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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 variable 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 identify 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, morphology, 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  2  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1  Overview of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.2  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2  1.3  Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . .  3  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  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  Summary of Landslides . . . . . . . . . . . . . . . . . . . . . . . . . . .  10  Data: Landslide Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . .  11  3.1  11  2.2  2.3 3  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii  3.1.1  Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11  3.1.2  Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12  3.1.3  Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12  3.1.4  Other Limitations . . . . . . . . . . . . . . . . . . . . . . . . . .  14  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  Error in Recorded Observations . . . . . . . . . . . . . . . . . . . . . .  18  3.3.1  Reliability of Reported Runout Characteristics . . . . . . . . . .  18  3.3.2  Incomplete Observations . . . . . . . . . . . . . . . . . . . . . .  19  Summary of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20  Models for Landslide Hazard Prediction . . . . . . . . . . . . . . . . . . . .  26  4.1  Predicting Landslide Runout . . . . . . . . . . . . . . . . . . . . . . . .  27  4.1.1  Laboratory Models . . . . . . . . . . . . . . . . . . . . . . . . .  28  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  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  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  Summary of Analysis of the Set of Landslides . . . . . . . . . . . . . . .  49  3.2  3.3  3.4 4  4.2  5  5.2  5.3  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  Summary of Tool Selection . . . . . . . . . . . . . . . . . . . . . . . . .  55  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  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  Summary of Back Analysis . . . . . . . . . . . . . . . . . . . . . . . . .  64  Analysis of Model Back Analyses and Parameter Selection . . . . . . . . .  66  8.1  Defining “Best” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66  8.1.1  Qualitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66  8.1.2  Quantitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  67  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  Summary of Parameter Performance . . . . . . . . . . . . . . . . . . . .  77  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  6.3 7  7.2  7.3 8  8.2  8.3 9  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 Charmon´etier, Is`ere, France . . . . . . . . . . . . . . . . . . . . . .  122  E.6 1442 Claps de Luc, Drˆome, 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 Charmon´etier, Is`ere, France . . . . . . . . . . . . . . . . . . . . . .  175  F.6  1442 Claps de Luc, Drˆome, 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. . . . . . . . . . . . . . . . . . . . . . . . . . . .  3.6  22  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  5.2  by the Hungr et al. 2001 system. . . . . . . . . . . . . . . . . . . . . . .  37  Number of events overall and in morphology subsets. . . . . . . . . . . .  38  5.3 V -α relationships determined by linear regressions. See Equation 4.1 for form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4  40  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. . . . . . . . . . . . . . . . . .  5.5  41  P-values of ANOVA between characteristics and mobility controlled for volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  43  5.6  Base average and influencing factor for a characteristic (independent variable) 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8.1 8.2 8.3  Interpretation of normalized runout for mobility indices. An event is overpredicted by at least double the observed runout distance when ∆L ≥ +100.  68  the specified mobility indices (with ∆L ≤ 100%). . . . . . . . . . . . . .  70  Mean normalized runout (∆), and standard deviation (σ ) of that mean for  Percentage of cases with absolute mean normalized runout that are excellentlymodelled (|∆| ≤ 5%) or well-modelled (|∆| ≤ 30%) for the specified mo-  bility indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4  63  70  Low f paired with high ξ over-predict mobility (green), mid-range parameters 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 = 3 most mobile), and velocity increases from left to right (ξ = 2000 ms = fastest). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8.5  Percentage of cases with under-estimation (∆ < −10%), excellent estima-  tion (∆ < |10%|), or over-estimation (∆ > +10%) of the specified mobility  8.6  71  indices (with ∆L ≤ 100%). . . . . . . . . . . . . . . . . . . . . . . . . .  73  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 modified linear regressions either excluding Tozawagawa, or excluding events prior to 1900, versus those determined by previous research. Compare to Table 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xii  113  F.1  Mathematically-selected parameters for Abbot’s Cliff. For case description, see Section E.1. For back analyses with user-selected parameters, see Table G.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.2  167  Mathematically-selected parameters for Arth-Goldau. For case description, see Section E.2. For back analyses with user-selected parameters, see Table G.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.3  Mathematically-selected parameters for Arvel. For case description, see Section E.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.4  169 171  Mathematically-selected parameters for Brazeau Lake. For case description, see Section E.4. For back analyses with user-selected parameters, see Table G.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.5  Mathematically-selected parameters for Charmon’etier. For case description, see Section E.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.6  175  Mathematically-selected parameters for Claps de Luc. For case description, see Section E.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.7  173  177  Mathematically-selected parameters for Eagle Pass. For case description, see Section E.7. For back analyses with user-selected parameters, see Table G.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.8  179  Mathematically-selected parameters for Elm. For case description, see Section E.8. For back analyses with user-selected parameters, see Table G.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.9  181  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 description, see Section E.13. . . . . . . . . . . . . . . . . . . . . . . . . .  191  F.14 Mathematically-selected parameters for Jonas Creek (south). For case description, see Section E.13. . . . . . . . . . . . . . . . . . . . . . . . . . xiii  193  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 description, 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 description, see Section E.18. For back analyses with user-selected parameters, see Table G.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  203  F.20 Mathematically-selected parameters for McAuley Creek. For case description, see Section E.19. . . . . . . . . . . . . . . . . . . . . . . . . .  205  F.21 Mathematically-selected parameters for Mount Cayley. For case description, 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 description, 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 description, 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 description, see Section E.23.  . . . . . . . . . . . . . . . . . . . . . . . . . . .  213  F.25 Mathematically-selected parameters for Mount Steele. For case description, see Section E.24.  . . . . . . . . . . . . . . . . . . . . . . . . . . .  215  F.26 Mathematically-selected parameters for Mystery Creek. For case description, see Section E.25.  . . . . . . . . . . . . . . . . . . . . . . . . . . .  217  F.27 Mathematically-selected parameters for Nomash River. For case description, 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 parameters, see Table G.17. . . . . . . . . . . . . . . . . . . . . . . . . . . xiv  221  F.29 Mathematically-selected parameters for Pink Mountain. For case description, see Section E.28.  . . . . . . . . . . . . . . . . . . . . . . . . . . .  223  F.30 Mathematically-selected parameters for Queen Elizabeth. For case description, see Section E.29. . . . . . . . . . . . . . . . . . . . . . . . . .  