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Landslide runout: statistical analysis of physical characteristics and model parameters McKinnon, Mika 2010

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Landslide Runout Statistical Analysis of Physical Characteristics and Model Parameters by Mika McKinnon B.A. Physics, University of California at Santa Barbara, 2005 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in THE FACULTY OF GRADUATE STUDIES (Geophysics) The University Of British Columbia (Vancouver) June 2010 c￿Mika McKinnon, 2010 Abstract Landslides are treacherous, but risk management actions based on improved prediction of landslide runout can reduce casualties and damage. Forty rapid flow-like landslides of vari- able volume, entrainment, and composition are used to develop a volume-runout regression, which is compared to those established in previous research. The cases are analyzed to iden- tify the most critical characteristics observable prior to failure which differentiate between events of high and low mobility. Mitigating long-runout flow-like landslides requires accurate hazard mapping, a task best accomplished through runout modelling. Current practice requires back-analyzing a set of cases consistent in scope with the target event, then applying the same rheology and parameters to forward modelling. This thesis determines which aspects of scope are most important to prioritize when selecting similar cases, as volume, movement type, mor- phology, and material have a more substantial influence on mobility than other physical characteristics. Statistical analysis of the performance of frictional and Voellmy rheologies over a range of parameters for the forty case studies provides the expected mean normalized runout and associated standard deviation, and recommendations for parameters to use in initial forward modelling of prospective events. ii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Landslides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Definition of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Anatomy of a Landslide . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Quantifying Mobility . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Mechanisms of Flow . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Excessive Runout of Catastrophic Landslides . . . . . . . . . . . . . . . 7 2.2.1 Internal Friction . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Basal Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.4 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Summary of Landslides . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Data: Landslide Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 iii 3.1.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.2 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.4 Other Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Categorization of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.1 Landslide Classification . . . . . . . . . . . . . . . . . . . . . . 14 3.2.2 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.3 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.4 Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.5 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Error in Recorded Observations . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 Reliability of Reported Runout Characteristics . . . . . . . . . . 18 3.3.2 Incomplete Observations . . . . . . . . . . . . . . . . . . . . . . 19 3.4 Summary of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4 Models for Landslide Hazard Prediction . . . . . . . . . . . . . . . . . . . . 26 4.1 Predicting Landslide Runout . . . . . . . . . . . . . . . . . . . . . . . . 27 4.1.1 Laboratory Models . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Mathematical Model Classification . . . . . . . . . . . . . . . . . . . . . 28 4.2.1 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2.2 Dynamic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4 Summary of Runout Models . . . . . . . . . . . . . . . . . . . . . . . . 35 5 Analysis of Real Landslide Behaviour . . . . . . . . . . . . . . . . . . . . . 36 5.1 Comparison to Previous Work . . . . . . . . . . . . . . . . . . . . . . . 36 5.1.1 Comparison of Scope . . . . . . . . . . . . . . . . . . . . . . . . 37 5.1.2 Relative Statistical Power . . . . . . . . . . . . . . . . . . . . . 38 5.1.3 Comparison of Sample Populations . . . . . . . . . . . . . . . . 38 5.2 Pre-failure Characteristics and Runout Behaviour . . . . . . . . . . . . . 41 5.2.1 Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.2.2 Evaluation of Imposed Categories . . . . . . . . . . . . . . . . . 42 5.2.3 Evaluation of Emergent Categories . . . . . . . . . . . . . . . . 44 5.2.4 Influence of Categories on Runout . . . . . . . . . . . . . . . . . 45 5.3 Summary of Analysis of the Set of Landslides . . . . . . . . . . . . . . . 49 iv 6 Tools: Selecting Runout Models . . . . . . . . . . . . . . . . . . . . . . . . 51 6.1 Proposed Models: DAN-W and DAN3D . . . . . . . . . . . . . . . . . . 52 6.2 Hypothetical Fluids and Rheologies . . . . . . . . . . . . . . . . . . . . 53 6.2.1 Frictional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2.2 Voellmy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.3 Summary of Tool Selection . . . . . . . . . . . . . . . . . . . . . . . . . 55 7 Method of Standardized Back Analysis . . . . . . . . . . . . . . . . . . . . 56 7.1 Method for Back Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 57 7.1.1 Step 1: Describe a Case History . . . . . . . . . . . . . . . . . . 58 7.1.2 Step 2: Build a Model . . . . . . . . . . . . . . . . . . . . . . . 59 7.1.3 Step 3: Run the Model . . . . . . . . . . . . . . . . . . . . . . . 59 7.1.4 Step 4: Select Best Parameters . . . . . . . . . . . . . . . . . . . 60 7.2 Example of Application of Back Analysis to 1969 Madison Canyon, U.S.A 61 7.2.1 Describe the Case History . . . . . . . . . . . . . . . . . . . . . 61 7.2.2 Build a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 7.2.3 Run the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.2.4 Select Best Parameters . . . . . . . . . . . . . . . . . . . . . . . 64 7.3 Summary of Back Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 64 8 Analysis of Model Back Analyses and Parameter Selection . . . . . . . . . 66 8.1 Defining “Best” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 8.1.1 Qualitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 8.1.2 Quantitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.2 Evaluating the Performance of Rheologies and Parameters . . . . . . . . 68 8.2.1 User-Selected versus Mathematically-Selected Parameters . . . . 68 8.2.2 Minimizing Normalized Runout and Maximizing Consistency . . 69 8.2.3 Counting Cases within Cutoff Criteria . . . . . . . . . . . . . . . 71 8.2.4 Evaluation within Categories . . . . . . . . . . . . . . . . . . . . 72 8.3 Summary of Parameter Performance . . . . . . . . . . . . . . . . . . . . 77 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9.2 Recommendations to Practitioners . . . . . . . . . . . . . . . . . . . . . 80 9.2.1 Forward Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 80 9.2.2 Cautions and Limitations . . . . . . . . . . . . . . . . . . . . . . 81 v 9.3 Implications to the Field . . . . . . . . . . . . . . . . . . . . . . . . . . 82 9.4 Directions for Future Research . . . . . . . . . . . . . . . . . . . . . . . 83 9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A Deformable Mass Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.1 Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.2 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.3 Internal Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.3.1 Continuum Models . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.3.2 Discontinuum Models . . . . . . . . . . . . . . . . . . . . . . . 101 A.3.3 Hybrid Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.4 Eulerian and Lagrangian Coordinate Systems . . . . . . . . . . . . . . . 101 A.5 Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.5.1 Geometric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.5.2 Mathematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.6 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 B Recommendations for Model Verification and Cross-Validation . . . . . . . 104 B.1 Randomization of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.2 Training Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.3 Correlating Observable Characteristics to Parameter Selection . . . . . . 105 B.4 Verification Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.5 Calculating Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 C Details on DAN Software Programs . . . . . . . . . . . . . . . . . . . . . . 107 C.1 Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 C.2 Momentum Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 C.2.1 Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 C.2.2 Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 108 C.3 Earth Pressure Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 108 C.4 Additional DAN-W Details . . . . . . . . . . . . . . . . . . . . . . . . . 109 C.5 Additional DAN3D Details . . . . . . . . . . . . . . . . . . . . . . . . . 111 C.6 Mathematical Manipulation of DAN-W Output Data . . . . . . . . . . . 111 vi D Sensitivity of the Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . 112 D.1 Impact of Relic Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 D.2 Impact of Tozawagawa . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 E Descriptions of Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 117 E.1 1988 Abbot’s Cliff, England . . . . . . . . . . . . . . . . . . . . . . . . 118 E.2 1806 Arth-Goldau, Schwyz, Switzerland . . . . . . . . . . . . . . . . . . 119 E.3 1922 Arvel, Vaud, Switzerland . . . . . . . . . . . . . . . . . . . . . . . 120 E.4 1933 Brazeau Lake, Alberta, Canada . . . . . . . . . . . . . . . . . . . . 121 E.5 1987 Charmonétier, Isère, France . . . . . . . . . . . . . . . . . . . . . . 122 E.6 1442 Claps de Luc, Drôme, France . . . . . . . . . . . . . . . . . . . . . 123 E.7 1999 Eagle Pass, British Columbia, Canada . . . . . . . . . . . . . . . . 124 E.8 1881 Elm, Sernaf Valley, Glarus, Switzerland . . . . . . . . . . . . . . . 126 E.9 1903 Frank Slide, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . 128 E.10 1915 Great Fall, England . . . . . . . . . . . . . . . . . . . . . . . . . . 129 E.11 1998 Hiegaesi, Fukushima Prefecture, Japan . . . . . . . . . . . . . . . . 130 E.12 1965 Hope Slide, British Columbia, Canada . . . . . . . . . . . . . . . . 131 E.13 Jonas Creek, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . . . . 133 E.14 2005 Kuzulu, Sivas Province, Turkey . . . . . . . . . . . . . . . . . . . . 134 E.15 La Madeleine, Savoie, France . . . . . . . . . . . . . . . . . . . . . . . . 135 E.16 2001 Las Colinas, Santa Tecla, El Salvador . . . . . . . . . . . . . . . . 136 E.17 2006 Luzon (Guinsaugon) Slide, Philippines . . . . . . . . . . . . . . . . 137 E.18 1969 Madison Canyon, Montana, United States . . . . . . . . . . . . . . 139 E.19 2002 McAuley Creek, British Columbia, Canada . . . . . . . . . . . . . 141 E.20 1984 Mount Cayley, British Columbia, Canada . . . . . . . . . . . . . . 142 E.21 1991 Mount Cook, New Zealand . . . . . . . . . . . . . . . . . . . . . . 143 E.22 1248 Mount Granier, Savoie, France . . . . . . . . . . . . . . . . . . . . 144 E.23 1984 Mount Ontake, Japan . . . . . . . . . . . . . . . . . . . . . . . . . 145 E.24 2007 Mount Steele, Yukon, Canada . . . . . . . . . . . . . . . . . . . . 146 E.25 Mystery Creek, British Columbia, Canada . . . . . . . . . . . . . . . . . 148 E.26 1999 Nomash River, British Columbia, Canada . . . . . . . . . . . . . . 149 E.27 1959 Pandemonium Creek, British Columbia, Canada . . . . . . . . . . . 151 E.28 2002 Pink Mountain, British Columbia, Canada . . . . . . . . . . . . . . 152 E.29 Queen Elizabeth, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . 154 E.30 Rockslide Pass, Northwest Territories, Canada . . . . . . . . . . . . . . . 155 vii E.31 1855 Rubble Creek, British Columbia, Canada . . . . . . . . . . . . . . . 156 E.32 1982 Sale Mountain, China . . . . . . . . . . . . . . . . . . . . . . . . . 157 E.33 1850 Seaford, England . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 E.34 1964 Sherman Glacier, Alaska, United States . . . . . . . . . . . . . . . 159 E.35 1946 Six de Eaux Froids, Switzerland . . . . . . . . . . . . . . . . . . . 160 E.36 Slide Mountain, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . . 161 E.37 2000 Tozawagawa, Niigata Prefecture, Japan . . . . . . . . . . . . . . . 162 E.38 1717 Triolet Glacier, Italy . . . . . . . . . . . . . . . . . . . . . . . . . . 163 E.39 2002 Zymoetz River, British Columbia, Canada . . . . . . . . . . . . . . 164 F Model Data: Mathematically-Selected Parameters . . . . . . . . . . . . . . 166 F.1 1988 Abbot’s Cliff, England . . . . . . . . . . . . . . . . . . . . . . . . 167 F.2 1806 Arth-Goldau, Schwyz, Switzerland . . . . . . . . . . . . . . . . . . 169 F.3 1922 Arvel, Vaud, Switzerland . . . . . . . . . . . . . . . . . . . . . . . 171 F.4 1933 Brazeau Lake, Alberta, Canada . . . . . . . . . . . . . . . . . . . . 173 F.5 1987 Charmonétier, Isère, France . . . . . . . . . . . . . . . . . . . . . . 175 F.6 1442 Claps de Luc, Drôme, France . . . . . . . . . . . . . . . . . . . . . 177 F.7 1999 Eagle Pass, British Columbia, Canada . . . . . . . . . . . . . . . . 179 F.8 1881 Elm, Sernaf Valley, Glarus, Switzerland . . . . . . . . . . . . . . . 181 F.9 1903 Frank Slide, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . 183 F.10 1915 Great Fall, England . . . . . . . . . . . . . . . . . . . . . . . . . . 185 F.11 1998 Hiegaesi, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 F.12 1965 Hope Slide, British Columbia, Canada . . . . . . . . . . . . . . . . 189 F.13 Jonas Creek (north), Alberta, Canada . . . . . . . . . . . . . . . . . . . . 191 F.14 Jonas Creek (south), Alberta, Canada . . . . . . . . . . . . . . . . . . . . 193 F.15 2005 Kuzulu, Turkey . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 F.16 La Madeleine, Savoie, France . . . . . . . . . . . . . . . . . . . . . . . . 197 F.17 2001 Las Colinas, Santa Tecla, El Salvador . . . . . . . . . . . . . . . . 199 F.18 2006 Luzon Slide, Philippines . . . . . . . . . . . . . . . . . . . . . . . 201 F.19 1969 Madison Canyon, Montana, United States . . . . . . . . . . . . . . 203 F.20 2002 McAuley Creek, British Columbia, Canada . . . . . . . . . . . . . 205 F.21 1984 Mount Cayley, British Columbia, Canada . . . . . . . . . . . . . . 207 F.22 1991 Mount Cook, New Zealand . . . . . . . . . . . . . . . . . . . . . . 209 F.23 1248 Mount Granier, Savoie, France . . . . . . . . . . . . . . . . . . . . 211 F.24 1984 Mount Ontake, Japan . . . . . . . . . . . . . . . . . . . . . . . . . 213 viii F.25 2007 Mount Steele, Yukon, Canada . . . . . . . . . . . . . . . . . . . . 215 F.26 Mystery Creek, British Columbia, Canada . . . . . . . . . . . . . . . . . 217 F.27 1999 Nomash River, British Columbia, Canada . . . . . . . . . . . . . . 219 F.28 1959 Pandemonium Creek, B.C., Canada . . . . . . . . . . . . . . . . . 221 F.29 2002 Pink Mountain, British Columbia, Canada . . . . . . . . . . . . . . 223 F.30 Queen Elizabeth, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . 225 F.31 Rockslide Pass, Northwest Territories, Canada . . . . . . . . . . . . . . . 227 F.32 1855 Rubble Creek, British Columbia, Canada . . . . . . . . . . . . . . . 229 F.33 1982 Sale Mountain, China . . . . . . . . . . . . . . . . . . . . . . . . . 231 F.34 1850 Seaford, England . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 F.35 1964 Sherman Glacier, Alaska, United States . . . . . . . . . . . . . . . 235 F.36 1946 Six de Eaux Froids (east lobe), Switzerland . . . . . . . . . . . . . 237 F.37 1946 Six de Eaux Froids (west lobe), Switzerland . . . . . . . . . . . . . 239 F.38 Slide Mountain, Alberta, Canada . . . . . . . . . . . . . . . . . . . . . . 241 F.39 2000 Tozawagawa, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . 243 F.40 1717 Triolet Glacier, Italy . . . . . . . . . . . . . . . . . . . . . . . . . . 245 F.41 2002 Zymoetz River, British Columbia, Canada . . . . . . . . . . . . . . 247 G Model Data: User-Selected Parameters . . . . . . . . . . . . . . . . . . . . 249 G.1 1988 Abbot’s Cliff, England . . . . . . . . . . . . . . . . . . . . . . . . 250 G.2 1806 Arth-Goldau, Schwyz, Switzerland . . . . . . . . . . . . . . . . . . 251 G.3 1933 Brazeau Lake, Alberta, Canada . . . . . . . . . . . . . . . . . . . . 252 G.4 1999 Eagle Pass, British Columbia, Canada . . . . . . . . . . . . . . . . 253 G.5 1881 Elm, Sernaf Valley, Glarus, Switzerland . . . . . . . . . . . . . . . 254 G.6 1915 Great Fall, England . . . . . . . . . . . . . . . . . . . . . . . . . . 255 G.7 1965 Hope Slide, British Columbia, Canada . . . . . . . . . . . . . . . . 257 G.8 2001 Las Colinas, Santa Tecla, El Salvador . . . . . . . . . . . . . . . . 258 G.9 1969 Madison Canyon, Montana, United States . . . . . . . . . . . . . . 260 G.10 1984 Mount Cayley, British Columbia, Canada . . . . . . . . . . . . . . 261 G.11 1991 Mount Cook, New Zealand . . . . . . . . . . . . . . . . . . . . . . 263 G.12 1248 Mount Granier, Savoie, France . . . . . . . . . . . . . . . . . . . . 264 G.13 1999 Nomash River, British Columbia, Canada . . . . . . . . . . . . . . 265 G.14 1959 Pandemonium Creek, B.C., Canada . . . . . . . . . . . . . . . . . 266 G.15 Rockslide Pass, Northwest Territories, Canada . . . . . . . . . . . . . . . 267 G.16 1855 Rubble Creek, British Columbia, Canada . . . . . . . . . . . . . . . 268 ix G.17 1982 Sale Mountain, China . . . . . . . . . . . . . . . . . . . . . . . . . 269 G.18 1850 Seaford, England . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 G.19 1964 Sherman Glacier, Alaska, United States . . . . . . . . . . . . . . . 271 G.20 1946 Six de Eaux Froids, Switzerland . . . . . . . . . . . . . . . . . . . 272 G.21 2000 Tozawagawa, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . 273 G.22 1717 Triolet Glacier, Italy . . . . . . . . . . . . . . . . . . . . . . . . . . 274 G.23 2002 Zymoetz River, British Columbia, Canada . . . . . . . . . . . . . . 275 H Normalized Runout of Modelled Mobility . . . . . . . . . . . . . . . . . . . 276 H.1 All Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 H.1.1 Mean Normalized Runout and Standard Deviation . . . . . . . . 278 H.1.2 Well- and Excellently-Modelled Events . . . . . . . . . . . . . . 281 H.1.3 Over- and Under-Estimation of Runout . . . . . . . . . . . . . . 284 H.2 Categorized by Magnitude Volume . . . . . . . . . . . . . . . . . . . . . 287 H.2.1 Mean Normalized Runout and Standard Deviation . . . . . . . . 287 H.2.2 Well- and Excellently-Modelled Events . . . . . . . . . . . . . . 290 H.2.3 Over- and Under-Estimation of Runout . . . . . . . . . . . . . . 293 H.3 Categorized by Movement Type . . . . . . . . . . . . . . . . . . . . . . 296 H.3.1 Mean Normalized Runout and Standard Deviation . . . . . . . . 296 H.3.2 Well- and Excellently-Modelled Events . . . . . . . . . . . . . . 299 H.3.3 Over- and Under-Estimation of Runout . . . . . . . . . . . . . . 302 H.4 Categorized by Morphology . . . . . . . . . . . . . . . . . . . . . . . . 305 H.4.1 Mean Normalized Runout and Standard Deviation . . . . . . . . 305 H.4.2 Well- and Excellently-Modelled Events . . . . . . . . . . . . . . 308 H.4.3 Over- and Under-Estimation of Runout . . . . . . . . . . . . . . 311 H.5 Categorized by Material . . . . . . . . . . . . . . . . . . . . . . . . . . 314 H.5.1 Source Material . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 H.5.2 Path Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 H.6 Histograms of Parameter Performance . . . . . . . . . . . . . . . . . . . 332 H.6.1 Performance of All Models . . . . . . . . . . . . . . . . . . . . . 332 H.6.2 Performance of Frictional Rheology by Parameter . . . . . . . . 333 H.6.3 Performance of Voellmy Rheology by Parameter . . . . . . . . . 343 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 x List of Tables 2.1 Theories to explain the excessive mobility of large landslides. . . . . . . . 8 3.1 Selection criteria for cases. . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Categories identified from the literature which may impact mobility, and classification options within the category identified from my case studies. See Table 3.4 for the number of cases with each characteristic. . . . . . . 16 3.3 Processes which produce debris. . . . . . . . . . . . . . . . . . . . . . . 17 3.4 Number of cases with specified characteristic and runout observation. . . 21 3.5 Landslide characteristics observable prior to failure for case studies A-L. See Table 3.6 for M-Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6 Landslide characteristics observable prior to failure for case studies M-Z. See Table 3.5 for A-L. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.7 Mobility characteristics for case studies A-R. See Table 3.8 for S-Z. . . . 24 3.8 Mobility characteristics for case studies S-Z. See Table 3.7 for A-R. . . . 25 5.1 Scope of events in the analyzed datasets. Movement types are classified by the Hungr et al. 2001 system. . . . . . . . . . . . . . . . . . . . . . . 37 5.2 Number of events overall and in morphology subsets. . . . . . . . . . . . 38 5.3 V -α relationships determined by linear regressions. See Equation 4.1 for form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.4 P-values from t-testing the regression coefficient and intercept of my linear regressions versus those determined by previous research. Regressions on subsets are compared to matching subsets. . . . . . . . . . . . . . . . . . 41 5.5 P-values of ANOVA between characteristics and mobility controlled for volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 xi 5.6 Base average and influencing factor for a characteristic (independent vari- able) and mobility index (dependent variable), controlled for volume. See Equation 5.1 for form, and Table 3.4 for the number of cases represented with each characteristic. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.1 Default DAN-W parameter values used in back analyses. . . . . . . . . . 59 7.2 User-selected parameters for Madison Canyon. This table is also located in Table G.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 8.1 Interpretation of normalized runout for mobility indices. An event is over- predicted by at least double the observed runout distance when ∆L≥+100. 68 8.2 Mean normalized runout (∆), and standard deviation (σ ) of that mean for the specified mobility indices (with ∆L≤ 100%). . . . . . . . . . . . . . 70 8.3 Percentage of cases with absolute mean normalized runout that are excellently- modelled (|∆| ≤ 5%) or well-modelled (|∆| ≤ 30%) for the specified mo- bility indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.4 Low f paired with high ξ over-predict mobility (green), mid-range param- eters predict runout well (x), and high f paired with low ξ under-predict runout (red). Model mobility decreases from top to bottom ( f = 0.05 = most mobile), and velocity increases from left to right (ξ = 2000m3s = fastest). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.5 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of the specified mobility indices (with ∆L≤ 100%). . . . . . . . . . . . . . . . . . . . . . . . . . 73 8.6 Recommended rheologies and parameters overall, and within categories of landslides. Recommendations for debris avalanches are excluded as morphology dominants behaviour. . . . . . . . . . . . . . . . . . . . . . 78 D.1 V -α relationships determined by linear regressions on all my case studies, excluding Tozawagawa, or events since 1900 only. See Equation 4.1 for form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 D.2 P-values from t-testing the regression coefficient and intercept of my mod- ified linear regressions either excluding Tozawagawa, or excluding events prior to 1900, versus those determined by previous research. Compare to Table 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 xii F.1 Mathematically-selected parameters for Abbot’s Cliff. For case descrip- tion, see Section E.1. For back analyses with user-selected parameters, see Table G.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 F.2 Mathematically-selected parameters for Arth-Goldau. For case descrip- tion, see Section E.2. For back analyses with user-selected parameters, see Table G.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 F.3 Mathematically-selected parameters for Arvel. For case description, see Section E.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 F.4 Mathematically-selected parameters for Brazeau Lake. For case descrip- tion, see Section E.4. For back analyses with user-selected parameters, see Table G.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 F.5 Mathematically-selected parameters for Charmon’etier. For case descrip- tion, see Section E.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 F.6 Mathematically-selected parameters for Claps de Luc. For case descrip- tion, see Section E.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 F.7 Mathematically-selected parameters for Eagle Pass. For case description, see Section E.7. For back analyses with user-selected parameters, see Ta- ble G.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 F.8 Mathematically-selected parameters for Elm. For case description, see Section E.8. For back analyses with user-selected parameters, see Ta- ble G.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 F.9 Mathematically-selected parameters for Frank Slide. For case description, see Section E.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 F.10 Mathematically-selected parameters for Great Fall. For case description, see Section E.10. For back analyses with user-selected parameters, see Section G.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 F.11 Mathematically-selected parameters for Hiegaesi. For case description, see Section E.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 F.12 Mathematically-selected parameters for Hope Slide. For case description, see Section E.12. For back analyses with user-selected parameters, see Table G.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 F.13 Mathematically-selected parameters for Jonas Creek (north). For case de- scription, see Section E.13. . . . . . . . . . . . . . . . . . . . . . . . . . 191 F.14 Mathematically-selected parameters for Jonas Creek (south). For case de- scription, see Section E.13. . . . . . . . . . . . . . . . . . . . . . . . . . 193 xiii F.15 Mathematically-selected parameters for Kuzulu. For case description, see Section E.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 F.16 Mathematically-selected parameters for La Madeleine. For case descrip- tion, see Section E.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 F.17 Mathematically-selected parameters for Las Colinas. For case description, see Section E.16. For back analyses with user-selected parameters, see Section G.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 F.18 Mathematically-selected parameters for Luzon Slide. For case description, see Section E.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 F.19 Mathematically-selected parameters for Madison Canyon. For case de- scription, see Section E.18. For back analyses with user-selected parame- ters, see Table G.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 F.20 Mathematically-selected parameters for McAuley Creek. For case de- scription, see Section E.19. . . . . . . . . . . . . . . . . . . . . . . . . . 205 F.21 Mathematically-selected parameters for Mount Cayley. For case descrip- tion, see Section E.20. For back analyses with user-selected parameters, see Section G.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 F.22 Mathematically-selected parameters for Mount Cook. For case descrip- tion, see Section E.21. For back analyses with user-selected parameters, see Table G.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 F.23 Mathematically-selected parameters for Mount Granier. For case descrip- tion, see Section E.22. For back analyses with user-selected parameters, see Table G.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 F.24 Mathematically-selected parameters for Mount Ontake. For case descrip- tion, see Section E.23. . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 F.25 Mathematically-selected parameters for Mount Steele. For case descrip- tion, see Section E.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 F.26 Mathematically-selected parameters for Mystery Creek. For case descrip- tion, see Section E.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 F.27 Mathematically-selected parameters for Nomash River. For case descrip- tion, see Section E.26. For back analyses with user-selected parameters, see Table G.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 F.28 Mathematically-selected parameters for Pandemonium Creek. For case description, see Section E.27. For back analyses with user-selected pa- rameters, see Table G.17. . . . . . . . . . . . . . . . . . . . . . . . . . . 221 xiv F.29 Mathematically-selected parameters for Pink Mountain. For case descrip- tion, see Section E.28. . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 F.30 Mathematically-selected parameters for Queen Elizabeth. For case de- scription, see Section E.29. . . . . . . . . . . . . . . . . . . . . . . . . . 225 F.31 Mathematically-selected parameters for Rockslide Pass. For case descrip- tion, see Section E.30. For back analyses with user-selected parameters, see Table G.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 F.32 Mathematically-selected parameters for Rubble Creek. For case descrip- tion, see Section E.31. For back analyses with user-selected parameters, see Table G.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 F.33 Mathematically-selected parameters for Sale Mountain. For case descrip- tion, see Section E.32. For back analyses with user-selected parameters, see Table G.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 F.34 Mathematically-selected parameters for Seaford. For case description, see Section E.33. For back analyses with user-selected parameters, see Ta- ble G.21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 F.35 Mathematically-selected parameters for Sherman Glacier. For case de- scription, see Section E.34. For back analyses with user-selected parame- ters, see Table G.22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 F.36 Mathematically-selected parameters for Six de Eaux Froids (east lobe). For case description, see Section E.35. For back analyses with user-selected parameters, see Section G.20. . . . . . . . . . . . . . . . . . . . . . . . . 237 F.37 Mathematically-selected parameters for Six de Eaux Froids (west lobe). For case description, see Section E.35. For back analyses with user-selected parameters, see Section G.20. . . . . . . . . . . . . . . . . . . . . . . . . 239 F.38 Mathematically-selected parameters for Slide Mountain. For case descrip- tion, see Section E.36. . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 F.39 Mathematically-selected parameters for Tozawagawa. For case descrip- tion, see Section E.37. For back analyses with user-selected parameters, see Table G.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 F.40 Mathematically-selected parameters for Triolet Glacier. For case descrip- tion, see Section E.38. For back analyses with user-selected parameters, see Table G.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 xv F.41 Mathematically-selected parameters for Zymoetz River. For case descrip- tion, see Section E.39. For back analyses with user-selected parameters, see Table G.26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 G.1 User-selected parameters for Abbot’s Cliff. For case description, see Sec- tion E.1. For back analyses with with mathematically-selected parameters, see Table F.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 G.2 User-selected parameters for Arth-Goldau. For case description, see Sec- tion E.2. For back analyses with with mathematically-selected parameters, see Table F.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 G.3 User-selected parameters for Brazeau Lake. For case description, see Sec- tion E.4. For back analyses with with mathematically-selected parameters, see Table F.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 G.4 User-selected parameters for Eagle Pass. For case description, see Sec- tion E.7. For back analyses with with mathematically-selected parameters, see Table F.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 G.5 User-selected parameters for Elm. For case description, see Section E.8. For back analyses with with mathematically-selected parameters, see Ta- ble F.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 G.6 User-selected parameters for Great Fall with frictional rheology, and with Voellmy rheology for f ≤ 0.17. For f ≥ 0.18, see Table G.7. . . . . . . . 255 G.7 User-selected parameters for Great Fall with Voellmy rheology for f ≥ 0.18. For f ≤ 0.17, see Table G.6. For case description, see Section E.10. For back analyses with with mathematically-selected parameters, see Ta- ble F.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 G.8 User-selected parameters for Hope Slide. For case description, see Sec- tion E.12. For back analyses with with mathematically-selected parame- ters, see Table F.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 G.9 User-selected parameters for Las Colinas without entrainment. For mod- elling with entrainment, see Table G.10. . . . . . . . . . . . . . . . . . . 258 G.10 User-selected parameters for Las Colinas with entrainment. For modelling without entrainment, see Table G.9. For case description, see Section E.16. For back analyses with with mathematically-selected parameters, see Ta- ble F.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 xvi G.11 User-selected parameters for Madison Canyon. For case description, see Section E.18. For back analyses with with mathematically-selected pa- rameters, see Table F.19. . . . . . . . . . . . . . . . . . . . . . . . . . . 260 G.12 User-selected parameters Mount Cayley without entrainment. For case de- scription, see Section E.20. For back analyses with with mathematically- selected parameters, see Table F.21. . . . . . . . . . . . . . . . . . . . . 261 G.13 User-selected parameters for Mount Cayley with entrainment to the spec- ified volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 G.14 User-selected parameters for Mount Cook. For modelling with entrain- ment, the event was split into two streamlines: the main path, and the tributary which ran out over Anzec Peak. For case description, see Sec- tion E.21. For back analyses with with mathematically-selected parame- ters, see Table F.22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 G.15 User-selected parameters for Mount Granier. For case description, see Section E.22. For back analyses with with mathematically-selected pa- rameters, see Table F.23. . . . . . . . . . . . . . . . . . . . . . . . . . . 264 G.16 User-selected parameters for Nomash River. For case description, see Sec- tion E.26. For back analyses with with mathematically-selected parame- ters, see Table F.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 G.17 User-selected parameters for Pandemonium Creek. For case description, see Section E.27. For back analyses with with mathematically-selected parameters, see Table F.28. . . . . . . . . . . . . . . . . . . . . . . . . . 266 G.18 User-selected parameters for Rockslide Pass. For case description, see Section E.30. For back analyses with with mathematically-selected pa- rameters, see Table F.31. . . . . . . . . . . . . . . . . . . . . . . . . . . 267 G.19 User-selected parameters for Rubble Creek. For case description, see Sec- tion E.31. For back analyses with with mathematically-selected parame- ters, see Table F.32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 G.20 User-selected parameters for Sale Mountain. For case description, see Section E.32. For back analyses with with mathematically-selected pa- rameters, see Table F.33. . . . . . . . . . . . . . . . . . . . . . . . . . . 269 G.21 User-selected parameters for Seaford. For case description, see Section E.33. For back analyses with with mathematically-selected parameters, see Ta- ble F.34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 xvii G.22 User-selected parameters for Sherman Glacier. For case description, see Section E.34. For back analyses with with mathematically-selected pa- rameters, see Table F.35. . . . . . . . . . . . . . . . . . . . . . . . . . . 271 G.23 User-selected parameters for Six de Eaux Froids. For back analyses with with mathematically-selected parameters, see Table F.36 (east lobe) and Table F.37 (west lobe). . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 G.24 User-selected parameters for Tozawagawa. For case description, see Sec- tion E.37. For back analyses with with mathematically-selected parame- ters, see Table F.39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 G.25 User-selected parameters for Triolet Glacier. For case description, see Sec- tion E.38. For back analyses with with mathematically-selected parame- ters, see Table F.40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 G.26 User-selected parameters for Zymoetz River. For case description, see Section E.39. For back analyses with with mathematically-selected pa- rameters, see Table F.41. . . . . . . . . . . . . . . . . . . . . . . . . . . 275 H.1 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%). . . . . . . . . . . . . . . . 278 H.2 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D. . . . . . . . . . . . . . . . . . . . . . . . . . 279 H.3 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α . . . . . . . . . . . . . . . . . . . . . . . . . . 280 H.4 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%). . . . . . . . . . . . . . . . . . . . . . . 281 H.5 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 H.6 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 H.7 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%). 284 H.8 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D. . . . . . . . . . . 285 H.9 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α . . . . . . . . . . . 286 xviii H.10 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%) by volume. . . . . . . . . . 287 H.11 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D by volume. . . . . . . . . . . . . . . . . . . . 288 H.12 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α by volume. . . . . . . . . . . . . . . . . . . . 289 H.13 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%) by volume. . . . . . . . . . . . . . . . . 290 H.14 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D by volume. . . . . . . . . . . . . . . . . . . . . . . . . . . 291 H.15 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α by volume. . . . . . . . . . . . . . . . . . . . . . . . . . . 292 H.16 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%) by volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 H.17 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D by volume. . . . . 294 H.18 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α by volume. . . . . 295 H.19 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%) by movement. . . . . . . . 296 H.20 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D by movement. . . . . . . . . . . . . . . . . . 297 H.21 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α by movement. . . . . . . . . . . . . . . . . . 298 H.22 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%) by movement. . . . . . . . . . . . . . . 299 H.23 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D by movement. . . . . . . . . . . . . . . . . . . . . . . . . 300 H.24 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α by movement. . . . . . . . . . . . . . . . . . . . . . . . . 301 H.25 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%) by movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 xix H.26 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D by movement. . . 303 H.27 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α by movement. . . 304 H.28 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%) by morphology. . . . . . . 305 H.29 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D by morphology. . . . . . . . . . . . . . . . . 306 H.30 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α by morphology. . . . . . . . . . . . . . . . . 307 H.31 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%) by morphology. . . . . . . . . . . . . . 308 H.32 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D by morphology. . . . . . . . . . . . . . . . . . . . . . . . 309 H.33 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α by morphology. . . . . . . . . . . . . . . . . . . . . . . . 310 H.34 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%) by morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 H.35 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D by morphology. . 312 H.36 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α by morphology. . 313 H.37 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%) by source material. . . . . 314 H.38 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D by source material. . . . . . . . . . . . . . . 315 H.39 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α by source material. . . . . . . . . . . . . . . . 316 H.40 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%) by source material. . . . . . . . . . . . . 317 H.41 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D by source material. . . . . . . . . . . . . . . . . . . . . . . 318 H.42 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α by source material. . . . . . . . . . . . . . . . . . . . . . . 319 xx H.43 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%) by source material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 H.44 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D by source material. 321 H.45 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α by source material. 322 H.46 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for L (with ∆L≤ 100%) by path material. . . . . . . 323 H.47 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for D by path material. . . . . . . . . . . . . . . . . 324 H.48 Mean deviation (∆) between model and observations, and standard devia- tion (σ ) of that mean for α by path material. . . . . . . . . . . . . . . . . 325 H.49 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for L (with ∆L≤ 100%) by path material. . . . . . . . . . . . . . 326 H.50 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for D by path material. . . . . . . . . . . . . . . . . . . . . . . . 327 H.51 Percentage of cases with absolute mean deviation (|∆|) within specified cut-offs for α by path material. . . . . . . . . . . . . . . . . . . . . . . . 