01 - -0.001 - j 0.0004-i 0.00094 llllllllj llllllllj llllllllj llllllllj 11 llllllj 11 llllllj llllllllj llllllllj llllllllj 11 llllllj llllllllj 0.001 0.10 10.0 1000 100000 100M Volume (cu m) 1000.00 - g 100.00 10.00 — 1.00 -0.10 -g 0.01 - j j j 0.001 - i 0.0004^ 0.00094 Figure 5.23 - Magnitude-cumulative frequency plot; Highway 1 without Band F llllllllj llllllllj llllllllj llllllllj llllllllj llllllllj llllllllj llllllllj Mil 0.001 0.10 10.0 1000 100000 Volume (cu m) 100M 132 Figure 5.24 - Magnitude-cumulative frequency plots for each route; events with unknown volumes distributed from 0.01 to 1 cubic m (a) Highway 99, Bands A and B 100.00 10.00 (0 CD >» v_ CD Q. i? c CD ZJ cr & > TO E O 1.00 0.10 — 0.01 llllllll I III TTTI TTl 0.001 0.10 10.0 1000 Volume (cubic m) TTTTTTT| 100000 133 Figure 5.24 - Magnitude-cumulative frequency plots for each route; events with unknown volumes distributed from 0.01 to 1 cubic m (b) BCR 100.00 — i 0.001 0.10 10.0 1000 100000 Volume (cubic m) 134 Figure 5.24 - Magnitude-cumulative frequency plots for each route; events with unknown volumes distributed from 0.01 to 1 cubic m (c) Highway 1 without Band F 100.00 — i 10.00 — 1.00 — 0.10 — 0.01 I I llllllj I lllllllj I I llllllj I lllllllj I lllllllj I lllllllj I 0.001 0.10 10.0 1000 Volume (cubic m) TTn 100000 135 Figure 5.24 - Magnitude-cumulative frequency plots for each route; events with unknown volumes distributed from 0.01 to 1 cubic m (d) CPR 100.00 10.00 — c 13 cr (D CD > '-4—< 03 E o 1.00 0.10 0.01 I lllllllj I lllllllj I lllllllj I lllllllj I lllllllj 11 llllllj I 0.001 0.10 10.0 1000 Volume (cu m) TT 100000 136 Figure 5.25 - Corrected magnitude-cumulative frequency plots for all routes CO (D >» i _ <D C L ly Q) ZJ CT £ > JCO - J E 100.0 "=q 10.0 LOO -=j o.io - H 0.01 - d o 0.001 - d 0.0001 - d 0.00001 0 — Highway 99, A and B - - • - - Highway 1, without F o - BCR C P R I llllllj 11 llllllj llllllllj llllllllj llllllllj llllllllj llllllllj 11 llllllj llllllllj I 0.001 1.00 1000 1M Volume (cubic m) 100M 137 Figure 5.26 - Corrected magnitude-cumulative frequency plots for all routes; 30 million cubic m events not shown ro CD <D CL iy c CD 3 CT £ CD > Zf E - J O 100.0 -_• 10.0 1.00 H 0.10 0.01 0.001 0.0001 0.00001 0.001 0 Highway 99, A and B - - • - - Highway 1, without F o BCR C P R i ilium i T 0.10 10.0 1000 Volume (cubic m) 100000 138 o o C O 141 142 143 o o I x: g> X jo" ro c Q. E CO in c <D in o x: o in XL O o c <D 3 cr cu c o ro o _o in > c 3 cr .2 o o co 3 C C co ro o o o co E XL o o CM CO ro CL CO co CN LO 3 CD O O O 00 O T t SJUOAO ;o joqiunN 144 Figure 5.30 - Magnitude-cumulative frequency plot for rock falls in plutonic rocks; Highway 99, Bands A and B 100.00 - g 10,00 - J 1.00 -0.10 - J 0.01 0.001 TT 111 mill 111 mill I I i i 0.10 10.0 Volume (cubic m) I I llllllj I II 1000 100000 Figure 5.31 - Magnitude-cumulative frequency plot for rock falls in plutonic rocks; BCR 100.00 -m 10.00 - g 1.00 0.10 - ~ 0.01 0.001 0.10 10.0 Volume (cubic m) I I llllllj I 1000 100000 Figure 5.32 - Magnitude-cumulative frequency plot for rock falls in plutonic rocks; Highway 1 without band F 100.00 - B 10.00 1.00 - J 0.10 -Z 0.01 -0.001 0.10 10.0 1000 Volume (cubic m) 100000 Figure 5.33 - Magnitude-cumulative frequency plots for rock falls in plutonic rocks on all routes 100.00 10.00 — ca o cu Q . c CD CT CD <4— CU > E o 1.00 0.10 — 0.01 o Highway 99 Slope = -0.41 • Highway 1 Slope = -0.69 A BCR Slope = -0.31 TT 0.001 lllllllj 11 llllllj I lllllllj I lllllllj I lllllllj I lllllllj I llllllll 0.10 10.0 1000 100000 Volume (cubic m) 146 Figure 5.34 - Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; Highway 99, Band A 100.00 -m 10.00 -1.00 -B 0.10 -~ 0.01 I I llllllj I I llllllj I I llllllj I I llllllj I I llllllj I I llllllj I I llllllj I I llllllj D.001 0.10 10.0 1000 100000 Volume (cubic m) Figure 5.35 - Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; BCR 100.00 -10.00 - J 1.00 -0.10 - J 0.01 0.001 I I llllllj I III 0.10 TTI 111 nun 111 mm 111 nun 10.0 1000 Volume (cubic m) Tmnij 100000 Figure 5.36 - Magnitude-cumulative frequency plot for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks; Highway 1 without band F 100.00 -10.00 1.00 - J 0.10 -Z 0.01 - I lllllllj I lllllllj I I llllllj I lllllllj I I llllllj I lllllllj I I llllllj I I llllllj 0.001 0.10 10.0 1000 100000 Volume (cubic m) Figure 5.37 - Magnitude-cumulative frequency plots for rock falls in sedimentary, volcanic, and non-foliated metamorphic rocks on all routes 100.00 10.00 — j o Highway 99 Slope = -0.43 • Highway 1 Slope = -0.56 A BCR Slope = -0.44 CO CD >. i_ CD Q. fr C CD CD »— ._ -t—t ro Z3 E o 1.00 — 0.10 0.01 TTTTT 0.001 lllllllj I lllllllj I lllllllj I I llllllj I llllllj I lllllllj I lllllllj 0.10 10.0 1000 100000 Volume (cubic m) 148 Figure 5.38 - Magnitude-cumulative frequency plot for rock falls in foliated metamorphic rocks; Highway 1 149 Figure 5.39 - Magnitude-cumulative frequency plots for rock falls in different rock types; Highway 99 Bands A and B 100.00 — i 10.00 Sedimentary, volcanic, and non-foliated metamorphic rocks co CD >-i— CD CL fr c CD 3 cr CD CD > j o 3 E 3 o 1.00 Plutonic rocks 0.10 0.01 I lllllllj I lllllllj II llllllj I M!llll| I lllllllj I lllllllj I lllllllj I lllllllj 0.001 0.10 10.0 1000 100000 Volume (cubic m) 150 Figure 5.40 - Magnitude-cumulative frequency plots for rock falls in different rock types; BCR 100.00 10.00 1.00 0.10 O Plutonic rocks Sedimentary, volcanic and non-foliated metamorphic rocks 0.01 0.001 lllllllj I lllllllj I I llllllj I lllllllj I lllllllj I III 0.10 10.0 1000 Volume (cubic m) 100000 151 Figure 5.41 - Magnitude-cumulative frequency plots for rock falls in various rock types; Highway 1 without Band F co cu a) CL c CD 3 cr 4 — CD > 3 E 3 o 100.00 — i 10.00 1.00 — 0.10 o Plutonic rocks Sedimentary, volcanic, and non-foliated metamorphic rocks • Foliated metamorphic rocks 0.01 I lllllllj I lllllllj I I llllllj I lllllllj I I llllllj I lllllllj I lllllllj I I llllllj 0.001 0.10 10.0 1000 100000 Volume (cubic m) 152 Figure 5.42 - Magnitude-cumulative frequency plot for rock falls on Highway 99 Zone 1; Horseshoe Bay to Squamish / 100.00 — , 10.00 co cu cu Q. c cu 3 cr cu cu > ro E 3 o 1.00 0.10 — 0.01 TTT] 0.001 llllllj I llllllll I lllllllj I lllllllj I lllllllj I lllllllj I lllllllj 0.10 10.0 1000 100000 Volume (cubic m) 153 Figure 5.43 - Magnitude-cumulative frequency plots for rock falls on BCR Zones 1, 2 and 4 100.00 co >> l_ CD CL fr c CD 3 CT S> s— ._ _CJj 3 E 3 o 10.00 1.00 — Zone 1 Q Horseshoe Bay to Squamish n Zone 2 i i Squamish to Whistler A Zone 4 A Pemberton to Lillooet 0.10 — 0.01 I llllllll I lllllllj I lllllllj 11 llllllj 11 llllllj I lllllllj I lllllllj I lllllllj 0.001 0.10 10.0 1000 100000 Volume (cubic m) 154 Figure 5.44 - Magnitude-cumulative frequency plots for rock falls on Highway 1 Zones 1 and 2 155 Figure 5.45 - Magnitude-cumulative frequency plots for rock falls on C P R Zones 1 to 4 co CD CD Q_ fr C CD 3 cr 4 — l E 3 o 100.00 10.00 — 1.00 — 0.10 0.01 o Zone 1 Vancouver to Hope + Zone 2 Hope to Lytton n Zone 3 i i Lytton to Thompson Zone 4 A Thompson to Kamloops I llllllll I llllllll I llllllll 11 llllllj I I lllllllj I 0.001 0.10 10.0 1000 Volume (cubic m) TP 100000 156 'E co 3 cr CO >% co m cu o JZ (0 Cl) o X E _co Is o o CD T J 3 rt 'c CO CO E T J C co cT c CU 3 cr cu co co E _ 3 o > I o o a: o1 o 5 o o o o CN O O o o (w ojqno) 8Lun|0A \e\o\ CO CD E _ 3 o > c «: o c "]~ I o h- < o r- < o TT o CN jo jeqtunN CO 'E CO 3 cr CO E o >i= o o i_ o cu T J 3 'c CD CO E T J C ca >« o c cu 3 cr cu o co cu E _ 3 O > "co «*— o o OH 1 o t5 ^ 1 1=5 o o o o ao o o o o TT ( I U ojqno) 9Lun|0A | B ; O X CO CD E _ 3 o > c o c o CO 1 - < Q 2 < tl o CN SJU9A3 jo jaqwriN c o c o :s c o CO T f 3 CO c cu > CU "a? O < c o \- < 5 T f 3 CO c cu > cu "cc? c o o co o o CN s}U8A3 jo jaqwnN SJU8A3 io jaqujnN 157 c o tr CD X I E cu 0_ _CD E p in cu E _ 3 O > o o or Fs 1- O •PS f » o o o CN O O (ui ojqno) aiun|OA |E}0i cu o o o r CU X I E cu D_ E o in cu E _ 3 O > I XL o o or - o - z - o - CO - < 5 c o o o o o CN o o o o (ui ojqno) 9iun|0A |ejoi in a XL O O (U TJ 3J 'E CD CD E co c cu 3 CT <U in CD E _ 3 O > c o E: 1 1 I_ 1 h 2 < CO o S J U 9 A 3 jaqiunN iS XL O 2 o cu 3 'E CD CO E XJ c co c 3 cr cu m a> E _ 3 O > c $ o c Q Z O CO < 5 < 2 LU c o o o CN s ; u 9 A 3 io JsqiuriN c o c o oo LO £ CD C cu > cu O to < c o LO 3 CD 1- Q cu > 0) "ST 1- to < < LL. o o CN O 00 O s ; u 9 A 3 ;o jeqwnN s i u 9 A 3 io jaqiunN 158 C L O X o -*—' cu > 3 o o c co > E o o o o cu TJ _ 3 "c C D CO E T3 C co fr c cu 3 C T CU in cu E _ 3 O > 1 o o or c/> cu E _ 3 O > a o c — Q — Z - O — w - < JZ - - » c : - -> o — < o o o o o o CM (LU Ojqno) awn|OA |B}o x I— Q O in cu E _ 3 O > I o o rr: o CM c o 0) C L o X E o o o cu "D 3 EE co co E co fr c cu 3 CT cu a z o CO < 5 < 2 O o o o C M ( w ojqno) euiniOA |B}0X in cu E _ 3 O > c «S o c I — B Q Z O CD < 2 < 2 u. o o CM c o SJU9A3 i,o jeqwriN tz o s}uaA3 io jaqwriN o L O 3 C O LL. in * — o —^* c cu < > cu -> < < — • LL -> c o L O L O 3 C O w —^' c cu > cu co c o o o CM O 00 O S}U9A3 io jaqwriN siueA3 ; o jaqujnN 159 <D CD T J •c m 0) a> o c CD CL CO o >» _ i E tn is o o CU T J 3 'E CO to E T J c to tz a> a> a> E _3 O > I X. o o or c o o o o co o o o (LU ojqno) 9iun|0A |BJOI in a> E _3 O > c o c c o 2 o o CN o o in OL O _o E to a) CO T J •c CQ in cu o c CU Q. CO E e o o o a> T J 3 E CO co E T J tz co cT rz cu 3 CT CU to CD E _3 o > I XL O O or Q — Z — 0 — CO I - < c o t ? 