225  F.31 Mathematically-selected parameters for Rockslide Pass. For case description, 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 description, 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 description, 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 Table G.21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  233  F.35 Mathematically-selected parameters for Sherman Glacier. For case description, see Section E.34. For back analyses with user-selected parameters, 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 description, see Section E.36.  . . . . . . . . . . . . . . . . . . . . . . . . . . .  241  F.39 Mathematically-selected parameters for Tozawagawa. For case description, 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 description, see Section E.38. For back analyses with user-selected parameters, see Table G.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xv  245  F.41 Mathematically-selected parameters for Zymoetz River. For case description, 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 Section 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 Section 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 Section 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 Section 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 Table 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 Table F.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  256  G.8 User-selected parameters for Hope Slide. For case description, see Section E.12. For back analyses with with mathematically-selected parameters, see Table F.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  257  G.9 User-selected parameters for Las Colinas without entrainment. For modelling 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 Table F.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xvi  259  G.11 User-selected parameters for Madison Canyon. For case description, see Section E.18. For back analyses with with mathematically-selected parameters, see Table F.19. . . . . . . . . . . . . . . . . . . . . . . . . . .  260  G.12 User-selected parameters Mount Cayley without entrainment. For case description, see Section E.20. For back analyses with with mathematicallyselected parameters, see Table F.21. . . . . . . . . . . . . . . . . . . . .  261  G.13 User-selected parameters for Mount Cayley with entrainment to the specified volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  262  G.14 User-selected parameters for Mount Cook. For modelling with entrainment, the event was split into two streamlines: the main path, and the tributary which ran out over Anzec Peak. For case description, see Section E.21. For back analyses with with mathematically-selected parameters, 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 parameters, see Table F.23. . . . . . . . . . . . . . . . . . . . . . . . . . .  264  G.16 User-selected parameters for Nomash River. For case description, see Section E.26. For back analyses with with mathematically-selected parameters, 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 parameters, see Table F.31. . . . . . . . . . . . . . . . . . . . . . . . . . .  267  G.19 User-selected parameters for Rubble Creek. For case description, see Section E.31. For back analyses with with mathematically-selected parameters, 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 parameters, 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 Table F.34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xvii  270  G.22 User-selected parameters for Sherman Glacier. For case description, see Section E.34. For back analyses with with mathematically-selected parameters, 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 Section E.37. For back analyses with with mathematically-selected parameters, see Table F.39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  273  G.25 User-selected parameters for Triolet Glacier. For case description, see Section E.38. For back analyses with with mathematically-selected parameters, 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 parameters, see Table F.41. . . . . . . . . . . . . . . . . . . . . . . . . . .  275  H.1 Mean deviation (∆) between model and observations, and standard deviation (σ ) of that mean for L (with ∆L ≤ 100%). . . . . . . . . . . . . . . .  278  tion (σ ) of that mean for D. . . . . . . . . . . . . . . . . . . . . . . . . .  279  H.2 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  282  H.5 Percentage of cases with absolute mean deviation (|∆|) within specified H.6 Percentage of cases with absolute mean deviation (|∆|) within specified  cut-offs for α. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.7 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  283  tion (∆ < |10%|), or over-estimation (∆ > +10%) of L (with ∆L ≤ 100%).  284  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D. . . . . . . . . . .  285  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α. . . . . . . . . . .  286  H.8 Percentage of cases with under-estimation (∆ < −10%), excellent estimaH.9 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  xviii  H.10 Mean deviation (∆) between model and observations, and standard deviation (σ ) of that mean for L (with ∆L ≤ 100%) by volume. . . . . . . . . .  287  tion (σ ) of that mean for D by volume. . . . . . . . . . . . . . . . . . . .  288  H.11 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D by volume. . . . . . . . . . . . . . . . . . . . . . . . . . .  291  H.14 Percentage of cases with absolute mean deviation (|∆|) within specified 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.17 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  293  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D by volume. . . . .  294  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α by volume. . . . .  295  tion (σ ) of that mean for L (with ∆L ≤ 100%) by movement. . . . . . . .  296  tion (σ ) of that mean for D by movement. . . . . . . . . . . . . . . . . .  297  H.18 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  H.19 Mean deviation (∆) between model and observations, and standard deviaH.20 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D by movement. . . . . . . . . . . . . . . . . . . . . . . . .  300  H.23 Percentage of cases with absolute mean deviation (|∆|) within specified 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xix  302  H.26 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D by movement. . .  303  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α by movement. . .  304  tion (σ ) of that mean for L (with ∆L ≤ 100%) by morphology. . . . . . .  305  tion (σ ) of that mean for D by morphology. . . . . . . . . . . . . . . . .  306  H.27 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  H.28 Mean deviation (∆) between model and observations, and standard deviaH.29 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D by morphology. . . . . . . . . . . . . . . . . . . . . . . .  309  H.32 Percentage of cases with absolute mean deviation (|∆|) within specified 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.35 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  311  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D by morphology. .  312  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α by morphology. .  313  tion (σ ) of that mean for L (with ∆L ≤ 100%) by source material. . . . .  314  tion (σ ) of that mean for D by source material. . . . . . . . . . . . . . .  315  H.36 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  H.37 Mean deviation (∆) between model and observations, and standard deviaH.38 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D by source material. . . . . . . . . . . . . . . . . . . . . . .  318  H.41 Percentage of cases with absolute mean deviation (|∆|) within specified H.42 Percentage of cases with absolute mean deviation (|∆|) within specified  cut-offs for α by source material. . . . . . . . . . . . . . . . . . . . . . . xx  319  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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.44 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  320  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D by source material.  321  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α by source material.  322  tion (σ ) of that mean for L (with ∆L ≤ 100%) by path material. . . . . . .  323  tion (σ ) of that mean for D by path material. . . . . . . . . . . . . . . . .  324  H.45 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  H.46 Mean deviation (∆) between model and observations, and standard deviaH.47 Mean deviation (∆) between model and observations, and standard deviaH.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  cut-offs for D by path material. . . . . . . . . . . . . . . . . . . . . . . .  