328 H.52 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of L (with ∆L≤ 100%) by path material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 H.53 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of D by path material. . 330 H.54 Percentage of cases with under-estimation (∆<−10%), excellent estima- tion (∆< |10%|), or over-estimation (∆>+10%) of α by path material. . 331 xxi List of Figures 2.1 Common terminology for landslide anatomy: source, deposit, crown, toe, and path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Common terminology for runout mobility: fahrböschung angle (α), travel angle (θ ), idealized runout angle (32◦), vertical height maximum (H) and of the center of mass (Hcom), horizontal length maximum (L) and of the center of mass (Lcom), and excessive length travelled beyond that expected of a simple sliding block (Le). See Figure C.3 for curvilinear runout dis- tance (D). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1 Original path topography may be uncertain for relic events. . . . . . . . . 15 3.2 Fahrböshung angle is easy to measure but prone to rounding error, while pacing off curvilinear distance is straightforward but tiring. . . . . . . . . 19 4.1 A point mass model of a gravity-driven block sliding down a plane inclined at slope angle β with a resisting frictional force. . . . . . . . . . . . . . . 33 5.1 My data and linear regression overlaid with regressions on separate data by Scheidegger and Corominas. See Figure 2 in Scheidegger (1973) and Figure 6 in Corominas (1996) for the respective author’s data. . . . . . . 39 5.2 Effectiveness of emergent grouping of landslides using cluster analysis to minimize differences in α . Results are similar for cluster analysis on other mobility indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.1 Real landslide materials are complicated, so are modelled as simple hypo- thetical fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 xxii 7.1 Back analysis is performed by varying input parameters until modelled runout is consistent with the observed real runout. Not all possibilities are sketched: runout distance and spreading vary independently, such that a model may produce a deposit that is both too short and too thin, too far and too thick, or any other inappropriate debris distribution and runout. . 58 7.2 Madison Canyon profile. This profile is also located in Section E.18. . . . 62 7.3 Raw output data for models ofMadison Canyon, with observations marked by a dashed line. For Voellmy rheologies, the friction angle calculated by θ = arctan( f ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). This figure is also located in Figure F.19. . . . . . . . . . . . . . 65 8.1 Histogram of the performance of frictional rheology with θb= 17◦ as mea- sured by the specified normalized index, across all case studies. See Sec- tion H.6 for other models. . . . . . . . . . . . . . . . . . . . . . . . . . . 74 8.2 Histogram of the performance of Voellmy rheology with f = 0.1 and ξ = 500m3s as measured by the specified normalized index, across all case studies. See Section H.6 for other models. . . . . . . . . . . . . . . . . . 75 C.1 DAN-W utilizes fixed-volume deformable blocks to calculate runout along a path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 C.2 Fixed width leads to error in flow depth for conditions with sloping side channels, and purely basal frictional resistance leads to neglecting resis- tance along channel walls. . . . . . . . . . . . . . . . . . . . . . . . . . 110 C.3 Curvilinear distance and required adjustment to model output data. . . . . 111 D.1 Effectiveness of emergent grouping of modern landslides using cluster analysis to minimize differences in α . Results are similar for cluster anal- ysis on other mobility indices (Figure 5.2). . . . . . . . . . . . . . . . . . 114 D.2 Theoretical and actual residuals for my V -α linear regression. Distance from the dashed line is indicative of poor fit. Case numbering is alphabeti- cal: Charmonétier (Section E.5), Las Colinas (Section E.16), and Tozawa- gawa (Section E.37). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 xxiii D.3 Residuals and leverage for my V -α linear regression. Points outside of the Cook’s distance are problematic as they are poorly fitting cases which influence the regression strongly. Case numbering is alphabetical: Char- monétier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Sec- tion E.37). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 E.1 Abbot’s Cliff profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 E.2 Arth-Goldau profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 E.3 Arvel profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 E.4 Brazeau Lake profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 E.5 Charmonétier profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 E.6 Claps de Luc profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 E.7 Eagle Pass profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 E.8 Elm profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 E.9 Frank Slide profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 E.10 Great Fall profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 E.11 Hiegaesi profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 E.12 Hope Slide profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 E.13 Jonas Creek profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 E.14 Kuzulu profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 E.15 La Madeleine profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 E.16 Las Colinas profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 E.17 Luzon Slide profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 E.18 Madison Canyon profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 139 E.19 McAuley Creek profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 E.20 Mount Cayley profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 E.21 Mount Cook profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 E.22 Mount Granier profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 E.23 Mount Ontake profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 E.24 Mount Steele profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 E.25 Mystery Creek profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 E.26 Nomash River profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 E.27 Pandemonium Creek profile. . . . . . . . . . . . . . . . . . . . . . . . . 151 E.28 Pink Mountain profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 E.29 Queen Elizabeth profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 154 xxiv E.30 Rockslide Pass profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 E.31 Rubble Creek profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 E.32 Sale Mountain profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 E.33 Seaford profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 E.34 Sherman Glacier profile. . . . . . . . . . . . . . . . . . . . . . . . . . . 159 E.35 Six de Eaux Froids profiles. . . . . . . . . . . . . . . . . . . . . . . . . . 160 E.36 Slide Mountain profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 E.37 Tozawagawa profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 E.38 Triolet Glacier profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 E.39 Zymoetz River profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 F.1 Raw output data for models of Abbot’s Cliff with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 F.2 Raw output data for models of Arth-Goldau with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 F.3 Raw output data for models of Arvel with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 172 F.4 Raw output data for models of Brazeau Lake with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 F.5 Raw output data for models of Charmonétier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 xxv F.6 Raw output data for models of Claps de Luc with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 F.7 Raw output data for models of Eagle Pass with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 F.8 Raw output data for models of Elmwith observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . 182 F.9 Raw output data for models of Frank Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 F.10 Raw output data for models of Great Fall with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 F.11 Raw output data for models of Hiegaesi with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 F.12 Raw output data for models of Hope Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 xxvi F.13 Raw output data for models of Jonas Creek (north) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 F.14 Raw output data for models of Jonas Creek (south) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 F.15 Raw output data for models of Kuzulu with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 196 F.16 Raw output data for models of La Madeleine with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 F.17 Raw output data for models of Las Colinas with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 F.18 Raw output data for models of Luzon Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 F.19 Raw output data for models of Madison Canyon with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 xxvii F.20 Raw output data for models of McAuley Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 F.21 Raw output data for models of Mount Cayley with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 F.22 Raw output data for models of Mount Cook with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 F.23 Raw output data for models of Mount Granier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 F.24 Raw output data for models of Mount Ontake with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 F.25 Raw output data for models of Mount Steele with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 F.26 Raw output data for models of Mystery Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 xxviii F.27 Raw output data for models of Nomash River with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 F.28 Raw output data for models of Pandemonium Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 F.29 Raw output data for models of Pink Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 F.30 Raw output data for models of Queen Elizabeth with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 F.31 Raw output data for models of Rockslide Pass with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 F.32 Raw output data for models of Rubble Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 F.33 Raw output data for models of Sale Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 xxix F.34 Raw output data for models of Seaford with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 F.35 Raw output data for models of Sherman Glacier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 F.36 Raw output data for models of Six de Eaux Froids (east) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 F.37 Raw output data for models of Six de Eaux Froids (west) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 F.38 Raw output data for models of Slide Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 F.39 Raw output data for models of Tozawagawa with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 F.40 Raw output data for models of Triolet Glacier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 xxx F.41 Raw output data for models of Zymoetz River with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 H.1 Histogram of the performance of both rheologies with any parameters as measured by the specified normalized index, across all case studies. . . . 332 H.2 Histogram of the performance of frictional rheology with Θb = 5◦ as mea- sured by the specified normalized index, across all case studies. . . . . . . 333 H.3 Histogram of the performance of frictional rheology with Θb = 10◦ as measured by the specified normalized index, across all case studies. . . . 334 H.4 Histogram of the performance of frictional rheology with Θb = 15◦ as measured by the specified normalized index, across all case studies. . . . 335 H.5 Histogram of the performance of frictional rheology with Θb = 17◦ as measured by the specified normalized index, across all case studies. . . . 336 H.6 Histogram of the performance of frictional rheology with Θb = 20◦ as measured by the specified normalized index, across all case studies. . . . 337 H.7 Histogram of the performance of frictional rheology with Θb = 25◦ as measured by the specified normalized index, across all case studies. . . . 338 H.8 Histogram of the performance of frictional rheology with Θb = 30◦ as measured by the specified normalized index, across all case studies. . . . 339 H.9 Histogram of the performance of frictional rheology with Θb = 35◦ as measured by the specified normalized index, across all case studies. . . . 340 H.10 Histogram of the performance of frictional rheology with Θb = 40◦ as measured by the specified normalized index, across all case studies. . . . 341 H.11 Histogram of the performance of frictional rheology with Θb = 45◦ as measured by the specified normalized index, across all case studies. . . . 342 H.12 Histogram of the performance of Voellmy rheology with f = 0.05, ξ = 100m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 H.13 Histogram of the performance of Voellmy rheology with f = 0.05, ξ = 500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 xxxi H.14 Histogram of the performance of Voellmy rheology with f = 0.05, ξ = 1000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 H.15 Histogram of the performance of Voellmy rheology with f = 0.05, ξ = 1500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 H.16 Histogram of the performance of Voellmy rheology with f = 0.05, ξ = 2000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 H.17 Histogram of the performance of Voellmy rheology with f = 0.1, ξ = 100m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 H.18 Histogram of the performance of Voellmy rheology with f = 0.1, ξ = 500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 H.19 Histogram of the performance of Voellmy rheology with f = 0.1, ξ = 1000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 H.20 Histogram of the performance of Voellmy rheology with f = 0.1, ξ = 1500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 H.21 Histogram of the performance of Voellmy rheology with f = 0.1, ξ = 2000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 H.22 Histogram of the performance of Voellmy rheology with f = 0.15, ξ = 100m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 H.23 Histogram of the performance of Voellmy rheology with f = 0.15, ξ = 500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 H.24 Histogram of the performance of Voellmy rheology with f = 0.15, ξ = 1000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 xxxii H.25 Histogram of the performance of Voellmy rheology with f = 0.15, ξ = 1500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 H.26 Histogram of the performance of Voellmy rheology with f = 0.15, ξ = 2000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 H.27 Histogram of the performance of Voellmy rheology with f = 0.2, ξ = 100m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 H.28 Histogram of the performance of Voellmy rheology with f = 0.2, ξ = 500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 H.29 Histogram of the performance of Voellmy rheology with f = 0.2, ξ = 1000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 H.30 Histogram of the performance of Voellmy rheology with f = 0.2, ξ = 1500m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 H.31 Histogram of the performance of Voellmy rheology with f = 0.2, ξ = 2000m 3 m as measured by the specified normalized index, across all case studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 xxxiii Acknowledgments “Yes,” said Eeyore. “However,” he said, brightening up a little, “we haven’t had an earthquake lately.” —Milne (1988) Thank you to my adviser, Oldrich Hungr, for sharing his kindness, wisdom, curiosity, and infinite patience while guiding me through finding my own balance between physics and engineering, and to my examining committee, Erik Eberhardt, Neil Balmforth, Stuart Sutherland, and Scott McDougall for their feedback and thought-provoking questions. I owe additional appreciation both to Scott, and to John Clague, for shaping my academic writing style through their own elegant examples, and with their edits demanding precision and conciseness. Statistician and code monkey Maciek Chudek rescued my data from an undignified heap, taming not-so-standard output into an orderly database. I deeply appreciate both his willingness to teach and his laughter as I became tangled in yet another quirk of statistics. I could not ask for a better partner in this adventure. As with every thesis, the author owes a debt to friends and family for their encourage- ment and support. I wish to particularly thank Vanessa Timmer for getting me back on track when I started to flounder and J. Joanne Kienholtz for pushing when I got lost in patterns of bark unaware of the forest. Deep gratitude is also owed to my first reader, Betty Morton, whose efforts brought clarity and conciseness to this manuscript. The final 3% push was made bearable by study buddies near and far: special appreciation to Allison Welch for sharing the dubious triumph of another page reorganized, spell-checked, and finalized day after day. As the thread tying together outrageous opportunities and beautiful learning experi- ences, this thesis is the best place to offer my appreciation to the people who have con- tributed to my adventure. Green College lived up to its motto, fostering budding interdisciplinary collaborations that will continue to bare fruitful discussion as long as the world has hazards. True inter- xxxiv disciplinary collaborations start in friendship and mutual trust in respective expertise – I look forward to exploring the relationship between disasters and economics, psychology, language, culture, geography, and politics now I have some free time! Kenny Gibbs and the rest of the gang at Stargate kept my imagination and orbital dy- namics in practice, presenting me with surreal and fantastic situations for whole new appli- cations of science. Thank you for making me your rocket scientist. The Victoria Institute of Earth and Planetary Sciences sent me roaming around Aus- tralia to learn about a far different (and mostly landslide-free) geologic setting; I extend my appreciation to the professors, students, and the Chudek family for welcoming me into their country. And thank you, my readers, for giving me a reason to write. May you find this thesis completely lacking in doom, death, and destruction. xxxv Chapter 1 Introduction We cannot continue to lurch from one disaster to another. —Brady (2004) 1.1 Overview of the Problem Landslides crash down mountainsides, wiping out infrastructure, destroying homes, and killing people. The risk grows ever more problematic as more people crowd into marginal land, increasing the likelihood of landslides impacting settlements. Efficiently predicting the hazard posed by a potential landslide can dramatically decrease this risk. The ability to predict the extent and intensity of a landslide before it happens enhances the capacity of decision-makers to protect human settlements and important resources. Ac- curate hazard maps that provide visual representation of the anticipated extent and intensity of the landslide hazard can provide essential information for this purpose. A hazard map may be constructed with data derived from runout analysis: reliable models of the runout distance, velocity profile, and deposit distribution of the projected landslide. Streamlining forward modelling is a key focus of this project, with the desired result of developing a protocol for more efficient runout analysis. This will result in more efficient hazard map construction, making the tool more accessible to decision-makers. Back analysis is a runout analysis of an event which already occurred: using software to model where a landslide flowed, how deep the deposit was, and how quickly it trav- elled. Forward modelling is using the same technique on an event that has yet to occur, predicting the hazard extent and intensity. Forward modelling currently relies on skilled professionals investing significant time to constrain model parameters through back analyz- ing similar historical events. In order to streamline this process, for this study I categorized 1 landslides which exhibit similar mobility behaviour by their physical characteristics, then back-analyzed the same landslides to determine the best-fit parameters for modelling each event. Model parameters are analyzed with respect to performance for each case, and in how they perform when applied to all cases. Parameters are recommended based on consis- tent high performance across cases, and within categories of cases defined by the physical characteristics of the event. Applying the categorization by the specified physical characteristics and using the rec- ommended parameters either for preliminary hazard mapping or a starting point in param- eter selection streamlines runout analysis, allowing expert practitioners to produce forward models more efficiently. 1.2 Scope This thesis: 1. describes 40 rapid flow-like landslide case studies; 2. identifies and evaluates criteria for categorizing events by runout behaviour; 3. back-analyses the cases using dynamic analysis software packages, DAN-W and DAN3D; and 4. recommends parameters for modelling cases within the defined categories. Choosing which aspects of an event are critically important to model and which aspects of the flow may be safely ignored is an art practiced by experienced landslide modellers. Without hard guidelines, each practitioner emphasizes modelling slightly different aspects of a flow, even when using the same software package. This noise makes it difficult to compare back analyses published by different authors because the lack of consistency in modelling may obscure real differences in landslide behaviour. For this project, all cases studies were back analyzed by a single author to eliminate the noise caused by various personal judgements. This consistency allows for comparison of parameter performance between case studies, and analysis of any links between best-fit parameters and landslide characteristics (morphology, movement type, material, and so on). Despite extensive studies comparing select characteristics, it is unclear which real char- acteristics will result in two landslides being accurately modelled using the same parame- ters. When back-analysing a set of landslides to constrain parameters for use in a forward model, practitioners are currently forced to subjectively prioritize which of a broad range of physical characteristics are most influential when setting the scope to determine which 2 cases are similar to the target event. By analyzing the relationship between physical charac- teristics and mobility, I am able to formalize which physical characteristics are most likely to predict events that exhibit similar mobility behaviour. Other practitioners may use these guidelines to prioritize characteristics when setting the scope of cases to back-analyse for constraining parameters in forward-modelling. Following this categorization by back-analyzing the case studies and investigating the parameters which are most appropriate for modelling cases within each category allows me to recommend specific parameters for use with landslides with specific physical character- istics. This streamlines forward modelling for other practitioners by providing them with clear guidelines for parameters when producing initial hazard maps, and with a starting point for parameter selection when producing more detailed hazard maps. Once it is possible to recommend parameters for runout analysis modelling based on the physical characteristics of the target landslide, it becomes more efficient to produce initial forward models for new cases. This decreases the time and cost of performing accurate runout analysis for use in hazard prediction and disaster mitigation, thus increasing the likelihood that the tool will be used. A good tool applied correctly will reduce damage and loss of life. 1.3 Organization of the Thesis I first investigated the phenomena of long-runout landslides, with a definition of terms and literature review (Chapter 2), summarization of my case studies (Chapter 3),a continued literature review with a survey of modelling (Chapter 4), and statistical analysis of the physical characteristics and mobility of the landslides (Chapter 5). I continue into the modelling portion of the thesis with a justification for the selection of my particular runout software, and briefly describe the program (Chapter 6) before laying out a method for back-analyses (Chapter 7). Finally, I analyze the results of the back- analyses of my case studies, both overall and categorized by select physical characteristics (Chapter 8). Finally, I outline recommendations and directions for future research (Chapter 9). 3 Chapter 2 Landslides The landslide brought me down. —Nicks (1975) 2.1 Definition of Terms Landslides are an erosional process of solid-liquid mixtures of (spatially and temporally) variable composition engaged in gravity-driven motion with free upper surfaces and poten- tially erodible basal surfaces (Iverson, 2005). 2.1.1 Anatomy of a Landslide Before discussing landslides further, it is necessary to establish common terms for describ- ing landslide anatomy. The boundary between the mass which fails and the mass which remains in place is the rupture surface (Varnes, 1978). The source is the volume of ini- tial movement, measured between the original ground and rupture surfaces, and the path is the area the landslide runs out over (Hungr, 2006). The deposit is the mass which comes to a rest, possibly with a larger volume than the initial failure through fragmentation1 or entrainment2 of additional material from the path (Figure 2.1). The crown of the landslide is the uppermost part of the rupture surface, and usually marks the maximum elevation of a landslide from which the total vertical drop in height (H) may be measured. The crown is also the starting point3 for measuring both the curvi- linear (D) and horizontal length (L) distances.These distances are measured to the toe of the deposit, the very farthest point the landslide runs out. 1See Section 2.2.4. 2See Section 2.2.1 and Section C.2.1. 3The “x = 0” of a landslide-oriented coordinate system. 4 Figure 2.1: Common terminology for landslide anatomy: source, deposit, crown, toe, and path. 2.1.2 Quantifying Mobility Although landslide runout may be directly measured by curvilinear distance or maximum vertical height (H) and horizontal length (L), the relative mobility is more easily compared through the use of angles or ratios. The fahrböschung angle (α) is the vertical angle between the top of the crown and the tip of the toe (Heim, 1932), a quantification of the relative runout per drop: tanα = H L (2.1) while the conceptually-similar travel angle depends on center of mass, measuring the angle between the center of mass of the source and the center of mass of the deposit (Figure 2.2). This makes the fahrböschung angle easier to measure in the field, and the travel angle easier to calculate mathematically4. Mobility may also be quantified by comparing observed runout to idealized runout of a block following Coulomb’s Law5, sliding along a surface with a coefficient of friction of tan32◦: Le = L− Htan32◦ (2.2) where excessive runout Le is any motion beyond that expected by the kinematics of friction 4See Legros (2002) for an analysis of the impact of using maximum versus center of mass measurements. 5See Section 4.2.2. 5 Figure 2.2: Common terminology for runout mobility: fahrböschung angle (α), travel angle (θ ), idealized runout angle (32◦), vertical height maximum (H) and of the center of mass (Hcom), horizontal length maximum (L) and of the center of mass (Lcom), and excessive length travelled beyond that expected of a simple sliding block (Le). See Figure C.3 for curvilinear runout distance (D). (Hsü, 1975)6, and may be further transformed into a dimensionless measure of relative mobility through the ratio between idealized and observed runout (Le/L). It is difficult to separate out only the horizontal length travelled in the field, but easy to measure length on post-event maps. However, to use excessive runout length as a mobility index, it is necessary to calculate idealized runout in addition to measuring length. 2.1.3 Mechanisms of Flow A flow is defined subjectively as moving in a fluid-like manner, as opposed to rigid masses that fall, slide or rotate. The mechanics of fluid-like landslides differ between floods, avalanches, and flows. Floods involve primarily free-flowing liquids with suspended sediments. They are dom- inated by fluid dynamics, with viscous drag, buoyancy, and turbulence playing an important role in behaviour (Iverson, 2005). Avalanches involve primarily the interaction of solid grains. They are dominated by solid kinematics, with collision, adhesion, and friction playing an important role in be- 6This assumes θb = 32◦ is a reasonable friction angle for dry, fragmented rock. 6 haviour as grains slide, roll, bounce, and fall (Iverson, 2005). As deformation occurs, cohesion may be neglected (Takahashi, 2009). Flows involve mixtures of liquids and solids. Both fluid and solid mechanisms, with pore fluid pressure, effective stress, and the proportion of solids to liquids playing an im- portant role. Turbulence is suppressed as the concentration of grains increases (Iver- son, 2005). Although the Varnes (1978) classification specifies all flows must exhibit internal deforma- tion, under the definition by Hungr et al. (2001) evidence of external fluid motion is by itself sufficient, irrelevant of specific kinematics. All the landslides in this thesis flow over a rigid bed, with a clear mechanical distinction between the landslide and the underlying bed. 2.2 Excessive Runout of Catastrophic Landslides Small landslides can be modelled by Coulomb’s Law using only the kinematics of sliding7, but the observed runout of very large landslides cannot be predicted in the same manner. The physics behind the excessive runout of catastrophic landslides is poorly understood: many mechanisms have been proposed (and occasionally discredited) to account for the unusually long runout of large landslides, but none have been widely accepted. Proposals include mechanisms for reducing internal or basal friction, geomorphic controls on the path, and physical consequences of volume (Table 2.1). 2.2.1 Internal Friction Internal friction may be reduced through mechanical fluidization of a landslide, allowing for longer runout as the landslide flows in fluid-like manner (Sassa, 1988). Theories for fluidization include interstitial fluids, dilation of the grain mass, spontaneous reduction of the internal friction angle, or vibrating the flow. Rock dust may theoretically act as an interstitial fluid, lubricating internal dynamics (Hsü, 1975), or producing buoyancy through collisions during highly concentrated grain flow (Bagnold, 1954). Disassociation of the underlaying material may produce carbon diox- ide, which may fluidize the mass (Erismann, 1979). The grain mass may be dilated through imparting high impulsive contact pressures (Davies, 1982), although dilation has not been observed to reduce friction. Internal fric- tion angles may theoretically spontaneously reduce at high rates of shear (Scheidegger, 7See Section 4.2.2. 7 Process Mechanism Result Reduce interstitial fluids (dust, gas) lubrication internal friction entrain saturated material increase liquid content internal collisions buoyancy high impulsive contact pressure dilation high shear spontaneous reduction earthquake or acoustic waves vibration Reduce air or water vapour cushion basal friction “ball bearing” fragments basal rolling limestone, gypsum, ice... smooth bed undrained loading fluidized bed melting (frictionite, water) lubrication grinding gouge Morphology channelized path low energy dissipation Volume confining and shear stress fragmentation fragmentation bulking release elastic energy entrainment larger deposit volume balance larger deposit Table 2.1: Theories to explain the excessive mobility of large landslides. 1975; Campbell, 1989), although this behaviour has also not been experimentally observed (Hungr & Evans, 2004). Vibration may occur through coincidence with earthquakes (such as an earthquake- triggered event) (McSaveney, 1978), or through acoustic vibration within the landslide (Collins & Melosh, 2003). Vibration has been experimentally demonstrated by shear tests to reduce friction angles (Melosh, 1979), but requires a undetermined continuous source of energy (Kobayashi, 1991) unless self-perpetuating (Collins & Melosh, 2003), and should not preferentially discriminate for large volumes (Hungr & Evans, 2004). Finally, entrainment of saturated material increases liquid content of a flow, reducing internal friction angle (Abele, 1994; Hungr & Evans, 2004; Crosta et al., 2009). 2.2.2 Basal Friction The mechanism driving reduced basal friction is most commonly theorized as a thin fluid layer along the base of the flow. This thin fluid layer may conceptualized as a cushion, basal rolling, smooth bed material or fluidization of the bed. 8 Cushions of trapped air (Shreve, 1966, 1968) or pressurized water vaporized by the heat of friction (Goguel & Pachoud, 1972) may be overridden or trapped, lubricating the flow. Cushion theories are contradicted by observation of long-runout events on the moon and Mars with minimal air or water to act as a lubricant (Hsü, 1975; Lucchitta, 1978), by failure to observe grading predicted by high gas pressures (Cruden & Hungr, 1986), and by failure to address how the cushion would not leak out from under the flow. Internal sorting producing a thin layer of “ball bearing” fragments could lubricate flow, but this effect would be inversely proportional to size as larger volumes would crush ball bearings (Erismann, 1986). The bed material could be originally smooth for events running out over limestone (Pollet & Schneider, 2004), gypsum (Watson & Wright 1969 as cited by Deganutti 2008), or glaciers (McSaveney, 1978, 2002), or made smooth by the heat of friction melting the underlaying material, producing a molten layer of “frictionite” to lubricate flow (Erismann, 1986; De Blasio & Elverhøi, 2008). However, these basal conditions would only apply to landslides running out over these path materials or for extremely thick landslides (where melted rock has been observed (Hungr & Evans, 2004)). Finally, the bed may become fluidized through undrained loading (Evans et al., 2006), melting (ice or snow to water, or rock to frictionite) (Masch et al., 1985), or grinding rock into a thin layer of gouge (akin to that observed in faults). 2.2.3 Morphology Geomorphic controls have a clearly observed relationship to energy dissipation and subse- quent runout, with channelized flows running out the farthest, free spreading flows running out an intermediate distance, and flows impeded by frontal impact traveling the shortest dis- tance (Nicoletti & Sorriso-Valvo, 1991). However, long runout has been observed in cases independent of channelized morphology, indicating that although a contributing mecha- nism, geomorphic control is insufficient to fully explain long runout phenomena. 2.2.4 Volume Finally, volume is also clearly related to runout, with larger volumes flowing a longer dis- tance. Volumes may be increased through fragmentation of the initial volume, or through entrainment of additional material. Fragmentation is volume-dependent as it increases pro- portionately to confining and shear stress, and has been observed to bulk flows by 18-35% 9 (Sherard, 1963)8. Fragmentation may also impart energy to the flow as the elastic energy of deformation is released through breaking (Davies & McSavenney, 1999; Davies & Mc- Saveney, 2002; Davies et al., 2006; Davies & McSaveney, 2009). The daunting task of extensively critiquing these theories has already been carried out9. I consistently analyze case studies to discriminate between these mechanisms, and clarify key characteristics, which predict exceptional mobility. 2.3 Summary of Landslides Fluid-like landslides may demonstrate a variety of physical mechanisms depending on the type of flow, but external evidence of fluid motion is sufficient to identify a fluid-like event. Landslides runout may continues beyond that predicted by the kinematics of friction and gravity. This excess mobility is theorized to relate to changes in internal friction or basal friction, and is certainly at least partially dependent on the path morphology and the volume of the event. 8See Locat et al. (2006) for a review and field study on fragmentation in rock avalanches. 9Notably by Legros (2002), Hungr & Evans (2004), and Deganutti (2008). 10 Chapter 3 Data: Landslide Case Studies Clearly people do not figure natural disaster risks into their decisions of where to live and where to retire. —Hartwig (2005) 3.1 Scope Characteristic Limiting Criteria Failure type single Volume Vf inal ≥ 1×106 m3 Velocity rapid or faster Movement fluid-like flows Material any Saturation no free-flowing water Table 3.1: Selection criteria for cases. All the landslide case studies analyzed in this thesis are large, rapid, single-failure fluid flows (Table 3.1). Flows may be dry or wet, but are not included if they exhibit freely flowing wa- ter, hyper-concentrated flows, or surges (which excludes most debris flows). 3.1.1 Availability To be included in this study, a full landslide de- scription including pre- and post-event topog- raphy and runout distance must be available in the literature. Descriptions preferably include some information about debris distribution and velocity observations. Independent field investigation or reinterpreting and verify- ing runout behaviour is beyond the scope of this thesis, so when the quantitative data of a well-described landslide differs between authors, the description that appears to have the broadest acceptance (usually the most-referenced or most recent publication) is used. Any misinterpretation or random error in field observations of the selected cases should not impact this study, as the large quantity of case studies should compensate for small 11 discrepancies in reported observations1. 3.1.2 Volume As discussed in Section 2.2, the exceptional runout of large landslides is fundamentally different than that of smaller landslides2. The cutoff on how big a “large” landslide needs to be in order to exhibit exceptional runout and fluidity is subject to debate. Hsü (1975) sets the lowest boundary, including all landslides with a volume V ≥ 0.5 million m3, while the highest cutoff is landslides of volume V ≥ 10 million m3 (Melosh, 1986; Wen et al., 2004). This thesis examines landslides with a final volume Vf ≥ 1 million m3 after entrainment (in keeping with volume limits supported by Erismann 1979, 1986; Abele 1994; Huppert & Dade 1998; von Poschinger 2002; Crosta et al. 2007), but includes events with smaller starting volumes. An additional advantage in modelling larger volumes is minimizing the impact of error from estimating the source volume, as errors of a few cubic meters are insignificant. Due to the relative infrequency of large-magnitude events, this limitation on scope sharply limits the available cases for this study. Similarly, if a sharp volume boundary exists, the utility of my results will be limited only to the rare instances when a community or infrastructure is threatened by a catastrophically large event. This will be discussed in greater depth in Section 5.2.4. 3.1.3 Velocity The velocity of a landslide changes throughout both space and time, thus a landslide does not exhibit only one constant velocity. Instead, reported velocities are of observed or cal- culated velocities at a specified point, or average velocities for an entire event. Retroactive velocity calculations are made from field elevation of scour from banking around the outside of curves or run-up against adverse slopes. Superelevation Superelevation is measured from the scour produced by material banking up the outside of the turn as a fluid traverses a curving path. The velocity is calculated through the use of the 1The impact of statistical outliers is discussed in Appendix D. 2Excepting Corominas (1996), who claims no clear minimum cutoff volume for an event to exhibit excessive mobility. 12 forced vortex equation: v= ￿ Rcg k ∆h b (3.1) where v is the flow velocity, Rc is the radius of the curvature of the flow centerline, g is the acceleration of gravity, ∆h is the superelevation height, b is the flow width, and k is a correction factor for viscosity and vertical sorting3. In the field, observed measurements may be reduced by measuring the banking angle β instead of superelevation height and flow width, where β = tan ∆hb . Producing a field measurement of a real channel’s radius of curvature may still present a challenge (Prochaska et al., 2008). Run-up Run-up is measured from the scour caused by material running up a slope before exhausting velocity and submitting to gravity. Similar to calculating the launch velocity of a projectile or hydraulic head from observations of maximum height, calculating velocity from run- up involves balancing initial velocity and gravitational acceleration converting kinetic to potential energy: v= ￿ 2gh (3.2) where v is the velocity, g is gravitational acceleration, and h is the run-up height. When a landslide overtops a small rise, the velocity is calculated in the same manner as for run-up, but the calculated velocity is the minimum velocity required to travel the vertical distance without exhausting momentum. Error Higher scour eliminates evidence of lower scour from when the flow travelled more slowly at the same point, so only the maximum velocity at that point may be calculated. Velocity may be overestimated if surges or splashing produces higher scour. The equations to calculate velocity neglect energy lost through friction or momentum exhausted in motion transverse to the slope. Neglecting friction when calculating veloc- ity from estimating the conversion of potential to kinetic energy (predicting from total drop) will result in over-estimates of velocity, while neglecting friction when estimating the conversion of kinetic into potential energy (measuring from run up) will result in under- estimates of velocity. Modified equations accounting for friction require the use of correc- tion factors from the percentage of energy lost to friction (Francis & Baker, 1977; Evans, 3The correction factor may be k = 1. 