2 o o CN O O (iu ojqno) 9iun|0A |B}oi CO a> E _3 o > cz o c I— o o CTJ < 2 < o CO f o S J U 9 A 3 ;o joquinN rz o x: —^. rz o CN LO LO 3 CO cz > cu co 1 _E Q Z o CO < c o co LO LO 3 CO > cu "cr? O o V- < o o CN O O CO o S1U8A3 io jequiniM s i u 9 A 3 jo jsquinN 160 Figure 5.54 - Magnitude-cumulative frequency plots for rock falls in different activity zones; Highway 99 bands A and B Figure 5.55 - Magnitude-cumulative frequency plots for rock falls in different activity zones; BCR 100.00 — i CO CD >> L -CD D. fr C CD ZJ cr CD CD > ro E ZJ o 10.00 — 1.00 — 0.10 0.01 o Active rock fall areas n Moderately active L_l rock fall areas A Inactive rock fall areas TTTTT 0.001 I I llllllj I I 0.10 llj 11 llllllj 11 llllllj 10.0 Volume (cubic m) lllllllj I III 1000 TT 100000 162 Figure 5.56 - Magnitude-cumulative frequency plots for rock falls in different activity zones; Highway 1 without Band F 163 CHAPTER 6 - DEBRIS FLOW MAGNITUDE-FREQUENCY RELATIONSHIPS 6.1 - Data Mapping As for the rock fall data, preliminary plots were constructed of the temporal and spatial distributions of debris flow events on each route. The number of debris flows in the database is much smaller than the number of fall and slide events. On CPR, no data was available for debris flows, and on CNR, only one debris flow was recorded, for which no location or magnitude estimate were given. This event occurred in 1946, and caused damage to the engine car and two rail cars. Each of Highway 99, Highway 1 and BCR have several debris flow records, with magnitude estimates. A histogram of the number of debris flows vs. location on Highway 99 is shown in Figure 6. la. Only four events were recorded on this route, all on creeks in the first 20 km north of Horseshoe Bay. All event records had magnitude estimates, ranging from 12500 to 17500 m3 (Figure 6. lb). It was not necessary to use a log scale to plot magnitude, as the difference between the minimum and maximum magnitudes was sufficiently small. Figure 6.1c shows the temporal distribution of these four debris flows, ranging from late 1981 to late 1983. Histograms showing the spatial distribution of all debris flow events, and only those for which magnitude estimates were given, were plotted for Highway 1 (Figure 6.2a and c). Volumes of these events are shown in Fig. 6.2b. All except one event occurred between km 125 and 150 (approximately Agassiz to Hope). The records of these events were found in a Thurber Engineering report on debris torrents in Walleach and Floods (Thurber, 1985). The other event, the magnitude of which is not known, occurred at Tank Hill, 12 km north of Lytton, in 1995. It should be noted that this event was the only debris flow in the MOTH landslide records for Highway 1. This suggests that debris flow events were not systematically recorded by MOTH, at least from the mid 1980s, when the above-mentioned events near Hope occurred. The temporal 164 distributions of all debris flows on Highway 1, and only those with known magnitudes, are shown in Figure 6.2d and e. BCR is the route on which most debris flows were recorded, over the greatest time period. Several of the debris flows recorded on BCR are the same as those which affected Highway 99. However, several other, smaller events were recorded at about mile 150 (near Lillooet). Most of these debris flows delayed BCR trains, and three caused damage to the tracks. The spatial and temporal distributions, and volumes of events, are shown in Figure 6.3. 6.2 - Sampling Intervals The definition of spatial bands of debris flow data was only necessary for BCR. Both the Highway 99 and Highway 1 debris flow records are concentrated in narrow zones, which appear to be homogeneous in terms of recording intervals. All events recorded on Highway 99 lie in the previously defined Band A (Figure 6. la). Assuming that the diligence of debris flow reporting on Highway 99 has been similar to that for rock falls and slides, only km 0 to 75 (Bands A and B) were considered in the debris flow magnitude-frequency analysis. On Highway 1, all except one event occurred between km 125 and 150 (Figure 6.2a). While one event on Highway 1 lies outside this zone, its magnitude is unknown. Therefore, only the events between km 125 and 150 were considered for magnitude-frequency analysis. On BCR, two bands were defined, separating the five data points recorded in the early to mid 1980s along the southern section of track from the denser population of events recorded near Lillooet between 1985 and 1992. The boundary between Bands A and B was placed at mile 100. Because debris flows in the study area are much less frequent than rock falls and slides, and because small-scale debris flows which do not affect the transportation routes may often go unreported, it was difficult to establish accurate sampling periods for uncensored data. The intervals chosen are rough estimates, based on the data available. In several cases, intervals were 165 chosen based on the sampling periods for rock falls of similar magnitudes, in the same area. This was done based on the assumption that if large rock falls were being diligently recorded in a certain area, it is likely that records of large debris flows would also be kept. The sampling interval for Highway 99 appears to have been consistent for debris flows of magnitudes greater than 10000 m3, from the middle 1900s to the present (Figure 6.1c). While no debris flows were reported after 1984, it can be assumed that this is due to the non-occurrence of events, rather than failure to report them. Due to the small number of events recorded, and the long return period on events of this magnitude, it was assumed that the consistency of reporting for debris flow events in this area was the same as that for rock fall and slide events. Therefore, a sampling interval of 39 years (1/1/1957 to 12/31/1995) was defined for debris flows with magnitudes of 10000 to 100000 m3 on Highway 99. Several extremely large-scale lahars at the Cheekye Fan were investigated by Hungr and Rawlings (1995) and Sobkowicz et al. (1995). Through field studies of the debris flow deposits in the area, it was determined that a total of about 20 million cubic metres of debris flow material had been deposited on the lower fan in three or more large events in the past 6000 years. The material of a very large event, the magnitude of which was estimated as 7 Mm 3, was dated at approximately 1300 years B.P. The deposits of two other events with magnitudes between 2 and 3 Mm 3 were found to post-date the 6000 year old Squamish River Diamicton. Other smaller events occurred in the same area, including two in the past 100 years. For the purposes of this study, it can be assumed that the three extremely large events would have reached the present location of Highway 99, somewhere near km 50. Therefore, the following data were added to the Highway 99 record: one event with a magnitude of 7 Mm 3, and a sampling interval of 1300 years (incremental annual frequency of 0.00077); and two events with magnitudes of 2 Mm 3, and sampling intervals of 6000 years (incremental annual frequencies of 0.00017). 166 It should be noted that these large-scale historical events are very different failure types than the debris flow records in the recent database. They involve failures in volcanic ash on the volcano slopes, not in Quaternary slopes. Therefore, the inclusion of these events in the magnitude-frequency relationships must be viewed with caution. On Highway 1, the number of debris flow events, and particularly, the number of years in which debris flows were recorded, again make it difficult to choose an appropriate sampling interval for uncensored data. All of the debris flow records in this area were obtained from a Thurber Engineering report completed in 1995 (Thurber, 1995). Since all recorded events had magnitudes from 1000 to 100000 m3, it was again decided that the start date used for rock falls and slides in the same magnitude range, and in the same area, would be appropriate. It was assumed that any reports of debris flows from at least that date forward were included in the Thurber report. However, because these debris flows were not recorded by MOTH, it is possible that debris flows after the completion of the Thurber report were not recorded. One debris flow in another section of the highway was recorded in 1995, but it cannot be assumed that the record for the area of highway between km 125 and 150 is complete up until 1995. Therefore, the end date for this area was chosen as 12/31/85, the end of the year in which the Thurber report was completed. The sampling interval for debris flows with magnitudes of 1000 to 100000 m3 on Highway 1, km 125 to 150, is then 29 years, giving each event an incremental frequency per year value of 0.034. Several debris flow records on Highway 1 did not include magnitude estimates. In researching these and other records, it became apparent that debris flows for which no magnitude estimate was made were not necessarily small events. Many of these events occurred many years ago, and estimates of magnitude were either not made, or have since been lost or disputed. Magnitudes of some events may be missing due to the difficulties in assessing the volumes of large, saturated soil masses, after the event has taken place, and much of the material has washed away. 167 Because it could not be assumed that events without magnitude estimates were small, these events could not be used in magnitude-frequency analysis. 34 debris flow events were recorded on BCR, from 1981 to 1992 (Figure 6.3d). Three of these events with magnitudes greater than 10000 m3, all in Band A, also affected Highway 99. The records of these events were not acquired from BCR, but from other sources describing the effect of the debris flows on both transportation routes (e.g. Church and Miles, 1987; Hungr, personal files). These three debris flows, which occurred in 1981 and 1983, are the only events in the record earlier than 1985. Therefore, it was assumed that, as in the case of the rock fall records, consistent recording of debris flow events on BCR began in 1985. However, in Band A, a notoriously hazardous slope failure area, recording of large-scale debris flows began at least a few years earlier. Although these records are not in the current BCR database, it was assumed that the sampling interval in Band A for very large debris flows is from about 1980 to the present. The sampling interval for all other events was defined as 12 years, from the beginning of 1985 to the end of 1996, which is the same interval used for all rockfall and slide events on BCR. As in the case of Highway 1, events without magnitude estimates were not used in magnitude-frequency analysis. The extremely large, historical lahars which affected the Howe Sound-Lillooet corridor (Hungr and Rawlings, 1995; Sobkowicz et al., 1995) were also included in the BCR Band A data set. Again, the volumes and dates assigned to these events were: one 7 Mm 3 events 1300 years B.P.; and two 2 Mm 3 events 6000 years B.P. Table 6.1 summarizes the sampling intervals chosen for each debris flow data set. 168 6.3 - Magnitude-Frequency Relationships The debris flow data for each transportation route was sorted in descending order of magnitude, and the incremental annual frequency values summed cumulatively. Magnitude-cumulative frequency curves were then plotted for each route (Figures 6.4 to 6.6). The quality of the Highway 99 curve is poor, due to the small size