327  H.50 Percentage of cases with absolute mean deviation (|∆|) within specified 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.53 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  329  tion (∆ < |10%|), or over-estimation (∆ > +10%) of D by path material. .  330  tion (∆ < |10%|), or over-estimation (∆ > +10%) of α by path material. .  331  H.54 Percentage of cases with under-estimation (∆ < −10%), excellent estima-  xxi  List of Figures 2.1  Common terminology for landslide anatomy: source, deposit, crown, toe, and path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2.2  5  Common terminology for runout mobility: fahrb¨oschung 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6  3.1  Original path topography may be uncertain for relic events. . . . . . . . .  15  3.2  Fahrb¨oshung angle is easy to measure but prone to rounding error, while pacing off curvilinear distance is straightforward but tiring. . . . . . . . .  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. . . . . . . . . . . . . . .  5.1  19  33  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. . . . . . .  5.2  39  Effectiveness of emergent grouping of landslides using cluster analysis to minimize differences in α. Results are similar for cluster analysis on other mobility indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6.1  44  Real landslide materials are complicated, so are modelled as simple hypothetical fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xxii  54  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 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. . . . . . . . . . . . . .  8.1  65  Histogram of the performance of frictional rheology with θb = 17◦ as measured by the specified normalized index, across all case studies. See Sec-  8.2  tion H.6 for other models. . . . . . . . . . . . . . . . . . . . . . . . . . .  74  Histogram of the performance of Voellmy rheology with f = 0.1 and 3 ξ = 500 ms 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 resistance 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 analysis 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 alphabetical: Charmon´etier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Section E.37). . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xxiii  115  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: Charmon´etier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Section 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 Charmon´etier 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.2  168  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.3  170  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).  F.4  172  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.5  174  Raw output data for models of Charmon´etier 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv  176  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.7  178  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  F.8  180  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: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green). . . . . . .  F.9  182  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xxvi  190  F.13 Raw output data for models of Jonas Creek (north) 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  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 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xxvii  204  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviii  218  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 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix  232  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 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 Raw output data for models of Six de Eaux Froids (west) 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxx  246  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 measured by the specified normalized index, across all case studies. . . . . . . H.3 Histogram of the performance of frictional rheology with Θb =  10◦  as  measured by the specified normalized index, across all case studies. . . . H.4 Histogram of the performance of frictional rheology with Θb =  15◦  H.5 Histogram of the performance of frictional rheology with Θb = H.6 Histogram of the performance of frictional rheology with Θb =  335  as  measured by the specified normalized index, across all case studies. . . . 20◦  334  as  measured by the specified normalized index, across all case studies. . . . 17◦  333  336  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. . . . H.8 Histogram of the performance of frictional rheology with Θb =  30◦  as  measured by the specified normalized index, across all case studies. . . . H.9 Histogram of the performance of frictional rheology with Θb =  35◦  H.10 Histogram of the performance of frictional rheology with Θb = H.11 Histogram of the performance of frictional rheology with Θb =  340  as  measured by the specified normalized index, across all case studies. . . . 45◦  339  as  measured by the specified normalized index, across all case studies. . . . 40◦  338  341  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 = 3 100 m 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 = 3 500 m 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 = 3 1000 m 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 = 3 1500 m 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 = 3 2000 m 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 = 3 100 m 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 = 3 500 m 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 = 3 1000 m 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 = 3 1500 m 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 = 3 2000 m 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 = 3 100 m 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 = 3 500 m 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 = 3 1000 m 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 = 3 1500 m 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 = 3 2000 m 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 = 3 100 m 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 = 3 500 m 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 = 3 1000 m 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 = 3 1500 m 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 = 3 2000 m 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 encouragement 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 experiences, this thesis is the best place to offer my appreciation to the people who have contributed 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 interxxxiv  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 dynamics in practice, presenting me with surreal and fantastic situations for whole new applications of science. Thank you for making me your rocket scientist. The Victoria Institute of Earth and Planetary Sciences sent me roaming around Australia 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. Accurate 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 travelled. 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 analyzing 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 consistent 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 recommended parameters either for preliminary hazard mapping or a starting point in parameter 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 characteristics will result in two landslides being accurately modelled using the same parameters. 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 characteristics 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 characteristics. 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 backanalyses 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 potentially erodible basal surfaces (Iverson, 2005).  2.1.1  Anatomy of a Landslide  Before discussing landslides further, it is necessary to establish common terms for describing 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 initial 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 curvilinear (D) and horizontal length (L) distances.These distances are measured to the toe of the deposit, the very farthest point the landslide runs out. 1 See  Section 2.2.4. Section 2.2.1 and Section C.2.1. 3 The “x = 0” of a landslide-oriented coordinate system. 2 See  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 fahrb¨oschung 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: tan α =  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 fahrb¨oschung 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 tan 32◦ : Le = L −  H tan 32◦  (2.2)  where excessive runout Le is any motion beyond that expected by the kinematics of friction 4 See 5 See  Legros (2002) for an analysis of the impact of using maximum versus center of mass measurements. Section 4.2.2.  