13 1989; Erismann & Abele, 2001). Both superelevation and run-up calculations are limited to estimating the maximum velocity of the center of mass. As the difference in height for the center of mass is smaller than the maximum drop (Hcom < H, see Figure 2.2), using H in run up calculations results in overestimating available kinetic energy, thus overestimating velocity4. Despite the difficulties in gathering a complete velocity profile for a given event, it is easy to distinguish between slow events and extremely rapid events. All landslides within this thesis are catastrophic, rapid events with velocities typically at least 5 m/s (Hungr, 2007). 3.1.4 Other Limitations Well-described relic landslides are included, but are treated with caution recognizing that piecemeal detachment may be difficult to distinguish, the initial topography may be un- certain, or the deposit may have eroded or been remobilized during the intervening time (Figure 3.1). Piecemeal detachment and retrogressive failures are not treated as the energy release is drawn out, talus from earlier movement smooths the path for later movement by filling in crevasses (Alean, 1985), and loading of talus does not generate pore pressure. 3.2 Categorization of Data In building case descriptions, I applied a priori categorization through describing physical characteristics that may be observed about a landslide in advance of failure. I applied common categories used to distinguish between landslides, identified from a survey of the literature and classification systems: volume, movement type, material, saturation, path morphology, and the triggering event that preceded the landslide (Table 3.2). 3.2.1 Landslide Classification Landslides are classified in many competing styles. As this project seeks to broadly dis- cuss landslide behaviour, a geomorphic perspective is preferable to strict movement-type divisions, and as all the landslides presented flow, I have elected to use the classification system presented by Hungr et al. (2001), a non-taxonomic structure encompassing move- ment mechanisms, material properties, velocity, and other properties with gradational dis- tinctions between characteristics allowing for subjective classification5. The landslides in 4For further discussion, see Erismann & Abele (2001). 5For extended definitions, please see Hungr et al. (2001). 14 Figure 3.1: Original path topography may be uncertain for relic events. this thesis are classified as follows: Flow Slides Flow slides involve loose saturated granular material, potentially with excess pore pressure, failing on moderately steep slopes. The source material must have a collapsive internal structure maintaining a moisture content in excess of the liquefaction limit, so the failure produces liquefaction (without entraining additional water), increasing mobility. Common settings for flow slides include lacustrine silt, loess, chalk or anthropogenic fills (hydraulic fills, mine tailings, and waste deposits). 15 Category Characteristic Category Characteristic Movement Type Rock Avalanche Material (Source) Rock Debris Avalanche Debris Flow Slide Chalk Saturation Dry Loess Wet Material (Path) Rock Morphology Unobstructed Debris Channelized Ash Impacted Clay Trigger Non-Violent Glacial Rain Talus Artificial Blast Urban Earthquake Table 3.2: Categories identified from the literature which may impact mobility, and classification options within the category identified from my case studies. See Table 3.4 for the number of cases with each characteristic. Debris Avalanches Debris avalanches involve unconfined shallow flow of variably saturated debris on a steep slope. Unconfined by channels and depleting local material, debris avalanches do not usu- ally repeat in the same location on short timescales6. Rock Avalanches Rock avalanches7 involve unconfined shallow flow of fragmented rock on a steep slope. Rock avalanches originate as a mass of rock in a rockslide or rock fall, fragmenting during failure, finally flowing as a semi-coherent mass. 3.2.2 Morphology Nicoletti & Sorriso-Valvo (1991) found that morphologies can be classified by the impact of the path topography on energy dissipation. Low-, medium- and high-energy dissipa- tive morphologies map to channelized, unobstructed, or impacted topographies.. A later analysis by Corominas (1996) originally categorized morphology into substantially more gradations in relation to deposit shape, form of run-up, and even ground cover, yet he too 6This is in contrast to debris flows, which re-occur periodically in the same channel. 7Also called sturzstroms (Heim, 1932). 16 eventually reduced to the same three major categorizations as the most pertinent to success- fully categorizing events into different mobility regimes. In accordance with the conclusions of Nicoletti & Sorriso-Valvo and Corominas, I too am categorizing morphology by dividing events to channelized, unobstructed, or im- pacted topographies. A channelized path morphology is characterized by topography which strongly confines the flow. The path of unobstructed morphology presents no obstructions, constraints, or barriers. Finally, impacted morphologies contain a significant barrier to flow, typically in the form of an opposing valley wall, hill, or other abrupt, adverse slope, which may halt or deflect flow. 3.2.3 Material Debris produced by... colluvium mass wasting residual soils weathering till glacial transport pyroclastic deposits explosive volcanism logs, stumps organic processes Table 3.3: Processes which produce debris. Flows are composed of a mixture of solids and liquids. The solids are particular masses, like debris or fragmented rock. The material distinction between debris and fragmented rock is gradational, with no specific cutoff for percentage compo- sition by grain size. Debris is any loose unsorted material (Table 3.3). Fragmented rock originates as an intact rock mass disin- tegrating during the landslide (Hungr et al., 2001). Partitioning of the observations into mutually exclusive categories allows for more straightforward analysis, yet a single landslide event may involve more than one material (for example, a rock avalanche running out over bare rock and then saturated debris). To manage this complication, two material categorizations were used: dominant source and path materials. 3.2.4 Saturation Flowing landslides may be wet or dry. Water may also have a heterogeneous distribution such that an otherwise dry mass is travelling on a thin saturated layer, and a precise cutoff would require in situ measurements of pore water pressure, a daunting and dangerous task. Therefore, I will also discuss water content subjectively without quantitative distinction be- 17 tween dry, moist, wet, and fully saturated events8.For this dataset, I labelled an event “wet” if it took place after a period of sustained heavy rain, was triggered by rainfall, entrained saturated material, or ran out over a creek (for instance, channelized by a stream); otherwise I labelled the event “dry.” 3.2.5 Trigger The trigger is the event which directly initiates failure. If a specific trigger is listed for an event, that trigger is listed. In some instances, a specific trigger could not be determined, but some triggers may be excluded. For example, the initiation may be directly observed with no abnormalities reported by the eyewitness, and examination of seismic records exclude earthquake triggers. In this instance, I classify the trigger as some undetermined event which did not involve a sudden injection of energy into the flow. I classify these events as having ”non-violent” triggers, as opposed to the violence inherent in an earthquake, artificial blast, or even volcanic trigger. When rain is specifically identified as the trigger for an event, it is listed as the trigger, although it also lacks in a sudden injection of energy (and thus may be a subcategory of non-violent triggers). 3.3 Error in Recorded Observations 3.3.1 Reliability of Reported Runout Characteristics This study is limited by published field observations of the case studies. Although theoreti- cally the reliability of all reported runout observations is perfect, real-world limitations can interfere. Although distanceD, length L, and fahrböschug angle α should all be comparable measures of runout, actual limitations in the field impact the reliability of the observations. Fahrböschung angle is the easiest to measure in the field, requiring only to stand at the toe of the landslide with an inclinometer, but is also the most prone to rounding error. A 0.1◦ difference is difficult to judge with the naked eye and rarely recorded in publications, yet may produce a profound difference on the actual runout experienced (Figure 3.2). In the field, D should be easier to measure in than L, requiring the observer to pace off the entire path of the landslide without needing to separate out horizontal versus vertical distance travelled, while the inverse is true in for extracting observations from post-event maps. For both, without highly detailed pre- and post-event observations, small topographic changes may be obscured by the deposit, or heterogeneous over the width of the event. This 8Although no landslide within this thesis has free flowing water with floating debris (debris floods). 18 Figure 3.2: Fahrböshung angle is easy to measure but prone to rounding error, while pacing off curvilinear distance is straightforward but tiring. source of error is compounded by path smoothing in computer modelling of an event. Few people are concerned with careful timekeeping when witnessing a catastrophe, making even the rare instances of eyewitness observations of velocity suspect. Post-hoc calculations based on field observations of run up or superelevation provide estimates of maximum velocities at a point, yet the flow may have been travelling faster at another location along the path without leaving an observable record. Although the underlaying cause of a landslide is frequently well-known, the actual trig- gering event may not be determined. The impact of failure for large landslides may result in a seismic signature, so even with seismic data it may be difficult to differentiate between landslides that were triggered by an earthquake and the seismic signature of the impacting mass. Confirming the reported landslide characteristics is beyond the scope of this study; I rely upon the recorded literature for runout observations. 3.3.2 Incomplete Observations Due to variability in landslide reporting, not all events have recorded values for all runout characteristics (as evident in Table 3.7 and Table 3.8). This is not problematic for user selection of parameters, but has a significant impact on rigid mathematical selection9, which 9Both user and mathematical selection of parameters is discussed in Section 7.1.4. 19 lacks the flexibility to compensate for incomplete input data10. Therefore, any case without a particular target characteristic is automatically excluded from mathematical parameter selection. As a result, later analysis of different target char- acteristics will include inconsistent subsets of cases, resulting in sample size varying for both proposed characteristics and target runout observations, thus variable statistical power (Table 3.4). 3.4 Summary of Data Full case histories are presented in Appendix E. Characteristics of a landslide that could theoretically be observed before failure are summarized in Table 3.5 and Table 3.6. These real landslide characteristics are analyzed in Chapter 5 to link mobility to physical characteristics. Measures of mobility recorded after failure are summarized in Table 3.7 and Table 3.8. I use these observations both in quantifying mobility while categorizing the landslides, and to judge my landslide runout models in Chapter 8. 10Technically, one may infer the missing data from similar complete cases. However, as I seek to identify what makes landslides similar, making assumptions about similarity to have complete data to draw conclusions about similarity would be circular reasoning. 20 Characteristic ntotal nD nL nα nvmax Any 40 19 35 27 11 Movement Type Rock Avalanche 29 16 26 28 9 Debris Avalanche 6 0 4 4 2 Flow Slide 5 2 5 5 0 Morphology Unobstructed 23 9 21 23 7 Channelized 8 5 7 7 3 Impact 9 4 7 9 1 Material Source Rock 29 11 24 29 8 Debris 7 6 7 6 3 Chalk 3 0 3 3 0 Loess 1 1 1 1 0 Path Rock 6 1 6 6 1 Debris 26 11 23 26 7 Ash 1 0 1 1 0 Clay 1 1 1 1 0 Snow & Ice 4 1 1 2 1 Talus 2 1 1 2 1 Saturation Dry 2 2 2 2 1 Wet 33 14 28 32 9 Unknown 5 2 5 5 1 Trigger Non-Violent & Rain 12 7 10 11 3 Artificial Blast 1 0 1 1 0 Earthquake 4 4 4 3 4 Unknown 23 7 20 22 4 Age Prehistoric 7 2 7 7 1 Historic 7 4 7 7 2 Modern (since 1900) 26 13 21 23 8 Table 3.4: Number of cases with specified characteristic and runout observation. 21 Landslide Movement Type Morphology Material Vi Trigger Saturation Source Path [Mm3] Abbot’s Cliff flow slide unobstructed chalk debris 0.28 wet Arth-Goldau rock avalanche unobstructed rock rock 24 rain wet Arvel debris avalanche unobstructed rock debris 0.61 non-violent wet Brazeau Lake rock avalanche unobstructed rock debris 4.5 wet Charmonétier debris avalanche channelized rock debris 0.13 rain wet Claps de Luc rock avalanche unobstructed rock rock 2 Eagle Pass debris avalanche impacted rock debris 0.07 wet Elm rock avalanche unobstructed rock debris 30 non-violent dry Frank Slide rock avalanche unobstructed rock debris 30 wet Great Fall flow slide unobstructed chalk debris 1.25 wet Hiegaesi rock avalanche unobstructed debris ash 50 rain wet Hope Slide rock avalanche impacted rock debris 47.3 wet Jonas Creek (north) rock avalanche unobstructed rock rock 2.1 Jonas Creek (south) rock avalanche unobstructed rock rock 4.5 Kuzulu rock avalanche channelized debris debris 12.5 non-violent wet La Madeleine rock avalanche unobstructed rock debris 71 wet Las Colinas flow slide impacted debris debris 0.1 dry Luzon Slide rock avalanche unobstructed debris debris 20 earthquake wet Table 3.5: Landslide characteristics observable prior to failure for case studies A-L. See Table 3.6 for M-Z. 22 Landslide Movement Type Morphology Material Vi Trigger Saturation Source Path [Mm3] Madison Canyon rock avalanche impacted rock debris 21.4 earthquake wet McAuley Creek rock avalanche channelized rock debris 7.4 wet Mount Cayley debris avalanche unobstructed rock debris 0.74 wet Mount Cook rock avalanche unobstructed rock snow & ice 11.8 non-violent wet Mount Granier rock avalanche unobstructed rock debris 500 rain wet Mount Ontake rock avalanche channelized debris debris 36 earthquake wet Mount Steele rock avalanche impacted rock snow & ice 30 wet Mystery Creek rock avalanche unobstructed rock debris 40 Nomash River rock avalanche channelized rock debris 0.3 wet Pandemonium Creek rock avalanche channelized rock debris 5 non-violent wet Pink Mountain rock avalanche unobstructed debris clay 0.74 non-violent wet Queen Elizabeth rock avalanche impacted rock rock 45 wet Rockslide Pass rock avalanche unobstructed rock rock 370 Rubble Creek rock avalanche channelized rock debris 25 wet Sale Mountain flow slide unobstructed loess talus 31 non-violent wet Seaford flow slide unobstructed chalk debris 0.15 blast wet Sherman snow & ice rock avalanche unobstructed rock snow & ice 60 earthquake wet Six de Eaux Froids rock avalanche impacted rock debris 8.4 wet Slide Mountain debris avalanche impacted rock debris 13 wet Tozawagawa rock avalanche impacted debris debris 19 wet Triolet snow & ice rock avalanche channelized rock snow & ice 9.8 wet Zymoetz River debris avalanche unobstructed rock talus 0.9 non-violent wet Table 3.6: Landslide characteristics observable prior to failure for case studies M-Z. See Table 3.5 for A-L. 23 Landslide D L H α Le Le/L vavg vmax [m] [m] [m] [◦] [m] [ %] [m/s] [m/s] Abbot’s Cliff 442 145 18 210 48 Arth-Goldau 6025 1265 12 4001 66 70 Arvel 363 258 35.5 -48 -14 Brazeau Lake 2700 18 2700 100 Charmonétier 600 520 40.9 -232 -39 Claps de Luc 800 370 25 208 26 Eagle Pass 31 Elm 2000 2017 613 16 1036 51 50 83.5 Frank Slide 3500 760 14 2284 65 28 45 Great Fall 628 150 13 388 62 Hiegaesi 67 25 11 27 40 Hope Slide 4240 1220 16 2288 54 Jonas Creek (north) 3250 880 17.1 1842 57 Jonas Creek (south) 2500 920 26.5 1028 41 Kuzulu 2300 3300 950 16 1780 54 8 14 La Madeleine 4500 1561 19 2002 44 Las Colinas 8000 715 160 12.6 459 64 Luzon Slide 4100 3800 810 12 2504 66 35 130 Madison Canyon 1280 1300 340 13 756 58 50 McAuley Creek 10 Mount Cayley 3460 1180 19 1572 45 70 Mount Cook 7500 55 Mount Granier 7500 7690 1520 12 5257 68 Mount Ontake 1300 400 400 100 22 31.7 Mount Steele 7000 5760 1860 18 2783 48 65 Mystery Creek 4000 4000 1250 15 1999 50 Nomash River 2270 560 13.5 1374 61 Pandemonium Creek 9000 8600 2000 13 5399 63 30 Pink Mountain 2000 1950 450 11.6 1230 63 Queen Elizabeth 2645 950 20 1125 43 Rockslide Pass 3000 6330 1000 8.5 4730 75 20 70 Rubble Creek 6900 4500 1060 13 2804 62 20 Table 3.7: Mobility characteristics for case studies A-R. See Table 3.8 for S-Z. 24 Landslide D L H α Le Le/L vavg vmax [m] [m] [m] [◦] [m] [ %] [m/s] [m/s] Sale Mountain 1120 1600 320 11 1088 68 19.8 Seaford 121 68 28 12 10 Sherman Glacier 5700 5950 1080 10 4222 71 26 67 Six de Eaux Froids 16 Slide Mountain 1650 420 14 978 59 Tozawagawa 454 100 230 66 -268 -268 Triolet Glacier 9000 7200 1860 14.5 4223 59 35 44 Zymoetz River 17 34 Table 3.8: Mobility characteristics for case studies S-Z. See Table 3.7 for A-R. 25 Chapter 4 Models for Landslide Hazard Prediction Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful. —Box & Draper (2007) When particular people, property, infrastructure, wildlife, or other resources are in dan- ger from a looming landslide, the assets are at risk. Landslide risk reduction relies on accurate hazard maps to guide mitigation, evacuation, or other remedial measures. Accu- rate hazard maps are built through predicting the distribution and intensity of an event in advance1. Rapid flow-like landslides challenge typical landslide mitigation measures because the potential destruction cannot often be prevented by stabilizing the source area (Hungr, 1995; Crosta & Agliardi, 2003). Instead, the most effective risk reduction techniques for this type of landslide are to accurately predict the expected runout and evacuate the projected flow path (Wen et al., 2004; Kilburn & Pasuto, 2003), or to construct structures to stop or deflect flow. Risk reduction depends on accurately predicting landslide runout, so the hazard assessment phase of mitigation is essential. Hazard assessment requires recognizing the hazard, then estimating the magnitude and intensity distribution. The probability of occurrence related to the expected magnitudes and distributions is then calculated, and included in a hazard assessment report. The next stage is risk assessment – determining the elements at risk, estimating vulnerability, calculating specific and total risks, and mitigating if necessary. For landslides, estimating magnitude 1Please see Fell, Ho, Lacasse, & Leroi (2005) for an in-depth framework for landslide risk assessment and management. 26 and intensity distribution is done through predicting the distance a flow will travel, the depth of the flow, and the velocity distribution within the flow. When the hazard assessment is inaccurate, the result may be catastrophic. In Vaiont, Italy, the hazard assessment greatly underestimated flow speed: when the landslide was much faster than projected, thousands of people died (Erismann, 1986). Even a perfect hazard assessment system is insufficient if it is not applied correctly. When landslide deposits are not recognized during initial surveys, entire settlements may be founded on relic landslide deposits, as in Lion’s Bay, British Columbia (Clague & Turner, 2003), and developments on the deposits of Flims and Elm landslides (Eisbacher & Clague, 1984). Although this thesis will improve the accuracy of predictive tools available for hazard assessment for rapid flow-like landslides, it will not replace field surveys by skilled geoscientists to identify unstable source areas and historic deposits. 4.1 Predicting Landslide Runout Physical experiments are usually preferred to models because models require more assump- tions than direct measurements, but for landslides, direct experiment is difficult, dangerous, expensive, and of limited utility. Landslides are frequently heterogeneous – an experi- menter inserting a probe into a flow needs to decide if a boulder, tree trunk, gravel, or murky sediment-laden water is most representative of the composition. Once isolated from a flow, velocity-dependent characteristics are lost from a sample, further reducing the usefulness of direct experiment, or even of small-scale laboratory tests. Some full-scale direct experi- ments with artificial landslides have been completed (Okura et al. 2000b, 2002; Ochiai et al. 2004; Moriwaki et al. 2004; and others), but a single event cannot be repeated carefully ad- justing only one factor, and even if it were, observing conditions is complicated by the danger of being in close proximity to a landslide and the difficulty of measuring a material with properties that change when observed in-situ or when isolated for measurement. As it is impractical to create controlled experimental conditions to directly measure out- comes, models are a powerful alternative for predicting landslide distribution and intensity. Models are conceptual representations of a phenomenon, unlike simulations which seek to directly imitate real processes. All good models explain the past, make predictions about the future, and are refutable, cost effective, and easy to use. All models are limited by the assumptions made in constructing them – as the number of assumptions increases, the accuracy and relevance of the model for exploring the phenomenon decreases. Models are also limited by the extent and quality of the input data: with poor quality input, the predic- 27 tions will be equally unreliable. When validated against field observations, mathematical modelling is a practical way to study landslide runout in combination with small-scale lab- oratory tests. 4.1.1 Laboratory Models Small-scale laboratory models of landslides are incredibly valuable for investigating scale- independent effects (Denlinger & Iverson, 2001) but are limited by the difficulty of account- ing for scaling thixotropy and flow heterogeneity. Thixotropy is a decrease in viscosity with agitation, characteristic of materials with a high static shear strength and low dynamic shear strength. Landslides exhibit scale-dependent thixotropy, becoming less viscous in motion when under constant shear yet rapidly solidifying when at rest, which is difficult to replicate with laboratory materials. Ward & Day (2006) found that even the slope friction coefficient between mass and slope is different between lab and field measurements of similar ma- terials. The same heterogeneity of flow material that makes field sampling impractical is equally difficult to replicate within a laboratory. 4.2 Mathematical Model Classification Different types of mathematical models are built using different assumptions about the phe- nomenon. These different assumptions lead to different limitations in the applicability of the model. Thus, each model has an appropriate usage and scope dictated by the underly- ing assumptions. As the number of assumptions underlaying a model increases, the scope narrows and accuracy and relevance of the model decreases. Assumptions may be in the underlying physics, mathematics, or computational techniques used by the model, and in the specified boundary conditions. Currently, all mathematical models in popular use for landslide runout modelling are deterministic: given fixed parameter input, an identical output is always produced. None of the models are probabilistic with a random aspect preventing repeatability between input and output, although best practice dictates using a deterministic model in a probabilistic manner by varying input parameters when generating data for constructing a hazard map2. 2A deterministic model used with a range of parameters produces a range of outputs. The input parameters and output predictions may be evaluated by an expert practitioner using professional judgment to select the most likely scenarios and manually assign probabilities. The output may then be used to produce a probabilistic hazard map. For more discussion, see Hungr et al. (2005). 28 4.2.1 Statistical Models Statistical mathematical models correlate physical properties of the landslide with the extent of the runout zone (McDougall & Hungr, 2004). Statistical analysis of empirical observa- tions establish probability relationships between characteristics of the failure region and runout behaviour. The scope of statistical models is limited by the scope of source cases: a target case must match the cases used to generate the model, so the model application is generally very narrow. Statistical models are subject to a high degree of approximation due to the difficulty in finding a comprehensive description of actual processes and ini- tial conditions (Crosta et al., 2006). Best practice dictates statistical models should only be applied in conditions similar to the events used in the statistical analysis (Rickenmann, 2005), preferably with events that are comparable in the initial volume, geometry, and de- tachment position of the unstable mass, conditions of the slope where movement, scouring, and deposition occurred, and total duration (Crosta et al., 2006). Statistical models make predictions by correlating pairs of observations3 This one-to- one correlation means models are limited to single point predictions as output (α) and cannot describe landslide motion dynamically or completely. This means the models cannot be used to predict velocity along the flow path, which is of great importance in determining hazard intensity. However, statistical models are very easy and quick to use, with very low computational demand because all the statistical analysis is done in advance and requires no additional adjustment for new target cases. Use of Volume to Predict Fahrböschung Angle Extensive research has correlated failure volume (V ) to fahrböschung angle (α) with data sets of various sizes and scopes (Scheidegger 1973; Hsü 1975; Lucchitta 1978; Corominas 1996; Rickenmann 2005; and many others). Relationships are of the form: log10 tanα = (intercept)+(slope) log10V (4.1) Scheidegger’s work is notable as an early example of calculating a relationship between volume and fahrböschung angle, and Corominas’s is notable for performing regressions on subsets with varying scope4. Scheidegger (1973) analyzed 33 landslides of 0.03 to 20,000 million m3, primarily prehistoric events described in Heim (1932), to build the first linear 3For landslide runout, a typical pairing is volume correlated with some runout index such as the fahrböschung angle. 4For more examples, see the review paper on statistical modelling by Rickenmann (2005). 29 regression to use volume to predict the fahrböschung angle. Corominas (1996) analyzed 204 landslides, differentiated into subcategories first by movement then by path morphol- ogy, to build statistical models with varying scope. Among other conclusions, he found no sharp volume cutoff for mobility, and that landslides of a range of velocities (slow to fast) could all exhibit excess runout. All the relationships described by these authors are statistically valid and consistent with empirical data given the source cases, so a practitioner must be careful in determining which model has the appropriate scope when deciding how to model a new target case. These particular examples will be discussed in more depth in Section 5.1. Using Volume to Predict Inundation Area It is unsurprising that landslides with larger volumes generally deposit over a larger area than smaller landslides. Fannin & Wise (2001) analyzed clear-cuts in British Columbia to develop a statistical relationship between initial volume, flow style, and expected inundation area for small-scale debris flows and avalanches. Similar studies have been undertaken for larger landslides (Iverson et al., 1998) This form of volume-balance relationship may be used in combination withV -α relationships predicting fahrböschung angle to create a rough hazard map for a target case. As a statistical model, the output is purely a probability correlation. Therefore, varying the input parameters to analyze the runout characteristics of a landslide if characteristics besides source volume change requires collecting additional sets of case histories limited to those characteristics and analyzing them to establish new statistical trends. For example, given a fixed set of case histories used to statistically correlate probable runout characteris- tics, if an expert practitioner wished to investigate how runout would change in relation to degree of saturation, entirely new models featuring cases divided by water content at time of failure would need to be created. Utility Statistical models have been created to relate almost any pair of observable landslide and runout characteristics, including the impact of mechanism, material, and morphology on runout, or predicting average or maximum runout velocity (Hsü 1975; Evans & Clague 1988; Nicoletti & Sorriso-Valvo 1991; Legros 2002 and many others). Although limited in scope by the necessity of comparing similar cases to perform statistical analysis, and in utility by producing only single data-point predictions, statistical models play a valuable 30 role in landslide runout analysis due ease of use. The models may be applied even while in the field to establish initial hazard characteristics for preliminary runout analysis, which may be later refined by other prediction models. 4.2.2 Dynamic Models Dynamic models are based on using physical relationships to establish runout character- istics, such as applying conservation of momentum to the kinematics of a failing mass. Dynamic models account for the progression of time and for terrain anomalies, and thus may be used to predict a complete description of landslide motion. All dynamic models rely on a basic axiom: although landslides are complex, it is possible to predict movement. Most analytic model fully describes motion from initiation to deposition (McDougall & Hungr, 2004)5. When determining an analytic solution is too complex, a compromise is made by using numerical methods to solve the governing equations, such as by iteratively time-stepping interactions to determine motion. Numerical models have the advantage of being based on general physical laws, while side-stepping the difficulty of finding an ana- lytic solution. All dynamic models use physical and mathematical relationships, but must remain con- sistent with empirical observations to be valid. This means that models must be verified against empirical data6 to determine the appropriate input parameters when making a pre- diction, which is a time-consuming task (Hungr, 1995; Iverson, 1997; Rickenmann, 2005). Currently, for each new target case, a small set of training cases with similar scope are used to constrain model parameters. This broadens the scope of applicability for dynamic models, yet decreases the usability by requiring time spent constraining parameters before each use. Dynamic models may be broadly sub-categorized by either treating the failing volume as a single mass interacting with the environment, or as many connected masses interacting both with each other and the environment. 5An exception is the flood modelling software FLO2Dwhich, when adapted to model debris flows, describes motion but not initiation (OBrien et al., 2009). 6Please see Appendix B for more discussion on model verification. 31 Point Mass Point mass7 models reduce a landslide to a single point, and calculate the dynamics along a prescribed flow path. This approach significantly reduces the complexity of a system, decreasing computational intensity at the expense of loss in detail. The models describe all forces acting on the mass through basic physics and simple flow resistance laws (Hürlimann et al., 2008), producing a complete description of the large-scale dynamics of the failing mass without addressing any internal dynamics. The classic point mass formulation is of a mass sliding down a plane using Coulomb’s Law of sliding friction (Körner, 1976) where the travel angle8 for a mass sliding down an inclined plane influenced only by friction and gravity is the equivalent coefficient of friction. For dry, rock fragments running out over bare rock, tanθ = tan32◦ ≈ 0.6. Then, by simple definition of terms and geometry, the runout distance may be easily predicted merely by estimating the total vertical drop H (Hsü, 1975): L= H tanθ (4.2) Coulomb’s Law works very well when applied to small-volume rockslides where move- ment is dominated by friction, making the runout analysis to predict hazard magnitude and intensity a straightforward calculation of the motion of a sliding block. The sliding block problem may be expanded to the form (Perla et al., 1980): dv dt = g(sinθ) = (µm cosβ )− v 2 k (4.3) where v is the flow velocity, t is time, g is gravitational acceleration, β is the slope angle9, µm is the sliding friction coefficient, and k is the turbulent friction coefficient10. The runout distance can only be modelled if the sliding friction coefficient is greater than the actual terrain slope of the depositional reach, µm ≥ tanθ , where as µm approaches tanθ the com- puted runout distance is increasingly sensitive to small changes in µm. The model must be 7Point mass models are also known as “lumped” mass models, for combining all elements within a system together, and describe the mass as a single meta-element. “Lumped” is a technical term within modelling, and is also used in several other subclassifications of dynamic models. To minimize confusion, conceptually identical alternate terminology will be used whenever possible. 8As the mass is treated as a single point (the center of mass), within the model travel angle and fahrböschung angle are identical. In practical application to the real world, the model may be used to predict the movement of the center of mass, thus the travel angle of the actual event. 9In application, the slope angle is the travel angle, as the horizontal distance the block slides isH tan(β ) = L, which means by definition, β = θ . 10Also called the “Mass to Drag” ratio (Perla et al., 1980). 32 Figure 4.1: A point mass model of a gravity-driven block sliding down a plane in- clined at slope angle β with a resisting frictional force. verified against observations, but relatively poor field data permit many combinations of µm and k unless additional restrictions are forced11. Other examples of point mass models are discussed in the review paper by Rickenmann (2005). Because the landslide is reduced to a single point, point mass models cannot com- pute the exact maximum runout distance, but only the displacement concerning the center of mass (Evans et al., 1994; Hungr, 1995). Volume is also not directly incorporated, so volume-dependent scenarios for hazard assessment and internal deformation cannot be an- alyzed directly. However, the simplicity of a point mass model allows analytical solutions, thus fast execution and analysis (Hürlimann et al., 2008). Deformable Mass Deformable mass models break the failing volume into elements that may interact with each other. This allows for modelling the source mass deforming throughout runout, incorporat- ing both solid (dislocation along a failure surface) and fluid (continuous flow) deformation, which are characteristic of landslides (Hungr, 1995). Deformable mass models incorporate 11Such as limiting the maximum velocity in relation to slope steepness. 33 varying depth and deposit area in the analysis, directly calculating intensity parameters used in hazard mapping. Thus, only minimal manual manipulation is required to convert model output into a hazard map. Deformable mass models produce the most complete description of movement, but are also the most computationally intensive of mathematical models. The complexity of apply- ing physical interactions to many mass-elements is too difficult for direct analytical relation- ships, so the models use iterative numerical solutions by time-stepping through analytical solutions. In addition to computational intensity, another drawback of deformable mass models is the time-intensive necessity of constraining rheological parameters12. For more discussion of distinctions between deformable mass models, see Appendix A. 4.3 Model Evaluation No tool is useful if it has not been properly calibrated, yet for landslide runout models, calibration is a tricky subject. Iverson (2003) rightly asserts that using back-analyses with post-hoc parameter selection merely proves model adaptability, while Crosta et al. (2006) presents a detailed description of further pitfalls of using back analyses for calibration: Calibration is hardly definitive when only geometrical information (deposit thickness, maximum or leading-edge runout distance, trim-line tilting derived velocities, runup distance or relief) is available and boundary conditions are complex or partially known (basal or lateral containment, free surface drag, basal scouring or entrainment and/or deposition during motion, water absorp- tion and material mixing, liquefaction, conditions of the material along the flow-path...). Additional constraints on model parameters can be provided by other field data such as flow duration, velocity estimates or measurements, or debris distribution to achieve a unique solution. This may be resolved for software models through verification instead of calibration, us- ing cross-validation to ensure the model is consistent with empirical data. Although beyond the scope of this thesis, a framework for enacting this solution is presented in Appendix B. For my purposes of purely back-analysis, it is sufficient that a technique exists that should be enacted before applying my results in forward prediction modelling. 12Discussed further in Chapter 7 34 4.4 Summary of Runout Models Identifying the potential runout of a landslide is complex, but a necessary aspect of hazard identification and risk analysis. Direct observation of landslide characteristics during an event is difficult and dangerous, and scaled laboratory models may not replicate key aspects of flow. Models present a powerful alternative in predicting runout when verified against empirical data. Models may be broadly classified into statistical models which make corre- lations to project runout, or dynamic models which describe motion in more detail. 35 Chapter 5 Analysis of Real Landslide Behaviour I’ll tickle your catastrophe. — Shakespeare The set of landslides selected and described in this thesis are worthy of independent statistical analysis prior to modelling. From comparing observed attributes such as volume and mobility, I can determine if my selection is consistent with sets analyzed by previ- ous authors, and assumably representative of the population of rapid flow-like landslides as a whole. By analyzing attributes observable before a failure such as movement type, morphology, and material, I can determine which characteristics are most linked to mobil- ity. This can guide future research investigations into which characteristics cause mobility (potentially differentiating between theories of excess mobility), or be used to widen the scope of statistical models to match only specific categories of characteristics instead of the more rigorous ideal of matching all observable characteristics. More immediately, this categorization of expected mobility dictated by easily identifiable characteristics allows me to analyze subgroups of case studies in later investigation of parameter selection for back analysis (Chapter 8). 5.1 Comparison to Previous Work In any endeavour, when analyzing select samples to draw conclusions about a larger dis- tribution, random sampling is essential in order to ensure the analysis is representative of the distribution in the real world. Unusual landslides1 are more interesting, thus reported more frequently than normal landslides. To counter this reporting bias, care was taken to 1Unusual events are those with either higher or lower than anticipated mobility for a given volume, ex- tremely large volumes, or large impact on human settlements or activities. 36 Movement Type Morphology Volume Scheidegger no constraints no constraints V ≥ 0.03×106 m3 Corominas debris avalanches, or unobstructed, no constraints debris flows impacted, or channelized McKinnon rock avalanches, unobstructed, Vf inal ≥ 106 m3 debris avalanches, or impacted, or flow slides channelized Table 5.1: Scope of events in the analyzed datasets. Movement types are classified by the Hungr et al. 2001 system. not select solely significantly unusual cases. The majority of my cases exhibit moderate excess mobility with 40%≤ Le/L≤ 70% (Table 3.4). The work of Scheidegger (1973) is notable as the first substantial effort at building a statistical model for landslide runout. Although many others have since gathered their own datasets for analysis, the work of Corominas (1996) stands out for building statistical mod- els differentiated by movement and morphology. These papers2 contain linear regressions of admirable statistical power, and are frequently cited in the literature. Therefore, I am using them as a standard against which to compare my own sample of landslides. 5.1.1 Comparison of Scope The scope of events analyzed by Scheidegger and Corominas are comparable to mine but do not overlap entirely (Table 5.1). Piecemeal detachment and retrogressive failures are not treated in any of our datasets. Notably, Scheidegger limits his cases by volume but with no other constraints, while Corominas and myself limit events to specified movement types and morphologies. The volumes of the cases analyzed by Corominas are unconfined, while the cases an- alyzed here are limited to catastrophic events with volume Vf inal ≥ 1 million m3 after en- trainment. The cases analyzed by Scheidegger follow the same constraint, except for one smaller case of V = 0.03 million m3. Entrainment of additional volume is not discussed by either author3. The landslides I analyzed include only those that exhibit fluid-like behaviour. Due to 2Both of which are first discussed in Section 4.2.1. 3Although Scheidegger does not differentiate between initial and final volumes for the cases in his analysis, independent case descriptions verify that entrainment did not substantially increase volume 37 Scheidegger Corominas McKinnon All 33 71 40 Unobstructed - 18 23 Channelized - 19 8 Impacted - 29 9 Table 5.2: Number of events overall and in morphol- ogy subsets. differences in classification systems, landslides where intact rock fragmented during failure are classified as debris avalanches by Corominas (using the Varnes 1978 classification sys- tem) and as rock avalanches in this study (using the Hungr et al. 2001 classification system). Unfortunately, Corominas’s subset also includes debris flows where surging is a dominant characteristic of motion, a behaviour excluded from my dataset, which prevents perfectly overlapping scopes. Scheidegger does not delineate events by movement, although it ap- pears most of the cases he analyzed are also rock avalanches. As I used the work of Corominas (and others) to guide my categorization strategy for morphology, the scope of our events directly overlap, and are identified with respect to channelized, unobstructed, and impacted morphologies. Scheidegger does not delineate events by morphology. 