of the data set. The slope of the entire curve, including the three large events, is -0.77. Without the lahar events, the slope is -2.6. However, the correlation coefficient for this regression is only 0.74, indicating that the linear approximation of the curve including only the four smaller events is poor. The Highway 1 data set is larger, and yields a much better magnitude-cumulative frequency curve (Figure 6.6). The whole curve is approximately linear, with a slope of -0.60. Although the BCR data set is the largest of the three, the magnitude-cumulative frequency curve is poorer than the Highway 1 curve (Figure 6.5). Without including the three historical events, there is an approximately linear section of the curve from about 765 to 17500 m3. The slope of this section is -0.66. The curve then curves strongly to a much flatter slope (-0.18) for smaller magnitudes. The reason for this could be a failure to report most small-magnitude events. Alternatively, some of the smaller events reported as mudslides or washouts, and labeled debris flows in the database, may not in fact be debris flow events. Although less accurately defined than the rock fall magnitude-frequency relationships, the debris flow curves can be used for approximations of debris flow probability, within given magnitude limits. On Highway 99 and Highway 1, no debris flows with magnitudes less than 1000 m3 were reported. Although several smaller debris flows were recorded on BCR, a good quality magnitude-frequency curve could not be established for magnitudes less than about 1000 m3. Therefore, these three curves can be used to assess debris flow probabilities only for events larger than 1000 m3. A plot of all three curves on the same set of axes is shown in Figure 6.7. 169 Table 6.2 summarizes the linear regression data for the three transportation routes. Interestingly, even though the slopes and intercepts are fairly rough estimates, they are fairly similar for the three routes. The data suggests that magnitude-cumulative frequency relationships for debris flows along the transportation routes in the study area can be described by a typical slope of about -0.6 to -0.8. 6.4 - Influence of Geology All four of the debris flow events recorded on Highway 99 occurred from km 5 to 15. The bedrock geology in this area is composed of Gambier Group volcanic and sedimentary rocks. Several steep cuts and natural slopes rise from the highway, into which numerous creeks and are incised. M Creek is incised almost completely into bedrock, while Alberta Creek and Charles Creek flow through till and colluvium slopes, as well as areas of bare rock. The gradients of these three creeks are approximately 25° in the lower reaches, and as high as 40° to 60° at higher elevations. The M Creek debris flow originated in a small gully in bedrock, at an elevation of 900 m. The event in Alberta Creek originated 600 m above the highway, in overburden. Continuous rock falls at the headwaters of Charles Creek, 950 m above the highway, were credited with causing two failures in talus, which became saturated and flowed down the creek to the highway. While all of these events occurred in volcanic and sedimentary rock, the bedrock geology does not seem to be as important as the geomorphology of the failure site. The conditions favourable for debris flows affecting the highway include fairly steep, narrow creeks with a supply of debris or rock fragments, and depositional fans at or near the highway. Instability at the creek headwaters, or at some source area above the highway, due to closely spaced jointing, and fracturing of bedrock, or steepness of colluvial slopes, serves to initiate debris flow events. Logging of the creek watersheds apparently has some effect in reducing the stability of the rock or 170 debris at source areas. The M Creek watershed was subjected to extensive clear-cutting prior to the debris flow. Three debris flows which affected BCR occurred in the same three creeks mentioned above. Most of the other events occurred near Lillooet, in the sheared greenstone-greenschist melange of the eastern Bridge River Complex. Details about creek or gully morphology were not available for these events, as most were reported simply as mudslides or washouts. The prominence of events in sheared, fractured, or closely jointed volcanic and sedimentary rocks indicates that this geological setting may be conducive to debris flows. However, two events were recorded at mile 38.8 and 63.7, which are both plutonic rock areas. The historical events noted by Hungr and Rawlings (1995) and Sobkowicz et al. (1995) all occurred in the young volcanic slopes of Mount Garibaldi. Failures in this material had to be extremely large to reach either the highway or the railway, as neither route actually traverses Garibaldi rocks. The lahars involved the collapse of the volcano slopes, and subsequent flow of massive amounts of material onto the Cheekye Fan. The deposits involved in these failures are poorly sorted pyroclastic breccias, up to 60% by volume of which are sand and silt (Hungr and Rawlings, 1995). The conical deposit of breccias, dipping outward at 10 to 12° are not welded nor cemented. Constant falls, slides and erosion serve to transport material from the headwall into the Cheekye River (Hungr and Rawlings, 1995). These geological conditions, and the removal of glacial ice support likely made the volcanic deposits susceptible to debris flows shortly after deglaciation (Hungr and Rawlings, 1995). All of the debris flows recorded on Highway 1 occurred in bedrock slopes. The events recorded in the Thurber Engineering report, from km 129.9 to 137.6, all occurred in natural creeks, with fans at the highway level. Again, the creeks all have fairly steep gradients above the fans, ranging from 20 to 50°. Several watersheds were affected by logging. The debris flow at km 278.6 occurred when overburden from the slope headscarp flowed into a natural gully. Again, it 171 seems that the geomorphology of the slope and creek or gully is more important than the type of bedrock, when considering debris flow susceptibility. 6.5 - Influence of Climate All four of the debris flows which occurred on Highway 99 involved heavy rain, and all occurred between October and February, inclusive. Therefore, freeze-thaw potentially also influenced each event. The Alberta Creek failure may have been initiated by a snow avalanche, with both heavy rainwater and meltwater contributing to the flowing mass. Of 26 debris flow records on BCR (including the above four), nine include a reference to rain at the time of the event, and nine more refer to heavy rain. Only one reports sunny, clear conditions at the time of the debris flow. Even if all failures with no record of climate occurred in clear conditions, the eighteen debris flows during rainy periods make up 69% of the BCR data set. Large storms in particular seem to have a great influence on debris flow frequency. Four events on BCR occurred on May 27, 1989, during heavy rains. Another 17 failures took place during heavy rains from August 10 to 15, 1991. The other five events in the data set occurred from October to February. This again suggests that apart from unusual storms, slopes on transportation routes in the southern Howe Sound-Lillooet corridor may be more frequent in the rainy winter season, during which freeze-thaw is also a concern. On Highway 1, 19 (86%) of the 22 debris flows recorded took place during or after major storms. 11 were recorded on January 4, 1984, and 8 on July 12, 1983. Of the other three events, one occurred in October, and two in January. This data indicates that heavy rain is a very important influence on debris flow frequency in the study area. In general, debris flows are more frequent in the rainy winter months, but storms in the summer are also capable of initiating failures. Of all events recorded on the three routes, it 172 can be roughly estimated that debris flows in the study area are about 3 to 4 times more likely to occur during storms or heavy rain, than in clear conditions. 173 Table 6.1 - Sampling intervals used to calculate debris flow frequency per year for each route segment and volume class Area Magnitude (m3) Start Year End Year Interval (yrs) Hwy. 99 (km 0-75) 10000-100000 Hwy. 1 (km 125-150) 1000-100000 B C R (mi. 0-100) B C R (mi. 0-100) B C R (mi. 100-160) 0-10000 10000-100000 0-100000 1957 1957 1985 1980 1985 1995 1985 1996 1996 1996 39 29 12 17 12 Table 6.2 - Magnitude-cumulative frequency slopes for debris flows on each route Correlation Route Corridor # of records Intercept Slope Coefficient Highway 99 km 0-75 H-L 7 1.96 -0.77 0.968 B C R H-L 12 1.75 -0.66 0.899 Highway 1 km 125-150 F-T 13 1.56 -0.60 0.911 174 Figure 6.1 - Locations, volumes and dates of debris flow events on Highway 99 (a) Spatial frequency of all events co •4-» C CO Lu cu XI E 3 "l r r r r~ r r r T T 10 km 15 20 (b) Debris flow volume vs. location ~ 30000 E o n 3 cu E _3 O > o 20000 10000 I I I I 10 km I I I I I I 15 20 (c) Dates of all events 1986 1984 1982 1980 I I I I I I I I I I I 10 km 15 20 175 Figure 6.2 - Locations, volumes and dates of debris flow events on Highway 1 (a) Spatial frequency of all events c <D LU CD XI E 3 100 150 200 Mile 250 300 (A -*—' C CD > LU CD X I E 3 (b) Spatial frequency of events with known volumes 100 150 200 km 250 300 E g xi 3 CD E i CO •*-» o 100000 - = -10000 -=J-1000 100 (c) Debris flow volume vs. location O O ^ — O o T 150 200 km 250 300 176 Figure 6.2 - Locations, volumes and dates of debris flow events on Highway 1 2000 1990 1980 1970 1960 100 (d) Dates of all events 150 200 km 250 300 1985 1984 1983 100 (e) Dates of events with known volumes oo 150 200 km 250 300 177 Figure 6.3 - Locations, volumes and dates of debris flow events on BCR (a) Spatial frequency of all events c CD CD XI E 3 50 100 Mile 150 200 (b) Spatial frequency of events with known volumes -•—. c CD > LU CD XI E 3 50 100 Mile 150 200 E g 3 O CD E _3 | CO -4-* O 100000 10000 — 1000 -d 100 10 -1 -(c) Debris flow volume vs. location 50 100 Mile 0 % 150 200 178 Figure 6.3 - Locations, dates and volumes of debris flow events on BCR (d) Dates of all events ro a> >-2000 1995 1990 1985 1980 1975 O o o 50 100 km < 3 O 0 O 150 200 (e) Dates of events with known volumes CO cu >-2000 1995 1990 1985 1980 1975 o <3O0O 50 100 Mile 150 200 179 Figure 6.4 - Magnitude-cumulative frequency plot for debris flows on Highway 99 10.000 - - . 