5  Figure 2.2: Common terminology for runout mobility: fahrb¨oschung 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). (Hs¨u, 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 dominated 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 be6 This  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 important role. Turbulence is suppressed as the concentration of grains increases (Iverson, 2005). Although the Varnes (1978) classification specifies all flows must exhibit internal deformation, 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 (Hs¨u, 1975), or producing buoyancy through collisions during highly concentrated grain flow (Bagnold, 1954). Disassociation of the underlaying material may produce carbon dioxide, 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 friction angles may theoretically spontaneously reduce at high rates of shear (Scheidegger, 7 See  Section 4.2.2.  7  Process  Mechanism  Result  Reduce internal friction  interstitial fluids (dust, gas) entrain saturated material internal collisions high impulsive contact pressure high shear earthquake or acoustic waves  lubrication increase liquid content buoyancy dilation spontaneous reduction vibration  Reduce basal friction  air or water vapour “ball bearing” fragments limestone, gypsum, ice... undrained loading melting (frictionite, water) grinding  cushion basal rolling smooth bed fluidized bed lubrication gouge  Morphology  channelized path  low energy dissipation  Volume  confining and shear stress fragmentation  fragmentation bulking release elastic energy larger deposit larger deposit  entrainment volume balance  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 earthquaketriggered 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 (Hs¨u, 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 subsequent 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 distance (Nicoletti & Sorriso-Valvo, 1991). However, long runout has been observed in cases independent of channelized morphology, indicating that although a contributing mechanism, 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 distance. Volumes may be increased through fragmentation of the initial volume, or through entrainment of additional material. Fragmentation is volume-dependent as it increases proportionately 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 & McSaveney, 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.  8 See  Locat et al. (2006) for a review and field study on fragmentation in rock avalanches. by Legros (2002), Hungr & Evans (2004), and Deganutti (2008).  9 Notably  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 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 water, hyper-concentrated flows, or surges (which excludes most debris flows).  3.1.1  Availability  To be included in this study, a full landslide description including pre- and post-event topog-  Characteristic  Limiting Criteria  Failure type  single  Volume  V f 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.  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. Hs¨u (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 V f ≥ 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 calculated 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 1 The  impact of statistical outliers is discussed in Appendix D.  2 Excepting Corominas (1996), who claims no clear minimum cutoff volume for an event to exhibit excessive  mobility.  12  forced vortex equation: v=  �  Rc g ∆h k 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 ∆h b . 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 runup 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 velocity 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 underestimates of velocity. Modified equations accounting for friction require the use of correction factors from the percentage of energy lost to friction (Francis & Baker, 1977; Evans, 3 The  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 uncertain, 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 discuss 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 movement mechanisms, material properties, velocity, and other properties with gradational distinctions between characteristics allowing for subjective classification5 . The landslides in 4 For 5 For  further discussion, see Erismann & Abele (2001). 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 Debris Avalanche Flow Slide Dry Wet Unobstructed Channelized Impacted Non-Violent Rain Artificial Blast Earthquake  Material (Source)  Rock Debris Chalk Loess Rock Debris Ash Clay Glacial Talus Urban  Saturation Morphology  Trigger  Material (Path)  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 usually 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 dissipative 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 6 This  7 Also  is in contrast to debris flows, which re-occur periodically in the same channel. called sturzstroms (Heim, 1932).  16  eventually reduced to the same three major categorizations as the most pertinent to successfully 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 impacted 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  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 composition by grain size. Debris is any loose unsorted material (Table 3.3). Fragmented rock originates as an intact rock mass disintegrating during the landslide (Hungr et al.,  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.  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 theoretically the reliability of all reported runout observations is perfect, real-world limitations can interfere. Although distance D, length L, and fahrb¨oschug angle α should all be comparable measures of runout, actual limitations in the field impact the reliability of the observations. Fahrb¨oschung 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 8 Although  no landslide within this thesis has free flowing water with floating debris (debris floods).  18  Figure 3.2: Fahrb¨oshung 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 triggering 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 9 Both  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 characteristics 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.  10 Technically,  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 Debris Avalanche Flow Slide  29 6 5  16 0 2  26 4 5  28 4 5  9 2 0  Morphology  Unobstructed Channelized Impact  23 8 9  9 5 4  21 7 7  23 7 9  7 3 1  Material  Source  Rock Debris Chalk Loess  29 7 3 1  11 6 0 1  24 7 3 1  29 6 3 1  8 3 0 0  Path  Rock Debris Ash Clay Snow & Ice Talus  6 26 1 1 4 2  1 11 0 1 1 1  6 23 1 1 1 1  6 26 1 1 2 2  1 7 0 0 1 1  Saturation  Dry Wet Unknown  2 33 5  2 14 2  2 28 5  2 32 5  1 9 1  Trigger  Non-Violent & Rain Artificial Blast Earthquake Unknown  12 1 4 23  7 0 4 7  10 1 4 20  11 1 3 22  3 0 4 4  Age  Prehistoric Historic Modern (since 1900)  7 7 26  2 4 13  7 7 21  7 7 23  1 2 8  Table 3.4: Number of cases with specified characteristic and runout observation.  21  22  Landslide  Movement Type  Morphology  Material Source Path  Vi [Mm3 ]  Abbot’s Cliff Arth-Goldau Arvel Brazeau Lake Charmon´etier Claps de Luc Eagle Pass Elm Frank Slide Great Fall Hiegaesi Hope Slide Jonas Creek (north) Jonas Creek (south) Kuzulu La Madeleine Las Colinas Luzon Slide  flow slide rock avalanche debris avalanche rock avalanche debris avalanche rock avalanche debris avalanche rock avalanche rock avalanche flow slide rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche flow slide rock avalanche  unobstructed unobstructed unobstructed unobstructed channelized unobstructed impacted unobstructed unobstructed unobstructed unobstructed impacted unobstructed unobstructed channelized unobstructed impacted unobstructed  chalk rock rock rock rock rock rock rock rock chalk debris rock rock rock debris rock debris debris  0.28 24 0.61 4.5 0.13 2 0.07 30 30 1.25 50 47.3 2.1 4.5 12.5 71 0.1 20  debris rock debris debris debris rock debris debris debris debris ash debris rock rock debris debris debris debris  Trigger  rain non-violent rain  non-violent  rain  non-violent  earthquake  Saturation wet wet wet wet wet wet dry wet wet wet wet  wet wet dry wet  Table 3.5: Landslide characteristics observable prior to failure for case studies A-L. See Table 3.6 for M-Z.  23  Landslide  Movement Type  Morphology  Material Source Path  Vi [Mm3 ]  Trigger  Saturation  Madison Canyon McAuley Creek Mount Cayley Mount Cook Mount Granier Mount Ontake Mount Steele Mystery Creek Nomash River Pandemonium Creek Pink Mountain Queen Elizabeth Rockslide Pass Rubble Creek Sale Mountain Seaford Sherman snow & ice Six de Eaux Froids Slide Mountain Tozawagawa Triolet snow & ice Zymoetz River  rock avalanche rock avalanche debris avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche rock avalanche flow slide flow slide rock avalanche rock avalanche debris avalanche rock avalanche rock avalanche debris avalanche  impacted channelized unobstructed unobstructed unobstructed channelized impacted unobstructed channelized channelized unobstructed impacted unobstructed channelized unobstructed unobstructed unobstructed impacted impacted impacted channelized unobstructed  rock rock rock rock rock debris rock rock rock rock debris rock rock rock loess chalk rock rock rock debris rock rock  21.4 7.4 0.74 11.8 500 36 30 40 0.3 5 0.74 45 370 25 31 0.15 60 8.4 13 19 9.8 0.9  earthquake  wet wet wet wet wet wet wet  debris debris debris snow & ice debris debris snow & ice debris debris debris clay rock rock debris talus debris snow & ice debris debris debris snow & ice talus  non-violent rain earthquake  non-violent non-violent  non-violent blast earthquake  non-violent  wet wet wet wet wet wet wet wet wet wet wet wet wet  Table 3.6: Landslide characteristics observable prior to failure for case studies M-Z. See Table 3.5 for A-L.  