5.1.2 Relative Statistical Power The number of cases analyzed determines the statistical power of a conclusion, where a larger datasets has greater power. Scheidegger analyzed the smallest number of cases, and thus has the smallest power. Although Corominas analyzed more cases overall than I did, the size of some of our subsets are similar and thus have similar statistical power (Table 5.2). 5.1.3 Comparison of Sample Populations Scheidegger, Corominas, and I performed linear regressions on our datasets to establish V -α relationships. Although this form of statistical mobility model is usually used to pre- dict runout, in this instance that usage is not recommended due to the scatter in my data (although it may still serve as a baseline for further modelling and analysis of the same data). Instead, I use these regressions to confirm that my sample set is consistent with that of previous research.4 4See Section D.2 for a sensitivity analysis of my regression. Although the exact numbers vary as cases are selectively excluded, the comparison with previous research remains the same. 38 !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Volume to alpha relationship − All Vol(m3) Ta n Al ph a 104 105 106 107 108 109 1010 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 8 1 McKinnon Scheidegger Corominas Figure 5.1: My data and linear regression overlaid with regressions on separate data by Scheidegger and Corominas. See Figure 2 in Scheidegger (1973) and Figure 6 in Corominas (1996) for the respective author’s data. If a population of landslides is defined as “landslides that behave similarly to each other,” I expect that any sample set drawn from that population will exhibit similar be- haviour to any other set drawn from the same population, with any variation in behaviour between sets accounted for by randomly selecting a slightly more or less mobile event. Likewise, I would expect sample sets drawn from another population of landslides that all behave in a different manner to reflect that change in behaviour, with far more variation in behaviour from the original sample set than could be accounted for by random selection alone. A simple way to index bulk behaviour of a set of landslides is to look at theV -α regres- sion constructed from that set. To investigate if my selection of landslides is drawn from the same population of landslides analyzed by the previous authors, I quantified the likelihood that similar relationships could occur entirely by chance (Table 5.3). Examining the slope and intercept independently, using a t-test 5 I conclude that my 5The central limit theorem requires that a regression coefficient be theoretically normally distributed with infinite samples, and practically t-distributed (similar to a wider normal distribution) with finite samples. A t- test assumes a t-distribution of the regression coefficients, and calculates the likelihood that a specific coefficient 39 landslides are drawn from the same population of landslides as those analyzed by Coromi- nas, yet it is highly unlikely that my landslides are drawn from the same population of events as those analyzed by Scheidegger (Table 5.4). Intercept Slope Scheidegger +0.623 -0.157 Corominas -0.012 -0.105 McKinnon +0.055 -0.084 Table 5.3: V -α relationships deter- mined by linear regressions. See Equation 4.1 for form. A low p-value indicates decreasing overlap be- tween the population of landslides used in my regres- sion and that of the previous work. A high p-value indicates a high probability that I drew landslides from the same parent population and that differences are due to randomly sampling different events from within that population. The very low p-values when comparing to Schei- degger indicates it is highly unlikely the differ- ence between our regressions are only from chance. Therefore, it is highly probable that he and I are sampling from different populations of landslides. As more than half the events analyzed by Scheidegger are prehistoric and 72% are from prior to 1900, it is plausible that the observations used in his statistical analysis are limited by erosion or obscuring of the original landslide deposits6. Six of the cases used by Scheidegger are also used in my analysis (Elm, Frank, Hope, Goldau, Madison Canyon, and Sherman Glacier), which may account for all of the limited overlap between sample populations. Of the other 27 events analyzed by Scheidegger, the remaining 13 from Heim (1932) and 2 from Shreve (1968) were previously investigated and found to not meet the scope requirements of the cases included in my analysis. Therefore, the conclusion that the cases studies we used in our regressions are not drawn from the same population affirms that my scope limitations are not arbitrary, and differentiate between landslide populations with distinctly different mobility characteristics. In contrast, the high p-values for the slope and intercept comparisons for the regressions performed by Corominas and myself, in combination with common sense and knowledge outside pure statistics, leads me to conclude that we are drawing from the same population of events. My conclusion is further substantiated by the continuation of high p-values when analyzing similar subsets. This indicates that not only are our samples from the same popu- lation, but that my method of classifying and dividing into subsamples continues to produce populations consistent with those analyzed by Corominas with his larger dataset. The low could result from purely random sampling. Higher probability of randomly calculating the same coefficient has a high p-value, low probability of selecting that specific coefficient has a low p-value. 6See Section 3.1.4 and Section 3.3.1 for more discussion of the pitfalls of using prehistoric events. 40 p-value for t-test on... Intercept Slope Scheidegger 0.02 0.04 Corominas 0.78 0.55 Unobstructed 0.25 0.80 Channelized 0.29 0.48 Impacted 0.19 0.18 Table 5.4: P-values from t-testing the regression coefficient and inter- cept of my linear regressions ver- sus those determined by previous research. Regressions on subsets are compared to matching subsets. p-value when comparing our regressions for impact morphologies may be due Corominas includes landslides that overrun small hills, while I consider that an unobstructed flow, and only categorize an event as occurring in impact morphology when the path includes sub- stantial terrain obstruction. When selecting a landslide dataset using similar constraints on scope as Corominas’s relatively recent and more statistically powerful sample, I indepen- dently established similar linear regressions. This lends confidence to further inferences from this sample. 5.2 Pre-failure Characteristics and Runout Behaviour I can statistically analyze my sample to determine which pre-failure observable charac- teristics most influence mobility, identifying which characteristics impact behaviour and defining groups of landslides that behave in a similar manner. By reducing the number of characteristics to the most influential few, the burden of finding historical events to verify a model is reduced to the more tractable task of categorizing the future event into one of the similar groups. Defining similar groups also clearly identifies which events are compa- rable, granting justification for excluding outliers that do not fit within the category when continuing to investigate my sample. 5.2.1 Categorization Categorization of landslides into sets with similar mobility behaviour may occur in two ways: by evaluating the impact of categories imposed a priori, or by performing a cluster analysis to detect emergent categories. The imposed categories I evaluated are: volume, movement type, path morphology, material, saturation, and the triggering event that pre- ceded the landslide (Table 3.2). For more discussion of imposed categories, see Section 3.2. For quantifying mobility, I use three indices: the total horizontal runout (L, in meters), 41 the proportion of runout that is excessively mobile beyond that expected if motion were dominated by friction (Le/L, dimensionless), and the fahrböschung angle (α , in degrees). For more discussion of these indices, see Section 2.1.2 and ??. Sample Size The sample size of landslides is small compared to the number of categories, and options within each category. This is unfortunate, but unavoidable given the rarity of large land- slides, the additional constraints on scope beyond volume, and my requirement for sufficient observational data to model the event. Provided that the analysis is treated with caution, general trends and patterns may still be determined. 5.2.2 Evaluation of Imposed Categories ANOVA Analysis of Variance (ANOVA) is a statistical technique that tests whether partitions of data into mutually exclusive categories accounts for more of the variance between observa- tions than could be expected from the same number of randomly selected partitions. In this instance, given a particular category, the landslides are sorted into mutually exclusive parti- tions (the options within the category). ANOVA calculates the variance within the partition, then averages those variances. This average is compared to the variance between partitions, where a large ratio between that variance and the average is indicative of more meaning- ful categorization. A p-value is assigned to index the probability that the variance (both within and between partitions) could happen by randomly sampling from the population of landslides. A set of landslides picked at random from the population without any characteristics that influence runout behaviour7 will have a high p-value (the variance between partitions is similar to that expected from chance alone). A set of landslides picked because of a specific characteristic that influences runout behaviour will have a low p-value (the variance between partitions is greater than that expected by chance alone). Although the p-value changes with respect to the dependent variable (L,Le/L,α) under consideration, the overall patterns remain the same independent of the index used to quantify mobility. 7For example, categorizing landslides alphabetically by name. 42 Importance of Categories Volume has a clear relationship with runout, yet my attempts at breaking volume into groups by order magnitude8 resulted in a worse-fitting relationship with a decrease in number of groups, and improved relationship with increasing groups up to the continuous, no-groups relationship of a linear regression. The fewer groups I assigned, the more poorly the rela- tionship fit reality. As I assigned more groups, the relationship imporved, with the best fit between model and reality described by the linear regression (Figure 5.1). p-values for... L Le/L α Movement 0.01 0.67 0.13 Morphology 0.42 0.29 0.29 Material Source 0.01 0.43 0.75 Path 0.02 0.95 0.84 Saturation 0.50 0.84 0.86 Trigger 0.69 0.93 0.71 Table 5.5: P-values of ANOVA between characteristics and mobility controlled for volume. The sampled cases are relatively few in number compared to the number of categories and options within the categories (partitions). Therefore, it is necessary to beware of coin- cidental relationships, where one character- istic is acting as an index for another due to sample-size limitations9. To avoid this, I analyzed categories independently and in combination with each other, with the most notable cross-influence being volume, which overpowers all other influences. When the influence of volume is con- trolled, the pre-failure observable characteris- tics with the greatest influence on mobility are movement type, material (both source and path), and morphology (Table 5.5). Although the p-value change, the trends remain across mobility indices. Trigger and saturation appear to have minimal impact on differentiating between runout behaviour. Comment on Mobility Indices Mobility is primarily indexed by L, Le/L and α , but I also analyzed any correlations with other measures of runout, D and vmax, to use different subsets of available data10. No pre- event observable characteristics appear to be correlated with expected maximum velocity (vmax) which is unconcerning given the scarcity maximum velocity data and the discrepancy between observed maximums at a point versus modelled maximums overall. More inter- 8Order-magnitude categorization follows the recommendations of Jakob 2005 for classification of debris flows by volume. 9For example, if all of the unobstructed morphologies also happen to be small-volume events, morphology could be a confounding proxy for volume. 10See Section 2.1.2 and Section 3.3 for discussion of the relative merits of these mobility indices. 43 estingly, correlations are present for horizontal length L but not for curvilinear distance D, which should logically be roughly equivalent (although not equal) for measuring runout. 5.2.3 Evaluation of Emergent Categories A cluster analysis assigns cases to a set number of categories, dividing the cases so those with most similar behaviour are in the same category by minimizing variance in mobility indices within each group. More and more clusters are attempted to minimize within-group variance, with absolute minimum variance achieved when the number of clusters is equal to the number of data points, with one item in each group. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2 4 6 8 10 12 14 0 10 00 20 00 30 00 40 00 Clusters for alpha N = 39 Number of Clusters W ith in gr ou ps  su m  o f s qu ar es Figure 5.2: Effectiveness of emergent grouping of landslides using cluster analysis to minimize differences in α . Results are similar for cluster analysis on other mobility indices. 44 For my data, the effectiveness of clustering rapidly fell off such that additional clus- ters produced diminishing returns on meaningful distinctions between groups after 3 to 4 clusters (Figure 5.2). By inspecting the cases within the defined clusters, I found the cate- gorization to be dominated by volume with no other clearly distinguishable characteristics common within a group. A modified form of cluster analysis controlling for the influence of volume may be attempted in future research. 5.2.4 Influence of Categories on Runout Within a category, it is possible to perform a linear regression to compare the influence of a given factor versus the remaining options within the category (Table 5.6). In this manner, while holding one option within a category fixed as the base average11, the coefficient of regression (B) is the amount by which a different option is likely to increase or decrease runout of an otherwise identical landslide such that: Bbase average+Binfluencing factor = average mobility for that factor (5.1) For example, when controlling for variation in volume, a landslide with unobstructed mor- phology will have, on average, L = 1635 m and α = 19.7◦, while a landslide identical in all other regards with channelized morphology will have L = 1635+ 1221 = 2856 m and α = 19.7−0.7 = 19.0◦12. As with any statistical average, outliers are an expected statical deviation and individual event behaviour may vary widely from the average13. Considering the complexity of landslide runout, it is absurd to use an incredibly simple model like this to predict mobility. Instead, this serves to quantify the relative impact of one characteristic versus another on mobility. Within this sample population some characteris- tics are underrepresented with only a few examples14, and thus only identifies interesting areas for future study when Bfactor is large relative to the base average. Influence on mo- bility is given using L, Le/L and α . If an effect is real, it should have an inverse impact on horizontal distance and fahrböschung angle. Volume Volume is by far the most dominant pre-failure observable characteristic influencing runout behaviour, and investigations of any other characteristics must be controlled for variation 11Graphically, as the intercept. 12Note: an increase in runout is measured by an increase L and Le/L and decrease α . 13For more discussion on the limitations and advantages of statistical models, see Section 4.2.1. 14For example, this data set contains only one instance of material = loess; see Table 3.4. 45 in volume. Decreasing fit proportional to number of partitions strongly implies a lack of hard volume cut-off for events that will or will not demonstrate excessive runout; however this dataset is limited to events over the debated fluidization cut-off of Vf inal ≥ 1 million m3 so a dataset without volume constraints should be analyzed to investigate if this con- straint is justified. Discovery of a hard constraint would place a firm physical limitations for investigation of mechanisms of exceptional mobility. As a hard constraint on minimum volume required to exhibit excess mobility seems unlikely both from the lack of distinctly separating events into groups of differing mobil- ity characteristics by imposing order of magnitude categorization, and from the previous research by Corominas (1996), an expansion of the sample set to include events of lower volumes increase the number of events available for analysis, and allow for the enhancement sets of cases currently underrepresented in this sample (Table 3.4; all events that are not a rock avalanche involving primarily rock running over unobstructed terrain would benefit this sample). Movement Type Movement type appears to have an impact on mobility, with flow slides having the most mobility, while rock avalanches and debris avalanches have progressively decreasing mo- bility. Although no flow slides within this sample have velocity observations, the same order holds true for velocity, with rock avalanches having an average higher maximum velocity than debris avalanches. However, the sample population is heavily biased to rock avalanches (nRock Avalanche= 29 versus nDebris Avalanche= 6 and nFlow Slide= 5), so this should be confirmed with a more diverse landslide population. Due to the limited number of large landslides, this is only possible by extending the sample population to events with smaller volumes. Morphology Analysis of this dataset is consistent with previous work by Nicoletti & Sorriso-Valvo (1991) and Corominas (1996): morphology is a strong contributing factor to runout be- haviour, with channelization increasing mobility and impact decreasing mobility. This trend does not remain constant across maximum velocity, with events in unobstructed terrain trav- elling on average far faster than events with substantial obstruction, and channelized events running out on average far slower. However, velocity is highly under-represented in this subset, with NUnobstructed = 7, NChannelized = 3, and NImpacted = 1, and unlike for most of my 46 subsets, this shortcoming is far easier to rectify with field visits. Expanding observations of velocity by morphology is usual, as the most frequent ob- served morphology (unobstructed) is also the least likely to produce maximum velocity es- timates by the nature of how velocity is calculated from field observations (Section 3.1.3). It is always possible to calculate maximum velocity for an event with impacted morphology (from run-up against the adverse slope), and frequently possible to calculate the maximum velocity for channelized events (from superelevation, although this requires confinement in channels with bends). However, as unobstructed morphologies by definition lack in ei- ther substantial run-up against adverse slopes, or channelization around bends, velocity estimates come from direct observation by eyewitnesses. Therefore, as unobstructed mor- phologies are the most-represented within this set with velocity estimates, it is not unlikely that future field visits can enhance case descriptions of events in channelized or impacted morphologies with maximum velocity estimates. Even within models with topographic-dependent scope (such as a scope of only chan- nelized runout, or only free runout, or only frontal impact impeding runout), statistical mod- els cannot explicitly account for buildings or other case-specific small-scale topographic changes. Material Events with rock sources are expected to run out the farthest, exhibiting approximately dou- ble the mobility of a similar event with a sediment or clay source. This is consistent with Ui (1983), who found volcanic dry avalanche deposits characterized in part by megablocks exhibited greater mobility that similar-volume avalanches of non-volcanic materials lacking megablocks. This mobility may be because the energy released by fragmentation enhances mobility. The rough relationship between particle size and runout (finer-particle sources have less mobility) may also hint at energy loss through increased internal friction or turbu- lence when a larger number of smaller particles are interacting. This could be investigated further by categorizing sources by particle size and performing a linear regression between particle size and mobility. Source material does not have an impact on maximum velocity. Although less influential, the impact of path material on mobility is more intuitive: events running out over glaciers travel the farthest (consistent with Evans & Clague 1988), then events over clay or bare rock, while events running out over talus, sediment and ash are expected to run less far (all lacking excess mobility entirely with Le < 0 m). An interesting avenue of further investigation would be to permit multiple materials, weighting material type with respect to its dominance in the runout region. On average, events running out over 47 bare rock have a marginally higher maximum velocity than events running out over glacier or debris, and a substantially higher maximum velocity than events running out over talus. The interaction of material and mobility is more complex than can be investigated by my coarse usage of a single source or path material. Further research should be done by creating separate categories for each material type (rock, debris, chalk, snow, and so on) with a single landslide potentially appearing in more than one category. Saturation Categorizing events by saturation was only minimally different for predicting runout be- haviour than if I had randomly allocated events into groups, yet on average wet events run out slower and about twice as far as dry events. This conclusion is extremely tentative due to the limited number of dry events within this sample. Saturation can only be determined during and shortly after an event, thus is often underreported in the literature. Further anal- ysis of a larger dataset15, or finer distinctions between levels of saturation (perhaps dividing between saturation from extended heavy rainfall, entraining saturated material, or running into flowing water) may clarify the relationship between degree of saturation and runout, if any exists. Triggers Previous research on earthquake-triggered landslides has focused primarily on mapping regions susceptible to seismically-triggered failures (Keefer, 1984), not on how the trigger may impact landslide runout. Work by Adushkin (2006) suggests that the violent trigger of an artificial blast alters V -α relationships; it is plausible that other violent triggers such as earthquakes or eruptions may have a similar effect. Unfortunately, triggers are notoriously underreported in the literature, so the subset of cases within this thesis with a recorded trigger is too small to draw meaningful conclusions. Further investigation focused on events with violent triggers – earthquakes, volcanic blasts, and artificial blasts – which may inject energy into a flow may help differentiate the validity of mobility theories16 involving converting elastic energy into kinetic energy through fragmentation. The frequency of earthquakes is of a different magnitude than that of the acoustic vibration demonstrated to enhance mobility, so even if a link between earth- quakes triggers and mobility is established, it will not directly support theories of reducing 15Again, due to the limited nature of case studies with large volumes, this may only be possible by including events with smaller volumes. 16See Section 2.2. 48 internal friction through vibration of the mass. From this limited dataset, trigger appears to have almost no impact on mobility. Events triggered by rain run out marginally farther than events triggered by earthquakes, while events triggered by earthquakes have higher maximum velocities on average. The single landslide triggered by an artificial blast has reduced mobility, consistent with Adushkin (2006). 5.3 Summary of Analysis of the Set of Landslides The set of landslides I am analyzing exhibits similar mobility characteristics to those ana- lyzed by Corominas (1996) in his research on categorizing mobility by classification then sub-classifying by morphology. It is likely my sample set is drawn from the same popu- lation of landslides he analyzed in his study with greater statistical power, supporting my assertion that the 40 cases are representative of the diversity in characteristics and behaviour of mobile landslides. Statistical analysis of both imposed and emergent categorization of landslides based on physical characteristics to determine groups of landslides with similar mobility behaviour confirms volume as the dominant factor in determining mobility, where increasing volume is linked to increasing mobility. In order of decreasing influence, movement type, morphol- ogy, and material also successfully categorize landslides into different mobility regimes, while saturation and trigger have minimal impact. Although volume has a strong influence on mobility, a lack of clear categorization by order magnitude, a continued high mobility even for events with initial volumes below one million m3, and previous research (Corominas, 1996) suggest that a hard constraint on the minimum volume required for excess mobility does not exist. This implies that removing the volume constraint from scope and expanding the sample set to events of smaller vol- umes will continue to select cases from a population of landslides which exhibit similar mobility characteristics. Removing the volume limitation will greatly increase sample size, as smaller volume events occur more frequently, and increase the likelihood of broadening the diversity of physical characteristics exhibited by landslides within the sample set. A more diverse sample set would both strengthen the statistical confidence in determine the relative impact of specific physical characteristics on mobility behaviour, and differentiate between behaviours regimes for events that are currently poorly represented. 49 Predictor Base Factor BL [m] BLe/L [%] Bα [ ◦] Bv [m/s] Movement Type Rock Avalanche 1544 15 20.5 53 Debris Avalanche -704 36 5.0 15 Flow Slide 977 15 -4.5 Morphology Unobstructed 1635 42 19.7 62 Channelized 1221 -3 -0.7 -41 Impacted -800 -44 5.9 -22 Material Source Rock 2642 42 20.9 49 Debris -2071 -43 3.1 0 Chalk -1782 0 -2.7 Loess -2668 17 -4.7 Path Rock 2124 44 22.1 71 Debris -468 -17 -0.3 -10 Ash -4232 -11 -5.3 Clay -6 20 -10.9 Snow & Ice 2367 6 -3.1 -15 Talus -2433 15 -5.6 -37 Saturation Dry 1060 56 15.2 78 Wet 818 -26 6.1 -28 Trigger Non-Violent 1857 44 19.1 41 Rain 110 -17 3.7 Artificial Blast -650 -29 6.4 Earthquake -980 12 -2.2 24 Table 5.6: Base average and influencing factor for a characteristic (independent variable) and mobility index (dependent vari- able), controlled for volume. See Equation 5.1 for form, and Table 3.4 for the number of cases represented with each characteristic. 50 Chapter 6 Tools: Selecting Runout Models Take calculated risks. That is quite different from being rash. —George S. Patton (1885 - 1945) When a field survey finds sufficient cause to anticipate a catastrophic event – observing widening fractures as a is torn mountain apart, a block poised on a sliding plane awaiting a trigger for failure – a mathematical model is used to predict runout characteristics. An ex- pert practitioner attempts to select the most appropriate modelling tool to produce the best prediction of the expected event (Erismann, 1986). Each mathematical model has differ- ent underlying assumptions and limitations, so selecting the appropriate model is equally as important as the selection of a constitutive model and parameters when attempting to accurately predict landslide runout. The model output data is interpreted by an expert prac- titioner in the construction of a hazard map, which is used to direct mitigation and risk reduction efforts. Models must be able to explain the past and predict the future. The model must have an appropriate scope such that the conditions under which the model is applicable encompasses the target event. All models must also be refutable: by producing results that may be tested, a model may be either repeatedly confirmed valid or possibly invalidated through contradictory results. Without the ability to be refuted, a model produces no truly testable results and is thus ineffective for scientific experimentation. Additionally, a model must be easily usable and cost-effective. Runout analysis investigates the magnitude and distribution of a landslide. This is the path the landslide traverses including the depth and velocity of flow, and the debris dis- tribution including area and depth. The metric for evaluating the fit of a landslide runout model is the closeness between the debris and velocity distribution of the real event and that 51 predicted by the model. In back analysis, model parameters are adjusted to produce results that match observations of the real event. In forward modelling, the model is used to predict the hazard distribution. 6.1 Proposed Models: DAN-W and DAN3D Many currently available dynamic models have the appropriate scope to assess rapid, flow- ing catastrophic landslides1. I am choosing to use the dynamic analysis software models, DAN-W and DAN3D, developed by Hungr (1995) and McDougall (2006) for use in pre- dicting the extent of motion and velocity of rapid landslides. I am electing to use these specific models because both rely on similar assumptions yet are mathematically different from each other, and previous work suggests that the models converge on similar parameters during back analysis of a case (McDougall & Hungr, 2003, 2004, 2005; McKinnon et al., 2008; and Geertsema et al. (2009) among others). This permits back analyses performed with either model to be comparable to each other. Conceptually, both models function by time-stepping the kinematics of fluid dynamics applied to fluid parcels. The DAN-W and DAN3D models concentrate on external aspects of behaviour, ignoring internal micro-mechanics. Actual landslides may have complex in- ternal motion such as turbulence. By concentrating on external aspects of behaviour only, the software may model landslide flow exclusively parallel to the bed, greatly simplifying internal motion. However, ignoring detailed internal material behaviour makes the models unsuitable for studying internal landslide behaviour such as material sorting, transporta- tion of intact blocks, or directing search-and-rescue efforts for victims (Petley, 2008). The models compensate for neglecting composition and internal mechanics by allowing for flex- ibility in describing the rheological character2 of the flow. Both approaches may be used to model landslides that entrain path material, and permit user-specified heterogenous flows with variable rheology. Both models treat landslides as instant fluids, while actual events may travel as a cohe- sive block for some distance before fragmenting. The instantaneous fluidization may result in the model flow spreading more quickly than the observed event, but the user can com- pensate for this effect by specifying the event be treated as a unified block for a set distance or time interval. See Appendix C for details on how the programs handle mass and momentum balance, 1See Section 4.2.2 for additional examples of dynamic models, and Section 3.1 for the scope of landslides analyzed for this project. 2Discussed further in Section 6.2. 52 and earth pressure equations. 6.2 Hypothetical Fluids and Rheologies Landslides are complex, both in material and in motion. It is challenging to gather direct evidence about the internal aspects of landslides, due to both variable composition and haz- ardous field conditions. However, a landslide expert may still make meaningful predictions about landslide behaviour by bypassing the intractable internal behaviour and concentrating on external behaviour. The term “flow-like” landslide implies a fluid material with significant basal and internal deformation as it flows over a resisting basal surface (Crosta et al. 2006; see Section 2.1.3). Flows can not be treated by kinematics of sliding3 but instead as concentrated cohesionless grains in a fluid medium (Hsü, 1975). Instead of attempting to mimic the heterogeneous mixture of real landslide rheology including mud, tree trunks, boulders, and anything else that is entrained in the flow through a complex simulation, the DANmodels use hypothetical fluids (Figure 6.1). Hypothetical fluids are theoretical constructs, simple homogeneous fluids designed to externally behave in a manner similar to real events4. The constitutive rheological model and the associated parameters play a fundamental role in the modelled dynamics (Hürlimann et al., 2008). The hypothetical fluids control only the basal rheology, with all modelled events acting a deformable mass flowing on a thin fluid basal layer. The bulk properties of the hypothetical fluids approximate the behaviours of the prototype mass; for this project the fluids are limited to frictional or Voellmy rheologies. 6.2.1 Frictional Basal shear stress is a function of effective normal stress at the base of the flow (Hungr, 1995). In frictional rheology, the basal shear stress τzx opposing motion is expressed as: τzx =−σz tanϕb (6.1) where σz is the total bed-normal stress at the base of the flow and ϕb is the bulk basal friction angle. The bulk basal friction angle can be expressed as basic components by: tanϕb = (1− ru) tanϕ (6.2) 3See Section 4.2.2. 4See Hungr (1995) or McDougall & Hungr (2004) for more detailed descriptions of the concept of hypo- thetical fluids. 53 (a) Complex heterogenous real mass parcels (b) Simple homogeneous ideal mass parcels Figure 6.1: Real landslide materials are complicated, so are modelled as simple hy- pothetical fluids. where ru is the pore pressure ratio and ϕ is the dynamic basal friction angle. As long as the pore pressure ratio may be assumed to have the constant value ru= uσ the total normal stress and shear stress maintain a fixed proportional relationship, and the basal stress relationship remains frictional. Overestimation of velocities and proximal-thickening of the deposit are characteristics of the frictional model (Körner, 1976; Hungr et al., 2005; McDougall, 2006). 6.2.2 Voellmy The Voellmy rheology combines frictional and turbulent models such that increasing veloc- ity results in increased drag (Körner, 1976) Mathematically, this is expressed as: τzx =−σz f + ρgνx 2 ξ (6.3) where f is the frictional coefficient, ρ is the material density, g is gravitational acceleration, νx is the depth-averaged flow velocity, and ξ is the turbulence term. Conceptually, ξ im- plicitly accounts for the thickness of an undrained layer overridden by a landslide, where the frictional resistance starts low and increases proportional to velocity squared (Bagnold, 54 1954; Hungr, 1995). The Voellmy model typically produces distal thickening of the deposit, and better sim- ulations of velocity than frictional rheology (Körner, 1976; Hungr et al., 2005; McDougall, 2006). A mathematical artifact of this rheology is unrealistic extended motion within the flow after the main event comes to a rest; it is necessary for a practitioner to exert judgement to determine when motion is complete. 6.3 Summary of Tool Selection Model characteristics dictate the applicability of that model to specific tasks. Although many models are appropriate for my task of consistently analyzing a large number of diverse landslides with flow-like behaviour, the combination of DAN-W and DAN3D allow me to easily model a single event using distinctly different mathematical techniques, and using different forms of input data, while still being able to compare results from both models. For my task of consistently analyzing a large number of diverse landslides, the ability to adapt the model to a particular case, ease of use, computational speed, affordability and accessibility of the software are all met by the DAN software suite. Ultimately, the exact model used is not relevant to the applicability of the results, as although the exact numbers will change based on how a particular program handles rheologies, the overarching concepts of how a physical characteristic relates to parameters should remain similar. As internal landslide mechanics and materials are too complicated to directly simulate, simplified homogenous hypothetical fluids model the bulk landslide behaviour. The two rheologies I am using are the frictional rheology controlled by the friction angle, and the Voellmy model controlled by friction and turbulence coefficients. 55 Chapter 7 Method of Standardized Back Analysis The road to wisdom? –Well, it’s plain and simple to express: Err and err and err again but less and less and less. —Hein (1966) Matching a model to a known landslide event with a measured volume, duration, and de- bris distribution is not an exact science. Determining which criteria are the most important to exactly model, and which are “good enough” requires expert judgment. For new land- slide researchers lacking in sufficient exposure to the wide range of landslide behaviours, it can be a daunting task to evaluate back-analyses. Even among experienced practitioners, deciding which back analysis best describes an event can be more a matter of a hunch than objective truth. This lack of consistency mandates working in isolation: even if a case study was thoroughly analyzed by a trusted peer, because of personal differences in technique and judgment, it must be re-analyzed by each new researcher wishing to include the case in their own collection of back-analyses verifying their landslide runout model, effectively dupli- cating efforts. This lack of consistency also renders meta-studies investigating published back-analyses to near-futile status, hindering efforts to cobble together larger datasets to use in distinguishing between theories of long runout mechanisms. 56 This lack of consistency is also costly because predictive models must be individually built in a time-consuming manner. Before forward-modelling a prospective event, similar historical events are back-analysed to establish a range of applicable model parameters. Those parameters are fed into the new model for forward modelling runout distribution and intensity. This is time-intensive, as an expert practitioner must not only construct the model for the landslide of interest, but also for many similar historic landslides, and then must conduct a parametric survey on all the models. If this process were streamlined and thus the tool more affordable, it is likely more planners would use it in determining their local hazards. Increased use of accurate prediction for landslide runout and anticipated intensity would lead to improved mitigation, reduced risk, and a decrease in the loss of life associated with landslides. I avoid the standardization problem by personally selecting parameters for all the pre- sented back analyses, producing a dataset that is internally consistent. Although other au- thors and other software programs may (indeed, probably will) produce different specific numbers for user-selected parameters, the general trends established through this process should be universally applicable. I also applied fixed-quantitative standards for judging the “best” back analyses (and related parameters), allowing for full reproducibility of results1. 7.1 Method for Back Analysis Any model is a hypothesis about the relationship between a set of fixed parameters and a set of variables. Given a set of parameters, the hypothesis implicit in the model is that the variables will take certain values. For landslide runout models, the variables are the measurable characteristics of runout – runout distance, thickness, velocities, and so on. Maximum runout distance is a clearly-defined measurement that may be taken in the field any time after the event with a high degree of accuracy for every single case study2 (and is frequently reported in published descriptions), while temporal characteristics such as ve- locity and event duration, must be measured during the event or retroactively calculated from indirect observations, so are more prone to inaccuracy3. Unfortunately, parameters for runout models are not as tractable, as they describe the properties of an imaginary fluid which behaves in a manner externally comparable to landslides4, but is not directly measur- able in the field or laboratories experiments. Instead, model parameters must be determined 1Both these techniques are discussed in more detail in Section 7.1.4 and Section 8.1. 2Excepting cases where the toe is subject to erosion, such as landslides damming rivers. 3Please see Section 3.1.3 for details. 4See Section 6.2 for details. 57 Figure 7.1: Back analysis is performed by varying input parameters until modelled runout is consistent with the observed real runout. Not all possibilities are sketched: runout distance and spreading vary independently, such that a model may produce a deposit that is both too short and too thin, too far and too thick, or any other inappropriate debris distribution and runout. through back analysis. Back analysis is a process by which the input rheology and parameters for a landslide model are varied until the modelled landslide runout (the output) is judged to be an adequate representation of the observed runout (Figure 7.1). By establishing a consistent framework for modelling methodology, back analyses may be compared and patterns extracted. 7.1.1 Step 1: Describe a Case History In order to perform a back analysis, my first step is to build a description of a real event. This case description must include the pre- and post-event topography, any observations of entrainment (locations, depths, volumes, or rates), and the source volume. Any observa- tions on velocities, runout distances, and debris distributions are also included, although the particular characteristics observed may vary from case to case. If a profile or contour map was not included in the reference papers, topography was extracted from publicly available databases. Landslides are located via visual inspection of satellite images on Google Maps, then a profile extracted by using the Path Profiler plugin along the runout path. A landslide is affected not just by the material that fails, but potentially by the material of the path it flows over or entrains or the geometry of the path. To allow analysis of potential links between pre-event observable characteristics and model parameters used to best-model the subsequent event, additional observations on geomorphology and material are also included in the case histories. 