1.000 -=J CD CD 1.0 100 10000 1M 10M Volume (cubic m) 180 Figure 6.5 - Magnitude-cumulative frequency plot for debris flows on BCR 10.000 1.00 100 10000 1M 10M Volume (cubic m) Figure 6.6 - Magnitude-cumulative frequency plot for debris flows on Highway 1 10.000 -=. 1.000 -=J co cu >» CD C L c cu ZJ cr 8> >*— cu > ro u E o 0.100 - d 0.010 0.001 - d 0.0001 TT TT TT 1.0 I llllllj I I 100 10000 Volume (cubic m) TT T T i i 1M 10M 182 Figure 6.7 - Magnitude-cumulative frequency plots for debris flows on all routes 10.00 — i o BCR - o Highway 1 - • Highway 99 1 10 100 1000 10000 100000 Volume (cubic m) 183 CHAPTER 7 - RISK ANALYSIS 7.1 - Rock fall Risk Calculations for Highway 99 and Highway 1 For the purposes of this study, risk represents the annual probability of at least one fatal accident occurring in a given zone, caused by slope failure. Using the magnitude-frequency relationships outlined above, and traffic statistics for the two highways, estimates of total risk for various sections of each route can be calculated. Bunce (1994) and Bunce et al. (1997) used the binomial theorem to calculate risk of rock fall death on a highway. However, Hungr and Beckie (1998) proposed that simple multiplication of conditional probabilities yields equally accurate results, provided accident probabilities are low. This approach was taken in the current research. Therefore, the formula used to calculate risk, for a given category of landslide magnitude, is as follows: P(A) - fh * P(S:H) * P(T:S) * P(I:S) * P(L:I), [7.1] where: P(A) is the annual probability of occurrence of a fatal accident in a given area; fh is the annual frequency of landslides in the area, in a single magnitude category; P(S:H) is the longitudinal encounter probability, defined as the probability of a vehicle being present within the length of the highway impacted by the landslide (the damage corridor), at the time the landslide occurs, as calculated below; P(T:S) is the temporal encounter probability, which equals 1.0, based on the assumption that vehicle flow with average intensity is continuous in time; P(I:S) is the lateral encounter probability, which describes the proportion of the route's width covered or affected by the landslide; and P(L:I) is the probability of death of at least one occupant, given impact. 184 The total annual risk of at least one landslide fatality in a given zone is then the sum of the risk values calculated for each magnitude category. Each of the terms in Equation [7.1] are related to rock fall magnitude. The frequency, f,, is derived from the magnitude-cumulative frequency curve by subtracting the cumulative frequencies for each of a series of successive magnitude classes. For example, the annual frequency of occurrence of rock falls with magnitude 0.1 m3 on Flighway 99, Zone 1, is: logFo., =b*log(0.1) + a = -0.435 *log(0.1) + 0.796 F 0.i =17.02 Similarly, the annual frequency of rock falls with magnitude 1.0 m3 in the same area is 6.25. Therefore, the annual frequency of rock falls with magnitudes 0.1 to 1.0 m3 is determined by subtracting 6.25 from 17.02, to give 10.77. The annual rock fall frequencies were calculated using this method for a series of magnitude classes, for each route in the study area. The longitudinal probability of encounter, P(S:H) is also dependent on rock fall magnitude, as the volume of the failed mass affects the damage corridor width. P(S:H) is calculated based on the geometrical relationships shown in Figure 7.1, assuming uniform average spacing between vehicles. P(S:H) = U + L , , [7.2] L d where Lv is the vehicle length (taken as 5.4 m for cars), Li is the damage corridor width, and L d is the average spacing between vehicles. L is estimated relative to the magnitude class of the slope 185 failure. Ld is dependent on the average velocity of vehicles (vavg, in m/hr), and the daily traffic volume (vpd). It is caluclated as follows (in metres): L d = v a y g * 24 hrs [7.3] vpd While traffic volumes and velocities are taken as averages, and do not allow for night and day differences, stoppages in traffic, etc., the linearity of the risk equation prevents any error from being compounded. Therefore, it is reasonable to use these average values for estimating risk. The lateral impact probability, P(I:S), is the probability that the vehicle will be impacted, given that it is within the landslide damage corridor when the failure occurs. Again, this value is related to rock fall magnitude, in that only a fraction of the route will be affected for small failures. For very small rock falls, less than one lane of a highway will be affected, making P(I:S) less than 0.5. For failures with magnitudes greater than 100 m3, it was assumed that any vehicle present in the corridor is likely to be impacted, and P(I:S) was taken as 1.0. The probability of death of a vehicle occupant, given impact, is probably the most difficult parameter to estimate. It was assumed for this study that for small rocks, P(L:I) is about 0.1 (Cruden, 1997). For events larger than 1000 m3, P(L:I) was assumed to be 1.0. A characteristic magnitude-cumulative frequency curve has been defined for rock falls on Highway 99, Zone 1. Because the data set for Zone 2 was not large enough to plot an adequate curve, a characteristic equation for the magnitude-cumulative frequency relationship could not be established for this zone. It would be inappropriate to use the same equation as for Zone 1 because the frequency of events in Zone 2 is significantly lower. In 1993, Highway 99 Zone 1, from Horseshoe Bay to Squamish (km 0 to 50), was characterized by a summer average daily traffic SADT) value of about 12000 vehicles. This value was calculated by taking an approximate average of 1993 SADT values from two BC MOTH 186 counting stations near Horseshoe Bay and Squamish. Because winter traffic values are likely to be lower than this, and because the risk analysis must consider traffic volumes throughout the sampling period, the average traffic density for this zone was taken to be 5000 vehicles per day (vpd). While this is only a rough estimate of the traffic volume, it is likely not useful to attempt to more accurately define the traffic densities, as it is still necessary to assume that the average density and average spacing of vehicles are constant, to keep the data manageable within the scope of this project. The average vehicle velocity was taken as 80 km/hr for all sections of both highways. Table 7.1 gives the values of all parameters in equation [7.1], for the rock falls and slides along Highway 99, Horseshoe Bay to Squamish. On Highway 1, characteristic magnitude-cumulative frequency curves have been defined for rock falls in Zones 1 and 2. Again, curves could not be defined for Zones 3 and 4, so no risk values are estimated for this section of the highway. For Zones 1 and 2, risks were calculated separately, using the specific magnitude-cumulative frequency equation, and traffic densities appropriate for each area. The Zone 2 curve has two distinct linear sections, and therefore, two equations were used in calculating risk. For events with volumes less than or equal to 1.0 m3, the curve has a slope of -0.28 and an intercept of 1.00. While this relatively flat slope may be in part due to data censoring for smaller events, it is likely that the effectiveness of ditches on the highway also contributes to the flat slope. Therefore, it was considered more appropriate to use a slope of -0.28 to calculate failure probabilities for events up to 1.0 m3, and a slope of-0.62 for events greater than 1.0 m3. Alternatively, failure probabilities could be estimated by reading values directly from the magnitude-cumulative frequency plot, but values corresponding to volumes beyond the limits of the graph would still have to be estimated using a linear approximation. Therefore, in this risk analysis, all probabilities were estimated based on linear approximations of the two curve segments. 187 Two zones of different traffic densities were chosen along the Highway 1 route, to coincide with the two geographic zones defined above. Similarly to Highway 99, the traffic densities used are based on averages of summer daily traffic volumes at various counting stations, provided by MOTH. These average densities are reduced to represent winter volumes as well. The estimated traffic density values (vpd) for each zone are: 4000 for Vancouver to Hope; and 3000 for Hope to Lytton. The Vancouver to Hope traffic density is estimated based on traffic volumes close to Hope. Only seven of the events recorded in Zone 1 occurred in the first 130 km of the Highway, where the heaviest traffic volumes are found. Therefore, the traffic volume farther along the highway, between Agassiz and Hope, is more appropriate for calculating risk, as the main concentration of slope failures in Zone 1 occurs in this area. The Equation [7.1] parameters and calculated risk values for rock fall on the two Highway 1 zones are given in Tables 7.2 and 7.3. The results of these risk calculations compare reasonably with the actual damage statistics collected in the rock fall database. On Highway 99, Zone 1, seven deaths due to rock falls were recorded in the database. While early rock fall records are incomplete, it can be assumed that any failures resulting in death would have been recorded fairly diligently. Therefore, 1964, the year of the earliest rock fall record in the database was used as the start of the sampling period for rock fall deaths on Highway 99. Although seven rock fall deaths were recorded from 1964 to 1996 (33 years), three of these deaths occurred during a single accident. Therefore, the total number of fatal accidents caused by rock falls is five, giving a return period of 6.6. This indicates a risk value somewhat higher than the calculated risk. However, one of the fatal accidents recorded in the database was not definitely rock fall related. The accident, which occurred in 1994, may have been a motor-vehicle accident with no rock fall involvement. If this accident is omitted from the record, the return period becomes 8.2 years (4 fatal accidents in 33 years). This is closer to the calculated return period of 9.9 years. The calculated risk is still somewhat low compared to the historical risk 188 on this section of the highway. This can be attributed to uncertainties in traffic volumes and various risk parameters, as well as assumptions regarding constant traffic flow. Another consideration is that rock fall