Landslide Abbot’s Cliff Arth-Goldau Arvel Brazeau Lake Charmon´etier Claps de Luc Eagle Pass Elm Frank Slide Great Fall Hiegaesi Hope Slide Jonas Creek (north) Jonas Creek (south) Kuzulu La Madeleine Las Colinas Luzon Slide Madison Canyon McAuley Creek Mount Cayley Mount Cook Mount Granier Mount Ontake Mount Steele Mystery Creek Nomash River Pandemonium Creek Pink Mountain Queen Elizabeth Rockslide Pass Rubble Creek  D [m]  2000  2300 8000 4100 1280  7500 7500 1300 7000 4000 9000 2000 3000 6900  L [m]  H [m]  α [◦ ]  Le [m]  Le /L [ %]  442 6025 363 2700 600 800  145 1265 258  210 4001 -48 2700 -232 208  48 66 -14 100 -39 26  2017 3500 628 67 4240 3250 2500 3300 4500 715 3800 1300  613 760 150 25 1220 880 920 950 1561 160 810 340  1036 2284 388 27 2288 1842 1028 1780 2002 459 2504 756  51 65 62 40 54 57 41 54 44 64 66 58  3460  1180  18 12 35.5 18 40.9 25 31 16 14 13 11 16 17.1 26.5 16 19 12.6 12 13 10 19  1572  45  520 370  vavg [m/s]  vmax [m/s]  70  50 28  83.5 45  8  14  35  130 50 70  55 7690 400 5760 4000 2270 8600 1950 2645 6330 4500  1520  12  1860 1250 560 2000 450 950 1000 1060  18 15 13.5 13 11.6 20 8.5 13  5257 400 2783 1999 1374 5399 1230 1125 4730 2804  68 100 48 50 61 63 63 43 75 62  22 65  31.7  30  20 20  70  Table 3.7: Mobility characteristics for case studies A-R. See Table 3.8 for S-Z.  24  Landslide Sale Mountain Seaford Sherman Glacier Six de Eaux Froids Slide Mountain Tozawagawa Triolet Glacier Zymoetz River  D [m]  L [m]  H [m]  1120 5700  1600 121 5950  320 68 1080  454 9000  1650 100 7200  420 230 1860  α [◦ ] 11 28 10 16 14 66 14.5 17  Le [m]  Le /L [ %]  vavg [m/s]  1088 12 4222  68 10 71  19.8  978 -268 4223  59 -268 59  vmax [m/s]  26  67  35  44 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 danger 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. Accurate 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 1 Please  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 assumptions than direct measurements, but for landslides, direct experiment is difficult, dangerous, expensive, and of limited utility. Landslides are frequently heterogeneous – an experimenter 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 experiments 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 adjusting 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 outcomes, 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 laboratory tests.  4.1.1  Laboratory Models  Small-scale laboratory models of landslides are incredibly valuable for investigating scaleindependent effects (Denlinger & Iverson, 2001) but are limited by the difficulty of accounting 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 materials. 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 phenomenon. 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 underlying 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 . 2 A 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 observations 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 initial 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 detachment 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-toone 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 Fahrb¨oschung Angle Extensive research has correlated failure volume (V ) to fahrb¨oschung angle (α) with data sets of various sizes and scopes (Scheidegger 1973; Hs¨u 1975; Lucchitta 1978; Corominas 1996; Rickenmann 2005; and many others). Relationships are of the form: log10 tan α = (intercept) + (slope) log10 V  (4.1)  Scheidegger’s work is notable as an early example of calculating a relationship between volume and fahrb¨oschung 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 3 For  landslide runout, a typical pairing is volume correlated with some runout index such as the fahrb¨oschung angle. 4 For more examples, see the review paper on statistical modelling by Rickenmann (2005).  29  regression to use volume to predict the fahrb¨oschung angle. Corominas (1996) analyzed 204 landslides, differentiated into subcategories first by movement then by path morphology, 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 with V -α relationships predicting fahrb¨oschung 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 characteristics, 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 (Hs¨u 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 characteristics, 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 analytic solution. All dynamic models use physical and mathematical relationships, but must remain consistent 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 prediction, 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. 5 An exception is the flood modelling software FLO2D which, when adapted to model debris flows, describes motion but not initiation (OBrien et al., 2009). 6 Please 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 (H¨urlimann 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 (K¨orner, 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, tan θ = tan 32◦ ≈ 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 (Hs¨u, 1975): L = H tan θ  (4.2)  Coulomb’s Law works very well when applied to small-volume rockslides where movement 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 v2 = g(sin θ ) = (µm cos β ) − dt 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 ≥ tan θ , where as µm approaches tan θ the com-  puted runout distance is increasingly sensitive to small changes in µm . The model must be 7 Point 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. 8 As the mass is treated as a single point (the center of mass), within the model travel angle and fahrb¨ oschung 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. 9 In application, the slope angle is the travel angle, as the horizontal distance the block slides is H tan(β ) = L, which means by definition, β = θ . 10 Also 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 inclined 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 compute 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 analyzed directly. However, the simplicity of a point mass model allows analytical solutions, thus fast execution and analysis (H¨urlimann 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, incorporating both solid (dislocation along a failure surface) and fluid (continuous flow) deformation, which are characteristic of landslides (Hungr, 1995). Deformable mass models incorporate 11 Such  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 applying physical interactions to many mass-elements is too difficult for direct analytical relationships, 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 absorption 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, using 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. 12 Discussed  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 correlations 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 previous 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 mobility. 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 distribution, 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 1 Unusual events are those with either higher or lower than anticipated mobility for a given volume, extremely large volumes, or large impact on human settlements or activities.  36  Movement Type  Morphology  Volume  Scheidegger Corominas  no constraints debris avalanches, or debris flows  V ≥ 0.03 × 106 m3 no constraints  McKinnon  rock avalanches, debris avalanches, or flow slides  no constraints unobstructed, impacted, or channelized unobstructed, impacted, or channelized  V f inal ≥ 106 m3  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 models 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 analyzed here are limited to catastrophic events with volume V f 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 2 Both  of which are first discussed in Section 4.2.1. 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 3 Although  37  Scheidegger  Corominas  McKinnon  33  71  40  Unobstructed  -  18  23  Channelized  -  19  8  Impacted  -  29  9  All  Table 5.2: Number of events overall and in morphology subsets.  