58 All descriptions of case histories are located in Appendix E. 7.1.2 Step 2: Build a Model I built a model for each landslide in DAN-W by first specifying the pre- and post-event profile, width, and entrainment (if any). For well-behaved events, one streamline is con- structed. For more complicated events involving a bifurcation of flow, two streamlines are constructed5. All the case studies presented here are modelled in DAN-W, and in DAN3D when digital elevation models are readily available. Grid files covering the area of interest for the path, source, and entrainment are input into DAN3D to build a 3-dimensional model. To account for fragmentation, the detached volume is bulked by 20% unless the lit- erature suggests a different bulking factor. Entrainment is only considered significant and included in the model if at least a 20% increase from the initial volume is observed (Ventrainment >Vbulking). All cases are modelled with default control and material settings (Table 7.1); only changes in the rheology and associated parameters are varied. Control Parameter Default Value Material Parameter Default Value number of elements 50 internal friction angle 35◦ time interval 0.02-0.1 s unit weight 20 smoothing coefficient 0.02 tip ratio 0.5 stiffness coefficient 0.05 stiffness ratio 5 centrifugal forces on boundary block geometry normal pressure term modified Table 7.1: Default DAN-W parameter values used in back analyses. 7.1.3 Step 3: Run the Model I held internal friction angle and unit weight constant for all materials (Table 7.1). All landslides are modelled using both frictional and Voellmy rheologies. I selected parameters through trial-and-error. After I evaluated the output of each run, I adjusted the input parameters and re-ran the model using an iterative process. For prac- 5Profiles are included along with case descriptions in Appendix E. 59 ticality, the friction angle is adjusted in ∆θb = 1◦ intervals, the friction coefficient is ad- justed in ∆ f = 0.01 intervals, and turbulence coefficient ∆ξ = 100 m3s intervals. In the two-parameter Voellmy rheology, first f is adjusted to alter runout distance, then ξ to ad- just velocity and timing. Without time or velocity data, the turbulence coefficient cannot be constrained. Proximal thickening is usually best-modelled by frictional rheologies and distal thickening by Voellmy rheologies. Runout distance increases inversely proportional to friction angle or friction coefficient, and velocity increases proportional to turbulence coefficient. In order to be able to statistically compare the input parameters, I also blindly ran all models in DAN-W with a fixed set of input parameters, retroactively identifying the best input parameters. The frictional rheology was run with friction angles 5◦ ≥ θb ≥ 45◦ in ∆θb = 5◦ intervals and θb = 17◦. The Voellmy rheology was run with friction coefficient 0.05 ≥ f ≥ 0.2 in ∆ f = 0.05 intervals, and the turbulence coefficient was run for ξ = 100 m 3 s and 500 m3 s ≥ ξ ≥ 2000 m 3 s in ∆ξ = 500 m3 s intervals. These models were all run without entrainment, as the purpose is not to create a detailed back analysis (as with user- selected parameters) but to use only information available prior to failure to test the efficacy of various parameters for forward-predicting hazard distribution and intensity6. 7.1.4 Step 4: Select Best Parameters I judged the back analyses against the case history descriptions, which may include runout distance, debris distribution, and velocity or time observations. If the observation data is limited, a range of parameters may be acceptable. Two main techniques were used to determine the best modelled runout for a case study: 1. User selection of parameters through expert judgement of the best combined total runout, debris distribution, velocity distribution, and in-motion behaviour. 2. Mathematical selection of parameters through minimizing the difference between the modelled and observed value of a runout index. In user selection, expert judgment is used to select which model best encompasses all aspects of a landslide’s behaviour, from in-motion velocities to deposit distribution. This is a time-consuming method but very tightly-fitting models of a real event are produced. Although the most flexible method, it is also the most difficult to replicate because each 6See Appendix F for further discussion on the choice to exclude entrainment from this portion of the back analyses. 60 expert may emphasize different aspects of observed behaviour and thus select different parameters. Mathematical selection is picking a single mobility index (such as curvilinear distance D), and selecting the back analysis that produced results most closely matching that single characteristic for each event. The speed, simplicity, and ease of repeatability of this tech- nique is severely hampered by the limitation of selecting parameters based entirely upon only one observed characteristic, when other characteristics may be vitally important to ac- curately model a particular event. The strength of this technique is its ability to consistently process a large volume of data. As more case studies are modelled using identical parame- ters, stronger assertions can be made about a particular parameter’s expected performance. Then, that parameter may be used in future prediction modelling with a clear expectation of how the model may deviate from the real event. The merits of qualitative and quantitative judging of back analysis are discussed further in Section 8.1. 7.2 Example of Application of Back Analysis to 1969 Madison Canyon, U.S.A Madison Canyon is an interesting an example of applying this methodology, as the observa- tion information includes data on all of the mobility indices, and the impacted morphology presents a choice in how to best represent the key aspects of an the path topography in a model. 7.2.1 Describe the Case History (This description is also located in Section E.18.) On 17 August 1969, the Hebgen Lake earthquake triggered the failure of V = 21.4 million m3 (bulked volume) of rock in Yellowstone National Park. The rock avalanche ran down Madison Canyon, across the valley floor, and 2000 m up the opposite wall before deflecting up and down along the valley, damming the river. The material ran out a curvilinear distance D = 1.28 km in less than 60 s. From run up, the flow reached up to a maximum velocity of 50 m/s. The mass traveled a horizontal distance L= 1300 m and dropped a vertical height H = 2200 m, with a fahrböschung angle α = 13◦.The rock avalanche left a deposit 1500 m wide(Hungr, 1995; Trunk & Dent, 1986). 61 0 500 1000 1500 19 00 20 00 21 00 22 00 23 00 Madison Canyon Distance (m) He igh t ( m .a .s. l.) 40 0 60 0 80 0 10 00 12 00 W idt h (m ) Figure 7.2: Madison Canyon profile. This profile is also located in Section E.18. 7.2.2 Build a Model At Madison Canyon, the impacted morphology defected flow along the valley. To reflect this, I may either model two streamlines, one flowing up-valley and the other down-valley after run-up, or I may have a single streamline with widening of the path at the valley floor. The mass coming to a rest almost immediately after deflecting down the opposing valley wall, with less than a third of total runout occurred along the valley. In order to prioritize the run-up over the valley spreading, I chose to model the event as a single streamline (Figure 7.2) with widening for valley spreading such that I could observe the impact of parameter selection on relative run-up height. 62 7.2.3 Run the Model The model was run both with user-selection of parameters (Table 7.2) and using the fixed parameters (Figure 7.3). Data is presented normalized with respect to the observed index. D L Le α vmax Observed 1280 m 1300 m 756 m 13◦ 50 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 15 11 -0 7 1.4 -17 Frictional 16 7 -4 -3 10.0 -20 Frictional 17 2 -8 -12 18.5 -24 Voellmy 0.2 100 3 -7 -10 16.4 -34 Voellmy 0.2 500 16 4 20 -9.8 -6 Voellmy 0.2 1000 18 7 27 -15.9 -7 Voellmy 0.2 1500 20 8 31 -19.5 -5 Voellmy 0.2 2000 21 9 32 -20.5 -5 Voellmy 0.2 4000 23 11 40 -26.3 -4 Voellmy 0.2 4500 24 12 41 -26.9 -4 Voellmy 0.2 5000 24 12 42 -27.7 -4 Voellmy 0.25 500 7 -3 -0 8.1 -13 Voellmy 0.25 1000 11 0 9 -0.2 -6 Voellmy 0.25 4000 14 3 16 -6.7 -13 Voellmy 0.27 500 4 -7 -8 14.7 -15 Voellmy 0.27 4000 11 -0 7 1.4 -17 Voellmy 0.28 500 3 -8 -11 18.0 -17 Voellmy 0.28 1000 7 -4 -2 9.8 -11 Voellmy 0.3 500 -0 -11 -18 25.0 -20 Voellmy 0.3 1000 3 -7 -10 16.4 -14 Voellmy 0.3 4000 5 -6 -6 13.3 -22 Table 7.2: User-selected parameters for Madison Canyon. This table is also located in Table G.11. 63 7.2.4 Select Best Parameters In user-selection of parameters (Table 7.2), the frictional rheology was quickly abandoned when it was apparent that appropriate runout distance could only be achieved at the expense of underestimating velocity by≈ 20%. With Voellmy rheology, although an extremely high turbulence coefficient (ξ = 4000m3s ) produces models very close to the observed velocity, increasing friction coefficients to achieve appropriate runout distances resulted in decreased velocity. Instead, in my judgement the best balance of mobility and velocity is modelled when using f = 0.2−0.25, ξ = 1000m3s which slightly over-estimates mobility and slightly under-estimates velocity. In mathematical selection of parameters (Figure 7.3), the lowest deviation horizontal runout distance, the fahrböschung angle, and velocity are with an extremely low friction angle (θb = 10◦), or with slightly lower friction coefficients than with the user-selected data ( f = 0.15, ξ = 1000m3s ). 7.3 Summary of Back Analysis Back analysis is an inherently deterministic process, matching a model to most closely reflect the observed runout characteristics. To do this, a user must first describe the event and build a model by inputting the pre- and post-event topographies. Finally, a model is run iteratively, with parameters adjusted in response to user-judgement of the suitability of the output. All cases are also run with a set of parameters selected a priori to have consistent input data for statistically evaluating the effectiveness of parameters across landslides. The results of modelling are discussed in Chapter 8, with the runout data for the 30 blind statistical rheologies presented in Appendix F and summarized in Appendix H, and the variable number of user-selected parameter runs are presented in Appendix G. 64 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●● ●● ● ● ● ●● 600 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ●● ●● ● ●●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●● ●● ● ● ● ●● 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ● ● ●● ● ● ●● 0 10 20 30 40 50 60 10 20 30 40 fri cti on  a ng le (d) vmax Figure 7.3: Raw output data for models of Madison Canyon, with observations marked by a dashed line. For Voellmy rheologies, the friction angle calculated by θ = arctan( f ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). This figure is also located in Figure F.19. 65 Chapter 8 Analysis of Model Back Analyses and Parameter Selection First weigh the considerations, then take the risks. — von Moltke In this chapter, I compare the traditional technique of qualitative user selection of pa- rameters and a new method of quantitative mathematical parameter selection for back anal- yses of my case studies. I then analyze the performance of individual parameters when modelling all cases, and subsets of cases as determined by movement type, morphology and material. 8.1 Defining “Best” When performing back-analyses, one needs to decide which rheology and parameters best models the target case. This may be done through qualitative or quantitative judgement of the model parameter performance. 8.1.1 Qualitative User selection of model parameters is a holistic process of expert judgment qualitatively judging the “best” rheology and associated parameters which most encapsulates the land- slide behaviour as a whole. This process involves comparison of observed and modelled characteristics including runout distance, debris distribution, and flow velocities as weighted by the expert’s opinion of the reliability of the reported observations. This process is ex- tremely flexible, involving so many subjective choices that the selection of a best rheology and associated parameters may vary substantially between practitioners. The cases pre- 66 sented here have all been back-analysed by a single practitioner in a consistent manner, using the same prioritization values and judgement to select the best model for each case. Although qualitative, it is possible to make relative comparisons about modelling landslide behaviour given pre-event characteristics. Even though exact numbers (particularly model parameters) may vary with other practitioners, the relative trends of increasing or decreas- ing parameter values in order to model landslides of a given categorization should remain consistent. 8.1.2 Quantitative Mathematically selected parameters are automatically evaluated by comparing the modelled mobility index to the reported observed index. Although it is technically possible to include multiple target observations simultaneously and weighing them by reliability, for simplic- ity only one target observation is evaluated at a time for this study. The normalization is quantified as a percentage: normalized index (∆) = indexmodelled− indexreal indexreal ×100 (8.1) Normalization is treated as a positive or negative, as over-estimating versus under-estimating runout mobility indices have substantially different consequences when using model pro- jections in engineering design. A negative normalized index implies under-estimating of the mobility index and a pos- itive normalized index is over-estimating the index. This is complicated by α being defined as the vertical angle, as the maximum measured value is at stability while the inverse is true of all other mobility indices (Table 8.1). For all indices, normalized index of 0% in- dicates a model that precisely matches the observed runout characteristic. A model that is within±30% of the observed runout is “well”-modelled, and within±10% is “excellently” modelled as a standard for this study. All of the landslides were modelled using the same rheologies and parameters1, and the normalized runout calculated for each model. Even by using a quantitative method comparing performance of a given model over a range of cases, it is still complicated to pick which model has best fit overall. For each mobility index, the “best” model is selected given: 1. minimum average normalized runout (low mean), 1Listed in Section 7.1.3. 67 Index Stable Under-Predict Exactly-Predict Over-Predict ∆α [%] ( 90◦αobs −1)×100 ≥ 0 0 ≤ 0 ∆L [%] −100 ≤ 0 0 ≥ 0 ∆Le [%] ( LobsLe obs −2)×100 ≤ 0 0 ≥ 0 ∆D [%] −100 ≤ 0 0 ≥ 0 Table 8.1: Interpretation of normalized runout for mobility indices. An event is over- predicted by at least double the observed runout distance when ∆L≥+100. 2. most consistent (least variation from the mean with a small standard deviation), and 3. largest count of landslides with normalized runout within specified cut-offs. 8.2 Evaluating the Performance of Rheologies and Parameters 8.2.1 User-Selected versus Mathematically-Selected Parameters The user-selected parameters produced smaller normalized runout than the mathematically- selected parameters, yet it is difficult to extract meaningful trends from the scattered results. The mathematically-selected parameters are easier to analyze for meaningful trends, yet have higher normalized runout than user-selected parameters. The mathematically-selected parameters were analyzed for the mean normalized runout and standard deviation from that mean, then analyzed for percentage of cases well- or excellently-modelled, and for over- and under-predicted runout. Debris Distribution One of the advantages of user selected parameters over mathematically selected parame- ters is that expert judgement may take the debris distribution into account when deciding which model best represents the observed event. Typically, frictional rheologies produce models with proximal thickening in the debris distribution, and Voellmy rheologies pro- duce distal thickened model deposits, yet my process of mathematically-selecting rheology for best-fit runout does not take preferred debris distribution into account2. For most of the user-selected rheologies and parameters, the modelled debris distribution is consistent with the observed distribution, while for the mathematically-selected rheology, the modelled dis- tribution is inconsistent with the observed distribution. 2In future research, this may be investigated by considering both maximal and center of gravity runout characteristics. 68 Velocity Like debris distribution, although methods for mathematically comparing modelled and observed velocity distributions is possible, they were not attempted for this project and thus the user-selected parameters fared far better at fully describing the modelled landslides. For mathematical selection of parameters, the normalized maximum velocity was calculated using the maximum velocity for the entire modelled landslide, not necessarily at the same location as the observed velocity, and was thus only used to determine if a model produced velocities of the appropriate magnitude. Although the small number of cases in my set with velocity observations makes all conclusions tentative, from Section 5.2.4, it is possible to generally position types of events with respect to velocity, and thus make determination between higher and lower turbulence coefficients. This will be discussed further in relation to parameter recommendations for events with specific characteristics. DAN-W and DAN3D The user-selected parameters for DAN3D are consistent with those selected for DAN-W. As the DAN3D model is more computationally demanding and digital elevation models are relatively difficult to acquire for many cases, no attempt was made to mathematically select parameters for this software. 8.2.2 Minimizing Normalized Runout and Maximizing Consistency Model rheologies and parameters which produce, on average, the tightest fit between model and observed mobility index are identified by minimizing average normalized runout. How- ever, because this is an average, the variation may be quite high: a model that vastly over- predicts runout for one case and under-predicts for another by the same magnitude may have a low mean normalized runout and high standard deviation from that mean. Because mean normalized runout is reported as a percentage, the standard deviation from that mean is in percentage points: the arithmetic difference between the percentage mean normalized runout and the percentage variation from that mean3. Consistency is maximized by minimizing variation4 The only frictional parameters which exhibit low variation are for stable models. 3The difference from 30% to 40% is 10 percentage points. 4Parameters that regularly produce stable models have extremely low variance, but are not of practical application, and thus are excluded from this discussion. 69 θb f ξ ∆L σ∆L ∆D σ∆D ∆α σ∆α [◦] [m 3 s ] [%] [%] [%] [%] [%] [%] 15 2 45 14 38 16 60 17 -6 47 -23 36 26 66 0.05 100 4 46 11 80 19 44 0.1 100 -5 46 -12 50 32 48 0.1 500 9 45 4 59 11 49 0.1 1000 17 45 15 70 3 46 0.15 1000 7 44 -5 48 13 50 0.15 1500 14 43 6 53 5 51 0.15 2000 13 43 3 50 5 49 0.2 2000 4 44 -9 41 16 54 Table 8.2: Mean normalized runout (∆), and standard deviation (σ ) of that mean for the specified mobility indices (with ∆L≤ 100%). Cases with... |∆L|≤ |∆D|≤ |∆α|≤ θb f ξ 5% 30% 5% 30% 5% 30% [◦] [m 3 s ] [%] [%] [%] [%] [%] [%] 15 14 60 6 50 23 64 17 14 49 17 50 5 49 0.05 100 14 57 17 67 8 56 0.05 500 11 60 17 31 18 67 0.05 1000 14 54 28 56 8 67 0.1 500 17 60 17 56 21 69 0.15 1000 14 63 11 50 13 74 0.15 1500 8 56 6 50 25 68 0.15 2000 11 63 11 61 10 77 Table 8.3: Percentage of cases with absolute mean normalized runout that are excellently-modelled (|∆| ≤ 5%) or well-modelled (|∆| ≤ 30%) for the specified mobility indices. The best overall parameters for minimizing normalized runout and variation across both mobility indices are listed in Table 8.2. Mean normalized runout and the standard deviation from the mean for all parameters are listed in Section H.1.1. 70 ξ [m3s ] f 100 500 1000 1500 2000 0.05 x x x 0.1 x x x 0.15 x 0.2 x x Table 8.4: Low f paired with high ξ over-predict mobility (green), mid-range param- eters predict runout well (x), and high f paired with low ξ under-predict runout (red). Model mobility decreases from top to bottom ( f = 0.05 = most mobile), and velocity increases from left to right (ξ = 2000m3s = fastest). 8.2.3 Counting Cases within Cutoff Criteria Another tactic for identifying the best runout parameters is to count the number of cases that are well- or excellently-modelled with a fixed set of parameters. Full counts for cases mod- elled to within 5%, 5-10%, and 10-30% of the observed runout are listed in Section H.1.2. The parameters which well- and excellently-predict all mobility indices are listed in Ta- ble 8.3. Neglecting velocity observations to constrain the turbulence coefficient, runout is most often well-modelled with ξ = 500 m3s . The difference in under-predicted and over-predicted landslide mobility may have sub- stantial impact on decision-making. Therefore, I also identified parameters that most of- ten over-predict, under-predict, or predict mobility to ±10% of observed mobility (Sec- tion H.1.3). For frictional rheologies, low friction angles (θb ≤ 10◦), with θb = 15− 17◦ predicting mobility to within ±10% for the largest percentage of cases for any friction an- gle, before the higher friction angles (17◦ ≥ θb) under-predicts mobility. Extremely high friction angles(25◦ ≤ θb ≤ 45◦) produce stable models for most cases while over-predicting L for the remainder. Using Voellmy rheology, models with low friction coefficients paired with high tur- bulence coefficients over-predict mobility while high friction coefficients paired with low turbulence coefficients under-predict mobility (Table 8.4). Velocity estimates are required to constrain the turbulence coefficient. When this is not possible, the turbulence coefficient that produces the best normalized runout when paired with the greatest range of friction coefficients is ξ = 1500 m3s . Alternately, the friction coefficients that most consistently produce the best normalized runout when paired with a range of turbulence coefficients (and thus over a range of velocities) are f = 0.05−0.1. When neglecting velocity constraints, parameters that most reliably predict mobility to 71 ±10% for the largest percentage of cases are listed in Table 8.5. All data is also presented visually in Section H.6, with histograms of model performance across all cases, and across categories of cases which have the same physical characteristics. From the histogram of the performance using frictional rheology with the friction an- gle fixed at θb = 17◦ for all cases, this model generally under-predicts runout, or very slightly over-predicts for most cases, with −50% ≤ ∆runout ≤ +10%, and that velocity is either slightly under-estimated with −30% ≤ ∆vmax ≤ −10%, or hugely over-estimated with ∆vmax ≥+90% (Figure 8.1). The two peaks for velocity are clarified when considering categories: rock avalanches run out faster than debris avalanches, and are better modelled with lower friction angles. Looking at a histogram for Voellmy rheology with the friction coefficient f = 0.1 and the turbulence coefficient ξ = 500m3s , most events are modelled to within ±30% for both mobility and velocity (Figure 8.2). 8.2.4 Evaluation within Categories The analysis of the impact of various pre-event observable characteristics in Section 5.2.4 indicated that magnitude volume, movement type, morphology, and material are the most influential characteristics for determining landslide mobility. Due to the bias in my sample set towards rock avalanches, rock sources, and sediment paths, and unobstructed morpholo- gies, this analysis is preliminary, and should be followed up with a similar analysis using a more diverse sample5. This sampling bias was an unintended consequence of the real distribution of landslide characteristics, where most catastrophically large landslides are rock avalanches running out over unobstructed terrain, so building a set with greater diver- sity may only be possible through removing the volume constraint and analyzing smaller events. To abbreviate discussion, I am using a holistic combination all the techniques to de- termine the best parameters instead of discussing each result individually. The reported parameters all have low mean normalized runout and variation from that mean, model a substantial percentage of cases to within ±30% of observed mobility, and neither over- nor under-estimate mobility. In addition, the parameters are also those which most distinguish between characteristics within a category, not those which are common to all landslides. 5In order to expand the sample set substantially, either a large number of catastrophic landslides will need to occur, or the volume constraint on scope may be dropped, as discussed in Section 5.2.4. 72 Cases with... ∆L ∆D ∆α θb f ξ −10% ↔ +10% −10% ↔ +10% −10% ↔ +10% [◦] [m 3 s ] [%] [%] [%] [%] [%] [%] 15 31 29 40 28 28 44 44 31 26 17 23 29 49 11 33 56 62 21 18 0.05 100 37 23 40 22 39 39 51 21 28 0.05 500 49 26 26 44 28 28 31 31 38 0.05 1000 57 26 17 50 28 22 21 38 41 0.1 500 37 23 40 33 22 44 41 28 31 0.1 1000 46 26 29 39 22 39 31 23 46 0.1 1500 56 25 19 50 17 33 18 20 62 0.15 500 34 14 51 28 22 50 56 18 26 0.15 1000 37 20 43 28 17 56 36 38 26 0.2 500 17 23 60 22 17 61 67 21 13 0.2 1000 29 29 43 22 28 50 59 15 26 Table 8.5: Percentage of cases with under-estimation (∆ < −10%), excellent estimation (∆ < |10%|), or over-estimation (∆ > +10%) of the specified mobility indices (with ∆L≤ 100%). 73 !L Fr eq ue nc y 0 2 4 6 8 10 $\theta_{b} =  17 ^{\circ}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (a) ∆L !" Fr eq ue nc y 0 2 4 6 8 10 $\theta_{b} =  17 ^{\circ}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (b) ∆α !D Fr eq ue nc y 0 2 4 6 8 10 $\theta_{b} =  17 ^{\circ}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (c) ∆D !vmax Fr eq ue nc y 0 2 4 6 8 10 $\theta_{b} =  17 ^{\circ}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (d) ∆vmax Figure 8.1: Histogram of the performance of frictional rheology with θb = 17◦ as measured by the specified normalized index, across all case studies. See Sec- tion H.6 for other models. 74 !L Fr eq ue nc y 0 2 4 6 8 10 $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (a) ∆L !" Fr eq ue nc y 0 2 4 6 8 10 $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (b) ∆α !D Fr eq ue nc y 0 2 4 6 8 10 $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (c) ∆D !vmax Fr eq ue nc y 0 2 4 6 8 10 $f = .1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$ <− 90 % (− 90 % ,− 70 % ) (− 50 % ,− 30 % ) (− 10 % ,1 0% ) (3 0% ,5 0% ) (7 0% ,8 0% ) >9 0% (d) ∆vmax Figure 8.2: Histogram of the performance of Voellmy rheology with f = 0.1 and ξ = 500m 3 s as measured by the specified normalized index, across all case studies. See Section H.6 for other models. 75 Magnitude Volume When categorizing volume to the nearest order of magnitude, no specific rheologies and pa- rameters produce better modelled runout for one category versus another. This is consistent with the difficulty in categorizing volume into discrete groups, as discussed in Section 5.2.2. Using frictional rheology, the friction angle is adjusted roughly inversely proportional to volume, such that as volume increases, the friction angle decreases (θb ∝ 1Vi ). See Sec- tion H.2 for complete data. Movement Type In frictional rheology, rock avalanches are best modelled with θb = 10−15◦ and flow slides with θb = 15−20◦. Debris avalanches are dominated by morphology, with two distinct cat- egories of behaviour depending on if the path is impacted or unobstructed6. For debris avalanches with impacted morphology, the events are best modelled with a high friction angle (θb = 35◦), while those with unobstructed morphologies are best modelled with ex- tremely low friction angles (θb = 5−17◦). In Voellmy rheology, rock avalanches are best modelled with a high friction coefficient and mid-range turbulence coefficients (consistent with mid-range average maximum veloc- ities), and flow slides with a lower turbulence coefficient7. As with frictional rheology, debris avalanches must be considered in conjunction with morphology. Debris avalanches in unobstructed morphologies (which have, on average, high maximum velocities) best modelled by high friction and turbulence coefficients ( f = 0.15, ξ ≥ 1000). Even when modelled with extremely high friction coefficients and low turbulence coefficients ( f = 0.2, ξ = 100), mobility is over-predicted for debris avalanches with impacted morphologies. See Section H.3 for complete data. Morphology Relative to channelized morphology, using frictional rheology landslides with unobstructed morphologies are best modelled with increased friction angles and events with impacted morphologies are best modelled with decreased friction angles. Using Voellmy rheology, cases with unobstructed morphology are best modelled using a wide range of parameters, with pairs of increasing friction and turbulence coefficients. However, as unobstructed mor- 6No channelized debris avalanches are represented in my sample, as by definition those events are more likely debris flows. 7My sample set lacks flow slides with velocity observations, so the turbulence coefficient cannot be properly constrained. 76 phologies have on average high maximum velocities, pairs with higher turbulence coeffi- cients are preferred. Cases with channelized morphologies are best modelled with mid- range friction and turbulence coefficients, while cases with impacted morphologies are best modelled with f = 0.1−0.15, ξ = 1500 m3s . See Section H.4 for complete data. Material For both source and path materials, rock is most consistently well-modelled using higher turbulence coefficients, and debris using a lower turbulence coefficient (especially ξ = 1000 m 3 s ). This is consistent with events running out over rock having, on average, higher maximum velocities than events running out over other path materials. When debris is the source material, the landslide mobility is usually overestimated. Due to the extremely small number of cases with debris as the source material within my sample, this subset should be investigated further to confirm results (possibly by expanding the scope to events without volume restrictions). See Section H.5 for complete data. 8.3 Summary of Parameter Performance Qualitative judgement when selecting runout parameters produces models that most closely reflect the actual runout of the observed event, but the parameter selection is difficult to gen- eralize to other cases. Quantitative judgement of mathematically selecting parameters with low mean normalized runout and standard deviations produces models that loosely match the observed runout, but are more easily generalized to other cases with clear expectations for parameter performance in relation to modelled mobility. This qualitative judgement is applied to all cases, and to cases within specific sub-categories. Although limited velocity observations make it difficult to distinguish between events best modelled with particular turbulence coefficients when using Voellmy rheology, earlier determination of the relative average maximum velocity of events with differing physical characteristics makes it possible to determine if higher or lower turbulence coefficients are more appropriate. A summary of the parameters which have the lowest mean normalized runout are shown in Table 8.6. These parameters perform with high consistency, with a low standard deviation. Determination of the appropriate rheology to use for a given landslide remains a sub- jective decision, with expert judgement required to determine if a frictional model with lower velocities and proximal thickening of the debris distribution, or a Voellmy model with higher velocities and distal thickening of the debris distribution, is more appropriate for a 77 Category θb f ξ [◦] [ m 3 s ] All 15-17 0.05 100 0.1 500 0.15 1000 Volume Decreasing ↑ Increasing ↓ Movement Type Rock Avalanches 10-15 0.15 500-1500 Flow Slides 15-20 0.1 100 0.2 1500 Morphology Channelized 0.1 500 0.15 1000 Unobstructed ↑ 0.2 1000-2000 Impacted ↓ 0.1-0.15 1500 Material Rock 0.05, 0.15 1500 Debris 0.05 100 Table 8.6: Recommended rheologies and parameters overall, and within categories of landslides. Recommendations for debris avalanches are excluded as morphology dominants behaviour. particular circumstance. Future work involving a similar analysis but including observa- tions from the center of mass to quantify debris distribution may produce recommendations for rheology selection based on physical characteristics. 78 Chapter 9 Conclusions Meanwhile, fears of universal disaster sank to an all-time low over the world. —Asimov (1975) 9.1 Summary of Results Landslide mobility behaviour is most powerfully influenced by volume, although movement type, morphology, and material play an influential role in distinguishing the mobility of events of similar volume. For forward modelling with the DAN software package, when using the frictional rhe- ology, θb = 10− 20◦ will be sufficient for most cases, with a decreasing friction angle for increasing volume or for events with impacted morphologies. In the rare instance when a landslide model is not stable for θb ≥ 25◦, it is highly likely that even friction angles as high as θb = 45◦ will over-predict mobility, and frictional rheology is inappropriate for modelling the event. When using Voellmy rheologies, although the friction coefficient f = 0.1 produces good models of mobility for most cases, rock avalanches, and events with unobstructed or channelized morphology are usually better modelled with higher friction coefficients, and events with debris as the dominant material are modelled better with a lower friction coeffi- cient. For most cases the turbulence coefficient is higher when modelling debris avalanches, events with unobstructed morphologies, or events with rock as the dominant material to reflect higher maximum velocities. If not velocity constraint is possible, ξ = 1500m3s pro- duces low normalized mobilities for all friction coefficients. 79 9.2 Recommendations to Practitioners When in the field, to perform a quick first-approximations of landslide runout hazard pre- diction, practitioners should select V -α statistical models built from landslides with similar movement types and morphologies as the target event. 9.2.1 Forward Modelling By its nature, back-analysis must be deterministic. It was dry or it was rainy. A large mass failed, or many smaller masses failed piece by piece. The landslide ran out over dry consolidated rock, or ash, or saturated sediments, or even ice. The landslide happened, and the model must reflect the determined runout. Future prediction should not be deterministic. It should be probabilistic – the failure is likely to occur during the rainy or dry season, the path will probably be dry debris or an icy glacier, the characteristics may be this or that. No guidelines can determine one golden parameter for all landslides, only provide a realistic range of parameters given probable conditions for the event. Common sense and expert judgement will always be required to apply a deterministic landslide model in a probabilistic manner in order to generate hazard maps. Once an expert identifies a prospective failure and its probable physical characteristics, the event is forward-modelled to determine the hazard area. Current Practice The current practice in forward-prediction modelling is to research several historical events similar to the target event over a range of physical characteristics. These historic events are then individually back-analysed, using expert judgement to selecting the best-fit rheologies and parameters. If the back-analysed parameters all fall within a similar range and a suffi- cient number of similar cases were used to justify robustness of the parameter performance, the parameters are applied to forward modelling the new case. This method requires significant time and effort on the part of the expert practitioner. Without consistent selection criteria for what determines best-fit, it is impossible to compare parameter selection between practitioners. Back analyses stand in isolation with little hope of comparison between events leading to theoretical breakthroughs in long-runout mecha- nisms. The large range of observed landslide characteristics make it also unlikely that other targets of future prediction analysis will match past projects, making even the selection and research of case histories unlikely to be reused by a single practitioner. 80 Proposed Revised Practice Although expert judgement of particular field conditions may still lead to emphasizing different physical characteristics, when no other considerations are present, landslides of similar volume, movement type, morphology, and material are more likely exhibit simi- lar mobility behaviour than landslides with other similar characteristics (such as sharing a common trigger). Once a landslide is categorized by its physical characteristics, it may be forward-modelled by using the recommended rheology and parameters with statistically-justified expecta- tions for normalized mean runout, and deviation from that mean (Table 8.6). By forward- modelling the target event using ranges of parameters associated with different probable conditions, a preliminary hazard map may be rapidly constructed for use in risk manage- ment. Although future research into mathematical selection of rheology by debris distribu- tion, at this time human judgement is required to identify the appropriate rheology for the given scenario. By recommending a specific set of parameters based on the physical characteristics of an event, the preliminary hazard map may be rapidly produced, reducing the cost to make landslide runout analysis a more accessible tool for decision makers. The recommended parameters also provide context-specific starting parameters so that an expert practitioner may fine-tune model parameters in the usual iterative process for parameter selection in the construction of a more detailed hazard map. 9.2.2 Cautions and Limitations This thesis is highly dependent on the accuracy of reported observations, from the recorded physical characteristics to accurate maps of pre- and post-event topography. No attempt was made to verify or reinterpret reported observations; minor errors are presumably compen- sated for by the large quantity of landslides analyzed. Statistical anomalies in the physical properties of the landslide were investigated, and found to have an insignificant impact on trends (changing precise numbers but not patterns) when excluded from the analysis of categorizing landslides into mobility behaviours by their physical characteristics, so were included throughout the analysis of model behaviour. Some subsets of events are underrepresented in the analyzed sample. Although this may be rectified in future research on an expanded sample without volume limitations on scope, at the current time recommendations for rock avalanches, events with unobstructed morphologies, and events involving rock as the dominant material are stronger, while all 81 other recommendations should be treated more cautiously. Expert judgement cannot be replaced by blind reliance on statistical data. All statistics are averages, and deviations from the mean are expected. Expert judgement is required to determine other physical characteristics play a dominate role in the behaviour of a particular event, and in determining the probable range of physical characteristics a future event might exhibit based on seasonal changes and the surrounding environment. Landslide runout analysis is an inherently blend of qualitative and quantitative techniques. 9.3 Implications to the Field Beyond streamlining the process of forward modelling prospective landslides, the quantita- tive technique used to compare model results has far-reaching consequences if it is adopted for formal reporting of back analyses in the literature. A change in reporting style to in- clude quantitative normalized runout characteristics in published back analyses will allow for meta-studies comparing the events and the models independent of the practitioner who performed the initial analyses. Any back analyses performed in DAN-W may be added to a verification set for even- tual formal model verification using cross-validation, while analyses performed using other software models may be more easily compared in higher-level analyses of the applicabil- ity of different styles of modelling to different scenarios. While the particular parameters recommended in this study have only been tested with the DAN package, it is logical that the same trends of decreasing friction angle when modelling larger-volume events, or using higher friction coefficients with impacted morphology than with channelized morphology will continue to hold agnostic of software provided the programs are designed for use with frictional and Voellmy rheologies. Finally, a growing pool of back analyses with a quantitative aspect to evaluating param- eters may lead to the emergence of groups of landslides which are modelled in a similar manner (both with best-fit parameters, and how the fit changes as the parameters are ad- justed). Emergent groups of events with similar mobility behaviour yet dissimilar (or at least not obviously similar) physical characteristics potentially share underlying mechani- cal processes of excess mobility, identifying target cases for differentiating between theories or insight into how multiple processes interact. 