frequency in the earlier years of the database may be affected by residual censoring, causing the estimated risk to be lower than historical values. The probability of a fatal accident occurring during a single trip from Vancouver to Squamish on Highway 99, PAV, can be calculated by dividing the P(A) value by the total number of trips per year. The number of trips per year is taken as the average number of vehicles per day on this part of the highway, multiplied by 365 days. Therefore, for Highway 99, Zone 1, PAV is equal to 5.5 x 10"8. This value falls well below the upper limits of acceptability proposed by Fell (1994), Morgan (1991), and Sobkowicz et al. (1995). The greatest proportion of risk on Highway 99 from Horseshoe Bay to Squamish results from rock falls with magnitudes between 100 and 1000 m3. Failures in the 10 to 100 m3 and 1 to 10 m3 ranges are the second and third greatest contributors to risk, respectively. The proportion of risk caused by rock falls in each magnitude range is shown graphically in Figure 7.2. On Highway 1, Zone 1, only one fatality due to rock fall has been recorded since 1980. Therefore, the return period on rock fall-related fatalities along this section of the highway is 17.0. This return period is significantly shorter than the calculated return period of 35.7. However, it is again not certain that this accident, which occurred in January, 1993, was caused by rock fall. If it was not, the record does not contain any rock fall fatalities in this area, and the calculated return period, which is longer than the sampling period, may be a reasonable estimate. The PAV value for Highway 1, Zone 1, is 1.9 x 10"8, which again can be considered acceptably according to several acceptability criteria. Similarly, on Highway 1, Zone 2, no rock fall deaths were recorded. The calculated return period on rock fall deaths is 15.0 years, which is two years shorter than the sampling period. Therefore, the risk estimate may be somewhat conservative, compared to historical statistics. 189 However, the estimated value does seem to be a reasonable value for average annual risk of death due to rock falls on Highway 1, from Hope to Lytton. The PAV value for Highway 1, Zone 2, is 6.1 x 10"8, again well within acceptability limits. On Highway 1, Zone 1, the greatest proportion of risk comes from rock falls with volumes from 100 to 1000 m3. Larger failures, with volumes from 1000 to 10000 m3, and 10000 to 100000 m3, make up the second and third greatest risk contributions, respectively. The largest proportion of rock fall risk in Zone 2 comes from smaller events, with magnitudes from 1 to 10 m3. Rock falls with volumes from 10 to 100 and 100 to 1000 m3 are also relatively large contributors to risk. This again displays the relative importance of smaller rock falls in the faulted, fractured rocks of the Fraser Canyon. In the more massive rocks of the Coast Mountains and the Fraser Lowland, larger rock falls are relatively more important. Figure 7.2 shows the risk of life posed by rock falls in each magnitude class on Highway 1 Zones 1 and 2. Another risk parameter which could be of interest is the risk of impact to large, multi-passenger vehicles. For example, a rock fall impacting a school bus could have severe consequences, due to the large number of people at risk. On Highway 99, near Squamish, approximately 2.5% of all vehicles are buses, according to BC MOTH 1993 traffic statistics. For the purposes of this risk analysis, this value was used to estimate the number of buses per day in each of Highway 99 Zone 1, Highway 1 Zone 1, and Highway 1 Zone 2. The average length of all buses was assumed to be 13.5 m. On Highway 99, from Horseshoe Bay to Squamish, the annual probability of a bus being impacted by a rock fall is 0.021, which gives a return period, R, of 47.0 years. The annual probability of a large rock fall (greater than 10 m3) impacting a bus is 0.003 (R = 334 years). The probability of a specific bus being impacted by a large rock fall on a single trip through this zone is then 6.6 x 10"8. 190 On Highway 1, from Vancouver to Hope, the annual probability of a rock fall impacting a bus is 0.0024 (R = 415). The annual probability of a large rock fall impacting a bus is 0.00094 (R = 1064 years), and the probability of a specific bus being impacted by a large rock fall during a single trip, is 2.6 x 10'8. From Hope to Lytton on Highway 1, the annual probability of a bus being impacted by a rock fall is 0.0079 (R = 127 years). The annual probability of a bus being impacted by a large rock fall is 0.0021 (R = 475 years), and the probability of a specific bus being impacted by a large rock fall during a single trip is 7.7 x 10 s. According to the risk acceptability criteria proposed by Sobkowicz et al. (1995), these risks are well below acceptability limits, even considering the fact that up to 40 people are potentially at risk. It should be noted that in estimating all of the above rock fall risks, no allowance was made for reductions in risks due to highway improvements, such as scaling, meshing and rock-bolting. Such efforts in some areas of the studied routes have been fairly intensive, and thus may have significantly affected risk values in recent years. Another factor to consider is the additional risk of death due to a moving vehicle striking a fallen rock. The risk analysis outlined above considers only the scenario in which moving vehicles are struck by falling rocks. The annual probability of an accident caused by a vehicle striking a fallen rock can be estimated using the decision sight distance, or the distance a vehicle travels in the time it takes for the driver to see a rock on the road, and stop or avoid the rock (Bunce et al., 1997). This value can be used instead of Lv, the average vehicle length, to estimate impact probabilities. However, P(L:I) values are likely to be lower, and more difficult to estimate, than for the falling rock scenario. This is partly because of the nature of the impact, and partly because the driver of a vehicle has a complex series of reactions after becoming aware of a rock on the road (Bunce et al., 1997). The probability of death may be reduced by the driver's awareness of the 191 rock, or it could be increased if this awareness causes the driver to lose control of the vehicle. Because of the additional assumptions required, risks were not calculated for this scenario. However, Bunce et al. (1997) found that the probabilities of impact from this scenario at the Argillite Cut are greater than those arising from the moving vehicle-falling rock scenario. Therefore, it is likely that the risk values estimated above for the current study area are also somewhat lower than for the moving vehicle-fallen rock scenario. 7.2 - Debris Flow Risk Calculations for Highway 99 and Highway 1 Because the data sets for debris flows on each route are significantly smaller than those for rock falls, it was more difficult to establish representative magnitude-cumulative frequency curves. Therefore, the risks calculated using the debris flow curves are less reliable than those calculated for rock falls. However, estimates of risk were calculated using the above method, for each of the two highways in the study area. The estimates used for spatial and temporal impact probabilities, and the probability of death given impact, were the same as those used in the rock fall risk calculations. For failures with volumes from 105 to 106 m3, a value of 100.0 m was used for Li , the damage corridor width. Again, these values are only rough estimates, based on the limited amount of data available in the database. The average vehicle velocity was again taken as 80 km/hr for both highways. For Highway 99, a representative magnitude-cumulative frequency relationship was established for debris flows greater than 1000 m3, from km 0 to 75. The slope of this curve is -0.77, and the intercept is 0.97. This relationship was used to calculate debris flow probabilities for the given area, in order to calculate risk. The traffic volume in this area was again estimated using MOTH data. The value used in calculating risk was 4000 vehicles per day. The Equation [7.1] parameters and calculated risk values for debris flows on Highway 99, km 0 to 75, are given in Table 7.4. 192 The representative magnitude-cumulative frequency curve for Highway 1, km 125 to 150, has a slope of-0.60 and an intercept of 0.911. The traffic volume in this area was estimated at 4500 vehicles per day. The Equation [7.1] parameters and calculated risk values for debris flows on Highway lj km 125 to 150, are given in Table 7.5. While twelve people have been killed by debris flows affecting Highway 99, since 1964, these deaths were caused by only three debris flows, giving a return period on fatal debris flow accidents of 11 years. The calculated risk to life from debris flows on Highway 99 is significantly lower than these historical statistics suggest. In part, the discrepancy in estimated and historical risks is due to the fact that risk was calculated based only on debris flows impacting highway users. Any fatalities from debris flows on the railway, or surrounding areas, including houses, were not considered in the analysis. Of the three fatal debris flows affecting Highway 99, only one, at M Creek in 1981, caused the death of highway users. The events at Charles Creek in 1981 and Alberta Creek in 1982 resulted in the death of a pedestrian, and two people in a house near the highway. Therefore, the return period on debris flows causing death to at least one person on Highway 99 is 33. Estimates of risks to people other than those on the transportation route in question would require detailed run-out analysis beyond the scope of the current research. The estimated return period of almost 300 years is still much longer than historical statistics suggest. This is likely due to the fact that debris flow accidents are not normally caused by failure material directly impacting moving vehicles. Instead, the normal scenario is that a bridge is washed out by the debris flow, posing danger to highway users after the event. Therefore, it may be more useful to estimate the probability of a bridge being washed out by a debris flow, and use traffic statistics, including the decision sight distance, to determine the probability of an accident resulting from the washout. Because many more recent highway bridges are designed for debris flows to run underneath them, it would be useful to analyse washout probabilities for each bridge individually, or for separate bridge categories, according to design. 