differences in classification systems, landslides where intact rock fragmented during failure are classified as debris avalanches by Corominas (using the Varnes 1978 classification system) 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 appears 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 predict 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 4 See  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  1  !  Tan Alpha  0.8  !  0.6  ! !  0.5  !  !  0.4  !  0.3  !  !  !  ! !  !  !  !  !  !  !  ! !!  !  0.2  ! !  !  ! ! ! ! !! !! ! ! !  !  !  0.1  McKinnon Scheidegger Corominas 104  105  106  107  108  109  1010  Vol(m3)  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 behaviour 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 the V -α regression 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  5 The 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 ttest 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 Corominas, yet it is highly unlikely that my landslides are drawn from the same population of events as those analyzed by Scheidegger (Table 5.4). A low p-value indicates decreasing overlap between the population of landslides used in my regression 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  Intercept  Slope  Scheidegger  +0.623  -0.157  Corominas  -0.012  -0.105  McKinnon  +0.055  -0.084  within that population.  Table 5.3: V -α relationships determined by linear regressions. See Equation 4.1 for form. degger indicates it is highly unlikely the differThe very low p-values when comparing to Schei-  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 population, 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. 6 See 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 intercept of my linear regressions versus 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 substantial terrain obstruction. When selecting a landslide dataset using similar constraints on scope as Corominas’s relatively recent and more statistically powerful sample, I independently 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 characteristics 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 comparable, 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 preceded 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 fahrb¨oschung 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 landslides, 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 observations 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 partitions (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 meaningful 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. 7 For  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 relationship 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). The sampled cases are relatively few in number compared to the number of categories  p-values for...  and options within the categories (partitions). Therefore, it is necessary to beware of coincidental relationships, where one characteristic 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  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  overpowers all other influences.  Table 5.5: P-values of ANOVA between characteristics and mobility controlled for volume. trolled, the pre-failure observable characterisWhen the influence of volume is con-  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 preevent 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 inter8 Order-magnitude categorization follows the recommendations of Jakob 2005 for classification of debris flows by volume. 9 For example, if all of the unobstructed morphologies also happen to be small-volume events, morphology could be a confounding proxy for volume. 10 See 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  Clusters for alpha to the number of data points, with one item in each group. N = 39  3000 2000  !  1000  Within groups sum of squares  4000  !  ! !  !  !  0  !  2  4  6  !  8  !  !  10  !  !  12  !  !  !  14  Number of Clusters  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 clusters 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 categorization 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 morphology 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 characteristics are underrepresented with only a few examples14 , and thus only identifies interesting areas for future study when B f actor is large relative to the base average. Influence on mobility is given using L, Le /L and α. If an effect is real, it should have an inverse impact on horizontal distance and fahrb¨oschung 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 11 Graphically,  as the intercept. an increase in runout is measured by an increase L and Le /L and decrease α. 13 For more discussion on the limitations and advantages of statistical models, see Section 4.2.1. 14 For example, this data set contains only one instance of material = loess; see Table 3.4. 12 Note:  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 V f inal ≥ 1 million m3 so a dataset without volume constraints should be analyzed to investigate if this constraint 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 mobility 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 mobility. 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 behaviour, with channelization increasing mobility and impact decreasing mobility. This trend does not remain constant across maximum velocity, with events in unobstructed terrain travelling 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 observed morphology (unobstructed) is also the least likely to produce maximum velocity estimates 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 either substantial run-up against adverse slopes, or channelization around bends, velocity estimates come from direct observation by eyewitnesses. Therefore, as unobstructed morphologies 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 channelized runout, or only free runout, or only frontal impact impeding runout), statistical models 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 double 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 turbulence 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 behaviour 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 analysis 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 earthquakes triggers and mobility is established, it will not directly support theories of reducing 15 Again, due to the limited nature of case studies with large volumes, this may only be possible by including events with smaller volumes. 16 See 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 analyzed 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 population 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, morphology, 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 volumes 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  Movement Type  Rock Avalanche Debris Avalanche Flow Slide  1544  Unobstructed  1635  Morphology  Factor  BL [m]  15 -704 977  Source  Rock Debris Chalk Loess  Path  Rock  2124  50 Dry  1060 Wet  Trigger  Non-Violent  56  1857 Rain Artificial Blast Earthquake  3.1 -2.7 -4.7 71  15.2  -10  -15 -37 78  6.1 19.1  -17 -29 12  0  -0.3 -5.3 -10.9 -3.1 -5.6  -26 44  110 -650 -980  -41 -22 49  22.1 -17 -11 20 6 15  818  62  20.9  44  15  -0.7 5.9  -43 0 17  -468 -4232 -6 2367 -2433  53  19.7  42  Bv [m/s]  5.0 -4.5  -3 -44  -2071 -1782 -2668  Debris Ash Clay Snow & Ice Talus Saturation  36 15  1221 -800 2642  Bα [◦ ] 20.5  42  Channelized Impacted Material  BLe /L [%]  -28 41  3.7 6.4 -2.2  24  Table 5.6: Base average and influencing factor for a characteristic (independent variable) 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.  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 expert practitioner attempts to select the most appropriate modelling tool to produce the best prediction of the expected event (Erismann, 1986). Each mathematical model has different 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 practitioner 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 distribution 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, flowing 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 predicting 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 internal 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, transportation 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 flexibility 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 cohesive 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 compensate 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, 1 See Section 4.2.2 for additional examples of dynamic models, and Section 3.1 for the scope of landslides analyzed for this project. 