82 9.4 Directions for Future Research As with any research, the conclusions of this study point in new directions for further re- search. Namely: Volume-Independent Sampling - A larger sample set may be gathered by removing the volume limitation on scope, thus bringing more diversity to the represented physical characteristics and strengthening the statistical power of conclusions. Enhanced Velocity Observations - The underrepresentation of velocity observations in the morphology subset can likely be rectified by field visits to determine run-up for impacted events, and superelevation around bends for channelized events. Model Verification - The back analyses performed function as a training set for cross- validation of the DAN-W software model. Any new cases (even forward-modelled events) may function as a verification set. Extension to Other Models - As the categorization is based on physical landslide char- acteristics, parameter recommendations may be made for other software models by applying the process from Chapter 7 and Chapter 8. Guided Automation - A hybrid of user- and mathematical parameter selection may be made to bring qualitative judgement to a quantitative process by using expert judge- ment to weight the reliability and importance of mobility indices. Inter- and Intra-User Studies - The variation in parameter selection between users can be investigated with an inter- and intra-user study by applying the quantitative evaluation of parameters to user-selected best-fit parameters between practitioners, and with a single practitioner’s selection repeated over time. 9.5 Summary Landslide mobility can be successfully categorized by physical characteristics. These same categories equally successfully distinguish events that are modelled with similar parame- ters. This allows for rapid first-order forward modelling of new events by following recom- mendations for parameter selection by probable physical characteristics of the events. Quantitative methods for parameter selection allow for comparison of back analyses performed by different practitioners, and allow for broad evaluation of parameter perfor- mance across landslides. 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Estimation of the sequence and size of the Tozawagawa landslide, Niigata, Japan, using aerial photographs. Landslides, 1(4), 299–303. → pages 162 Yanase, H., Ochiai, H., & Matuura, S. (1985). A large-scale landslide on Mt. Ontake due to the Naganoken-Seibu Earthquake, 1984. In Procedures from the 4th Iinternational Conference and Field Workshop on Landslides, Tokyo, (p. 323). → pages 145 Yilmaz, I., Ekemen, T., Yildrim, M., Keskin, I., & Özdemir, G. (2006). Failure and flow development of a collapse induced complex landslide: the 2005 Kuzulu (Koyulhisar, Turkey) landslide hazard. Environmental Geology, 49(3), 467–476. → pages 134 Zhang, Z.-Y., Chen, S.-M., & Tao, L.-J. (2002). Catastrophic Landslides: Effects, Occurrence, and Mechanisms, chap. 1983 Sale Mountain landslide, Gansu Province, China, (pp. 149–163). Geological Society of America Reviews Engineering Geology. → pages 157 97 Appendices 98 Appendix A Deformable Mass Models Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that the danger does lie in logic, not in imagination. —Chesterton (1908) Deformable mass models (Section 4.2.2) allow for deformation and interaction of mass elements within the landslide volume. Distinctions may be made between deformable mod- els in how they treat scale, composition, internal deformation, coordinate systems, dimen- sionality, and continuity. A.1 Scale Models must be used to investigate behaviours on scales equal to or greater than the repre- sentative computational element volumes (blocks, smoothed particles) of real components (grains, logs, boulders). Even discontinuum models1 use representative elements: modelled particles and real life particles are usually not modelled at a 1:1 ratio as even small volume landslides may have millions of components2. The tiny movements of the real components is implicitly included within the stress calculations for element volumes, so that stress must not fluctuate significantly in response to movement of the individual components (Iverson, 2005). 1See Section A.3.2. 2An event of V = 103 m3 may have more than 1010 individual grains (Iverson, 2005). 99 A.2 Composition Deformable mass models may feature either homogeneous (“lumped state”3) or heteroge- neous (“distributed state”) mass compositions. The failure mass may be homogeneous, with a non-varying rheological composition, reducing computational intensity at the ex- pense of accuracy. The failure mass may instead be heterogeneous, with each element within a system separately described with spatially varying rheological composition, in- creasing computationally intensity, but allowing for finer-grained distinctions for improved accuracy. Many landslide runout models compromise between techniques, describing sets of elements (such as the failing volume, the entrainment volume, and the runout path) as internally homogeneous yet rheologically distinct from each other. As the number of dis- tinct rheologically homogeneous sets increases, the complexity the model increases as it approaches a distributed state model, increasing both computational intensity and accuracy. A.3 Internal Deformation The distinction in how deformable models treat internal deformation is split between contin- uum and discontinuum techniques. Continuum models do not permit internal deformation while discontinuum and hybrid models do. A.3.1 Continuum Models A continuum model4 distributes a substance throughout the space it occupies, treating land- slides as a single externally deformable mass that is not internally deformable. Mathemat- ical solutions use finite-element and finite-difference techniques applied to mass and mo- mentum conservation, using purely kinematic analysis of the pull of gravity and frictional resistance to estimate travel distance where turbulence is a marginal effect. Common uses of continuummodels in landslide runout use depth-averaged open-channel fluid flow, such as the DAN-W (Hungr, 1995), DAN3D (McDougall, 2006) and RASH3D(Poisel et al., 2008), and many unnamed models (for example, Savage & Hutter (1991), Iverson (1997), and Crosta et al. (2006)). The models are ideal for investigating the influence of pore pressure and shear on changing the apparent friction angle, but are difficult to adapt to dry soil flows (Okura et al., 2000a). 3Another technical use of “lumped”, not to be confused with “lumped mass” models. 4Also called “continuous mass” models, or, confusingly, “lumped mass models” for “lumping” the mass- elements together, in contradiction to the term’s use in describing point-mass models as described in Sec- tion 4.2.2. 100 A.3.2 Discontinuum Models Discontinuummodels5 treat landslides as an assembly of interacting particles rolling, bounc- ing, sliding, or free falling down a surface(Poisel et al., 2008). Mathematical solutions often utilize distinct-element and discrete-element techniques. Particle collisions between each mass-element are individually modelled, then time-stepped and modelled again, iteratively processed until the flow comes to a rest. This is a computationally intensive process (Wal- ton, 1993), but with variable element size, even very small topographic and structural details may be retained, reducing the danger of over-simplifying the model. Discontinuummodels permit internal deformation, allowing for toe deformation (Evans et al., 1994), distinguishing between landslides where internal layout is preserved or de- formed into a sheet of jumbled debris (Hsü, 1975) and clearly modelling laminar layers and stress transfer between grains (Ting et al., 1989). Discontinuum models are particularly good at modelling dry particle flow (Okura et al., 2000a) by analyzing the behaviour be- tween colliding grains (Cundall & Strack, 1979). Examples include the Particle Flow Code models, PFC2D and PFC3D, and unnamed models that use energy and momentum balance or rigid inelastic collisions and ballistic trajectories (Straub, 1997). A.3.3 Hybrid Models Hybrid models6 are blends of continuum and discontinuum modelling techniques. An ex- ample is the DAN3D application of smooth particle hydrodynamics, where a continuous body of individual mass-elements interacts through the application of hydrodynamic rela- tionships7. A.4 Eulerian and Lagrangian Coordinate Systems The classes of mathematical solutions to the kinematic equations may use Eulerian or La- grangian coordinate systems, and be 1-, 2-, or 3-dimensional solutions. Eulerian coordi- nates use a fixed reference frame, and are used in most earlier landslide models and some modern models using a computational mesh. Lagrangian coordinates use a moving refer- ence frame (commonly attached to the landslide), and are used with most modern landslide models after an application to landslide runout was proposed by Potter (1973). Savage & Hutter (1989) compare the impact of using Eulerian or Lagrangian coordinate systems in 5Also called “discontinuous mass,” “discrete mass,” or “granular” models. 6Also called “coupled” models. 7Please see Section C.5 for more details. 101 landslide runout modelling. A.5 Dimensionality A.5.1 Geometric Deformable mass models may be 2- or 3-dimensional models. The simpler 2-dimensional models either calculate the runout over a linear runout path that is manually extrapolated over the study area to produce hazard maps, or calculate the runout over a specified path and extrapolate flow over a manually-input width, where probable channelization or spreading into fans is determined in advance by expert judgment. The more computationally intensive 3-dimensional models use a digital elevation model as input and project the probable runout path and width without additional manual adjustment. The output of 3-dimensional models may be directly used to generate intensity maps, since velocity and flow depths are modelled within the entire study area. A.5.2 Mathematic Dimensionality may also refer to the mathematical solution to the physical flow equations used within the model, which may be 1-, 2-, or 3-dimensional. Full 3-dimensional solutions to the kinematic equations (most commonly flow equations) are computationally extremely intensive to solve mathematically. The most common 2-dimensional solution is to depth- average by assuming a small depth gradient. Depth-averaging may oversimplify events where vertical sorting is a major component, such as in rock avalanches where grain size decreases with depth (Crosta et al., 2006). A.6 Continuity Continuity is maintained explicitly through fixing the volume of (rigid or deformable) blocks, or implicitly through the use of a computational mesh or smooth particle hydro- dynamics (McDougall & Hungr, 2003). For computational meshes, the repetitive structure of a lattice is exploited to reduce computational intensity. This enables modelling events over wide areas quickly (Okura et al., 2000a). By converting the individual elements to a mesh, topographic and structural features smaller than the mesh spacing may be lost (Okura et al., 2000a), and large dis- placements or deformations can excessively distort the mesh (Crosta et al., 2006) reducing accuracy of the output. Examples of continuous models utilizing mesh computational tech- 102 niques are the models of storm surges (Miyazaki et al. 1961 via Okura et al. 2000a), the Titan2D model (Sheridan et al., 2005), or modifications of block-volume continuity mod- els to use meshes (such as Savage & Hutter (1989) modified by Gray, Wieland, & Hutter (1999), Hungr (1995) modified by Chen & Lee (2000), and Iverson (1997) modified by Denlinger & Iverson (2001)). 103 Appendix B Recommendations for Model Verification and Cross-Validation A tacit rite of passage for the mathematician is the first sleepless night caused by an unsolved problem. —Reznick (1994) As discussed in Section 8.2, all models must be consistent with empirical data. Al- though calibration of any tool is logical, software models are instead verified through cross- validation. Cross-validation is a method of testing the hypothesis, “Inputing specific param- eters into this software model will predict landslide runout characteristics.” Cross validation is beyond the scope of this thesis; the following is a detailed framework on how cross vali- dation may be applied to any dynamic analysis software (including DAN-W or DAN3D)1. Cross validation is a process of verifying a model through the use of training and verifi- cation data. To do this for landslide runout models, a comprehensive collection of landslide case studies are randomly sorted into either the training set or the verification set. All the case studies in the training set are then used to estimate model parameters through back- analysis in the usual manner, adjusting the parameters until the model produces results consistent with the empirical observations. The resulting parameters are then statistically analyzed to determine robust input parameters. These input parameters are tested in the verification set by fixing the input parameters and verifying that model output is consistent with the empirical data. If the model and parameters are valid, the runout analyses of the verification set will be consistent with the empirical data without any adjustment of the pa- rameters. Once the model is verified, the parameters may be applied in forward prediction 1A detailed review of cross-validation methods as applied to astronomical models is presented in Arlot & Celisse (2009). 104 models with statistically quantified confidence and error. B.1 Randomization of Sets In models where data is gathered in advance, and the model is generated through statisti- cal analysis within the data seeking correlations, the separation of data into training and verification sets may be done post-hoc through random assignment. This is not possible in for landslide modelling, as the data for the verification stage requires inputs determined by the training stage, thus cases must be randomly assigned to training and verification sets in advance of gathering data. B.2 Training Set With the training set, the implicit model hypothesis (“A relationship between model pa- rameters and landslide runout characteristics”) is assumed correct. If the combination of kinematic descriptions of movement and rheological descriptions of fluids are accurate, by fixing model output to match real world observed characteristics, the parameters required to produce that result may be inferred through back-analysis of event. Using ad-hoc parame- ter adjustment to match real-world results uses training data to teach a relationship between input parameters and output characteristics. B.3 Correlating Observable Characteristics to Parameter Selection Once parameters have been inferred through back-analyses of the training cases, it is possi- ble to correlate the input parameters to pre-event observable landslide characteristics. This relationship is a new hypothesis linking pre-failure characteristics to model parameters. (This step is within the scope of this thesis, and is discussed in greater detail in Section 5.2). B.4 Verification Set Up to this stage, the original hypothesis, “Inputing specific parameters into this software model will predict landslide runout characteristics,” has not been tested, merely assumed correct in order to correlate pre-event observable characteristics to specific inferred param- eters. In order to test the hypothesis and validate the inferred data, the parameters must now be fixed a priori and tested against a fresh case studies, the verification set. For each case within the verification set, the pre-event observable characteristics are 105 used to predict software model parameters. The parameters are input into the model to perform a runout analysis of the event. Essentially, all future-prediction exercises are veri- fication cases where the predicted runout characteristics cannot be evaluated until the event actually happens. To speed up the process, a verification set may use entirely events that have already taken place to compare the fit of the model to reality: how closely the predicted (modelled) runout characteristics match the real (observed) runout characteristics. A statistical analysis of the difference between prediction and the real values results in a concrete measure of the accuracy of a software model, and allowing for rigorous compar- isons between models using alternative runout prediction techniques, including laboratory models, statistical models, and other software models. B.5 Calculating Error Cross-validation tests two hypotheses simultaneously – correlating pre-event observable characteristics to software parameters, and the dynamic software model relating parameters to runout characteristics. It is not directly obvious which hypothesis is contributing how much error to a final prediction. Inaccuracy may come from either the execution of the original software model, or the intermediary model linking characteristics to rheologies (Section B.3). As the correlation between characteristics and parameters is generated post-hoc, it is possible to measure its error separately for a given set of training data.2 It is possible to partition the error calculated from the verification data (Section B.4), and removing that error from total error to approximate the error of the software model in predicting runout characteristics. 2Although this has an implicit assumption with associated error: for a framework on establishing that axiom see the discussion in Section 5.1. 106 Appendix C Details on DAN Software Programs Basically, anything goes, as long as it’s not obscene, doesn’t offend or present a safety hazard. —Mark Giuffre The dynamic analysis software packages DAN-W and DAN3D are briefly described in Section 6.1. C.1 Mass Balance The DAN-W model maintains continuity through deformable blocks of fixed volume with interpolation from spline smoothing, and DAN3D uses meshless smooth particle hydrody- namics. Neither model contains numerical dampening. C.2 Momentum Balance The momentum balance for the DAN models is based on depth-averaged Saint Venant shallow-water equations calculated at reference columns. In DAN-W, these reference columns are fixed-volume blocks, while in DAN3D the reference columns are distributed through the landslide mass and advected with flow. C.2.1 Entrainment Both models permit entrainment of additional materials into the flow. Entraining stationary path material transfers momentum through solid collisions and fluid thrust (Hungr, 1995; McDougall & Hungr, 2005). The entrained material is assumed to have the same constant bulk density as the overrid- ing landslide. This assumption is valid for events that initiate in the same surfical deposits 107 that are encountered along the path, but snow or ice have significantly different bulk densi- ties as the overriding material (McDougall & Hungr, 2003, 2005). The DAN-W model allows for entrainment through user-input entrainment depth, and computationally determines the rate of entrainment proportional to flow depth and veloc- ity such that full entrainment for any given point occurs when the point is overun by the entire current flow volume. The relationship between entrainment and flow depth is consis- tent with physical changes in stress conditions proceeding failure of path material (Hungr, 1995). The DAN3D model allows for entrainment through a user-input digital elevation model of the entrainment volume, and a user-specified displacement-dependent natural exponen- tial growth rate E, which may be determined through trial-and-error or a priori calculation: ∂b ∂ t = Ehv (C.1) where the bed erosion velocity ∂b∂ t is empirically constrained, h is flow depth, and v is flow velocity. C.2.2 Flow Conditions Both models use modified Saint Venant Equations assuming shallow flow conditions. Shal- low flow requires flow parallel to the bed and a small depth gradient. The flow may be nonuniform and unsteady, but must be incompressible. The basal flow is subject to a thin layer of shear, with velocity elsewhere approximately constant, and the upper surface stress- free1. The unmodified equations are subject to instability from hydraulic shock when the flow encounters an abrupt change in the path slope, but this may be fixed through weighted velocity averaging (Hungr, 2009). Bed normal stress may not be assumed hydrostatic over complex terrain (McDougall & Hungr, 2003), but any component proportional to velocity is negligible (Hungr, 1995). C.3 Earth Pressure Equations Active earth pressure when the flow is expanding, and passive earth pressure conditions when the flow is compressing (Hungr, 2009). 1See Hungr (2009) for a more in-depth discussion of the assumptions in determining internal stress condi- tions. 108 The DAN-W model allows for Rankine, Savage-Hutter, and modified Savage-Hutter earth pressure equations as of version 9.0 of the software (Hungr, 2009) updated 03-03- 2009. DAN3D uses Savage-Hutter earth pressure equations2. C.4 Additional DAN-W Details DAN-W utilizes a 1-dimensional Lagrangian flow solution applied to fixed-volume de- formable blocks to calculate runout along a user-prescribed 2-dimensional3 flow path (Fig- ure C.1). The analyses in this thesis are performed with DAN-W version 9.0 updated 03- 03-2009. Figure C.1: DAN-W utilizes fixed-volume deformable blocks to calculate runout along a path. The manually input fixed path width may lead to error relating to flow depth and mo- mentum loss. The user-input path and width are fixed, which does not truly reflect con- ditions for flows with sloping sides in cross section since the actual width is proportional to depth while the modelled width is fixed (see Figure C.2. The basal resisting force is modelled along floor only, and treats the flow as fixed width irrespective of flow depth. The resisting force is only applied along the base of the flow, which does not truly reflect condi- tions for channelized flow where the actual event involves resisting forces along the walls. However, the error is less than 10% even for elliptical channels where widthdepth > 5 (Hungr, 1995). The runout path is input as a linear feature with a manually-input width and no changes horizontal direction. Thus, DAN-W does not model momentum loss in bends, which may be substantial (Fannin & Wise, 2001; Rickenmann, 2005). This compounds the error of 2See Pirulli, Bristeau, Mangeney, & Scavia (2007) for greater discussion on the importance of using the appropriate earth pressure equations. 3Technically, a 2 12 - or quasi-3-dimensional as the model permits manually-input widths. 109 (a) Elliptical channel (b) Rectangular channel (c) Triangular channel (d) Unconfined channel (e) Complex channel (f)Modelled channel Figure C.2: Fixed width leads to error in flow depth for conditions with sloping side channels, and purely basal frictional resistance leads to neglecting resistance along channel walls. 110 applying basal force along the floor only, as the model does not incorporate energy loss when the channel rapidly narrows or experiences a sudden change in flow direction (Hungr, 1995). Please see Hungr (1995) and Hungr (2009) for a full description of the model. C.5 Additional DAN3D Details DAN3D utilizes a 2-dimensional Lagrangian flow solution applied to smooth particle hy- drodynamics to calculate runout along a user-prescribed 3-dimensional digital elevation model. The analyses in this thesis are performed with DAN3D beta version updated 06-13- 2006. (McDougall & Hungr, 2004, 2005; McDougall, 2006) Please see McDougall (2006) for a full description of the model. C.6 Mathematical Manipulation of DAN-W Output Data Minimal mathematical manipulation is required to convert the DAN-W output for use in this thesis, most notably by converting D and L measurements of front and rear points to overall D and L measurements (Figure C.3). Figure C.3: Curvilinear distance and required adjustment to model output data. 111 Appendix D Sensitivity of the Statistical Analysis A mathematician is a device for turning coffee into theorems. — Paul Erdos D.1 Impact of Relic Cases As observations of relic events are less reliable, I also repeated my analyses excluding all events which occurred prior to 1900. Although the exact numbers change, the trends in p-values when performing a t-test on the modified regression (??) compared to previous research remain the same (Table D.2). I also checked the ANOVA and cluster categorizations: again, although the particular numbers changed, the trends are the same (Figure D.1). Similarly, for linear regressions on the impact of various characteristics on runout behaviour, movement type continues to have the greatest influence on mobility, and the only alterations on the linear regressions between characteristic and mobility index are that debris or talus on the path increases mobility. D.2 Impact of Tozawagawa In the linear regression to develop a V -α relationship for my data (Figure 5.1), Tozawa- gawa stands out for the unusually large dependent variable, α = 66◦. When comparing Intercept Slope All Cases 0.055 -0.084 Excluding Tozawagawa 0.117 -0.097 Only events since 1900 -0.039 -0.072 Table D.1: V -α relationships determined by linear regressions on all my case studies, excluding Tozawagawa, or events since 1900 only. See Equa- tion 4.1 for form. 112 p-values Except Tozawagawa Events since 1900 T-test on... Intercept Slope Intercept Slope Scheidegger 0.02 0.00 0.08 0.13 Corominas 0.43 0.74 0.94 0.55 Unobstructed 0.25 0.80 0.38 0.67 Channelized 0.29 0.48 0.36 0.49 Impact 0.29 0.83 0.50 0.61 Table D.2: P-values from t-testing the regression coefficient and intercept of my mod- ified linear regressions either excluding Tozawagawa, or excluding events prior to 1900, versus those determined by previous research. Compare to Table 5.4. individual cases to the linear regression, although the fit for Tozawagawa is extremely poor (Figure D.2), but it is exerting very little leverage on the regression (Figure D.3). This means that excluding Tozawagawa from calculating my V -α relationship makes very little difference. If I exclude Tozawagawa, the regression and subsequent t-test comparison are modified to Table D.1 and Table D.2. As the trends in p-values are identical to that discussed in Section 5.1, I decided to simplify discussion by not excluding any cases from the linear regression. 113 !! ! ! ! ! ! ! ! ! ! ! ! ! ! 2 4 6 8 10 12 14 0 10 00 20 00 30 00 Clusters for alpha N = 25 Number of Clusters W ith in gr ou ps  su m  o f s qu ar es Figure D.1: Effectiveness of emergent grouping of modern landslides using cluster analysis to minimize differences in α . Results are similar for cluster analysis on other mobility indices (Figure 5.2). 114 ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! −2 −1 0 1 2 −1 0 1 2 3 4 5 Theoretical Quantiles St an da rd ize d re sid ua ls lm(log10(tan(d2$alpha * (pi/180))) ~ log10(d2$volume_initial)) Normal Q−Q 37 5 16 Figure D.2: Theoretical and actual residuals for my V -α linear regression. Distance from the dashed line is indicative of poor fit. Case numbering is alphabetical: Charmonétier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Sec- tion E.37). 115 0.00 0.02 0.04 0.06 0.08 0.10 0.12 −2 −1 0 1 2 3 4 5 Leverage St an da rd ize d re sid ua ls ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! lm(log10(tan(d2$alpha * (pi/180))) ~ log10(d2$volume_initial)) Cook's distance 0.5 1 Residuals vs Leverage 37 5 16 Figure D.3: Residuals and leverage for my V -α linear regression. Points outside of the Cook’s distance are problematic as they are poorly fitting cases which in- fluence the regression strongly. Case numbering is alphabetical: Charmonétier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Section E.37). 116 Appendix E Descriptions of Case Studies Even the largest avalanche is triggered by small things. —Vernor Vinge The case histories summarized in Section 3.4 are more fully described here, with as- sociated model profiles. Data on back analyses with mathematically- and user-selected parameters are in Appendix F and Appendix G respectively. 117 E.1 1988 Abbot’s Cliff, England In 1988, V = 0.28 million m3 of chalk failed from a beach cliff. The chalk flowed down the cliff and across the beach without entraining additional material. The mass traveled horizontal length L= 442 m and dropped a vertical height H = 145 m, with a fahrböschung angle α = 18◦ (Hutchinson, 2002). 0 100 200 300 400 0 20 40 60 80 10 0 12 0 Abbots Cliff Distance (m) He igh t ( m .a .s. l.) W idt h = 12 7 m Figure E.1: Abbot’s Cliff profile. For back analyses, see Table F.1 and Table G.1. 118 E.2 1806 Arth-Goldau, Schwyz, Switzerland On 2 September 1806, V = 20−30 million m3 of shale failed from Rossberg Massif in the Alps. Although the rock avalanche did not entrain significant additional material, it ran out into and partially deposited in Lauerz See, displacing a wave of mud, trees, and water. The material ran out at an average velocity of 70 m/s with the mass travelling a horizontal length L= 6025 m and dropping a height H = 1265 m to a fahrböschung angle α = 12◦. The rock avalanche deposited to an average thickness of 25-100 m. The event killed 457 people and destroyed approximately 300 buildings (Heim, 1932; Eisbacher & Clague, 1984; Crosta & Agliardi, 2003). 1000 2000 3000 4000 5000 6000 40 0 60 0 80 0 10 00 12 00 14 00 16 00 Goldau Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 25 00 W idt h (m ) Figure E.2: Arth-Goldau profile. For back analyses, see Table F.2 and Table G.2. 119 E.3 1922 Arvel, Vaud, Switzerland On 14 March 1922, V = 0.614 million m3 of limestone failed in the Alps (45◦ 1’ 50” N, 6◦ 2’ 8” E). The rock avalanche ran out over alluvial sediments, damming the Rhône River. The mass travelled horizontal length L = 337 m and dropped a vertical height H =240 m, with a fahrböschung angle α = 35.5◦ (a nose of disturbed debris continued to αdisturbed = 19.5◦). The deposit exhibits proximal thickening with depths of 5-33 m, where two-thirds of the material deposited in a talus cone and one-third spread into the valley. The resulting infrastructure damage included destroyed sheds and a cable car, and damage to roads, a railway line, and water channel (Locat et al., 2006; Crosta et al., 2009). 100 200 300 400 500 40 0 45 0 50 0 55 0 60 0 Arvel Distance (m) He igh t ( m .a .s. l.) W idt h = 10 0 m Figure E.3: Arvel profile. For back analyses, see Table F.3. 120 E.4 1933 Brazeau Lake, Alberta, Canada In 1933, Vi = 4.5 million m3 failed from a slope in Jasper National Park (52◦ 24’ 36” N, 117◦ 03’ 56” W). The rock avalanche flowed down the slope, plowing through forest, and depositing just short of entering the lake. The mass traveled horizontal length L= 2700 m, with a fahrböschung angle α = 18◦. The rock avalanche ran out over a total area 0.9 km2, leaving a deposit 500 m wide. The deposit is uniform thickness between 5-6 m deep with conical molards, with minor distal thickening to 5-8 m at the toe. The deposit diverted the creek from the southeast of the fan to the northwest (Cruden, 1982). 0 500 1000 1500 2000 2500 18 00 20 00 22 00 24 00 26 00 Brazeau Lake Distance (m) He igh t ( m .a .s. l.) 30 0 35 0 40 0 45 0 50 0 55 0 60 0 W idt h (m ) Figure E.4: Brazeau Lake profile. For back analyses, see Table F.4 and Table G.3. 121 E.5 1987 Charmonétier, Isère, France On 24 August 1987, after heavy rain V = 0.13 million m3 of amphiboles failed from the northeast flank of Massif de Taillefer (45◦ 1’ 50” N, 6◦ 2’ 8” E).The rock avalanche was channelized over sediments, entraining insignificant additional material. The mass travelled horizontal length L= 600 m and dropped a vertical height H = 520 m, with a fahrböschung angle α = 41◦. The landslide left a talus cone deposit (Locat et al., 2006; Couture et al., 1997). 0 200 400 600 70 0 80 0 90 0 10 00 11 00 12 00 Charmonetier Distance (m) He igh t ( m .a .s. l.) 20 0 40 0 60 0 80 0 10 00 12 00 W idt h (m ) Figure E.5: Charmonétier profile. For back analyses, see Table F.5. 122 E.6 1442 Claps de Luc, Drôme, France In 1442, V = 2 million m3 of limestone failed in the Alps (44◦ 22’ 12” N, 5◦ 16’ 12” E). The rock avalanche spread over sediments, but did not entrain significant additional material. The mass travelled horizontal length L = 800 m and dropped a vertical height H = 370 m, with a fahrböschung angle α = 25◦ (Locat et al., 2006; Couture et al., 1997). 0 200 400 600 800 60 0 70 0 80 0 90 0 Claps de Luc Distance (m) He igh t ( m .a .s. l.) W idt h = 10 50  m Figure E.6: Claps de Luc profile. For back analyses, see Table F.6. 123 E.7 1999 Eagle Pass, British Columbia, Canada On May 1999, Vi = 0.074 million m3 of gneiss failed from upper valley slopes in Eagle Pass in the Monashee Mountains (118◦ 22’ 30” W, 50◦ 58’ 00” N). The debris avalanche partly deposited on a bench, where the remaining material mobilized and entrained glacial till and colluvial material to a depth of 0.25 m. The mobilized material overtopped the crest and flowed down the main slope over a cliff to deposit on the frozen surface of Clanwilliam Lake. The rock slide-debris avalanche affected a total volume Vf = 0.12 million m3 with a maximum 0.94 million m3 in motion at any time. Superelevation indicates the material was traveling at 8 m/s along the left margin at the crest of the bench. The mass travelled out to a fahrböschung angle α = 31◦. The debris avalanche deposited over 0.016 km2 on the ice to an average thickness of 2.2 m (Hungr & Evans, 2004). 200 400 600 800 1000 1200 60 0 70 0 80 0 90 0 10 00 11 00 Eagle Pass Distance (m) He igh t ( m .a .s. l.) 50 10 0 15 0 20 0 W idt h (m ) Figure E.7: Eagle Pass profile. 124 For back analyses, see Table F.7 and Table G.4. 125 E.8 1881 Elm, Sernaf Valley, Glarus, Switzerland On 11 September 1881, two small rockfalls preceded the failure of V = 11 million m3 of rock from Tschingelwald Ridge in the Alps. The rock avalanche did not entrain signifi- cant additional material. The material disintegrated, launched off an outcrop, was briefly airborne, turned, and ran out through the community of Elm. The material ran out D = 2 km in 45-55 s at an average velocity of 20-50 m/s up to a maximum velocity of 83.5 m/s. The mass travelled a horizontal length L = 2017 m and dropped vertical distance H = 613 m with a fahrböschung angle α = 16◦. The deposit is 1500 m long and 400-500 m wide with a depth 5-50 m with proximal thickening. The rock avalanche killed 115 people (Heim, 1932; Hsü, 1978; Eisbacher & Clague, 1984). 0 500 1000 1500 2000 10 00 11 00 12 00 13 00 14 00 15 00 Elm Distance (m) He igh t ( m .a .s. l.) 20 0 25 0 30 0 35 0 40 0 45 0 W idt h (m ) Figure E.8: Elm profile. 126 This event was modelled in trajectory launch mode. For back analyses, see Table F.8 and Table G.5. 127 E.9 1903 Frank Slide, Alberta, Canada On 29 April 1903, V = 30 million m3 of limestone failed from east face of Turtle Mountain in the Rocky Mountains (49◦ 36’ N, 114◦ 24’ 43” W). The rock avalanche ran down the mountain, through the town of Frank, and up the opposite side of the valley over limestone and saturated alluvium. The material ran out with an average velocity of 28-45 m/s. The mass ran out horizontal length L= 3500 m and dropped height H = 760 m with a fahrböschung angleα = 14◦. The rock avalanche ran out over a total area 2.67 km2 to an average thickness of 13.7 m. The event resulted in 70 fatalities, destroyed the coal mine and several buildings, and buried the Canadian Pacific rail line and the main road (McConnell & Brock, 2003; Anderson, 1979; Cruden & Hungr, 1986; Locat et al., 2006). 500 1000 1500 2000 2500 3000 3500 14 00 16 00 18 00 20 00 Frank Slide Distance (m) He igh t ( m .a .s. l.) 80 0 10 00 12 00 14 00 16 00 18 00 W idt h (m ) Figure E.9: Frank Slide profile. For back analyses, see Table F.9. 128 E.10 1915 Great Fall, England In 1915, V = 1.05−1.25 million m3 of chalk failed from a beach cliff. The rock avalanche flowed down the cliff and across the beach. The mass traveled horizontal length L= 628 m and dropped a vertical height H = 150 m, with a fahrböschung angle α = 13◦ (Hutchinson, 2002). 0 200 400 600 800 50 10 0 15 0 20 0 Great Fall Distance (m) He igh t ( m .a .s. l.) W idt h = 59 0 m Figure E.10: Great Fall profile. For back analyses, see Table F.10 and Section G.6. 129 E.11 1998 Hiegaesi, Fukushima Prefecture, Japan Between 26 and 31 August 1998, V = 50 million m3 of loamy volcanic ash and pumice layer failed and ran out over a rice paddy. The event is part of a temporal and spacial cluster of events near Nishigo village. The rock avalanche traveled horizontal length L= 48 m, 64 m, and 67 m in three lobes. The mass dropped a vertical height H = 25 m with a fahrböschung angle α = 11◦ (Wang et al., 2002). 0 20 40 60 80 100 0 5 10 15 20 Hiegaesi Distance (m) He igh t ( m .a .s. l.) W idt h = 23  m Figure E.11: Hiegaesi profile. For back analyses, see Table F.11. 130 E.12 1965 Hope Slide, British Columbia, Canada On 9 January 1965, V = 47.3 million m3 of metamorphic rock and snow failed from south- west slope of Johnson Peak in the southern Coast Mountains (49◦ 23’ 00” N, 121◦ 26’ 20” W). The rock avalanche flowed down the slope, across the highway, ran 822 m up the oppo- site wall, flowing back and spreading along the valley. The event entrained lesser quantities of snow and saturated soil. The mass travelled horizontal length L = 4240 m and dropped a vertical height H = 1220, with a fahrböschung angle α = 16◦. The deposit has an average thickness of 18 m up to a maximum 79 m. The rock avalanche buried 4.5 km of BC Highway 3, and resulted in 4 fatalities (Bruce & Cruden, 1977; Mathews & McTaggart, 1978). 0 500 1000 1500 2000 2500 80 0 10 00 12 00 14 00 16 00 18 00 Hope Slide Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 W idt h (m ) Figure E.12: Hope Slide profile. 131 For back analyses, see Table F.12 and Table G.8. 132 E.13 Jonas Creek, Alberta, Canada Two prehistoric rock avalanches occurred near Jasper in the Rocky Mountains (52◦ 26’ 00” N, 117◦ 24’ 30” W). The north slide failed thousands of years ago, and the south slide failed hundreds of years ago. An unfailed mass of Vi = 2.1 million m3 hangs between the source areas. The north slide, Vnorth = 2.1 million m3 of quartzite traveled horizontal length Lnorth = 3250 m and dropped a vertical height Hnorth = 880 m, with a fahrböschung angle αnorth = 17.1◦. The deposit covers 2.59 km2. The south slide, Vsouth = 4.5 million m3 of quartzite traveled horizontal length Lsouth = 2500 m and dropped a vertical height Hsouth = 920 m, with a fahrböschung angle αsouth = 26.5◦. The deposit covers 4.66 km2. No velocity estimates have been made for either event (Bruce, 1978; Bruce & Cruden, 1980; Locat et al., 2006). 0 500 1000 1500 2000 2500 3000 16 00 18 00 20 00 22 00 24 00 26 00 Jonas Creek (north) Distance (m) He igh t ( m .a .s. l.) 40 0 50 0 60 0 70 0 W idt h (m ) (a) (north) 500 1000 1500 2000 16 00 18 00 20 00 22 00 24 00 Jonas Creek (south) Distance (m) He igh t ( m .a .s. l.) 40 0 45 0 50 0 55 0 60 0 65 0 70 0 W idt h (m ) (b) (south) Figure E.13: Jonas Creek profiles. For back analyses of the older north slide, see Table F.13. For back analyses of the younger south slide, see Table F.14. 133 E.14 2005 Kuzulu, Sivas Province, Turkey On 17 March 2005, V = 12.5 million m3 of highly weathered volcanic tuffs failed in the Sivas Province. Another, smaller failure on 22 March is not modelled. The debris flow slid down a highly channelized V-shaped limestone valley. It did not entrain additional material. The material ran out over D= 2300 km in 300 s at an average velocity of 8 m/s up to a maximum velocity of 14 m/s. Eyewitness indicates the material was traveling at 13.6 m/s at the village. The mass travelled horizontal length L= 3300 m and dropped a vertical height H = 950 m, with a calculated fahrböschung angle α = 16◦. The deposit dammed the river to an average thickness of 25-30 m (Yilmaz et al., 2006; Ulusay et al., 2007). 0 500 1000 1500 2000 2500 3000 80 0 10 00 12 00 14 00 16 00 Kuzulu Distance (m) He igh t ( m .a .s. l.) 10 0 20 0 30 0 40 0 50 0 60 0 70 0 W idt h (m ) Figure E.14: Kuzulu profile. For back analyses, see Table F.15. 134 E.15 La Madeleine, Savoie, France Approximately 7,600 years ago, Vi71 million m3 of schist failed in the Maurienne Valley in the Alps (45◦ 17’ 14” N, 6◦ 57’ 52” E). The rock avalanche ran down the valley walls, entraining material to a final volume Vf = 125 million m3. The mass travelled horizontal length L = 4500 m and dropped a vertical height H = 1561 m, with a fahrböschung angle α = 19◦. The rock avalanche ran 150 m up the opposite valley wall before damming the Arc River in a hummocky deposit (Couture et al., 1997; Pollet & Schneider, 2004; Locat et al., 2006). 0 1000 2000 3000 4000 15 00 20 00 25 00 30 00 La Madeleine Distance (m) He igh t ( m .a .s. l.) W idt h = 60 0 m Figure E.15: La Madeleine profile. For back analyses, see Table F.16. 135 E.16 2001 Las Colinas, Santa Tecla, El Salvador On 13 January 2001, an earthquake triggered the failure of Vi = 0.1025 million m3 of vol- canic tephra from the northern flank of Báslamo Ridge in the Coridillern del Balasamo (89◦ 17’ 13” W, 13◦ 39’ 57” N). The flow slide ran down the 35◦ slope and into the flat Neuva San Salvador where it was channeled by buildings in urbanized terrain. The flow slide en- trained 0.082 million m3 between elevations 1076 to 1030 m.a.s.l and 0.081 million m3 between elevations 1030 to 90 m.a.s.l, ending with Vf = 0.1835 million m3. The material ran out over D = 8 km. The mass traveled horizontal length L = 715 m and dropped a vertical height H = 160 m, with a fahrböschung angle α = 12.6◦. The flow slide left a dry deposit 450 m long and 100 m wide to an average thickness of 2-6 m. The event resulted in 485 fatalities (Crosta et al., 2005). 0 200 400 600 800 1000 95 0 10 00 10 50 Las Colinas Distance (m) He igh t ( m .a .s. l.) 40 60 80 10 0 12 0 14 0 W idt h (m ) Figure E.16: Las Colinas profile. For back analyses, see Table F.17 and Section G.8. 136 E.17 2006 Luzon (Guinsaugon) Slide, Philippines On 17 February 2006, Vi = 15 million m3 failed from the slope above the village of Luzon. Between 380 to 280 m.a.s.l, the rock avalanche entrained material to a depth of 22 m for a final volume Vf = 20 million m3. The event flowed over the village and dammed at least four streams. The material ran out overD= 4.1 km at an average velocity of 35 m/s up to a maximum velocity of 120-130 m/s. The mass traveled horizontal length L = 3800 m and dropped a vertical height H = 810 m, with a α = 12◦. The rock avalanche ran out over a total area 3.2 km2. The event resulted in 139 confirmed fatalities, and 980 missing presumed dead (Lagmay et al., 2006; Catane et al., 2007; Evans et al., 2007). 0 1000 2000 3000 4000 5000 0 20 0 40 0 60 0 80 0 Luzo  Slide Distance (m) He igh t ( m .a .s. l.) 10 0 15 0 20 0 25 0 W idt h (m ) Figure E.17: Luzon Slide profile. 137 For back analyses, see Table F.18. 138 E.18 1969 Madison Canyon, Montana, United States On 17 August 1969, the Hebgen Lake earthquake triggered the failure of V = 21.4 million m3 of dolomite, schist, and gneiss in Yellowstone National Park. The rock avalanche slid down the canyon, across the floor, and 2000 m up the opposite wall, spreading up and down along the valley and damming the river. The material ran out a curvilinear distance D = 1.28 km in less than 60 s. From run up, the flow reached up to a maximum velocity of 50 m/s. The mass traveled a horizontal distance L= 1300 m and dropped a vertical height H = 2200 m, with a fahrböschung angle α = 13◦.The rock avalanche left a deposit 1500 mwide (Hungr, 1995; Trunk &Dent, 1986). 0 500 1000 1500 19 00 20 00 21 00 22 00 23 00 Madison Canyon Distance (m) He igh t ( m .a .s. l.) 40 0 60 0 80 0 10 00 12 00 W idt h (m ) Figure E.18: Madison Canyon profile. 139 For back analyses, see Table F.19 and Table G.11. 