193 On Highway 1, no debris flow fatalities are recorded in the database. Therefore, it is impossible to compare the estimated risk to life with historical results. It can be assumed that the return period on debris flow deaths on Highway 1 is greater than 30 years, which is the length of the database record for debris flows. This agrees with the estimated return period of 87.0 years, but it is not possible to conclude that the estimated risks are suitable, as an upper limit on the historical return period cannot be determined. It is reasonable to assume that the limited quality of the magnitude-frequency relationship for Highway 1 again may result in unreliable risk estimates. However, it should be noted that the Highway 1 magnitude-frequency curve is of higher quality than the Highway 99 curve. Again, the ability to estimate debris flow risks on Highway 1 will likely improve if future events are recorded consistently, thus lengthening the sampling period for useful debris flow records. The estimated risks again involve only fatalities caused by debris flow material directly impacting highway users. Further analysis of the probabilities of bridge washouts would provide a more complete picture of debris flow risks on the highway. The greatest proportion of risk to life on both Highway 99 and Highway 1, caused by direct impact of highway vehicles by debris flow material, is posed by debris flows with volumes from 1000 to 10000 m3. The relative risk decreases for increasing magnitude, up to 106 m3, which is the largest volume considered in the analysis. Both the Highway 99 and Highway 1 risk estimates for debris flows may be somewhat accurate in terms of risks only to people in vehicles on the highways, directly affected by debris flows. However, the ability to estimate risks using this method is likely to improve with continued diligence of reporting and recording debris flow events in the future. Analysis of debris flow runout, and the probabilities of bridge washouts, could be very useful in determining more realistic estimates of total risk from debris flows to all highway users. 194 7.3 - Rock fall risk calculations for BCR and CPR 7.3.1 - Passenger Trains Risk due to rock falls on BCR and CPR were calculated using the same method as for the two highways. However, some differences exist between the highways and railways, in terms of traffic patterns and vulnerabilities. On BCR, the maximum number of trains per day is fourteen, only in certain areas, and during the summer. Risk to life was calculated for passenger trains only, which involved an even lower number of trains per day. As for Highway 99 and Highway 1, risk was calculated separately for the geographic zones discussed in section 5.7. Therefore, the calculations could be made using the number of trains per day for each particular zone. Calculations were only possible for Zones 1, 2, and 4, due to the inadequate data set in Zone 3. To account for the seasonal variation in traffic, an average number of trains per day was taken for each zone, reducing the peak seasonal value based on the number of months certain trains do not run. The peak traffic volume was further reduced to account for trains running only on certain days of the week. Therefore, P(A), the calculated annual risk of at least one person being killed by rock fall on BCR, is an over-estimate for the winter months, and for Mondays and Tuesdays, but an under-estimate for the peak summer season and all other days of the week. The magnitude-cumulative frequency curve established for BCR, Zone 1, has a slope of -0.29 and an intercept of 0.05. Using these values, hazard values were calculated using the method described in section 7.1. P(S:H) values for each magnitude class were calculated using the same Li values as those used in the highway risk calculations. The average number of trains per day was estimated at 2.7, based on BCR 1998 timetables. Also based on BCR timetables, the average train velocity was estimated at 45 km/hr, which accounts for stops along the route. 195 The probability of death given impact, P(L:I), was again the most arbitrary and difficult parameter to estimate. Based on the fact that rock fragments as small as 0.03 m3 can cause train derailments (Abbott et al., 1998), P(L:I) values for all magnitude ranges above 0.01 m3 were assumed to be about one tenth of the values as those used for the highway analyses, multiplied by the average number of train passengers. The reason for not using the same values as for the highways, multiplied by the number of passengers, is that compared to highway vehicles, passenger trains were assumed to be sturdier and less susceptible to effects such as driver error. In the landslide database, the greatest number of fatalities from any one slope failure on BCR is nine, indicating that even a major accident is not likely to result in the death of a large proportion of passengers. For BCR trains in Zone 1, the average number of passengers is approximately 300 (Lorraine Poyer, 1998, personal communication). The average length of a BCR passenger train is approximately 175 m (Brad Follett, 1998, personal communication). The Equation [7.1] parameters and calculated risk values for rock falls on BCR, Zone 1, are given in Table 7.6. The BCR, Zone 2 magnitude-cumulative frequency curve for rock falls has a slope of -0.24 and an intercept of 0.26. The average number of trains per day in this area is 2. The Equation [7.1] parameters and calculated risk values for rock falls on BCR, Zone 2, are given in Table 7.7. The magnitude-cumulative frequency curve for rock falls on BCR, Zone 4 has two distinct sections. For volumes less than or equal to 100 m3, the curve has a slope of -0.24 and an intercept of 0.81. For volumes greater than 100 m3, the slope is -0.67, and the intercept is 1.63. The average number of trains per day in this area is approximately 2.5. The Equation [7.1] parameters and calculated risk values for rock falls on BCR, Zone 4, are given in Table 7.8. No rock fall deaths have been recorded on BCR in the sixteen year sampling period covered by the database. Therefore, estimated risk values can not be compared with historical •196 values, except to note that all estimated return periods on rock fall deaths on BCR are greater than sixteen years. PAV values can again be calculated for each zone, by dividing P(A) by the total number of trips per year. For BCR Zone 1, PAV is equal to 8.5 x 10"6. Zone 2 and Zone 4 have PAV values of 1.4 x 10"5 and 5.5 x 10"5, respectively. All of these values are below the upper limits of most proposed acceptability criteria. The reliability of these risk estimates is affected by uncertainty in estimating P(L:I), and the many assumptions required to estimate average traffic volumes. However, the estimated risk values are very useful in comparing relative risks posed by rock falls of different magnitudes. Figure 7.3 shows that for all three BCR Zones analysed, the greatest proportion of risk results from rock falls with volumes from 100 to 1000 m3. Slightly smaller failures, with magnitudes from 1 to 100 m3, are also relatively great contributors to risk. 7.3.2 - Freight Trains Rock falls which impact freight trains on BCR, rather than passenger trains, do not pose a large threat to life. Therefore, it is more useful to calculate risk to freight trains in terms of major accidents, instead of fatalities. The same probabilities of failure used in the risk calculations for passenger trains can be used in the freight train analyses. However, the number of trains per day, and the average train speed and length are different. An average of six freight trains per day run on BCR from mile 0 to 157. The average velocity is 40 km/hr, and the average length is about 2200 m (Brad Follett, 1998, personal communication). For the risk analysis of major accidents caused by rock falls impacting freight trains, it was again assumed that traffic is uniformly distributed in time and space, and that the length and velocity of all trains are equal to the average length and velocity. 197 To calculate the annual risk of a major accident or derailment in a given area, P(A)i, the term P(L:I) is replaced by the probability of a major accident resulting from a rock fall impact, P(L:I)i. While this is again a difficult and arbitrary parameter to estimate, here it was assumed that for any rock falls smaller than 1.0 m3, no serious accident would result. It was also assumed that a major accident would result from any rock falls greater than 1000 m3 impacting a freight train. Therefore P(L:I)i for all events greater than 1000 m3 was assumed to be 1.0. Tables 7.9, 7.10, and 7.11 give the risk analysis parameters and risk estimates for major freight train accidents caused by rock falls on BCR Zones 1, 2, and 4. It should be stressed that these estimated risks are very rough estimates, due to the number of assumptions which had to be made, and the uncertainty in estimating the probability of a major accident, given impact. The risk values should be regarded as examples of the risk analysis procedure, and should not be taken as absolute measures of risk on these railways. The estimated risks of major freight train accidents, or derailments, caused by rock falls on BCR, are low compared to historical values. The database contains records of one derailment in Zone 1, one in Zone 2, and two in Zone 4, in the past 16 years. This discrepancy may be due to uncertainty in estimating P(L:I)i, the probability of a major freight train accident given impact. Further study of the susceptibility of trains to derailment or other major accidents, given impact, would likely help to improve these risk estimates. Another factor is that the estimated risks refer only to accidents caused by moving trains hit by falling rock. They do not take into consideration the risks posed by trains striking rock on the track which has previously fallen. Because CPR does not operate any passenger trains in British Columbia, no estimates of risk to life due to rock falls were made. Instead, risks of major freight train accidents caused by rock falls in each of the four CPR zones were estimated, using the same method as for BCR. No information was available from CPR regarding the average number of trains per day traversing the 198 section of