2 Discussed 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 hazardous 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 (Hs¨u, 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 DAN models 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 (H¨urlimann 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 tan ϕb  (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: tan ϕb = (1 − ru ) tan ϕ 3 See  (6.2)  Section 4.2.2. Hungr (1995) or McDougall & Hungr (2004) for more detailed descriptions of the concept of hypothetical fluids. 4 See  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 hypothetical 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 = σu 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 (K¨orner, 1976; Hungr et al., 2005; McDougall, 2006).  6.2.2  Voellmy  The Voellmy rheology combines frictional and turbulent models such that increasing velocity results in increased drag (K¨orner, 1976) Mathematically, this is expressed as: ρgνx 2 τzx = −σz f + 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 implicitly 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 simulations of velocity than frictional rheology (K¨orner, 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 debris 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 landslide 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 duplicating 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 presented back analyses, producing a dataset that is internally consistent. Although other authors 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 velocity 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 measurable in the field or laboratories experiments. Instead, model parameters must be determined 1 Both  these techniques are discussed in more detail in Section 7.1.4 and Section 8.1. cases where the toe is subject to erosion, such as landslides damming rivers. 3 Please see Section 3.1.3 for details. 4 See Section 6.2 for details. 2 Excepting  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 observations 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 constructed. 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 literature 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 time interval smoothing coefficient tip ratio stiffness coefficient stiffness ratio centrifugal forces boundary block geometry pressure term  50 0.02-0.1 s 0.02 0.5 0.05 5 on normal modified  internal friction angle unit weight  35◦ 20  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 prac5 Profiles  are included along with case descriptions in Appendix E.  59  ticality, the friction angle is adjusted in ∆θb = 1◦ intervals, the friction coefficient is ad3 justed in ∆ f = 0.01 intervals, and turbulence coefficient ∆ξ = 100 m s intervals. In the two-parameter Voellmy rheology, first f is adjusted to alter runout distance, then ξ to adjust 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 = 3 m3 m3 m3 100 m s and 500 s ≥ ξ ≥ 2000 s in ∆ξ = 500 s intervals. These models were all run without entrainment, as the purpose is not to create a detailed back analysis (as with userselected 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 6 See  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 technique is severely hampered by the limitation of selecting parameters based entirely upon only one observed characteristic, when other characteristics may be vitally important to accurately 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 parameters, 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 observation 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 fahrb¨oschung angle α = 13◦ .The rock avalanche left a deposit 1500 m wide(Hungr, 1995; Trunk & Dent, 1986).  61  800 Width (m) 400  1900  600  2000  2100  Height (m.a.s.l.)  2200  1000  2300  1200  Madison Canyon  0  500  1000  1500  Distance (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 Observed Rheology  θb  Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  15 16 17  f  0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.27 0.27 0.28 0.28 0.3 0.3 0.3  ξ  100 500 1000 1500 2000 4000 4500 5000 500 1000 4000 500 4000 500 1000 500 1000 4000  L  Le  α  vmax 50 m/s  1280 m  1300 m  756 m  13◦  ∆D  ∆L  ∆Le  ∆α  ∆vmax  11 7 2 3 16 18 20 21 23 24 24 7 11 14 4 11 3 7 -0 3 5  -0 -4 -8 -7 4 7 8 9 11 12 12 -3 0 3 -7 -0 -8 -4 -11 -7 -6  7 -3 -12 -10 20 27 31 32 40 41 42 -0 9 16 -8 7 -11 -2 -18 -10 -6  1.4 10.0 18.5 16.4 -9.8 -15.9 -19.5 -20.5 -26.3 -26.9 -27.7 8.1 -0.2 -6.7 14.7 1.4 18.0 9.8 25.0 16.4 13.3  -17 -20 -24 -34 -6 -7 -5 -5 -4 -4 -4 -13 -6 -13 -15 -17 -17 -11 -20 -14 -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 3 turbulence coefficient (ξ = 4000 ms ) 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 3 when using f = 0.2−0.25, ξ = 1000 ms 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 fahrb¨oschung angle, and velocity are with an extremely low friction angle (θb = 10◦ ), or with slightly lower friction coefficients than with the user-selected data 3 ( f = 0.15, ξ = 1000 ms ).  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  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ● ●●  ●● ●  ● ●● ● ●  600  800  1000  ●  ● ●  ●  ●  ●  ●  ●  ● ●  ●  10  ●  10  ●  1200  ●  ● ●  ●  ● ●  ● ●  1400  10  ● ●  ● ●●  ●  ●  ●  ●  ●  ● ●  15  20  (b) α  (a) L  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ● ●●  ●  ● ●● ● ●  ● ●  800  1000  1200  ● ●● ●  10  ●  10  friction angle  25  ●  ●  ●  ●  ●  ●  ●  ●  ● ●  ● ●● ● ●  ● ●  ● ●  1400  0  (c) D  10  20  30  40  ●●● ●  50  ● ●●●  60  (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 parameters and a new method of quantitative mathematical parameter selection for back analyses 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 landslide 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 extremely flexible, involving so many subjective choices that the selection of a best rheology and associated parameters may vary substantially between practitioners. The cases pre66  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 decreasing 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 simplicity only one target observation is evaluated at a time for this study. The normalization is quantified as a percentage: normalized index (∆) =  indexmodelled − indexreal × 100 indexreal  (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 projections in engineering design. A negative normalized index implies under-estimating of the mobility index and a positive 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% indicates 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), 1 Listed  in Section 7.1.3.  67  Index ∆α [%] ∆L [%] ∆Le [%] ∆D [%]  Stable  Under-Predict  Exactly-Predict  Over-Predict  ( αobs − 1) × 100 −100 Lobs ( Le obs − 2) × 100 −100  ≥0 ≤0 ≤0 ≤0  0 0 0 0  ≤0 ≥0 ≥0 ≥0  90◦  Table 8.1: Interpretation of normalized runout for mobility indices. An event is overpredicted 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 mathematicallyselected 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 overand under-predicted runout. Debris Distribution One of the advantages of user selected parameters over mathematically selected parameters 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 produce 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 distribution is inconsistent with the observed distribution. 2 In 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. However, because this is an average, the variation may be quite high: a model that vastly overpredicts 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. 3 The  difference from 30% to 40% is 10 percentage points. that regularly produce stable models have extremely low variance, but are not of practical application, and thus are excluded from this discussion. 4 Parameters  69  θb [◦ ]  f  15 17 0.05 0.1 0.1 0.1 0.15 0.15 0.15 0.2  ξ 3 m [ s ]  ∆L [%]  σ∆L [%]  ∆D [%]  σ∆D [%]  ∆α [%]  σ∆α [%]  100 100 500 1000 1000 1500 2000 2000  2 -6 4 -5 9 17 7 14 13 4  45 47 46 46 45 45 44 43 43 44  14 -23 11 -12 4 15 -5 6 3 -9  38 36 80 50 59 70 48 53 50 41  16 26 19 32 11 3 13 5 5 16  60 66 44 48 49 46 50 51 49 54  Table 8.2: Mean normalized runout (∆), and standard deviation (σ ) of that mean for the specified mobility indices (with ∆L ≤ 100%). Cases with... θb f ξ 3 m ◦ [ ] [ s ] 15 17 0.05 0.05 0.05 0.1 0.15 0.15 0.15  100 500 1000 500 1000 1500 2000  |∆L| ≤ 5% 30% [%] [%] 14 14 14 11 14 17 14 8 11  60 49 57 60 54 60 63 56 63  |∆D| ≤ 5% 30% [%] [%] 6 17 17 17 28 17 11 6 11  50 50 67 31 56 56 50 50 61  |∆α| ≤ 5% 30% [%] [%] 23 5 8 18 8 21 13 25 10  64 49 56 67 67 69 74 68 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  3  f 0.05 0.1 0.15 0.2  100  500  x  x x  ξ [ ms ] 1000 1500 x x x x  2000  x x  Table 8.4: Low f paired with high ξ over-predict mobility (green), mid-range parameters 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), 3 and velocity increases from left to right (ξ = 2000 ms = 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 modelled 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 Table 8.3. Neglecting velocity observations to constrain the turbulence coefficient, runout is 3 most often well-modelled with ξ = 500 m s . The difference in under-predicted and over-predicted landslide mobility may have substantial impact on decision-making. Therefore, I also identified parameters that most often over-predict, under-predict, or predict mobility to ±10% of observed mobility (Section 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 angle, 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 turbulence 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 3 coefficients is ξ = 1500 m s . 