140 E.19 2002 McAuley Creek, British Columbia, Canada Between May and June 2002, V = 7.4 million m3 of gneissic rock failed in the Interior Plateau. The event was part of the same temporal cluster of events as the Zymoetz River landslide. Most of the rock avalanche deposited at the toe of the source slope, damming McAuley Creek while one million m3 of the debris continued down the valley over saturated glacial till in a 1.6 km long, thin distal deposit to a fahrböschung angle α = 10◦. (Evans et al., 2003; McDougall, 2006). 0 500 1000 1500 2000 10 00 11 00 12 00 13 00 14 00 15 00 McAuley Creek Distance (m) He igh t ( m .a .s. l.) 10 0 20 0 30 0 40 0 50 0 W idt h (m ) Figure E.19: McAuley Creek profile. For back analyses, see Table F.20. 141 E.20 1984 Mount Cayley, British Columbia, Canada In 1984,Vi = 0.74 million m3 of pyroclastic material failed from Mount Cayley. The debris avalanche travelled roughly along Avalanche Lake, closely along Turbid Creek, damming Squamish River. The event entrained 0.2 million m3 at a rate of 526 m3/m over Avalanche Creek, ending with Vf = 1.08 million m3. The material reached a maximum velocity of 70 m/s. Superelevation indicates the ma- terial was traveling at 42 m/s at midpath. The mass traveled horizontal length L = 3460 m and dropped a vertical height H = 1180 m, with a fahrböschung angle α = 19◦ (Evans et al., 2001; Hungr, 2006). 0 1000 2000 3000 4000 40 0 60 0 80 0 10 00 12 00 14 00 16 00 Mount Cayley Distance (m) He igh t ( m .a .s. l.) 50 10 0 15 0 20 0 25 0 30 0 W idt h (m ) Figure E.20: Mount Cayley profile. For back analyses, see Table F.21 and Section G.10. 142 E.21 1991 Mount Cook, New Zealand In 1991, Vi = 11.8 million m3 of rock, snow, and ice failed from the east face of Mount Cook. The rock avalanche flowed down Grand Plateau where a third of the mass ran up Anzec Peak and the remainder continued down Hochstetter Glacier and Tasman Glacier, running 70 m up a moraine wall before coming to a rest. The rock avalanche entrained ice, snow, rock to a final volume Vf = 60−80 million m3. The material ran out a curvilinear distance D = 7.5 km. From seismic data, the event completed in 15-120 s, and eyewitnesses report movement for up to 900 s. The average velocity for the center of mass was 55 m/s, and 60 m/s for the toe (McSaveney, 2002). 0 2000 4000 6000 8000 10 00 15 00 20 00 25 00 30 00 35 00 Mou t Cook Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 25 00 W idt h (m ) Figure E.21: Mount Cook profile. The event is modelled in DAN-W either as the whole mass over the glacier streamline without entrainment, or as with two paths, the main streamline running over the glaciers and a secondary streamline overtopping Anzec Peak, with entrainment to a depth of 9 m throughout both paths. For back analyses, see Table F.22 and Table G.14. 143 E.22 1248 Mount Granier, Savoie, France On 24 November 1248,Vi = 200 million m3 of limestone failed fromMount Granier Massif in the Alps. The rock avalanche flowed down the slope, overtopped a moraine, and came to a rest against a lower moraine without entraining additional material. The material ran out a horizontal length L = 7690 m and vertical height H = 1520 m, with a fahrböschung angle α = 12◦. The rock avalanche ran out over a total area 15-20 km2, leaving a deposit 7 km long and 2 km wide to an average thickness of 20 m. The event buried the town of St. André and possibly smaller hamlets, killing 1,500 to 5,000 people (Goguel & Pachoud, 1972; Cruden & Antoine, 1984; Eisbacher & Clague, 1984). 1000 2000 3000 4000 5000 6000 7000 50 0 10 00 15 00 Mou t Granier Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 25 00 30 00 W idt h (m ) Figure E.22: Mount Granier profile. For back analyses, see Table F.23 and Table G.15. 144 E.23 1984 Mount Ontake, Japan On 14 September 1984, the Naganoken-Seibu earthquake triggered the failure of Vi = 30.5− 36 million m3 of volcanic ash with pumice from the south flank of Mount Kenga- nine Pea. The rock avalanche ran out along Denjo, Nigorikawa, and Otaki rivers (Inokuchi, 1985; Yanase et al., 1985). The mass ran out curvilinear distance D= 1.3 km, travelling horizontal length L= 400 m. 0 1000 2000 3000 4000 5000 18 00 20 00 22 00 24 00 Mount Ontake Distance (m) He igh t ( m .a .s. l.) 0 20 0 40 0 60 0 80 0 10 00 12 00 14 00 W idt h (m ) Figure E.23: Mount Ontake profile. For back analyses, see Table F.24. 145 E.24 2007 Mount Steele, Yukon, Canada On 24 July 2007, Vi = 30 million m3 of rock and ice failed from north face of Mount Steele in the Saint Elias Mountains (140◦ 18’ 38”W, 61◦ 05’ 35” N). Part of a temporal and spacial cluster of 18 events, the main event occurred at 18:25 local time. The rock avalanche flowed down the slope, across the glacier, and ran up a ridge before falling back. It did not entrain significant additional material. From eyewitness and seismic data, the material ran out a curvilinear distance D = 0.7 km in 100 s at an average velocity of 35-65 m/s. The mass traveled a maximum horizontal distance of more than L = 5760 m, and dropped a vertical distance Hdeposit = 1860m (al- though the maximum descent over the glacier was Hmax = 2160 m), with a fahrböschung angle αdeposit = 18◦. The rock avalanche ran out over a total area 3.66 km2 (Lipovsky et al., 2008). 0 2000 4000 6000 8000 25 00 30 00 35 00 40 00 45 00 Mount Steele Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 W idt h (m ) Figure E.24: Mount Steele profile. 146 For back analyses, see Table F.25. 147 E.25 Mystery Creek, British Columbia, Canada Approximately 880 years ago, V = 40 million m3 of foliated hard intrusive rock failed from the east side of Green River Valley north of Whistler (50◦ N 123◦ W). The rock avalanche flowed down the slope, overtopped a 150 m ridge and came to rest at the present- day location of Highway 99. The material ran out over curvilinear distance D = 4 km with a fahrböschung angle α = 15◦. The rock avalanche ran out over a total area of 1.2 km2 (Evans et al., 1994; Hungr et al., 1999; Nichol et al., 2002). 0 1000 2000 3000 4000 40 0 60 0 80 0 10 00 12 00 14 00 16 00 Mystery Creek Distance (m) He igh t ( m .a .s. l.) 50 0 60 0 70 0 80 0 90 0 10 00 11 00 12 00 W idt h (m ) Figure E.25: Mystery Creek profile. For back analyses, see Table F.26. 148 E.26 1999 Nomash River, British Columbia, Canada On 25 or 26 April 1999, Vi = 0.30 million m3 of limestone failed from upper slope of a glacial valley in the Insular Mountains near Zeballos on the western coast of Vancouver Island (126◦ 42’ 00” W, 49◦ 59’ 00” N). The rock avalanche flowed down slope, across the valley floor, changed direction by 90◦ and followed the river until coming to a rest. The event traveled over glacial till, colluvial, and alluvial materials, entraining ∆V = 0.36 million m3 of saturated material along the lower slopes, ending with Vf = 0.66 million m3. Superelevation indicates the material was traveling at 22.5 m/s at the first bend (at ap- proximately L = 776 m), 23 m/s at the second bend, and less than 2 m/s in the final bends of the path. The mass traveled horizontal length L= 2270 m and dropped a vertical height H = 560 m, with a fahrböschung angle α = 13.5◦ (Guthrie et al., 2003; Hungr & Evans, 2004). 0 500 1000 1500 2000 2500 40 0 50 0 60 0 70 0 80 0 Nomash River Distance (m) He igh t ( m .a .s. l.) 0 50 10 0 15 0 20 0 25 0 30 0 W idt h (m ) Figure E.26: Nomash River profile. 149 For back analyses see Table F.27 and Table G.16. 150 E.27 1959 Pandemonium Creek, British Columbia, Canada In 1959, Vi = 5 million m3 of quartz diorite failed from a rock spur of a cirque headwall near Pandemonium Creek in the southern Coast Mountains (52◦ 01’ N, 125◦ 46’ W). The rock avalanche flowed down the cirque, crossed Pandemonium Creek, was deflected by or ran up the opposing valley wall, and continued down the valley, depositing in Knot Lakes. It did not entrain additional material (Evans & Hungr, 1989; Erismann & Abele, 2001). The material ran out over D = 9.0 km in 300 s at an average velocity of 30 m/s. The upper zone of the event had an average velocity of 74 m/s, slowing to an average velocity of 22 m/s in the lower zone. From run up and superelevation data, the material was traveling 81-100 m/s entering the run-up zone at Pandemonium Creek, and 21-38 m/s in the eastern Pandemonium Valley. The mass traveled at least horizontal length L= 8600 m and dropped a vertical height H = 2000 m, with a fahrböschung angle α = 13◦. The deposit has distal thickening up to 20 m (Evans & Hungr, 1989). 0 2000 4000 6000 8000 10 00 15 00 20 00 25 00 Pandemonium Creek Distance (m) He igh t ( m .a .s. l.) 20 0 25 0 30 0 35 0 40 0 45 0 50 0 W idt h (m ) Figure E.27: Pandemonium Creek profile. For back analyses see Table F.28 and Table G.17. 151 E.28 2002 Pink Mountain, British Columbia, Canada Between 30 June and 6 July 2002, Vi = 0.74 million m3 of colluvium, soil, sandstone, and shale failed from a gentle slope in the Rocky Mountain foothills of the upper Peace River Valley (122◦ 52’ W, 57◦ 94’ N). The rock avalanche ran over a road, entered Two Bit Creek, and came to a rest. The rock avalanche entrained 0.196 million m3 of clay-rich saturated colluvium over the slope from the toe of source scar to elevation 1050 m. The final volume was Vf = 1.04 million m3 (Geertsema et al., 2006). The material ran out over curvilinear distance D= 2 km. The mass traveled horizontal length L = 1950 m and dropped a vertical height H = 450 m, with a fahrböschung angle α = 11.6◦. The rock avalanche ran out over a total area 0.434 km2, leaving a deposit 320 m wide with an average thickness of 1-2 m with distal thickening up to 4 m. The event buried a forestry road (Geertsema et al., 2006). 0 500 1000 1500 2000 0 10 0 20 0 30 0 40 0 50 0 Pink Mountain Distance (m) He igh t ( m .a .s. l.) 15 0 20 0 25 0 30 0 W idt h (m ) Figure E.28: Pink Mountain profile. 152 For back analyses see Table F.29. 153 E.29 Queen Elizabeth, Alberta, Canada V = 45 million m3 of limestone failed from the Rocky Mountains (52◦ 52’ 36” N, 117◦ 42’ W). The rock avalanche ran 190 m up the opposite valley wall, falling back to fill the valley and dam a lake. The mass travelled horizontal length L = 2645 m and dropped a vertical height H = 950 m, for a calculated fahrböschung angle α = 20◦ (Locat et al., 2006). 0 500 1000 1500 2000 18 00 20 00 22 00 24 00 26 00 Queen Elizabeth Distance (m) He igh t ( m .a .s. l.) W idt h = 50 0 m Figure E.29: Queen Elizabeth profile. For back analyses see Table F.30. 154 E.30 Rockslide Pass, Northwest Territories, Canada In Rockslide Pass, Vi = 370-450 million m3 of limestone and dolomite failed from bedding plane above a U-shaped valley in the Mackenzie Mountains (127◦ 45’ W, 63◦ 20’ N). The rock avalanche traversed the valley as an intact block for nearly 4.5 km, disintegrated, and spread both up and down the valley. No additional material was entrained. The material ran out over D > 3 km at an average velocity of at least 20 m/s. Run- up indicates the material was traveling at 40 to 70 m/s near the beginning of the path. The mass traveled horizontal length L = 6330 m and dropped height H = 1000 m, with a fahrböschung angle α = 8.5◦. The rock avalanche ran out over a total area 1.2 km2, leaving a deposit with an average thickness of 175 m. The deposit ramp has distal thickening up to 200 m followed by a thin downstream lobe with distal thickening to 4 m (McLellan & Kaiser, 1984). The event is modelled as a block for the first 4.5 km. 0 1000 2000 3000 4000 5000 6000 40 0 60 0 80 0 10 00 12 00 Rockslide Pass Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 25 00 W idt h (m ) Figure E.30: Rockslide Pass profile. For back analyses see Table F.31 and Table G.18. 155 E.31 1855 Rubble Creek, British Columbia, Canada In 1855,Vi = 25 million m3 of glacial dacitic lava failed from headwall of the Barrier, north of Vancouver. The rock avalanche flowed over granitic rocks and alluvial sediments along Rubble Creek without entraining significant additional material. The material ran out over D = 6.9 km in 300-600 s at an average velocity of 20 m/s. Superelevation indicates the material was traveling at 29.4 m/s at the first curve, 22.2 m/s at the second curve, and 29.5 m/s at the third curve. The mass traveled horizontal length L= 4500 m and dropped a vertical heightH = 1060 m, with a fahrböschung angle α = 13◦. The rock avalanche ran out over a total area 1.1 km2, leaving a deposit 3.5 m long and 200- 350 m wide thickening up to 15 m. The event eventually led to a court ruling barring residential development in the area (Moore et al., 1978; Hungr et al., 1999). 0 1000 2000 3000 4000 5000 0 20 0 40 0 60 0 80 0 10 00 Rubble Creek Distance (m) He igh t ( m .a .s. l.) 10 00 10 05 10 10 10 15 W idt h (m ) Figure E.31: Rubble Creek profile. For back analyses see Table F.32 and Table G.19. 156 E.32 1982 Sale Mountain, China In 1982,Vi =million m3 of loess failed from Sale Mountain. A larger volume slumped over a short distance, immediately followed by a smaller flow slide running out over the deposit and into the valley without entraining additional material. The material ran out in 55 s at an average velocity of 7-19.8 m/s over the deposit from a recent slump. The mass traveled horizontal length L = 1600 m and dropped a vertical height H = 320 m, with a fahrböschung angle α = 11◦. The flow slide ran out over a total area 1.3 km2 to an average thickness of 24 m. The deposit has proximal thickening up to 70 m (Zhang et al., 2002). 0 500 1000 1500 20 00 20 50 21 00 21 50 22 00 22 50 Sale Mountain Distance (m) He igh t ( m .a .s. l.) 0 20 0 40 0 60 0 80 0 10 00 W idt h (m ) Figure E.32: Sale Mountain profile. For back analyses, see Table F.33 and Table G.20. 157 E.33 1850 Seaford, England In 1850, an artificial blast triggered the failure ofVi= 0.153 million m3 of chalk from a cliff. The chalk flowed down the cliff and across the beach. It did not entrain additional material. The mass traveled horizontal length L = 121 m and dropped a vertical height H = 68 m, with a fahrböschung angle α = 28◦ (Hutchinson, 2002). 50 100 150 200 250 20 30 40 50 60 70 80 Seaford Distance (m) He igh t ( m .a .s. l.) W idt h = 13 5 m Figure E.33: Seaford profile. For back analyses see Table F.34 and Table G.21. 158 E.34 1964 Sherman Glacier, Alaska, United States On 27 March 1964, V = 10− 60 million m3 of rock, snow, and ice failed from Shattered Peak (60◦ 32’ 16” N 145◦ 6’ 25” W). The rock avalanche flowed in all directions from the peak, with the majority crossing Andes Glacier, splitting on a 150 m high spur 1 km from the source. A quarter of the mass overtopped the spur with the remainder flowing around, rejoining into one flow spreading across and down Sherman Glacier. The material ran out over curvilinear distanceD= 5.7 km in 216 s at an average velocity of 26 m/s, and was traveling at least 67 m/s as it overran the spur. The mass travelled a horizontal length L= 5950 m and dropped a vertical height H = 1080 m, with a calculated fahrböschung angle α = 10◦. The rock avalanche ran out over a total area 8.25 km2, leaving a deposit 200 m wide with an average thickness of 1.65 m up to a maximum 10 m (Shreve, 1966; Bull & Marangunic, 1966; McSaveney, 1978). 0 1000 2000 3000 4000 5000 6000 40 0 60 0 80 0 10 00 Sh rman Glacier Distance (m) He igh t ( m .a .s. l.) 50 0 10 00 15 00 20 00 25 00 W idt h (m ) Figure E.34: Sherman Glacier profile. For back analyses see Table F.35 and Table G.22. 159 E.35 1946 Six de Eaux Froids, Switzerland On 30 May 1946, an earthquake triggered the failure of V = 4.2 million m3 of limestone from Andins Valley near Rawyl, Valais in the Alps. The rock avalanche flowed down the slope, deflected east and west along the valley, filled Luchet Lake and buried Serin pasture. It did not entrain significant additional material. The eastern down-valley flow of approximately 3 million m3 traveled 1.5 km from the toe of the source slope, while the remaining 2 million m3 western flow travelled up-valley. The rock avalanche ran out to a fahrböschung angle α = 16◦, and left a deposit 2000 m long and 400 m wide (Hungr & McDougall, 2009). 0 500 1000 1500 0 10 0 20 0 30 0 40 0 50 0 60 0 Six de Eaux Froids (left) Distance (m) He igh t ( m .a .s. l.) 10 0 15 0 20 0 25 0 W idt h (m ) (a) (west) 0 500 1000 1500 2000 2500 0 20 0 40 0 60 0 80 0 Six de Eaux Froids (right) Distance (m) He igh t ( m .a .s. l.) 20 0 30 0 40 0 50 0 W idt h (m ) (b) (east) Figure E.35: Six de Eaux Froids profiles. For back analyses with mathematically-selected parameters, see Table F.36 (east lobe) and Table F.37 (west lobe). For back analyses with user-selected parameters, see Sec- tion G.20 (both lobes). 160 E.36 Slide Mountain, Alberta, Canada V = 13 million m3 of limestone failed from Slide Mountain in the Rocky Mountains (53◦ 5’ 50” N, 117◦ 38’ 24” W). The rock avalanche ran out over rock before entraining glacial and fluvial sediments, but not to significant additional volume. The mass travelled horizontal length L= 1650 m and dropped a vertical heightH = 420 m, for a calculated fahrböschung angle α = 14.5◦. The rock avalanche ran 120 m up a gentle incline before damming the Fiddle River with a deposit area 1.3 km2 to an average depth of 25 m (Locat et al., 2006). 0 500 1000 1500 16 00 17 00 18 00 19 00 20 00 Slide Mountain Distance (m) He igh t ( m .a .s. l.) W idt h = 50 0 m Figure E.36: Slide Mountain profile. For back analyses see Table F.38. 161 E.37 2000 Tozawagawa, Niigata Prefecture, Japan On 5 January 2000,V = 0.19 million m3 failed in the Niigata Prefecture. The mass traveled a total distance D= 454 m, travelling a horizontal length L= 100 m and dropped a vertical height H = 230 m for a calculated fahrböschung angle α = 66◦. The deposit dammed the Tozawaga River, with a deposit maximum width of 35 m and depth of 15-20 m (Yamagishi et al., 2004; Sassa, 2005). 0 100 200 300 400 25 0 30 0 35 0 40 0 45 0 50 0 Tozawagawa Distance (m) He igh t ( m .a .s. l.) 80 10 0 12 0 14 0 16 0 W idt h (m ) Figure E.37: Tozawagawa profile. For back analyses see Table F.39 and Table G.24. 162 E.38 1717 Triolet Glacier, Italy In 1717, Vi = 7.3− 9.8 million m3 of rock, snow, and ice failed from cirque headwall on Mont Blanc in the Alps (7◦ 0’ 13” E, 45◦ 53’ 45” N). The rock avalanche flowed down the slope over a glacier, splashed up the valley side, then continued down the river valley. The rock avalanche entrained boulders, water, and ice, depositing withVf = 10−15 million m3. The material ran out over curvilinear distance D= 9.0 km at an average velocity of 35 m/s up to a maximum velocity of 44 m/s. The mass traveled horizontal length L = 7200 m and dropped a vertical height H = 1860 m, with a fahrböschung angle α = 14.5◦. The deposit has an average thickness of 2.5-3.4 m (Noetzli et al., 2006; Deline & Kirkbride, 2009; Deline, 2009). The event resulted in seven fatalities, killed 120 oxen and cows, and destroyed a lot of cheese (Grove, 2004). 0 2000 4000 6000 8000 20 00 25 00 30 00 35 00 Triolet Glacier Distance (m) He igh t ( m .a .s. l.) 0 50 0 10 00 W idt h (m ) Figure E.38: Triolet Glacier profile. For back analyses see Table F.40 and Table G.25. 163 E.39 2002 Zymoetz River, British Columbia, Canada On 8 June 2002, Vi = 0.72 million m3 of volcanic bedrock failed from a small, steep tribu- tary of the Skeena River in the north Coast Mountains (128◦ 18’ W, 54◦ 26’ N). The debris avalanche traveled down the source slope, partly depositing in a cirque basin, and continued down the tributary over snow, talus, and bare rock. The event entrained 0.5 million m3 of snow, saturated glacial till, and organics at a rate of 3.3×10−4 m−1 below 880 m elevation, ending with Vf = 1.4 million m3. The material reached a maximum velocity of 34 m/s. Superelevation indicates the ma- terial was traveling at 26 m/s at the first major curve of the path. The mass ran out to a fahrböschung angle α = 17◦. Half the mass deposited in a cirque basin at the head of the valley with an average thickness of 3 m, and the other half deposited along Glen Falls Creek and a fan damming the Zymoetz River. The event triggered a debris flow and severed a Pa- cific Northern Gas pipeline (Schwab et al., 2003; Boultbee et al., 2006; McDougall, 2006). 0 1000 2000 3000 4000 20 0 40 0 60 0 80 0 10 00 12 00 14 00 Zymoetz River Distance (m) He igh t ( m .a .s. l.) 0 50 10 0 15 0 20 0 25 0 30 0 W idt h (m ) Figure E.39: Zymoetz River profile. 164 For back analyses see Table F.41 and Table G.26. 165 Appendix F Model Data: Mathematically-Selected Parameters Any statistics can be extrapolated to the point where they show disaster. — Sowell (1996) The following summarizes back-analyses of the case studies described in Appendix E where a fixed range of parameters are modelled and runout is quantitatively judged as defined in Section 8.1.2. The purpose is identify and recommend parameters for use in forward- prediction of similar events. All the models exclude entrainment, even when entrainment is a significant portion of the volume. This is because the purpose of these back analyses is not to create a detailed model of the past event (as it is with user-selected parameters, Appendix G), but instead to use only information available before a failure in order to test the efficacy of various parameters in forward-predicting hazard distribution and intensity. This technique may be updated to include entrainment when field investigation of potential failure sites also includes identifying likely entrainment locations, depths, and volumes as part of standard procedures. Note that for cases with recorded maximum velocities, the comparison between obser- vation and model is for the maximum modelled velocity anywhere along the runout path, not at the specified observed location. See Table 8.1 for interpretation of deviation for mobility indices. 166 F.1 1988 Abbot’s Cliff, England D L Le α vmax Observed 442 m 210 m 18◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 72 185 -57.8 Frictional 10 28 67 -25.9 Frictional 15 -5 -6 2.2 Frictional 17 -14 -25 11.9 Frictional 20 -24 -46 24.6 Frictional 25 -35 -68 42.2 Frictional 30 -41 -80 54.1 Frictional 35 -48 -94 69.8 Frictional 40 -55 -109 90.2 Frictional 45 -63 -124 117.9 Voellmy 0.05 100 13 32 -13.8 Voellmy 0.05 500 43 105 -37.2 Voellmy 0.05 1000 43 104 -37.0 Voellmy 0.05 1500 69 175 -55.5 Voellmy 0.05 2000 61 152 -49.7 Voellmy 0.1 100 -3 -1 -0.2 Voellmy 0.1 500 32 76 -28.8 Voellmy 0.1 1000 43 105 -37.2 Voellmy 0.1 1500 45 109 -38.2 Voellmy 0.1 2000 52 129 -43.7 Voellmy 0.15 100 -13 -24 11.3 Voellmy 0.15 500 15 37 -15.7 Voellmy 0.15 1000 23 56 -22.4 Voellmy 0.15 1500 24 58 -22.9 Voellmy 0.15 2000 30 72 -27.4 Voellmy 0.2 100 -22 -41 21.2 Voellmy 0.2 500 0 5 -3.2 Voellmy 0.2 1000 7 20 -9.2 Voellmy 0.2 1500 8 22 -10.0 Voellmy 0.2 2000 12 29 -13.0 Table F.1: Mathematically-selected parameters for Abbot’s Cliff. For case descrip- tion, see Section E.1. For back analyses with user-selected parameters, see Ta- ble G.1. 167 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● 200 300 400 500 600 700 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●●●●● ●●●● ●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● 300 400 500 600 700 800 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.1: Raw output data for models of Abbot’s Cliff with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 168 F.2 1806 Arth-Goldau, Schwyz, Switzerland D L Le α vmax Observed 6025 m 4001 m 12◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 13 -0 20.2 Frictional 10 -16 -12 -9.9 Frictional 15 -31 -43 30.3 Frictional 17 -40 -55 46.1 Frictional 20 -61 -76 69.8 Frictional 25 -70 -85 84.9 Frictional 30 -71 -85 86.5 Frictional 35 -71 -85 87.0 Frictional 40 -72 -86 87.8 Frictional 45 -72 -86 88.1 Voellmy 0.05 100 -28 -37 22.5 Voellmy 0.05 500 -25 -33 16.8 Voellmy 0.05 1000 -25 -32 15.2 Voellmy 0.05 1500 -7 1 -18.2 Voellmy 0.05 2000 85 -643 412.3 Voellmy 0.1 100 -33 -46 34.2 Voellmy 0.1 500 -23 -28 10.1 Voellmy 0.1 1000 -23 -27 9.6 Voellmy 0.1 1500 -18 -17 -4.5 Voellmy 0.1 2000 -14 -8 -13.8 Voellmy 0.15 100 -36 -50 39.6 Voellmy 0.15 500 -27 -36 21.0 Voellmy 0.15 1000 -22 -26 7.1 Voellmy 0.15 1500 -20 -21 0.2 Voellmy 0.15 2000 -23 -27 9.6 Voellmy 0.2 100 -38 -53 43.3 Voellmy 0.2 500 -32 -44 32.1 Voellmy 0.2 1000 -27 -36 22.0 Voellmy 0.2 1500 -25 -32 15.5 Voellmy 0.2 2000 -24 -29 12.1 Table F.2: Mathematically-selected parameters for Arth-Goldau. For case description, see Section E.2. For back analyses with user-selected parameters, see Table G.2. 169 ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●●● 2000 4000 6000 8000 10000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●●●● ●●●● ● ●●●●● 10 20 30 40 50 60 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ●●● ●●●● 5000 10000 15000 20000 25000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 0 20 40 60 80 100 120 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.2: Raw output data for models of Arth-Goldau with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 170 F.3 1922 Arvel, Vaud, Switzerland D L Le α vmax Observed 363 m -21 m 35.5◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 -67 839 66.0 Frictional 10 100 16265 88.1 Frictional 15 100 3722 38.4 Frictional 17 100 3098 33.1 Frictional 20 100 1519 16.2 Frictional 25 59 -771 -28.8 Frictional 30 26 -531 -25.1 Frictional 35 9 -258 -16.1 Frictional 40 -7 13 -4.8 Frictional 45 -19 331 10.6 Voellmy 0.05 100 100 9878 71.1 Voellmy 0.05 500 100 21049 96.3 Voellmy 0.05 1000 100 19075 93.2 Voellmy 0.05 1500 100 4055 41.0 Voellmy 0.05 2000 100 19112 93.3 Voellmy 0.1 100 100 3130 33.4 Voellmy 0.1 500 100 19707 94.2 Voellmy 0.1 1000 100 4953 47.4 Voellmy 0.1 1500 100 24221 100.4 Voellmy 0.1 2000 100 9760 70.7 Voellmy 0.15 100 100 1600 17.2 Voellmy 0.15 500 100 8750 66.9 Voellmy 0.15 1000 100 11455 76.3 Voellmy 0.15 1500 100 6049 54.1 Voellmy 0.15 2000 100 -27 -8.3 Voellmy 0.2 100 100 74 -6.3 Voellmy 0.2 500 100 6600 57.0 Voellmy 0.2 1000 100 2671 29.0 Voellmy 0.2 1500 100 3881 39.7 Voellmy 0.2 2000 100 4830 46.6 Table F.3: Mathematically-selected parameters for Arvel. For case description, see Section E.3. 171 ●● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ● ●●● ● ●● ● ● 200 400 600 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ● ●●● ● ●● ● ● 30 40 50 60 70 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ● ●●● ● ●● ● ● 0 1000 2000 3000 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● 50 100 150 200 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.3: Raw output data for models of Arvel with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 172 F.4 1933 Brazeau Lake, Alberta, Canada D L Le α vmax Observed 2700 m 18◦ Rheology θb f ξ ∆L ∆α Frictional 5 29 -69.8 Frictional 10 15 -35.3 Frictional 15 6 -17.5 Frictional 17 -3 -5.6 Frictional 20 -16 8.8 Frictional 25 -35 28.7 Frictional 30 -56 61.8 Frictional 35 -84 76.6 Frictional 40 -89 84.5 Frictional 45 -90 88.6 Voellmy 0.05 100 -6 -1.7 Voellmy 0.05 500 -1 -7.6 Voellmy 0.05 1000 -1 -8.6 Voellmy 0.05 1500 16 -37.4 Voellmy 0.05 2000 3 -14.1 Voellmy 0.1 100 -11 3.6 Voellmy 0.1 500 -4 -4.1 Voellmy 0.1 1000 -1 -8.6 Voellmy 0.1 1500 11 -27.2 Voellmy 0.1 2000 -5 -2.9 Voellmy 0.15 100 -34 28.1 Voellmy 0.15 500 -11 3.9 Voellmy 0.15 1000 -0 -8.8 Voellmy 0.15 1500 5 -16.9 Voellmy 0.15 2000 1 -11.4 Voellmy 0.2 100 -40 35.9 Voellmy 0.2 500 -21 13.2 Voellmy 0.2 1000 -8 0.7 Voellmy 0.2 1500 -2 -6.3 Voellmy 0.2 2000 1 -11.5 Table F.4: Mathematically-selected parameters for Brazeau Lake. For case descrip- tion, see Section E.4. For back analyses with user-selected parameters, see Ta- ble G.3. 173 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●● ● ●●●● ● ●●●●● 5 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● 20 40 60 80 100 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.4: Raw output data for models of Brazeau Lake with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 174 F.5 1987 Charmonétier, Isère, France D L Le α vmax Observed 600 m -232 m 40.9◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 51 -348 -68.7 Frictional 10 51 -344 -68.0 Frictional 15 53 -384 -75.6 Frictional 17 54 -409 -80.4 Frictional 20 57 -459 -89.8 Frictional 25 63 -575 -111.2 Frictional 30 75 -896 -162.1 Frictional 35 8 -15 -4.3 Frictional 40 -54 -46 3.5 Frictional 45 -67 -50 9.0 Voellmy 0.05 100 18 -45 -11.0 Voellmy 0.05 500 22 -60 -14.1 Voellmy 0.05 1000 27 -87 -19.3 Voellmy 0.05 1500 30 -113 -24.2 Voellmy 0.05 2000 33 -133 -27.9 Voellmy 0.1 100 17 -41 -10.1 Voellmy 0.1 500 21 -56 -13.2 Voellmy 0.1 1000 17 -40 -10.0 Voellmy 0.1 1500 28 -98 -21.3 Voellmy 0.1 2000 30 -113 -24.1 Voellmy 0.15 100 16 -38 -9.4 Voellmy 0.15 500 20 -51 -12.2 Voellmy 0.15 1000 21 -59 -13.8 Voellmy 0.15 1500 17 -42 -10.4 Voellmy 0.15 2000 24 -71 -16.2 Voellmy 0.2 100 15 -33 -8.5 Voellmy 0.2 500 18 -46 -11.1 Voellmy 0.2 1000 22 -63 -14.6 Voellmy 0.2 1500 20 -54 -12.8 Voellmy 0.2 2000 20 -51 -12.3 Table F.5: Mathematically-selected parameters for Charmon’etier. For case descrip- tion, see Section E.5. 175 ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ● ●● 200 400 600 800 1000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●● ●●● ●● ●●●● −20 −10 0 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ●●● ●● ●● ●●●● ●●●● 500 1000 1500 2000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ●● 50 100 150 200 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.5: Raw output data for models of Charmonétier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 176 F.6 1442 Claps de Luc, Drôme, France D L Le α vmax Observed 800 m 208 m 25◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 29 -469 89.9 Frictional 10 45 -1173 145.2 Frictional 15 23 -296 65.9 Frictional 17 11 -83 23.9 Frictional 20 1 -9 2.4 Frictional 25 -15 -29 4.2 Frictional 30 -31 -73 17.2 Frictional 35 -45 -115 35.1 Frictional 40 -64 -143 56.7 Frictional 45 -76 -136 64.8 Voellmy 0.05 100 35 -701 113.7 Voellmy 0.05 500 61 -2272 181.8 Voellmy 0.05 1000 73 -2268 177.7 Voellmy 0.05 1500 57 -1997 175.3 Voellmy 0.05 2000 63 -2474 186.0 Voellmy 0.1 100 30 -498 93.3 Voellmy 0.1 500 59 -2125 178.5 Voellmy 0.1 1000 58 -2070 177.2 Voellmy 0.1 1500 58 -2065 177.0 Voellmy 0.1 2000 55 -1833 170.8 Voellmy 0.15 100 13 -115 31.4 Voellmy 0.15 500 56 -1909 173.0 Voellmy 0.15 1000 55 -1851 171.3 Voellmy 0.15 1500 56 -1879 172.1 Voellmy 0.15 2000 52 -1642 164.8 Voellmy 0.2 100 -23 -44 7.7 Voellmy 0.2 500 55 -1799 169.8 Voellmy 0.2 1000 52 -1615 163.9 Voellmy 0.2 1500 48 -1359 154.0 Voellmy 0.2 2000 54 -1761 168.6 Table F.6: Mathematically-selected parameters for Claps de Luc. For case descrip- tion, see Section E.6. 177 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●● ● ●●● 200 400 600 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ● ●●● ● ●●● ● 30 40 50 60 70 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ●●●● ● ●●● ● 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● 0 2000 4000 6000 8000 10000 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.6: Raw output data for models of Claps de Luc with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 178 F.7 1999 Eagle Pass, British Columbia, Canada D L Le α vmax Observed 31◦ Rheology θb f ξ ∆α Frictional 5 -52.3 Frictional 10 -45.6 Frictional 15 -27.3 Frictional 17 -19.1 Frictional 20 -17.9 Frictional 25 -5.7 Frictional 30 7.6 Frictional 35 15.3 Frictional 40 27.3 Frictional 45 38.8 Voellmy 0.05 100 4.4 Voellmy 0.05 500 -0.4 Voellmy 0.05 1000 2.5 Voellmy 0.05 1500 -13.6 Voellmy 0.05 2000 -19.4 Voellmy 0.1 100 7.7 Voellmy 0.1 500 1.5 Voellmy 0.1 1000 -0.3 Voellmy 0.1 1500 -6.8 Voellmy 0.1 2000 -16.4 Voellmy 0.15 100 8.9 Voellmy 0.15 500 3.4 Voellmy 0.15 1000 -3.3 Voellmy 0.15 1500 0.4 Voellmy 0.15 2000 -13.5 Voellmy 0.2 100 9.6 Voellmy 0.2 500 5.0 Voellmy 0.2 1000 -1.8 Voellmy 0.2 1500 -1.6 Voellmy 0.2 2000 -0.2 Table F.7: Mathematically-selected parameters for Eagle Pass. For case description, see Section E.7. For back analyses with user-selected parameters, see Table G.4. 179 ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● 200 400 600 800 1000 1200 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●●● ●●●●● ●●● ●● ●●●● 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● 200 400 600 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.7: Raw output data for models of Eagle Pass with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 180 F.8 1881 Elm, Sernaf Valley, Glarus, Switzerland D L Le α vmax Observed 2000 m 2017 m 1036 m 16◦ 84 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 49 36 83 -32.1 8 Frictional 10 51 38 90 -34.7 -2 Frictional 15 24 12 29 -10.4 -9 Frictional 17 8 -5 -1 1.9 -12 Frictional 20 -9 -21 -32 20.2 -17 Frictional 25 -27 -38 -66 50.3 -26 Frictional 30 -38 -50 -89 80.4 -36 Frictional 35 -46 -57 -102 103.8 -48 Frictional 40 -51 -63 -112 126.1 -63 Frictional 45 -58 -69 -122 152.6 -68 Voellmy 0.05 100 19 7 19 -6.4 -14 Voellmy 0.05 500 49 36 84 -32.2 1 Voellmy 0.05 1000 58 45 109 -42.9 3 Voellmy 0.05 1500 66 52 134 -53.5 6 Voellmy 0.05 2000 70 55 145 -58.3 8 Voellmy 0.1 100 -1 -13 -17 10.5 -20 Voellmy 0.1 500 42 29 66 -25.1 -4 Voellmy 0.1 1000 51 38 90 -34.9 -2 Voellmy 0.1 1500 58 45 109 -42.9 -0 Voellmy 0.1 2000 57 44 107 -42.0 2 Voellmy 0.15 100 -11 -23 -35 22.6 -26 Voellmy 0.15 500 29 17 38 -13.7 -10 Voellmy 0.15 1000 42 29 66 -24.9 -8 Voellmy 0.15 1500 48 35 80 -30.8 -7 Voellmy 0.15 2000 51 38 89 -34.4 -6 Voellmy 0.2 100 -18 -29 -48 33.1 -31 Voellmy 0.2 500 12 0 7 -1.7 -16 Voellmy 0.2 1000 26 14 33 -11.9 -13 Voellmy 0.2 1500 33 20 46 -16.9 -13 Voellmy 0.2 2000 36 24 54 -20.0 -11 Table F.8: Mathematically-selected parameters for Elm. For case description, see Sec- tion E.8. For back analyses with user-selected parameters, see Table G.5. 181 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●● ●●●●● ●●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ● 30 40 50 60 70 80 90 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.8: Raw output data for models of Elm with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: pur- ple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 182 F.9 1903 Frank Slide, Alberta, Canada D L Le α vmax Observed 3500 m 2284 m 14◦ 45 m/s Rheology θb f ξ ∆L ∆Le ∆α ∆vmax Frictional 5 3 23 -44.1 173 Frictional 10 -8 -10 -9.4 142 Frictional 15 -12 -21 3.1 115 Frictional 17 -18 -33 16.1 105 Frictional 20 -29 -53 38.6 90 Frictional 25 -46 -78 74.5 64 Frictional 30 -54 -91 104.9 31 Frictional 35 -60 -102 133.4 -15 Frictional 40 -74 -108 163.7 -43 Frictional 45 -83 -111 200.3 -73 Voellmy 0.05 100 -30 -54 40.4 33 Voellmy 0.05 500 -15 -28 10.9 114 Voellmy 0.05 1000 -18 -33 16.1 138 Voellmy 0.05 1500 1 16 -37.1 149 Voellmy 0.05 2000 -19 -35 18.0 155 Voellmy 0.1 100 -40 -69 59.9 28 Voellmy 0.1 500 -15 -28 10.9 103 Voellmy 0.1 1000 -14 -25 7.6 126 Voellmy 0.1 1500 -4 2 -22.3 136 Voellmy 0.1 2000 -15 -28 11.4 143 Voellmy 0.15 100 -46 -77 73.2 23 Voellmy 0.15 500 -23 -41 24.8 92 Voellmy 0.15 1000 -13 -23 5.8 114 Voellmy 0.15 1500 -10 -14 -4.8 124 Voellmy 0.15 2000 -12 -21 3.4 130 Voellmy 0.2 100 -49 -81 81.9 17 Voellmy 0.2 500 -29 -52 37.3 81 Voellmy 0.2 1000 -20 -36 19.7 101 Voellmy 0.2 1500 -15 -27 10.0 111 Voellmy 0.2 2000 -13 -22 4.8 117 Table F.9: Mathematically-selected parameters for Frank Slide. For case description, see Section E.9. 183 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●●●● ●●●● ● ●●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● 1000 1500 2000 2500 3000 3500 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 40 60 80 100 120 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.9: Raw output data for models of Frank Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 184 F.10 1915 Great Fall, England D L Le α vmax Observed 628 m 388 m 13◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 30 27 7.7 Frictional 10 51 75 -22.0 Frictional 15 13 -2 24.6 Frictional 17 3 -20 37.9 Frictional 20 -8 -40 56.5 Frictional 25 -20 -61 81.3 Frictional 30 -27 -74 99.6 Frictional 35 -33 -86 120.5 Frictional 40 -45 -100 145.8 Frictional 45 -51 -108 165.1 Voellmy 0.05 100 30 26 8.2 Voellmy 0.05 500 37 41 -0.8 Voellmy 0.05 1000 35 36 2.0 Voellmy 0.05 1500 70 133 -58.2 Voellmy 0.05 2000 33 33 3.9 Voellmy 0.1 100 4 -18 36.0 Voellmy 0.1 500 44 55 -9.5 Voellmy 0.1 1000 49 69 -18.5 Voellmy 0.1 1500 59 95 -34.7 Voellmy 0.1 2000 47 63 -14.5 Voellmy 0.15 100 -5 -34 51.0 Voellmy 0.15 500 27 21 10.8 Voellmy 0.15 1000 38 44 -2.5 Voellmy 0.15 1500 44 57 -10.8 Voellmy 0.15 2000 48 65 -15.6 Voellmy 0.2 100 -12 -46 63.3 Voellmy 0.2 500 10 -8 28.2 Voellmy 0.2 1000 20 8 18.5 Voellmy 0.2 1500 25 17 13.5 Voellmy 0.2 2000 28 22 10.6 Table F.10: Mathematically-selected parameters for Great Fall. For case description, see Section E.10. For back analyses with user-selected parameters, see Sec- tion G.6. 185 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 400 600 800 1000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●● ● ●●●●● ●●●●● 5 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 200 400 600 800 1000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 25 30 35 40 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.10: Raw output data for models of Great Fall with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 186 F.11 1998 Hiegaesi, Japan D L Le α vmax Observed 67 m 27 m 11◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 51 166 -7.3 Frictional 10 46 146 3.1 Frictional 15 3 44 38.6 Frictional 17 -8 14 57.9 Frictional 20 -27 -26 84.2 Frictional 25 -49 -62 115.5 Frictional 30 -62 -86 155.7 Frictional 35 -62 -87 157.5 Frictional 40 -62 -88 159.5 Frictional 45 -63 -88 160.4 Voellmy 0.05 100 15 77 20.4 Voellmy 0.05 500 51 168 -7.9 Voellmy 0.05 1000 52 171 -9.6 Voellmy 0.05 1500 52 172 -10.3 Voellmy 0.05 2000 52 171 -10.0 Voellmy 0.1 100 8 59 30.5 Voellmy 0.1 500 48 153 -0.4 Voellmy 0.1 1000 52 174 -11.5 Voellmy 0.1 1500 52 174 -11.3 Voellmy 0.1 2000 51 168 -8.1 Voellmy 0.15 100 3 44 38.4 Voellmy 0.15 500 19 92 12.2 Voellmy 0.15 1000 30 115 6.4 Voellmy 0.15 1500 45 142 4.6 Voellmy 0.15 2000 46 146 3.1 Voellmy 0.2 100 -5 24 50.4 Voellmy 0.2 500 9 62 28.6 Voellmy 0.2 1000 13 74 22.1 Voellmy 0.2 1500 15 79 19.6 Voellmy 0.2 2000 16 82 18.1 Table F.11: Mathematically-selected parameters for Hiegaesi. For case description, see Section E.11. 187 ●● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ●●● 40 60 80 100 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ●●●● ●●●●● ●●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ●●● 40 60 80 100 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ●● 2 4 6 8 10 12 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.11: Raw output data for models of Hiegaesi with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 188 F.12 1965 Hope Slide, British Columbia, Canada D L Le α vmax Observed 4240 m 2288 m 16◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 -40 -66 46.6 Frictional 10 -40 -67 48.6 Frictional 15 -39 -63 42.8 Frictional 17 -38 -60 37.5 Frictional 20 -39 -62 40.4 Frictional 25 -43 -76 60.7 Frictional 30 -58 -94 88.2 Frictional 35 -61 -97 94.2 Frictional 40 -65 -96 90.8 Frictional 45 -65 -96 90.5 Voellmy 0.05 100 -40 -65 45.6 Voellmy 0.05 500 -40 -65 45.4 Voellmy 0.05 1000 -39 -64 43.2 Voellmy 0.05 1500 -39 -64 44.2 Voellmy 0.05 2000 -39 -65 44.9 Voellmy 0.1 100 -40 -65 45.8 Voellmy 0.1 500 -39 -64 44.6 Voellmy 0.1 1000 -40 -66 46.1 Voellmy 0.1 1500 -40 -66 47.1 Voellmy 0.1 2000 -40 -65 45.8 Voellmy 0.15 100 -40 -66 46.2 Voellmy 0.15 500 -40 -65 45.6 Voellmy 0.15 1000 -39 -65 45.1 Voellmy 0.15 1500 -40 -65 45.8 Voellmy 0.15 2000 -40 -66 46.4 Voellmy 0.2 100 -40 -67 48.7 Voellmy 0.2 500 -40 -66 46.6 Voellmy 0.2 1000 -40 -65 45.7 Voellmy 0.2 1500 -40 -65 45.6 Voellmy 0.2 2000 -40 -65 45.9 Table F.12: Mathematically-selected parameters for Hope Slide. For case descrip- tion, see Section E.12. For back analyses with user-selected parameters, see Table G.8. 189 ●● ● ● ● ● ● ● ● ● ●●● ●●● ●● ●●● 1600 1800 2000 2200 2400 2600 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ●● ●● ●●● ●●● 22 24 26 28 30 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●●● ●●● ●● ●●● 2800 3000 3200 3400 3600 3800 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● 0 20 40 60 80 100 120 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.12: Raw output data for models of Hope Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 190 F.13 Jonas Creek (north), Alberta, Canada D L Le α vmax Observed 3250 m 1842 m 17.1◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 7 48 -54.4 Frictional 10 2 16 -27.2 Frictional 15 -7 -22 6.4 Frictional 17 -9 -28 11.9 Frictional 20 -18 -48 27.0 Frictional 25 -34 -71 46.4 Frictional 30 -50 -93 75.7 Frictional 35 -83 -103 102.7 Frictional 40 -83 -103 102.7 Frictional 45 -83 -103 102.7 Voellmy 0.05 100 -10 -33 15.7 Voellmy 0.05 500 -9 -30 13.2 Voellmy 0.05 1000 -10 -32 15.3 Voellmy 0.05 1500 -7 -23 7.6 Voellmy 0.05 2000 -8 -28 11.5 Voellmy 0.1 100 -11 -37 19.2 Voellmy 0.1 500 -9 -30 13.7 Voellmy 0.1 1000 -9 -30 13.9 Voellmy 0.1 1500 -10 -31 14.6 Voellmy 0.1 2000 -10 -33 15.8 Voellmy 0.15 100 -31 -67 43.0 Voellmy 0.15 500 -10 -34 17.0 Voellmy 0.15 1000 -7 -24 8.6 Voellmy 0.15 1500 -8 -27 10.9 Voellmy 0.15 2000 -9 -29 12.8 Voellmy 0.2 100 -37 -75 51.2 Voellmy 0.2 500 -19 -48 27.4 Voellmy 0.2 1000 -8 -27 11.1 Voellmy 0.2 1500 -6 -21 5.5 Voellmy 0.2 2000 -6 -21 5.8 Table F.13: Mathematically-selected parameters for Jonas Creek (north). For case de- scription, see Section E.13. 191 ●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ●●● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●●●● ●●●●● ●●●● 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ●●● ● ● ● ● 1000 1500 2000 2500 3000 3500 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ●● ●● 0 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.13: Raw output data for models of Jonas Creek (north) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 192 F.14 Jonas Creek (south), Alberta, Canada D L Le α vmax Observed 2500 m 1028 m 26.5◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 36 181 -80.0 Frictional 10 17 58 -41.3 Frictional 15 9 25 -30.9 Frictional 17 13 40 -35.7 Frictional 20 6 13 -27.2 Frictional 25 -20 -48 -7.2 Frictional 30 -45 -88 11.7 Frictional 35 -80 -101 23.5 Frictional 40 -84 -100 21.9 Frictional 45 -84 -100 21.9 Voellmy 0.05 100 -0 -7 -20.8 Voellmy 0.05 500 1 -2 -22.1 Voellmy 0.05 1000 1 -3 -22.1 Voellmy 0.05 1500 -0 -5 -21.1 Voellmy 0.05 2000 4 7 -25.2 Voellmy 0.1 100 -3 -14 -18.5 Voellmy 0.1 500 -2 -11 -19.5 Voellmy 0.1 1000 4 6 -24.8 Voellmy 0.1 1500 8 21 -29.6 Voellmy 0.1 2000 12 35 -34.2 Voellmy 0.15 100 -6 -20 -16.4 Voellmy 0.15 500 -5 -19 -16.8 Voellmy 0.15 1000 1 -3 -21.9 Voellmy 0.15 1500 5 10 -26.0 Voellmy 0.15 2000 7 18 -28.6 Voellmy 0.2 100 -20 -47 -7.4 Voellmy 0.2 500 -11 -32 -12.7 Voellmy 0.2 1000 -4 -15 -18.1 Voellmy 0.2 1500 1 -3 -22.0 Voellmy 0.2 2000 6 14 -27.4 Table F.14: Mathematically-selected parameters for Jonas Creek (south). For case description, see Section E.13. 