the railway within the study area, the average train length, or the average train velocity. Therefore, several assumptions were necessary in estimating accident risks. It was assumed that the average train length and velocity were the same as those used in the BCR calculations, namely 2200 m and 40 km/hr. The average number of trains per day in each zone was assumed to be 10. It should be noted that the resulting risk estimates may be unrelieable due to the unavailability of this information, but that the risk analysis methodology can be used to more accurately assess risks, given the appropriate data. The estimated risks can also be used to assess relative risks within various zones on the railway. The magnitude-cumulative frequency curve for rock falls on CPR, Zone 1, has a slope of -0.64 and an intercept of 0.27, for events greater than 1 m3. Although the relationship is curved for smaller magnitudes, it was assumed that this was at least in part the result of residual censoring, and that it would not be unreasonable to use the above slope and intercept to calculate probabilities for rock falls of all volumes. This assumption was made for each of the four zones. The Zone 2 curve has a slope of-0.54 and an intercept of 0.64; the Zone 3 curve has a slope of -0.63 and an intercept of 0.98; and the Zone 4 curve has a slope of -0.44 and an intercept of 0.030. Tables 7.12 to 7.15 give the risk analysis parameters and risk estimates for major freight train accidents caused by rock falls on CPR Zones 1 to 4. Damage statistics for CPR were not available, so the estimated risks can not be compared with historical values. It should also be noted again that the estimated risks concern only accidents caused by rock falls derectly impacting moving trains, not by trains striking fallen rock on the track. Because of these factors, and the uncertainty in estimating several parameters in the risk analysis, the calculated risks are most useful not as absolute values, but as an example of the risk analysis procedure, and as a means of comparing relative risks posed by rock falls of different magnitudes. 199 On CPR from Vancouver to Hope, small rock falls with volumes from 1.0 to 10 m3 pose the greatest proportion of risk. This contrasts with the Highway 1, Zone 1 results, which show that larger events pose the greatest risk. A possible explanation for this discrepancy is the fact that the Highway 1, Zone 1 data set is very small. Therefore, the importance of large events may be overestimated by the occurrence of a small number of large rock falls. The greatest proportion of risk on CPR from Hope to Lytton, and from Lytton to Thompson, is also posed by rock falls with volumes from 1 to 10 m3. Events from 1 to 10 m3, and arger rock falls, with volumes from 10 to 100 m3, are both the greatest contributors to risk on CPR from Thompson to Kamloops. Figure 7.4 shows the relative risks posed by rock falls of various volume classes in each CPR zone. 7.4 - Debris flow risk calculations for BCR Debris flow risks on BCR were calculated using the same method as for Highway 99 and Highway 1. The magnitude-cumulative frequency curve for debris flows on BCR has a slope of -0.66 and an intercept of 1.75, for events greater than 1000 m3. The average number of trains per day running from mile 0 to 160 is approximately 2.5. Table 7.16 gives the Equation [7.1] values and risks to life due to debris flows on BCR. No debris flow deaths have been recorded on BCR in the past sixteen years. Therefore, the estimated return period on debris flow deaths of 12.0 may be somewhat conservative, especially since the calculated risk refers only to people in BCR trains killed by direct impact from debris flows. This discrepancy may be a result of inaccurate estimates of P(L:I), which is the most arbitrary and difficult parameter to determine. The greatest proportion of risk to life on BCR is again posed by debris flows with volumes from 1000 to 10000 m3, and the relative risk decreases for increasing magnitude. 200 The probability of a major freight train accident caused by debris flows can be calculated similarly to the rock fall case, by multiplying the probability of failure and spatial probability of impact by the probability of a major accident given impact. Again, the number of trains per day throughout the route is approximately 6, the average train length is 2200 m, and the average train velocity is 40 km/hr. 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P ^. 0 . © © © ©| © © © r -© © ' © © © © o u o _o rJ 2 5? m M tf 0 3 c o en o CO •c - O a) •a i-cS cn S o 3 u cn 2 v o 3 cd T 3 'C V DH s tt tt ST sr WO sr wo sr E^ ed 3 B B < I c eu' u fa 1 4 em . . es es S u oo v d © >n T t CO fN rH VD CN N^: CN CO VD T t CO VD i - H o 00 © o © o o o © ' o © © © CO CO CO © © © VD CN T t l T t U - ) VD! © © © ! © © © O © © " ° . ° . © : « - ) © © ' CN >n CN VD © CN T t r H O © © © © © © © © © O © rH 2 -r 6 • © © © © © © © • © © © © T J O V — fc IS u es *» mi > D- PES e fc fc C/3 B sr s r o r o f~ CO «/•> Tf" Tf ro' •/"> r—l CN CN 1—H f~ CO Tf Tf CO VD —I O O O O O O O o o o o o o o © o T f T f T f o o o o o o B <! fa B cu §1 CU WD »> es es S o P <=>. o V ) o o CN >/-> •—1| CN VO O CN T t ; - H o o © ©' o o o o o o O O r-H 2 T 6 i o o o o o o o o o o o 210 Figure 7.1 - longitudinal probability of encounter Landslide Path i p i i i ^ i i L i j I I 1 U i L,/2 i i L,/2 « H >j j< > A : B : 1 L d < » Li = Landslide damage corridor width L v = Vehicle length L d = Average vehicle spacing in each lane Encounter probability (in each lane): A Lv+L Encounter probability (both lanes): 211 Figure 7.2 - Highway rock fall risks according to volume class (a) Highway 99, Zone 1 0.03 0.02 0.01 0.00 0.001 0.01 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) 0.008 0.004 0.000 (b) Highway 1, Zone 1 0.001 0.01 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) 0.02 0.01 0.00 (c) Highway 1, Zone 2 0.001 0.O1 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) Figure 7.3 - Rock fall risks on BCR according to volume class o_ 0.003 0.002 0.001 0.000 (a) BCR, Zone 1 ~1 . 0.001 0.01 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) o_ 0.003 0.002 0.001 0.000 (b) BCR, Zone 2 0.001 0.01 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) 0.03 (c) BCR, Zone 4 < 0.02 0.01 0.00 0.001 0.01 0.1 1.0 10 100 1000 10000 100000 Volume class (cubic m) 213 Figure 7.4 - Risks of freight train accidents due to rock falls on CPR, according to volume class < oT 0.010 0.005 0.000 (a) CPR, Zone 1 0.001 0.1 10 1000 Volume class (cubic m) 100000 (b) CPR, Zone 2 0.020 — | S 0.010 1 1 o- 1 0.001 0.1 10 1000 100000 Volume class (cubic m) (c) CPR, Zone 3 0.05 — | S 0.03 : 1 , -o-0.001 0.1 10 1000 100000 Volume class (cubic m) 0.004 (d) CPR, Zone 4 < CL 0.002 0.000 0.001 0.1 10 1000 Volume class (cubic m) 100000 214 CHAPTER 8 - CONCLUSIONS Slope failures on British Columbia transportation routes have caused at least twenty-six deaths; numerous injuries; damage to vehicles, roads, tracks, and other equipment and structures; and costly delays to traffic. To reduce the damaging effects of slope failures, it is necessary to quantify risk, as the product of the probability of failure, and the consequences arising from the possible failure. Consequences can be expressed in terms of lives lost, damage caused, or cost imposed by the failure. While extensive fieldwork is common in estimating the probability of slope failure in a given area, this may be impractical for extensive study areas. It has been shown that failure probabilities can be adequately estimated by compiling records of past events within the study area, and using them to forecast future failures. To calculate the probability of failure by this method, it is necessary to establish frequency-magnitude relationships for slope failures within a given area of study. This can only be accomplished if slope failure records including volume estimates are available over a reasonable number of years. The research presented here serves to emphasize the need for complete, accurate and systematic recording of slope failures in problem areas. Problems in predicting probabilities arise when records are censored, or when volume estimates are not included. In the past, record censoring appears to have been most significant for small-scale failures, and for failures in generally non-problematic areas. Slope failure records were collected for five transportation routes through the major corridors in southwestern British Columbia, including: Highway 99 and BCR, from Horseshoe Bay to Lillooet, in the Howe Sound-Lillooet corridor; and Highway 1, CPR, and CNR, from Vancouver to Kamloops, in the Fraser-Thompson corridor. A large number of failure records were available for each route. However, very few CNR records included volume estimates. A total of 3220 rock falls and 56 debris flows have been recorded in a large database. Of these, 1738 rock fall records and 43 debris flow records contain volume estimates. Recording 215 consistency has improved over time throughout the study area. However, in some areas, consistent recording has begun too recently for magnitude-frequency relationships to be accurately defined. Sampling intervals over which rock fall recording was fairly consistent were defined for rock falls in a series o f volume classes, for separate sections o f each route. Thus, incremental annual frequency values could be assigned to each event. These frequency values were summed cumulatively to establish magnitude-cumulative frequency relationships for each route. It was possible to establish rock fall magnitude-cumulative frequency curves for all routes except C N R , although certain portions o f Highway 99 and Highway 1 were omitted due to inadequate data. A l l curves showed power-law relationships for volumes spanning at least three orders o f magnitude. I f historical rock avalanches are included in the curves, the linear sections span eight to ten orders o f magnitude. Curvature o f the magnitude-frequency relationships for volumes below 1 m 3 is likely due to residual censoring, and the effectiveness o f highway and railway ditches. Based on the curves plotted for each route, it was established that the rock fall magnitude-cumulative frequency slopes for routes through the Howe Sound-Lillooet corridor were flatter than those through the Fraser-Thompson corridor. This was thought to be a result o f the structural differences in the geology of the two