193 ●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ●●●●● ●●●● ●●●●● 5 10 15 20 25 30 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 20 40 60 80 100 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.14: Raw output data for models of Jonas Creek (south) with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 194 F.15 2005 Kuzulu, Turkey D L Le α vmax Observed 2300 m 3300 m 1780 m 16◦ 14 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 350 100 384 -66.4 597 Frictional 10 118 47 89 -32.7 482 Frictional 15 43 -6 -5 -1.4 273 Frictional 17 26 -18 -25 9.9 145 Frictional 20 -51 -69 -74 16.7 19 Frictional 25 -76 -85 -86 9.7 5 Frictional 30 -76 -85 -86 9.7 -2 Frictional 35 -76 -85 -86 9.7 -11 Frictional 40 -76 -85 -86 9.7 -20 Frictional 45 -76 -85 -86 9.7 -29 Voellmy 0.05 100 143 64 117 -36.5 328 Voellmy 0.05 500 264 100 256 -49.6 530 Voellmy 0.05 1000 283 100 280 -52.4 586 Voellmy 0.05 1500 297 100 300 -54.8 608 Voellmy 0.05 2000 309 100 318 -57.1 620 Voellmy 0.1 100 86 24 51 -24.4 249 Voellmy 0.1 500 47 -3 1 -4.5 420 Voellmy 0.1 1000 192 98 170 -41.6 482 Voellmy 0.1 1500 226 100 209 -44.9 506 Voellmy 0.1 2000 244 100 230 -46.9 522 Voellmy 0.15 100 76 17 39 -20.9 153 Voellmy 0.15 500 88 26 54 -25.4 325 Voellmy 0.15 1000 101 34 69 -28.8 383 Voellmy 0.15 1500 110 41 80 -31.1 414 Voellmy 0.15 2000 118 46 89 -32.7 434 Voellmy 0.2 100 46 -4 -1 -3.4 91 Voellmy 0.2 500 53 1 9 -8.4 211 Voellmy 0.2 1000 57 4 14 -10.9 271 Voellmy 0.2 1500 60 6 18 -12.5 305 Voellmy 0.2 2000 62 7 21 -13.8 331 Table F.15: Mathematically-selected parameters for Kuzulu. For case description, see Section E.14. 195 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●●●●● 2000 4000 6000 8000 10000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ● ●●●● ●●●●● ●●●●● 6 8 10 12 14 16 18 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●●●●● 2000 4000 6000 8000 10000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 40 60 80 100 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.15: Raw output data for models of Kuzulu with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 196 F.16 La Madeleine, Savoie, France D L Le α vmax Observed 4500 m 2002 m 19◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 66 210 -67.9 Frictional 10 59 173 -56.1 Frictional 15 37 89 -28.3 Frictional 17 47 124 -39.9 Frictional 20 43 110 -35.2 Frictional 25 -34 -76 44.9 Frictional 30 -43 -92 59.7 Frictional 35 -50 -102 71.1 Frictional 40 -58 -115 88.6 Frictional 45 -67 -121 103.5 Voellmy 0.05 100 18 35 -10.1 Voellmy 0.05 500 44 110 -35.4 Voellmy 0.05 1000 54 153 -49.5 Voellmy 0.05 1500 22 45 -13.4 Voellmy 0.05 2000 62 190 -61.7 Voellmy 0.1 100 14 24 -6.2 Voellmy 0.1 500 45 114 -36.5 Voellmy 0.1 1000 46 120 -38.7 Voellmy 0.1 1500 49 131 -42.4 Voellmy 0.1 2000 51 140 -45.2 Voellmy 0.15 100 0 -5 4.8 Voellmy 0.15 500 20 40 -11.7 Voellmy 0.15 1000 35 80 -25.2 Voellmy 0.15 1500 38 91 -28.9 Voellmy 0.15 2000 42 103 -33.1 Voellmy 0.2 100 8 12 -1.7 Voellmy 0.2 500 8 12 -1.9 Voellmy 0.2 1000 79 287 -92.3 Voellmy 0.2 1500 19 38 -10.9 Voellmy 0.2 2000 21 42 -12.5 Table F.16: Mathematically-selected parameters for La Madeleine. For case descrip- tion, see Section E.15. 197 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●●● ● ● ● ● ● ● ●●● 2000 3000 4000 5000 6000 7000 8000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ●● ●●●●● ●●●●● ●● ●● 0 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●●● ● ● ● ● ● ● ●●● 1000 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ●● ●● ● ●● ●● 0 500 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.16: Raw output data for models of La Madeleine with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 198 F.17 2001 Las Colinas, Santa Tecla, El Salvador D L Le α vmax Observed 8000 m 715 m 459 m 12.6◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 -86 36 63 -35.2 Frictional 10 -89 7 17 -15.3 Frictional 15 -92 -34 -44 24.6 Frictional 17 -93 -46 -60 42.7 Frictional 20 -95 -61 -77 67.6 Frictional 25 -96 -77 -92 104.4 Frictional 30 -97 -85 -97 128.3 Frictional 35 -99 -101 -101 102.1 Frictional 40 -99 -102 -101 100.5 Frictional 45 -99 -102 -101 100.6 Voellmy 0.05 100 -92 -24 -30 12.3 Voellmy 0.05 500 -88 14 26 -19.3 Voellmy 0.05 1000 -86 38 67 -36.7 Voellmy 0.05 1500 -86 41 74 -40.2 Voellmy 0.05 2000 -86 34 59 -33.0 Voellmy 0.1 100 -93 -42 -54 36.0 Voellmy 0.1 500 -91 -16 -17 3.1 Voellmy 0.1 1000 -89 8 17 -15.7 Voellmy 0.1 1500 -87 22 39 -24.3 Voellmy 0.1 2000 -87 30 52 -29.6 Voellmy 0.15 100 -94 -52 -67 52.0 Voellmy 0.15 500 -92 -34 -44 24.4 Voellmy 0.15 1000 -91 -18 -20 5.5 Voellmy 0.15 1500 -90 -8 -6 -4.0 Voellmy 0.15 2000 -90 -2 3 -9.2 Voellmy 0.2 100 -95 -61 -77 67.6 Voellmy 0.2 500 -93 -45 -58 39.8 Voellmy 0.2 1000 -93 -36 -46 26.9 Voellmy 0.2 1500 -92 -30 -37 18.7 Voellmy 0.2 2000 -92 -25 -31 13.7 Table F.17: Mathematically-selected parameters for Las Colinas. For case descrip- tion, see Section E.16. For back analyses with user-selected parameters, see Section G.8. 199 ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 200 400 600 800 1000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●●● ●●●●● ●●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 200 400 600 800 1000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● 0 10 20 30 40 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.17: Raw output data for models of Las Colinas with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 200 F.18 2006 Luzon Slide, Philippines D L Le α vmax Observed 4100 m 3800 m 2504 m 12◦ 130 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 28 33 65 -45.0 -35 Frictional 10 5 9 16 -12.3 -51 Frictional 15 -38 -38 -54 47.6 -63 Frictional 17 -53 -53 -69 62.2 -67 Frictional 20 -64 -65 -81 83.1 -76 Frictional 25 -84 -85 -93 100.8 -87 Frictional 30 -85 -86 -95 113.2 -94 Frictional 35 -85 -86 -95 113.2 -98 Frictional 40 -85 -86 -95 113.2 -100 Frictional 45 -85 -86 -95 113.2 -100 Voellmy 0.05 100 -20 -18 -25 15.9 -70 Voellmy 0.05 500 -9 -7 -8 2.0 -54 Voellmy 0.05 1000 3 7 13 -10.3 -48 Voellmy 0.05 1500 11 15 26 -19.3 -45 Voellmy 0.05 2000 11 15 27 -19.7 -42 Voellmy 0.1 100 -25 -24 -34 23.7 -73 Voellmy 0.1 500 -17 -15 -20 11.2 -59 Voellmy 0.1 1000 -8 -5 -5 0.6 -54 Voellmy 0.1 1500 -1 2 5 -5.5 -51 Voellmy 0.1 2000 3 7 12 -9.9 -49 Voellmy 0.15 100 -36 -36 -51 43.0 -77 Voellmy 0.15 500 -23 -22 -31 21.0 -64 Voellmy 0.15 1000 -16 -14 -19 10.5 -60 Voellmy 0.15 1500 -12 -9 -12 4.8 -58 Voellmy 0.15 2000 -9 -6 -7 1.7 -57 Voellmy 0.2 100 -49 -49 -65 57.2 -81 Voellmy 0.2 500 -34 -34 -47 38.4 -70 Voellmy 0.2 1000 -29 -28 -39 28.6 -66 Voellmy 0.2 1500 -25 -24 -33 23.3 -65 Voellmy 0.2 2000 -23 -21 -29 19.8 -64 Table F.18: Mathematically-selected parameters for Luzon Slide. For case descrip- tion, see Section E.17. 201 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ●●●●● ●●●●● ●●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 0 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.18: Raw output data for models of Luzon Slide with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 202 F.19 1969 Madison Canyon, Montana, United States D L Le α vmax Observed 1280 m 1300 m 756 m 13◦ 50 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 8 -3 1 6.8 21 Frictional 10 12 1 10 -1.2 2 Frictional 15 10 -1 4 3.7 -14 Frictional 17 2 -9 -14 20.8 -22 Frictional 20 -7 -17 -34 42.8 -33 Frictional 25 -19 -29 -60 75.3 -55 Frictional 30 -32 -42 -81 107.0 -84 Frictional 35 -45 -54 -90 119.6 -100 Frictional 40 -45 -54 -90 119.6 -100 Frictional 45 -45 -54 -90 119.6 -100 Voellmy 0.05 100 8 -3 1 6.9 -15 Voellmy 0.05 500 15 3 18 -8.1 13 Voellmy 0.05 1000 22 10 35 -22.6 19 Voellmy 0.05 1500 21 9 34 -22.1 21 Voellmy 0.05 2000 11 -0 8 0.8 22 Voellmy 0.1 100 11 0 8 0.1 -20 Voellmy 0.1 500 18 6 26 -14.9 6 Voellmy 0.1 1000 15 3 17 -7.8 11 Voellmy 0.1 1500 21 9 34 -22.0 12 Voellmy 0.1 2000 1 -10 -16 23.0 13 Voellmy 0.15 100 8 -3 1 6.9 -26 Voellmy 0.15 500 14 2 15 -5.5 -2 Voellmy 0.15 1000 10 -1 7 1.8 2 Voellmy 0.15 1500 19 7 29 -17.7 3 Voellmy 0.15 2000 9 -2 2 5.8 4 Voellmy 0.2 100 2 -8 -12 19.0 -31 Voellmy 0.2 500 15 4 19 -9.6 -10 Voellmy 0.2 1000 18 7 27 -15.9 -7 Voellmy 0.2 1500 20 8 31 -19.5 -5 Voellmy 0.2 2000 21 9 32 -20.5 -5 Table F.19: Mathematically-selected parameters for Madison Canyon. For case de- scription, see Section E.18. For back analyses with user-selected parameters, see Table G.11. 203 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●● ●● ● ● ● ●● 600 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ●● ●● ● ●●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●● ●● ● ● ● ●● 800 1000 1200 1400 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ● ● ●● ● ● ●● 0 10 20 30 40 50 60 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.19: Raw output data for models of Madison Canyon with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 204 F.20 2002 McAuley Creek, British Columbia, Canada D L Le α vmax Observed 10◦ Rheology θb f ξ ∆α Frictional 5 16.2 Frictional 10 -8.2 Frictional 15 59.2 Frictional 17 75.4 Frictional 20 101.5 Frictional 25 140.9 Frictional 30 174.9 Frictional 35 318.6 Frictional 40 256.1 Frictional 45 256.1 Voellmy 0.05 100 -25.8 Voellmy 0.05 500 -30.7 Voellmy 0.05 1000 -2.9 Voellmy 0.05 1500 -91.8 Voellmy 0.05 2000 -14.1 Voellmy 0.1 100 38.2 Voellmy 0.1 500 -22.9 Voellmy 0.1 1000 -14.1 Voellmy 0.1 1500 -37.4 Voellmy 0.1 2000 -46.8 Voellmy 0.15 100 63.8 Voellmy 0.15 500 8.9 Voellmy 0.15 1000 -8.6 Voellmy 0.15 1500 -15.2 Voellmy 0.15 2000 -20.7 Voellmy 0.2 100 83.8 Voellmy 0.2 500 46.3 Voellmy 0.2 1000 37.1 Voellmy 0.2 1500 31.8 Voellmy 0.2 2000 28.0 Table F.20: Mathematically-selected parameters for McAuley Creek. For case de- scription, see Section E.19. 205 ●● ● ● ● ● ● ● ● ● ●●● ●● ● ●● ●● ● ● ●●● ● ● ●●● 500 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ●●● ●●●●● ●●●●● 0 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ●● ● ● ● ● ●●● ● ● ●●● 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● 0 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.20: Raw output data for models of McAuley Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 206 F.21 1984 Mount Cayley, British Columbia, Canada D L Le α vmax Observed 3460 m 1572 m 19◦ 70 m/s Rheology θb f ξ ∆L ∆Le ∆α ∆vmax Frictional 5 62 201 -70.6 62 Frictional 10 46 122 -43.0 26 Frictional 15 24 51 -17.8 5 Frictional 17 10 18 -6.7 -3 Frictional 20 -27 -34 7.1 -15 Frictional 25 -49 -72 32.1 -35 Frictional 30 -63 -91 52.7 -50 Frictional 35 -75 -103 76.4 -67 Frictional 40 -88 -106 98.3 -91 Frictional 45 -90 -106 101.9 -97 Voellmy 0.05 100 21 43 -15.2 -32 Voellmy 0.05 500 24 50 -17.6 5 Voellmy 0.05 1000 27 59 -20.6 19 Voellmy 0.05 1500 32 73 -25.5 25 Voellmy 0.05 2000 28 62 -21.6 29 Voellmy 0.1 100 15 29 -10.5 -34 Voellmy 0.1 500 18 36 -12.6 -0 Voellmy 0.1 1000 23 47 -16.4 12 Voellmy 0.1 1500 26 57 -20.1 18 Voellmy 0.1 2000 29 65 -22.6 21 Voellmy 0.15 100 -39 -55 18.5 -38 Voellmy 0.15 500 -22 -26 3.2 -5 Voellmy 0.15 1000 15 30 -10.5 6 Voellmy 0.15 1500 20 40 -14.2 11 Voellmy 0.15 2000 23 49 -17.2 13 Voellmy 0.2 100 -43 -62 24.5 -41 Voellmy 0.2 500 -38 -54 17.6 -11 Voellmy 0.2 1000 -25 -31 5.3 -1 Voellmy 0.2 1500 8 14 -5.3 2 Voellmy 0.2 2000 14 26 -9.4 5 Table F.21: Mathematically-selected parameters for Mount Cayley. For case descrip- tion, see Section E.20. For back analyses with user-selected parameters, see Section G.10. 207 ●● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●●● ●●●●● ●●●●● 5 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●●● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● 0 1000 2000 3000 4000 5000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● 0 20 40 60 80 100 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.21: Raw output data for models of Mount Cayley with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 208 F.22 1991 Mount Cook, New Zealand D L Le α vmax Observed 7500 m Rheology θb f ξ ∆D Frictional 5 57 Frictional 10 87 Frictional 15 4 Frictional 17 5 Frictional 20 -3 Frictional 25 -50 Frictional 30 -59 Frictional 35 -65 Frictional 40 -73 Frictional 45 -76 Voellmy 0.05 100 -1 Voellmy 0.05 500 3 Voellmy 0.05 1000 4 Voellmy 0.05 1500 4 Voellmy 0.05 2000 4 Voellmy 0.1 100 -7 Voellmy 0.1 500 -5 Voellmy 0.1 1000 -2 Voellmy 0.1 1500 4 Voellmy 0.1 2000 4 Voellmy 0.15 100 -10 Voellmy 0.15 500 -9 Voellmy 0.15 1000 -6 Voellmy 0.15 1500 -2 Voellmy 0.15 2000 3 Voellmy 0.2 100 -60 Voellmy 0.2 500 -14 Voellmy 0.2 1000 -9 Voellmy 0.2 1500 -5 Voellmy 0.2 2000 -2 Table F.22: Mathematically-selected parameters for Mount Cook. For case descrip- tion, see Section E.21. For back analyses with user-selected parameters, see Table G.14. 209 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● 2000 4000 6000 8000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ●●●●● ●●●●● ●●●●● 25 30 35 40 45 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ●●● ● ● ● ● ● ●● 2000 4000 6000 8000 10000 12000 14000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ● ●●● 50 100 150 200 250 300 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.22: Raw output data for models of Mount Cook with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 210 F.23 1248 Mount Granier, Savoie, France D L Le α vmax Observed 7500 m 7690 m 5257 m 12◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 -3 -8 6 -35.8 Frictional 10 -20 -24 -21 -15.0 Frictional 15 -56 -58 -60 2.8 Frictional 17 -61 -63 -66 8.0 Frictional 20 -66 -68 -71 13.2 Frictional 25 -70 -72 -75 17.7 Frictional 30 -71 -73 -77 19.6 Frictional 35 -72 -73 -77 19.8 Frictional 40 -76 -77 -81 26.3 Frictional 45 -77 -79 -83 29.0 Voellmy 0.05 100 -5 -10 2 -32.7 Voellmy 0.05 500 -1 -5 11 -40.6 Voellmy 0.05 1000 -4 -8 5 -34.9 Voellmy 0.05 1500 3 -2 19 -49.0 Voellmy 0.05 2000 -7 -11 -1 -30.5 Voellmy 0.1 100 -16 -20 -15 -19.9 Voellmy 0.1 500 -7 -11 -0 -30.6 Voellmy 0.1 1000 -2 -7 8 -37.7 Voellmy 0.1 1500 -0 -5 12 -41.8 Voellmy 0.1 2000 1 -4 14 -44.0 Voellmy 0.15 100 -37 -40 -37 -17.3 Voellmy 0.15 500 -19 -23 -19 -16.7 Voellmy 0.15 1000 -14 -18 -12 -22.2 Voellmy 0.15 1500 -12 -16 -9 -24.7 Voellmy 0.15 2000 -11 -15 -7 -26.2 Voellmy 0.2 100 -46 -49 -48 -7.7 Voellmy 0.2 500 -41 -44 -42 -13.4 Voellmy 0.2 1000 -39 -42 -39 -15.4 Voellmy 0.2 1500 -38 -41 -39 -16.1 Voellmy 0.2 2000 -38 -41 -38 -16.4 Table F.23: Mathematically-selected parameters for Mount Granier. For case descrip- tion, see Section E.22. For back analyses with user-selected parameters, see Table G.15. 211 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●● 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●●●●● ●●●●● ●●●● 6 8 10 12 14 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●● 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ● ●●● 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.23: Raw output data for models of Mount Granier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 212 F.24 1984 Mount Ontake, Japan D L Le α vmax Observed 1300 m 400 m 32 m/s Rheology θb f ξ ∆D ∆L ∆vmax Frictional 5 287 100 41 Frictional 10 100 100 5 Frictional 15 39 100 -25 Frictional 17 31 100 -42 Frictional 20 27 100 -48 Frictional 25 20 100 -53 Frictional 30 19 100 -57 Frictional 35 19 100 -67 Frictional 40 19 100 -85 Frictional 45 19 100 -87 Voellmy 0.05 100 258 100 5 Voellmy 0.05 500 341 100 27 Voellmy 0.05 1000 360 100 32 Voellmy 0.05 1500 373 100 42 Voellmy 0.05 2000 381 100 48 Voellmy 0.1 100 127 100 -5 Voellmy 0.1 500 178 100 20 Voellmy 0.1 1000 182 100 11 Voellmy 0.1 1500 189 100 12 Voellmy 0.1 2000 194 100 12 Voellmy 0.15 100 78 100 -17 Voellmy 0.15 500 87 100 -10 Voellmy 0.15 1000 99 100 -8 Voellmy 0.15 1500 101 100 -5 Voellmy 0.15 2000 104 100 -3 Voellmy 0.2 100 49 100 -29 Voellmy 0.2 500 53 100 -22 Voellmy 0.2 1000 55 100 -19 Voellmy 0.2 1500 55 100 -17 Voellmy 0.2 2000 56 100 -14 Table F.24: Mathematically-selected parameters for Mount Ontake. For case descrip- tion, see Section E.23. 213 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●● ● ● ●●● ●●● 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●●● ●●●● 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●● ● ● ●●● ●●● 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●●●● ● ● ● ●● 10 20 30 40 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.24: Raw output data for models of Mount Ontake with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 214 F.25 2007 Mount Steele, Yukon, Canada D L Le α vmax Observed 7000 m 5760 m 2783 m 18◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 38 42 116 -48.1 Frictional 10 28 37 67 -20.6 Frictional 15 19 29 26 1.4 Frictional 17 -11 -4 -16 9.9 Frictional 20 -18 -13 -37 23.0 Frictional 25 -28 -25 -66 44.8 Frictional 30 -38 -38 -91 67.8 Frictional 35 -50 -51 -110 91.2 Frictional 40 -59 -62 -123 116.7 Frictional 45 -72 -76 -124 137.6 Voellmy 0.05 100 -27 -23 -63 42.1 Voellmy 0.05 500 -18 -13 -37 23.2 Voellmy 0.05 1000 12 20 6 9.4 Voellmy 0.05 1500 20 30 29 0.2 Voellmy 0.05 2000 20 31 32 -1.2 Voellmy 0.1 100 -31 -28 -73 49.9 Voellmy 0.1 500 -21 -16 -46 29.7 Voellmy 0.1 1000 -15 -10 -29 16.9 Voellmy 0.1 1500 13 23 11 7.7 Voellmy 0.1 2000 19 29 26 1.7 Voellmy 0.15 100 -33 -31 -79 55.6 Voellmy 0.15 500 -23 -19 -53 34.6 Voellmy 0.15 1000 -17 -11 -32 19.3 Voellmy 0.15 1500 -13 -7 -20 11.8 Voellmy 0.15 2000 10 18 2 11.1 Voellmy 0.2 100 -35 -34 -84 60.8 Voellmy 0.2 500 -25 -22 -60 39.7 Voellmy 0.2 1000 -19 -14 -42 26.2 Voellmy 0.2 1500 -16 -11 -30 18.2 Voellmy 0.2 2000 -14 -8 -24 14.0 Table F.25: Mathematically-selected parameters for Mount Steele. For case descrip- tion, see Section E.24. 215 ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2000 3000 4000 5000 6000 7000 8000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●● ●●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 2000 4000 6000 8000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● 40 60 80 100 120 140 160 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.25: Raw output data for models of Mount Steele with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 216 F.26 Mystery Creek, British Columbia, Canada D L Le α vmax Observed 4000 m 4000 m 2000 m 15◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 76 64 181 -66.0 Frictional 10 43 33 86 -29.5 Frictional 15 11 2 13 3.5 Frictional 17 1 -9 -8 15.3 Frictional 20 -12 -22 -34 32.3 Frictional 25 -25 -35 -61 57.7 Frictional 30 -35 -44 -85 89.9 Frictional 35 -54 -62 -103 119.7 Frictional 40 -71 -77 -106 133.9 Frictional 45 -78 -83 -112 168.4 Voellmy 0.05 100 -26 -35 -62 59.4 Voellmy 0.05 500 26 17 46 -12.5 Voellmy 0.05 1000 36 26 69 -22.5 Voellmy 0.05 1500 57 46 124 -44.2 Voellmy 0.05 2000 43 33 88 -30.1 Voellmy 0.1 100 -26 -36 -64 61.3 Voellmy 0.1 500 13 3 17 1.5 Voellmy 0.1 1000 32 22 59 -18.3 Voellmy 0.1 1500 41 31 81 -27.5 Voellmy 0.1 2000 46 36 95 -32.9 Voellmy 0.15 100 -27 -37 -67 64.4 Voellmy 0.15 500 1 -9 -9 15.5 Voellmy 0.15 1000 18 8 27 -3.7 Voellmy 0.15 1500 25 16 44 -11.6 Voellmy 0.15 2000 30 20 55 -16.5 Voellmy 0.2 100 -28 -38 -69 67.3 Voellmy 0.2 500 -9 -19 -29 28.3 Voellmy 0.2 1000 5 -5 -0 10.5 Voellmy 0.2 1500 12 2 14 2.9 Voellmy 0.2 2000 15 6 22 -1.2 Table F.26: Mathematically-selected parameters for Mystery Creek. For case descrip- tion, see Section E.25. 217 ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●●● ●●●●● ●●●●● 5 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● 20 40 60 80 100 120 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.26: Raw output data for models of Mystery Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 218 F.27 1999 Nomash River, British Columbia, Canada D L Le α vmax Observed 2270 m 1374 m 13.5◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 89 169 -63.2 Frictional 10 25 45 -21.9 Frictional 15 -30 -42 27.0 Frictional 17 -41 -58 45.8 Frictional 20 -53 -76 73.2 Frictional 25 -64 -93 114.4 Frictional 30 -70 -103 148.4 Frictional 35 -74 -109 175.5 Frictional 40 -80 -114 206.0 Frictional 45 -87 -114 236.4 Voellmy 0.05 100 -56 -82 84.8 Voellmy 0.05 500 -19 -24 12.8 Voellmy 0.05 1000 3 9 -7.0 Voellmy 0.05 1500 18 34 -17.9 Voellmy 0.05 2000 30 54 -25.1 Voellmy 0.1 100 -67 -98 128.4 Voellmy 0.1 500 -50 -71 65.0 Voellmy 0.1 1000 -34 -47 32.0 Voellmy 0.1 1500 -20 -25 13.5 Voellmy 0.1 2000 -5 -3 -0.2 Voellmy 0.15 100 -69 -101 141.6 Voellmy 0.15 500 -57 -82 85.5 Voellmy 0.15 1000 -45 -64 53.3 Voellmy 0.15 1500 -36 -51 36.4 Voellmy 0.15 2000 -29 -39 24.6 Voellmy 0.2 100 -71 -103 150.5 Voellmy 0.2 500 -61 -88 100.5 Voellmy 0.2 1000 -52 -74 70.4 Voellmy 0.2 1500 -46 -65 55.2 Voellmy 0.2 2000 -41 -58 45.6 Table F.27: Mathematically-selected parameters for Nomash River. For case descrip- tion, see Section E.26. For back analyses with user-selected parameters, see Table G.16. 219 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●●● ●●●●● 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 2000 3000 4000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 30 40 50 60 70 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.27: Raw output data for models of Nomash River with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 220 F.28 1959 Pandemonium Creek, B.C., Canada D L Le α vmax Observed 9000 m 7800 m 4639 m 13◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 54 72 145 -58.1 Frictional 10 19 33 58 -19.7 Frictional 15 -23 -16 -23 21.8 Frictional 17 -40 -35 -48 38.5 Frictional 20 -52 -49 -67 61.2 Frictional 25 -79 -79 -90 87.3 Frictional 30 -86 -86 -96 111.2 Frictional 35 -89 -89 -100 149.3 Frictional 40 -93 -93 -102 182.8 Frictional 45 -94 -95 -103 201.4 Voellmy 0.05 100 -9 -0 1 7.4 Voellmy 0.05 500 -1 9 16 -0.5 Voellmy 0.05 1000 1 12 21 -2.6 Voellmy 0.05 1500 3 14 24 -4.5 Voellmy 0.05 2000 7 18 31 -7.6 Voellmy 0.1 100 -45 -41 -55 45.1 Voellmy 0.1 500 -32 -27 -37 29.6 Voellmy 0.1 1000 -11 -3 -3 10.2 Voellmy 0.1 1500 -11 -2 -2 9.1 Voellmy 0.1 2000 -8 1 4 5.8 Voellmy 0.15 100 -53 -50 -68 62.7 Voellmy 0.15 500 -49 -46 -62 54.7 Voellmy 0.15 1000 -36 -31 -42 34.3 Voellmy 0.15 1500 -33 -27 -37 29.8 Voellmy 0.15 2000 -22 -14 -21 20.2 Voellmy 0.2 100 -57 -55 -74 73.2 Voellmy 0.2 500 -54 -51 -70 65.4 Voellmy 0.2 1000 -49 -45 -62 54.2 Voellmy 0.2 1500 -46 -42 -57 47.2 Voellmy 0.2 2000 -41 -36 -49 39.6 Table F.28: Mathematically-selected parameters for Pandemonium Creek. For case description, see Section E.27. For back analyses with user-selected parameters, see Table G.17. 221 ●● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● 0 2000 4000 6000 8000 10000 12000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●● ●●●●● ●●●●● 5 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● 0 2000 4000 6000 8000 10000 12000 14000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 50 100 150 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.28: Raw output data for models of Pandemonium Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 222 F.29 2002 Pink Mountain, British Columbia, Canada D L Le α vmax Observed 2000 m 1950 m 1230 m 11.6◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 71 70 134 -59.7 Frictional 10 34 34 54 -16.5 Frictional 15 -7 -9 -17 27.2 Frictional 17 -24 -26 -41 48.1 Frictional 20 -54 -56 -71 73.8 Frictional 25 -85 -86 -94 107.0 Frictional 30 -87 -88 -95 114.7 Frictional 35 -87 -88 -95 114.7 Frictional 40 -87 -88 -95 114.7 Frictional 45 -87 -88 -95 114.7 Voellmy 0.05 100 -1 -3 -7 19.7 Voellmy 0.05 500 12 10 14 6.3 Voellmy 0.05 1000 25 24 36 -6.7 Voellmy 0.05 1500 33 32 52 -15.3 Voellmy 0.05 2000 34 33 53 -16.2 Voellmy 0.1 100 -8 -10 -17 27.8 Voellmy 0.1 500 0 -1 -5 17.9 Voellmy 0.1 1000 12 11 15 5.5 Voellmy 0.1 1500 21 20 29 -2.7 Voellmy 0.1 2000 26 26 39 -8.4 Voellmy 0.15 100 -12 -14 -24 33.6 Voellmy 0.15 500 -7 -8 -16 26.3 Voellmy 0.15 1000 1 -1 -3 17.2 Voellmy 0.15 1500 7 6 7 10.4 Voellmy 0.15 2000 12 11 15 5.6 Voellmy 0.2 100 -16 -18 -30 38.4 Voellmy 0.2 500 -13 -15 -25 34.4 Voellmy 0.2 1000 -8 -10 -18 28.3 Voellmy 0.2 1500 -4 -6 -12 23.4 Voellmy 0.2 2000 -1 -3 -7 19.7 Table F.29: Mathematically-selected parameters for Pink Mountain. For case descrip- tion, see Section E.28. 223 ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● 500 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●●● ●●●●● 5 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 20 40 60 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.29: Raw output data for models of Pink Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 224 F.30 Queen Elizabeth, Alberta, Canada D L Le α vmax Observed 2645 m 1125 m 20◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 -1 62 -45.7 Frictional 10 -10 11 -17.0 Frictional 15 -19 -21 0.4 Frictional 17 -22 -32 6.9 Frictional 20 -31 -48 14.8 Frictional 25 -34 -60 24.2 Frictional 30 -37 -70 32.7 Frictional 35 -44 -104 63.7 Frictional 40 -65 -114 81.2 Frictional 45 -65 -114 81.2 Voellmy 0.05 100 -35 -62 25.7 Voellmy 0.05 500 -14 -7 -7.1 Voellmy 0.05 1000 -15 -8 -6.3 Voellmy 0.05 1500 -3 48 -38.0 Voellmy 0.05 2000 -15 -10 -5.2 Voellmy 0.1 100 -35 -61 25.1 Voellmy 0.1 500 -14 -7 -7.2 Voellmy 0.1 1000 -12 2 -12.1 Voellmy 0.1 1500 1 74 -52.5 Voellmy 0.1 2000 -13 -1 -10.6 Voellmy 0.15 100 -34 -60 24.2 Voellmy 0.15 500 -18 -19 -0.5 Voellmy 0.15 1000 -14 -6 -7.9 Voellmy 0.15 1500 -2 53 -40.7 Voellmy 0.15 2000 -12 4 -13.5 Voellmy 0.2 100 -36 -64 27.4 Voellmy 0.2 500 -22 -30 5.9 Voellmy 0.2 1000 -8 20 -22.5 Voellmy 0.2 1500 -7 23 -24.1 Voellmy 0.2 2000 -16 -11 -4.8 Table F.30: Mathematically-selected parameters for Queen Elizabeth. For case de- scription, see Section E.29. 225 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●●● 1000 1500 2000 2500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ● ●●●● ● ●●●● ● ●●●● ● 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●●● 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● 0 20 40 60 80 100 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.30: Raw output data for models of Queen Elizabeth with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 226 F.31 Rockslide Pass, Northwest Territories, Canada D L Le α vmax Observed 3000 m 6330 m 4730 m 8.5◦ 70 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 -9 -65 -79 121.9 -52 Frictional 10 -38 -78 -96 232.8 -70 Frictional 15 -50 -84 -104 328.4 -86 Frictional 17 -54 -86 -106 367.5 -90 Frictional 20 -57 -88 -108 400.9 -95 Frictional 25 -59 -88 -109 422.0 -100 Frictional 30 -59 -88 -109 422.0 -100 Frictional 35 -59 -88 -109 422.0 -100 Frictional 40 -59 -88 -109 422.0 -100 Frictional 45 -59 -88 -109 422.0 -100 Voellmy 0.05 100 -8 -64 -78 119.6 -52 Voellmy 0.05 500 116 -6 -5 4.6 -46 Voellmy 0.05 1000 133 3 6 -3.6 -45 Voellmy 0.05 1500 142 7 11 -7.9 -45 Voellmy 0.05 2000 148 9 15 -10.5 -45 Voellmy 0.1 100 -28 -74 -90 185.4 -60 Voellmy 0.1 500 -21 -71 -86 160.1 -56 Voellmy 0.1 1000 -20 -70 -85 154.7 -56 Voellmy 0.1 1500 -19 -70 -85 152.7 -55 Voellmy 0.1 2000 -19 -70 -85 151.6 -55 Voellmy 0.15 100 -36 -78 -95 222.9 -68 Voellmy 0.15 500 -34 -77 -94 212.5 -66 Voellmy 0.15 1000 -34 -77 -94 210.9 -66 Voellmy 0.15 1500 -33 -76 -93 210.4 -65 Voellmy 0.15 2000 -33 -76 -93 210.1 -65 Voellmy 0.2 100 -42 -81 -99 262.6 -76 Voellmy 0.2 500 -41 -80 -98 256.5 -75 Voellmy 0.2 1000 -41 -80 -98 255.6 -75 Voellmy 0.2 1500 -41 -80 -98 255.3 -75 Voellmy 0.2 2000 -41 -80 -98 255.2 -75 Table F.31: Mathematically-selected parameters for Rockslide Pass. For case descrip- tion, see Section E.30. For back analyses with user-selected parameters, see Table G.18. 227 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● 1000 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●● ●●● ●● 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● 1000 2000 3000 4000 5000 6000 7000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ●● 0 10 20 30 40 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.31: Raw output data for models of Rockslide Pass with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 228 F.32 1855 Rubble Creek, British Columbia, Canada D L Le α vmax Observed 6900 m 4500 m 2804 m 13◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 194 100 -607 342.2 Frictional 10 5 44 12 37.3 Frictional 15 -46 -23 -34 26.1 Frictional 17 -54 -36 -52 42.6 Frictional 20 -64 -51 -70 63.8 Frictional 25 -73 -64 -86 95.4 Frictional 30 -79 -72 -94 118.6 Frictional 35 -82 -78 -100 143.9 Frictional 40 -86 -83 -103 168.8 Frictional 45 -88 -87 -108 209.4 Voellmy 0.05 100 -32 -1 -2 3.5 Voellmy 0.05 500 -28 4 7 -3.1 Voellmy 0.05 1000 -12 28 35 -7.1 Voellmy 0.05 1500 6 45 10 40.2 Voellmy 0.05 2000 281 100 -921 392.2 Voellmy 0.1 100 -38 -10 -18 15.2 Voellmy 0.1 500 -33 -3 -5 5.2 Voellmy 0.1 1000 -28 5 9 -5.0 Voellmy 0.1 1500 -25 8 17 -11.8 Voellmy 0.1 2000 -14 26 35 -9.9 Voellmy 0.15 100 -53 -34 -50 40.1 Voellmy 0.15 500 -42 -17 -27 21.0 Voellmy 0.15 1000 -34 -5 -8 7.7 Voellmy 0.15 1500 -30 1 1 1.7 Voellmy 0.15 2000 -29 4 6 -2.4 Voellmy 0.2 100 -64 -51 -70 63.6 Voellmy 0.2 500 -52 -33 -48 38.3 Voellmy 0.2 1000 -46 -23 -34 26.1 Voellmy 0.2 1500 -41 -15 -25 19.8 Voellmy 0.2 2000 -38 -11 -19 16.1 Table F.32: Mathematically-selected parameters for Rubble Creek. For case descrip- tion, see Section E.31. For back analyses with user-selected parameters, see Table G.19. 229 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● 2000 4000 6000 8000 10000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●●● ●●●●● ●●●●● 10 20 30 40 50 60 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●●● ● ● ● ●●● ● ●●●● 0 5000 10000 15000 20000 25000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ●●●● ● ●●● 0 100 200 300 400 500 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.32: Raw output data for models of Rubble Creek with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 230 F.33 1982 Sale Mountain, China D L Le α vmax Observed 1120 m 1600 m 1088 m 11◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 221 100 246 -81.2 Frictional 10 210 100 230 -76.0 Frictional 15 6 0 6 -8.7 Frictional 17 10 3 12 -17.0 Frictional 20 101 38 -49 128.1 Frictional 25 55 34 58 -35.5 Frictional 30 59 37 62 -36.7 Frictional 35 -100 -69 -86 110.8 Frictional 40 -100 -69 -86 110.8 Frictional 45 -100 -69 -86 110.8 Voellmy 0.05 100 73 49 80 -42.3 Voellmy 0.05 500 71 45 74 -40.5 Voellmy 0.05 1000 285 100 297 -73.5 Voellmy 0.05 1500 280 100 292 -72.3 Voellmy 0.05 2000 480 100 639 -180.2 Voellmy 0.1 100 -18 -16 -18 8.9 Voellmy 0.1 500 80 51 84 -43.2 Voellmy 0.1 1000 29 15 31 -25.5 Voellmy 0.1 1500 24 12 25 -23.2 Voellmy 0.1 2000 94 61 98 -46.8 Voellmy 0.15 100 -28 -23 -29 19.4 Voellmy 0.15 500 18 8 20 -20.9 Voellmy 0.15 1000 -26 -21 -26 15.3 Voellmy 0.15 1500 84 54 87 -44.1 Voellmy 0.15 2000 -24 -20 -24 13.9 Voellmy 0.2 100 -41 -32 -44 40.5 Voellmy 0.2 500 -5 -7 -2 -7.7 Voellmy 0.2 1000 -5 -7 -2 -7.3 Voellmy 0.2 1500 -96 -66 -80 88.8 Voellmy 0.2 2000 33 18 35 -27.0 Table F.33: Mathematically-selected parameters for Sale Mountain. For case descrip- tion, see Section E.32. For back analyses with user-selected parameters, see Table G.20. 231 ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ●●● ● ● ● ●● ● ●● ● 1000 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ●● ●●● ●● ●● ●● ●● −10 −5 0 5 10 15 20 25 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ● ● ●● ● ●● ● 0 1000 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ●● ● ●● ● 0 50000 100000 150000 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.33: Raw output data for models of Sale Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 232 F.34 1850 Seaford, England D L Le α vmax Observed 121 m 12 m 28◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 100 2445 -72.5 Frictional 10 100 1343 -50.0 Frictional 15 87 732 -31.9 Frictional 17 74 578 -25.8 Frictional 20 60 413 -18.0 Frictional 25 47 235 -8.2 Frictional 30 56 356 -15.0 Frictional 35 39 131 -1.8 Frictional 40 27 -51 10.6 Frictional 45 17 -199 21.9 Voellmy 0.05 100 100 1460 -52.8 Voellmy 0.05 500 100 2123 -66.5 Voellmy 0.05 1000 100 1894 -62.0 Voellmy 0.05 1500 100 2603 -75.5 Voellmy 0.05 2000 100 1860 -61.3 Voellmy 0.1 100 100 1125 -44.4 Voellmy 0.1 500 100 1613 -56.1 Voellmy 0.1 1000 100 1795 -60.0 Voellmy 0.1 1500 100 1862 -61.3 Voellmy 0.1 2000 100 1895 -62.0 Voellmy 0.15 100 100 892 -37.5 Voellmy 0.15 500 100 1175 -45.8 Voellmy 0.15 1000 100 1261 -48.0 Voellmy 0.15 1500 100 1313 -49.3 Voellmy 0.15 2000 100 1353 -50.3 Voellmy 0.2 100 86 720 -31.5 Voellmy 0.2 500 99 867 -36.7 Voellmy 0.2 1000 100 932 -38.8 Voellmy 0.2 1500 100 967 -39.9 Voellmy 0.2 2000 100 994 -40.7 Table F.34: Mathematically-selected parameters for Seaford. For case description, see Section E.33. For back analyses with user-selected parameters, see Table G.21. 233 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●●● 150 200 250 300 350 400 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●●●●● ●●●●● ●●●●● 10 15 20 25 30 35 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ●●● 150 200 250 300 350 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● 18 20 22 24 26 28 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.34: Raw output data for models of Seaford with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 234 F.35 1964 Sherman Glacier, Alaska, United States D L Le α vmax Observed 5700 m 5950 m 4222 m 10◦ 67 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 13 7 19 -24.7 32 Frictional 10 -35 -39 -40 7.9 15 Frictional 15 -61 -63 -72 57.0 -3 Frictional 17 -66 -68 -78 74.8 -10 Frictional 20 -71 -73 -85 103.6 -21 Frictional 25 -78 -79 -92 148.2 -33 Frictional 30 -82 -84 -97 187.2 -42 Frictional 35 -86 -87 -100 223.2 -48 Frictional 40 -89 -90 -102 263.2 -64 Frictional 45 -93 -93 -103 299.6 -72 Voellmy 0.05 100 -67 -69 -79 81.4 -24 Voellmy 0.05 500 -37 -40 -42 10.6 2 Voellmy 0.05 1000 -34 -37 -38 5.9 12 Voellmy 0.05 1500 -30 -34 -33 1.0 18 Voellmy 0.05 2000 -26 -30 -28 -3.8 22 Voellmy 0.1 100 -72 -74 -86 109.2 -27 Voellmy 0.1 500 -63 -65 -73 61.6 -3 Voellmy 0.1 1000 -51 -54 -59 32.3 5 Voellmy 0.1 1500 -43 -46 -49 19.0 10 Voellmy 0.1 2000 -38 -42 -44 12.5 13 Voellmy 0.15 100 -75 -77 -89 128.2 -32 Voellmy 0.15 500 -67 -69 -79 79.6 -8 Voellmy 0.15 1000 -61 -63 -71 54.9 -1 Voellmy 0.15 1500 -56 -59 -65 42.5 2 Voellmy 0.15 2000 -52 -55 -61 34.8 5 Voellmy 0.2 100 -77 -79 -92 143.5 -35 Voellmy 0.2 500 -70 -72 -83 95.9 -14 Voellmy 0.2 1000 -65 -68 -77 73.8 -8 Voellmy 0.2 1500 -63 -65 -74 63.1 -4 Voellmy 0.2 2000 -61 -63 -71 56.3 -2 Table F.35: Mathematically-selected parameters for Sherman Glacier. For case de- scription, see Section E.34. For back analyses with user-selected parameters, see Table G.22. 235 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 1000 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●●● ●●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 1000 2000 3000 4000 5000 6000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 30 40 50 60 70 80 90 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.35: Raw output data for models of Sherman Glacier with observations marked with a dashed line. For Voellmy rheologies, the friction angle cal- culated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 236 F.36 1946 Six de Eaux Froids (east lobe), Switzerland D L Le α vmax Observed 16◦ Rheology θb f ξ ∆α Frictional 5 -69.8 Frictional 10 -1.7 Frictional 15 -0.6 Frictional 17 13.0 Frictional 20 28.2 Frictional 25 48.4 Frictional 30 67.8 Frictional 35 94.6 Frictional 40 128.6 Frictional 45 164.5 Voellmy 0.05 100 7.6 Voellmy 0.05 500 -2.9 Voellmy 0.05 1000 -1.1 Voellmy 0.05 1500 -29.8 Voellmy 0.05 2000 -1.8 Voellmy 0.1 100 48.2 Voellmy 0.1 500 -2.7 Voellmy 0.1 1000 -3.6 Voellmy 0.1 1500 -20.4 Voellmy 0.1 2000 1.2 Voellmy 0.15 100 56.2 Voellmy 0.15 500 4.2 Voellmy 0.15 1000 -5.3 Voellmy 0.15 1500 -10.5 Voellmy 0.15 2000 -6.0 Voellmy 0.2 100 63.1 Voellmy 0.2 500 20.6 Voellmy 0.2 1000 7.7 Voellmy 0.2 1500 4.2 Voellmy 0.2 2000 -4.2 Table F.36: Mathematically-selected parameters for Six de Eaux Froids (east lobe). For case description, see Section E.35. For back analyses with user-selected parameters, see Section G.20. 237 ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● 500 1000 1500 2000 2500 3000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●● ●●● ● ●●●● ●●●●● 10 20 30 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● 500 1000 1500 2000 2500 3000 3500 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●●● ● 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.36: Raw output data for models of Six de Eaux Froids (east) with observa- tions marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 238 F.37 1946 Six de Eaux Froids (west lobe), Switzerland D L Le α vmax Observed 16◦ Rheology θb f ξ ∆α Frictional 5 21.7 Frictional 10 12.6 Frictional 15 5.3 Frictional 17 18.7 Frictional 20 35.4 Frictional 25 59.4 Frictional 30 76.2 Frictional 35 101.6 Frictional 40 134.4 Frictional 45 170.8 Voellmy 0.05 100 49.2 Voellmy 0.05 500 25.0 Voellmy 0.05 1000 24.2 Voellmy 0.05 1500 -33.2 Voellmy 0.05 2000 20.9 Voellmy 0.1 100 65.5 Voellmy 0.1 500 18.7 Voellmy 0.1 1000 22.6 Voellmy 0.1 1500 -17.7 Voellmy 0.1 2000 23.6 Voellmy 0.15 100 72.6 Voellmy 0.15 500 18.4 Voellmy 0.15 1000 14.7 Voellmy 0.15 1500 -3.2 Voellmy 0.15 2000 20.0 Voellmy 0.2 100 78.4 Voellmy 0.2 500 27.9 Voellmy 0.2 1000 10.7 Voellmy 0.2 1500 9.3 Voellmy 0.2 2000 1.8 Table F.37: Mathematically-selected parameters for Six de Eaux Froids (west lobe). For case description, see Section E.35. For back analyses with user-selected parameters, see Section G.20. 239 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ●● ● ● ●● ● 500 1000 1500 2000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●● ● ●●●● ●●●● ● ●●●●● 10 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ●● ● ● ●● ● 1000 1500 2000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● 20 40 60 80 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.37: Raw output data for models of Six de Eaux Froids (west) with obser- vations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 240 F.38 Slide Mountain, Alberta, Canada D L Le α vmax Observed 1650 m 978 m 14◦ Rheology θb f ξ ∆L ∆Le ∆α Frictional 5 -43 -81 90.9 Frictional 10 -13 -20 13.1 Frictional 15 -27 -52 47.9 Frictional 17 -33 -63 62.3 Frictional 20 -40 -76 82.1 Frictional 25 -48 -91 108.3 Frictional 30 -54 -101 131.4 Frictional 35 -60 -113 161.9 Frictional 40 -66 -121 189.4 Frictional 45 -72 -126 215.5 Voellmy 0.05 100 -48 -91 108.2 Voellmy 0.05 500 -26 -49 44.6 Voellmy 0.05 1000 -38 -71 73.8 Voellmy 0.05 1500 -5 3 -9.2 Voellmy 0.05 2000 -35 -65 65.7 Voellmy 0.1 100 -51 -96 120.1 Voellmy 0.1 500 -28 -53 49.9 Voellmy 0.1 1000 -18 -33 27.1 Voellmy 0.1 1500 -12 -16 9.4 Voellmy 0.1 2000 -24 -45 40.2 Voellmy 0.15 100 -54 -101 129.9 Voellmy 0.15 500 -35 -66 67.0 Voellmy 0.15 1000 -25 -47 42.4 Voellmy 0.15 1500 -20 -37 31.3 Voellmy 0.15 2000 -17 -30 23.9 Voellmy 0.2 100 -55 -104 138.6 Voellmy 0.2 500 -40 -76 81.9 Voellmy 0.2 1000 -33 -62 60.4 Voellmy 0.2 1500 -29 -54 50.6 Voellmy 0.2 2000 -26 -49 44.6 Table F.38: Mathematically-selected parameters for Slide Mountain. For case de- scription, see Section E.36. 241 ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 600 800 1000 1200 1400 1600 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●●●● ● ●●●●● ●●●●● 15 20 25 30 35 40 45 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 800 1000 1200 1400 1600 1800 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 40 50 60 70 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.38: Raw output data for models of Slide Mountain with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 242 F.39 2000 Tozawagawa, Japan D L Le α vmax Observed 454 m 100 m -268 m 66◦ Rheology θb f ξ ∆D ∆L ∆Le ∆α Frictional 5 3 100 -110 -54.3 Frictional 10 3 100 -110 -54.3 Frictional 15 6 100 -121 -57.2 Frictional 17 7 100 -123 -57.7 Frictional 20 6 100 -122 -57.5 Frictional 25 5 100 -119 -56.8 Frictional 30 3 100 -113 -55.0 Frictional 35 -38 100 -100 -51.4 Frictional 40 -42 100 -97 -50.3 Frictional 45 -46 100 -100 -51.4 Voellmy 0.05 100 3 100 -112 -54.8 Voellmy 0.05 500 5 100 -119 -56.8 Voellmy 0.05 1000 4 100 -114 -55.4 Voellmy 0.05 1500 43 100 -227 -80.6 Voellmy 0.05 2000 4 100 -114 -55.4 Voellmy 0.1 100 4 100 -114 -55.5 Voellmy 0.1 500 4 100 -115 -55.7 Voellmy 0.1 1000 4 100 -115 -55.5 Voellmy 0.1 1500 33 100 -204 -76.8 Voellmy 0.1 2000 3 100 -113 -55.0 Voellmy 0.15 100 4 100 -116 -55.8 Voellmy 0.15 500 5 100 -116 -56.0 Voellmy 0.15 1000 4 100 -116 -55.8 Voellmy 0.15 1500 27 100 -185 -72.9 Voellmy 0.15 2000 4 100 -113 -55.2 Voellmy 0.2 100 5 100 -117 -56.1 Voellmy 0.2 500 5 100 -119 -56.6 Voellmy 0.2 1000 5 100 -117 -56.3 Voellmy 0.2 1500 21 100 -169 -69.4 Voellmy 0.2 2000 5 100 -117 -56.2 Table F.39: Mathematically-selected parameters for Tozawagawa. For case descrip- tion, see Section E.37. For back analyses with user-selected parameters, see Table G.24. 243 ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● 200 250 300 350 400 450 500 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●● ●● ●●● ● ●●● ● ●●●● 15 20 25 30 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ●● ● 300 400 500 600 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ●● ● 0 10 20 30 40 50 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.39: Raw output data for models of Tozawagawa with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 244 F.40 1717 Triolet Glacier, Italy D L Le α vmax Observed 9000 m 7200 m 4223 m 14.5◦ 44 m/s Rheology θb f ξ ∆D ∆L ∆Le ∆α ∆vmax Frictional 5 6 25 42 -18.9 197 Frictional 10 5 24 40 -18.1 144 Frictional 15 -33 -24 -38 25.4 63 Frictional 17 -52 -47 -69 53.0 60 Frictional 20 -77 -77 -91 79.7 55 Frictional 25 -82 -82 -98 111.3 49 Frictional 30 -84 -85 -102 133.6 40 Frictional 35 -86 -87 -105 156.1 30 Frictional 40 -87 -89 -107 178.8 19 Frictional 45 -89 -91 -108 200.3 6 Voellmy 0.05 100 -25 -14 -22 13.0 11 Voellmy 0.05 500 -24 -13 -20 11.5 48 Voellmy 0.05 1000 -14 -0 0 -0.7 73 Voellmy 0.05 1500 -5 12 19 -9.5 101 Voellmy 0.05 2000 3 21 35 -16.2 146 Voellmy 0.1 100 -31 -22 -35 22.7 8 Voellmy 0.1 500 -29 -19 -31 19.9 42 Voellmy 0.1 1000 -26 -15 -25 14.8 61 Voellmy 0.1 1500 -22 -10 -16 8.6 78 Voellmy 0.1 2000 -15 -2 -3 0.8 122 Voellmy 0.15 100 -77 -76 -91 78.6 6 Voellmy 0.15 500 -36 -28 -45 30.4 37 Voellmy 0.15 1000 -32 -23 -37 24.7 45 Voellmy 0.15 1500 -29 -18 -30 18.8 54 Voellmy 0.15 2000 -25 -14 -23 13.2 88 Voellmy 0.2 100 -81 -82 -98 109.6 3 Voellmy 0.2 500 -52 -47 -68 52.5 32 Voellmy 0.2 1000 -40 -32 -50 35.4 40 Voellmy 0.2 1500 -37 -29 -45 31.0 43 Voellmy 0.2 2000 -34 -25 -40 26.8 45 Table F.40: Mathematically-selected parameters for Triolet Glacier. For case descrip- tion, see Section E.38. For back analyses with user-selected parameters, see Table G.25. 245 ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● 2000 4000 6000 8000 10 20 30 40 fri cti on  a ng le (a) L ● ● ● ● ● ● ● ● ● ● ●●●●● ●●●●● ●●●●● ●●●●● 15 20 25 30 35 40 10 20 30 40 fri cti on  a ng le (b) α ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● 2000 4000 6000 8000 10 20 30 40 fri cti on  a ng le (c) D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● 60 80 100 120 10 20 30 40 fri cti on  a ng le (d) vmax Figure F.40: Raw output data for models of Triolet Glacier with observations marked with a dashed line. For Voellmy rheologies, the friction angle calculated by f = tan(θ), and turbulence coefficients are identified by colour (ξ = 100: red, ξ = 500: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). 246 F.41 2002 Zymoetz River, British Columbia, Canada D L Le α vmax Observed 17◦ 34 m/s Rheology θb f ξ ∆α ∆vmax Frictional 5 19.8 511 Frictional 10 14.2 350 Frictional 15 -11.8 132 Frictional 17 3.9 119 Frictional 20 23.4 86 Frictional 25 49.8 47 Frictional 30 76.4 17 Frictional 35 104.1 -33 Frictional 40 124.8 -63 Frictional 45 145.2 -89 Voellmy 0.05 100 49.9 5 Voellmy 0.05 500 -14.9 94 Voellmy 0.05 1000 -20.3 141 Voellmy 0.05 1500 -21.0 110 Voellmy 0.05 2000 47.4 162 Voellmy 0.1 100 57.3 1 Voellmy 0.1 500 3.3 81 Voellmy 0.1 1000 -11.4 132 Voellmy 0.1 1500 -13.4 103 Voellmy 0.1 2000 -19.4 150 Voellmy 0.15 100 67.5 -3 Voellmy 0.15 500 15.2 60 Voellmy 0.15 1000 4.6 119 Voellmy 0.15 1500 0.1 97 Voellmy 0.15 2000 -10.1 139 Voellmy 0.2 100 72.6 -8 Voellmy 0.2 500 19.4 49 Voellmy 0.2 1000 11.7 94 Voellmy 0.2 1500 8.5 87 Voellmy 0.2 2000 10.8 120 Table F.41: Mathematically-selected parameters for Zymoetz River. For case descrip- tion, see Section E.39. For back analyses with user-selected parameters, see Table G.26. 247 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 0 2000 4000 6000 8000 10 20 30 40