corridors. The faulted, fractured rocks of the Fraser-Thompson corridor produced a relative abundance of small-scale failures, while the more massive Howe Sound-Lillooet rocks resulted in a relative abundance of medium to large slides. Characteristic slopes could be approximated for the magnitude-cumulative frequency curves through the two transportation corridors. For the Howe Sound-Lillooet corridor, a slope of about -0.4 to -0.5 is appropriate, while a slope of about -0.6 to -0.7 is suitable for the Fraser-Thompson corridor. To assess the influence of geology on the shapes of the rock fall magnitude-cumulative frequency curves, each route was separated into sections of similar lithology. Separate curves 216 were then plotted for only those sections through plutonic rocks, only those through sedimentary, volcanic and non-foliated metamorphic rocks, and those through foliated metamorphic rocks. In general, the rock type alone did not seem to have a major influence on the shapes of the curves, as the slopes remained very similar for all rock types along a single transportation route. As rock type alone did not appear to be of primary importance in defining characteristic rock fall magnitude-cumulative frequency slopes within the study area, each route was then broken into geographic zones. These zones were defined based partially on rock type, but also on structural and phsyiographic setting. Here, differences in the slopes of the curves became visible, apparently influenced by changes in the structural characteristics of the rocks. Curves representing sections of the routes through faulted, sheared and fractured rocks tended to be steeper than those representing sections through more massive rocks. A slope of about -0.25 to -0.55 was considered appropriate for fairly massive rocks with widely spaced joints, such as those throughout the southern section of the Howe Sound-Lillooet Corridor, and the northeastern section of the Fraser-Thompson corridor. For faulted, sheared and fractured rocks such as those through the Fraser Canyon, and near the Downtown Fault, a slope of about -0.55 to -0.75 appeared to be suitable. The effects of climate on rock fall frequency were studied by analysing rainfall, snowfall, and freeze-thaw statistics for various sections of each corridor. Precise conclusions could not be drawn regarding the role of climate on rock fall and slide frequency in most areas. It was noted that rock fall frequencies were generally positively influenced by rain, snow and freeze-thaw. However, the influence of these climatic effects was highly variable. Failures were generally fewer in arid areas, but the differences in geological setting may have been a greater influence than climate. Freeze-thaw appeared to be the most important climatic influence in the drier areas of the routes, namely the Thompson River Valley, and the northern section of the Howe Sound-Lillooet corridor. 217 Differences in magnitude-frequency curves based on rock fall activity were studied by separating each route into 'active', 'moderately active', and 'inactive' sections. Magnitude-cumulative frequency curves were then plotted for each category. This analysis did not yield any evidence that rock fall activity affected the shape of the magnitude-cumulative frequency curve for any given area. Therefore, it was concluded that structural setting was the most important influence on magnitude-frequency relationships for rock falls and slides in this study area. It was then considered appropriate to calculate risk for various sections of each route, defined as above, based on lithology, structural setting, and physiography. Although the debris flow data sets were much smaller than the rock fall data sets, debris flow magnitude-cumulative frequency relationships could be roughly defined for events over 1000 m3, for certain sections of Highway 99, Highway 1, and BCR. The slopes of all curves are between -0.6 and -0.8. Conditions positively influencing debris flow frequency include: steep, narrow gullies or streams; depositional fans near the route; instability at the headwaters; and heavy rain. Risk to life due to slope failure was calculated by multiplying the probability of failure by the probability of at least one fatality resulting from the possible failure. Rock fall probability was calculated from the rock fall magnitude-cumulative frequency curves for each zone, by subtracting the cumulative frequencies for each of a series of successive volume classes. Debris flow probabilities were calculated similarly, using the debris flow magnitude-cumulative frequency plots for events greater than 1000 m3 in volume. The probability of death was calculated as the product of the longitudinal encounter probability, the temporal encounter probability, the lateral encounter probability, and the probability of death given impact. These parameters were estimated based on average traffic volumes and speeds, and an assumption of continuous traffic flow. Estimates of damage corridor widths, necessary to calculate the longitudinal encounter probability, were made 218 based on the available information in the slope failure database. The probability of death given impact was the most arbitrary parameter, but was selected where possible based on past events, and previous research. Because of insufficient data in some areas along the two highways, rock fall risk estimates could only be calculated for Highway 99, Zone 1 and Highway 1, Zones 1 and 2. The calculated annual risk of fatality due to rock falls and slides on Highway 99, Zone 1, was 0.10, indicating a return period, R, of 9.9 years. For Highway 1, Zone 1, the calculated annual risk was 0.028 (R = 35.7 years), and for Highway 1, Zone 2, the calculated annual risk was 0.067 (R = 15.0 years). These values represent approximate estimates of annual risk to life on the respective highway sections, and are not intended as exact risk values. It should also be noted that the risk analysis does not take into account any recent improvements to highway slopes, which may have led to a reduction in risk. For example, the frequency of rock falls on Highway 99, Zone 1, appeared to decrease in the most recent years of the data set. Based on the fatality and injury statistics available in the database, these rock fall risk estimates are reasonable. They are somewhat conservative, which is likely due to the fact that risk due to fallen rock on the highways was not considered in the risk analysis. Estimated annual specific risks to highway users are well below proposed acceptability limits. The greatest proportion of risk on Highway 99, from Horseshoe Bay to Squamish, and on Highway 1, from Vancouver to Hope, is posed by rock falls with magnitudes from 100 to 1000 m3. Smaller failures, with volumes from 1 to 10 m3, are the greatest contributors to risk on Highway 1, from Hope to Lytton. Annual risk to life due to debris flows on Highway 99, km 0 to 75, was estimated at 0.0034 (R = 296 years). On Highway 1, km 125 to 150, the estimated annual risk was 0.012 (R = 87 years). The non-conservatism of these values can be attributed to the fact that risk to life due to bridges being washed out by debris flows was not considered in the risk analysis. Further study of 219 bridge characteristics, and probability of bridge failure given impact by a debris flow, would help to establish more complete debris flow risk estimates. The greatest proportion of risk on both Highway 99 and Highway 1 is posed by debris flows at the lower end of the magnitude scale, with volumes from 1000 to 10000 m3. Annual risk to life due to rock falls on BCR were calculated similarly to rock fall risks on the two highways. It was assumed that failures under 0.01 m3 posed no risk to life. Probability of death given impact was again very difficult to estimate, particularly because the large number of passengers had to be considered. The estimated risks to life due to rock falls on the BCR Zones with adequate data sets were: 0.008 for Zone 1 (R = 120 years); 0.01 for Zone 2 (R = 97 years); and 0.05 for Zone 4 (R = 20 years). The corresponding specific annual risks to railway users are all below the upper limits of most proposed acceptability criteria. Again, risks due to fallen rock on the railway were not considered in the risk analysis. The greatest proportion of rock fall risk on all BCR zones is posed by failures with volumes from 100 to 1000 m3. Risks of major freight train accidents due to rock falls on BCR and CPR were calculated by estimating the probability of a major accident, given impact, instead of the probability of death, given impact. These estimates in particular are only rough estimates, which should be viewed as examples of the risk analysis procedure, not absolute values of risk. On BCR, the estimated annual risks of major freight train accidents caused by rock falls are: 0.006 for Zone 1 (R = 160 years); 0.011 for Zone 2 (R = 91 years); and 0.044 for Zone 4 (R = 23 years). These values are non-conservative compared to historical values, likely due to uncertainty in the probability of an accident, given impact, and the fact that risks due to fallen rock on the railway were not considered. On CPR, the estimated annual risks of major freight train accidents caused by rock falls are: 0.010 for Zone 1 (R = 100 years); 0.028 for Zone 2 (R = 36 years); 0.053 for Zone 3 (R = 19 220 years); and 0.0076 for Zone 4 (R = 131 years). Because some traffic statistics were unavailable from CPR, these values represent only rough estimates of rock fall risk. However, the risk analysis is useful in indicating the relative risks for different sections of the railway. According to these risk estimates, the areas at highest risk from rock falls are in the Fraser and Thompson Canyons, from Hope to Thompson. The greatest proportion of rock fall risk on CPR Zones 1, 2, and 3, are posed by small failures, with magnitudes from 1.0 to 10 m3. In Zone 4, rock falls with volumes from 1 to 100 m3 are the greatest contributors to risk. The annual risk of death due to debris flows on BCR was estimated at 0.083 (R = 12 years). This risk value may be high, due to difficulty in estimating the probability of death, given impact. The estimated annual risk of freight train accidents caused by debris flows was 0.008 (R = 123 years). The greatest proportion of risk is posed by small debris flows, with volumes from 1000 to 10000 m3. 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