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 angle 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 3 the turbulence coefficient ξ = 500 m , most events are modelled to within ±30% for both s  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 morphologies, 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 diversity 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 determine 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. 5 In 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  θb [◦ ]  Cases with... f ξ 3 m [ s ]  15 17  73  0.05 0.05 0.05 0.1 0.1 0.1 0.15 0.15 0.2 0.2  100 500 1000 500 1000 1500 500 1000 500 1000  −10% [%]  ∆L ↔ [%]  +10% [%]  −10% [%]  ∆D ↔ [%]  +10% [%]  −10%  ∆α ↔  +10%  31 23 37 49 57 37 46 56 34 37 17 29  29 29 23 26 26 23 26 25 14 20 23 29  40 49 40 26 17 40 29 19 51 43 60 43  28 11 22 44 50 33 39 50 28 28 22 22  28 33 39 28 28 22 22 17 22 17 17 28  44 56 39 28 22 44 39 33 50 56 61 50  44 62 51 31 21 41 31 18 56 36 67 59  31 21 21 31 38 28 23 20 18 38 21 15  26 18 28 38 41 31 46 62 26 26 13 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%).  $\theta_{b} = 17 ^{\circ}$  $\theta_{b} = 17 ^{\circ}$  !"  6  (30%,50%)  (70%,80%)  >90%  (70%,80%)  >90%  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  >90%  (70%,80%)  (30%,50%)  (30%,50%)  (a) ∆L  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  0  0  2  4  Frequency  6 4 2  Frequency  8  8  10  10  !L  $\theta_{b} = 17 ^{\circ}$  (b) ∆α!vmax  $\theta_{b} = 17 ^{\circ}$  6 4  Frequency  6  2  4  (c) ∆D  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  >90%  (70%,80%)  (30%,50%)  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  0  0  2  Frequency  8  8  10  10  !D  (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 Section H.6 for other models.  74  $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$  $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$  !L  8  (30%,50%)  (70%,80%)  >90%  (30%,50%)  (70%,80%)  >90%  (−10%,10%)  $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$  $f = 0.1 $, $\xi = 500 \frac{\mbox{m}^{3}}{\mbox{s}}$  !D  !vmax  (b) ∆α  6  (c) ∆D  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  >90%  (70%,80%)  (30%,50%)  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  0  0  2  2  4  4  6  Frequency  8  8  10  10  (a) ∆L  Frequency  (−50%,−30%)  (−90%,−70%)  <−90%  >90%  (70%,80%)  (30%,50%)  (−10%,10%)  (−50%,−30%)  (−90%,−70%)  <−90%  0  0  2  2  4  6  Frequency  6 4  Frequency  8  10  10  !"  (d) ∆vmax  Figure 8.2: Histogram of the performance of Voellmy rheology with f = 0.1 and ξ = 3 500 ms 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 parameters 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 ∝ tion H.2 for complete data.  1 Vi ).  See Sec-  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 categories 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 extremely 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 velocities), 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 mor6 No channelized debris avalanches are represented in my sample, as by definition those events are more likely debris flows. 7 My 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 coefficients are preferred. Cases with channelized morphologies are best modelled with midrange friction and turbulence coefficients, while cases with impacted morphologies are best 3 modelled with f = 0.1 − 0.15, ξ = 1500 m s . 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 = 3 1000 m 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 generalize 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 subjective 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  All  15-17  0.05 0.1 0.15  ξ 3 [m s ] 100 500 1000  0.15 0.1 0.2  500-1500 100 1500  0.1 0.15 0.2 0.1-0.15  500 1000 1000-2000 1500  0.05, 0.15 0.05  1500 100  Volume Decreasing Increasing Movement Type Rock Avalanches Flow Slides  ↑ ↓ 10-15 15-20  Morphology Channelized Unobstructed Impacted Material Rock Debris  ↑ ↓  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 observations 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 rheology, 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 coefficient. 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 3 reflect higher maximum velocities. If not velocity constraint is possible, ξ = 1500 ms produces 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 prediction, 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 sufficient 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 mechanisms. 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 similar 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 expectations for normalized mean runout, and deviation from that mean (Table 8.6). By forwardmodelling the target event using ranges of parameters associated with different probable conditions, a preliminary hazard map may be rapidly constructed for use in risk management. Although future research into mathematical selection of rheology by debris distribution, 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 compensated 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 quantitative 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 include 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 eventual formal model verification using cross-validation, while analyses performed using other software models may be more easily compared in higher-level analyses of the applicability 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 parameters 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 adjusted). Emergent groups of events with similar mobility behaviour yet dissimilar (or at least not obviously similar) physical characteristics potentially share underlying mechanical 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 research. 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 crossvalidation 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 characteristics, 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 judgement 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 parameters. This allows for rapid first-order forward modelling of new events by following recommendations 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 performance across landslides. 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Acoustic fluidization: a new geologic process? Journal of Geophysical Research, 84, 7513–7520. → pages 8 Milne, A. (1988). Winnie the Pooh. McClelland & Stewart Ltd. → pages xxxiv Miyazaki, M., Ueno, T., & Unoki, S. (1961). Theoretical investigations of typhoon surges along the Japanese coast. Oceanographical Magazine, 13(1), 51–75. → pages 103 Moore, D., Mathews, W., Shilts, W., Nickling, W., Naqvi, S., Rao, V., Hussain, S., Narayana, B., Rogers, J., Satyanarayana, K., et al. (1978). The Rubble Creek landslide, southwestern British Columbia. Canadian Journal of Earth Sciences, 15(7), 1039–1052. → pages 156 Moriwaki, H., Inokuchi, T., Hattanji, T., Sassa, K., Ochiai, H., & Wang, G. (2004). Failure processes in a full-scale landslide experiment using a rainfall simulator. Landslides, 1(4), 277–288. → pages 27 Nichol, S. L., Hungr, O., & Evans, S. G. (2002). Large-scale brittle and ductile toppling of rock slopes. Canadian Geotechnical Journal, 39(4), 773. → pages 148 Nicks, S. (1975). Landslide. Song. → pages 4 Nicoletti, P., & Sorriso-Valvo, M. (1991). Geomorphic controls of the shape and mobility of rock avalanches. Bulletin of the Geological Society of America, 103(10), 1365. → pages 9, 16, 17, 30, 46 Noetzli, J., Huggel, C., Hoelzle, M., & Haeberli, W. (2006). GIS-based modelling of rock-ice avalanches from Alpine permafrost areas. Computational Geosciences, 10(2), 161–178. → pages 163 Ochiai, H., Okada, Y., Furuya, G., Okura, Y., Matsui, T., Sammori, T., Terajima, T., & Sassa, K. (2004). A fluidized landslide on a natural slope by artificial rainfall. Landslides, 1(3), 211–219. → pages 27  93  Okura, Y., Kitahara, H., Ochiai, H., Sammori, T., & Kawanami, A. (2002). Landslide fluidization process by flume experiments. Engineering Geology, 66(1-2), 65–78. → pages 27 Okura, Y., Kitahara, H., & Sammori, T. (2000a). Fluidization in dry landslides. Engineering Geology, 56, 347–360. → pages 100, 101, 102, 103 Okura, Y., Kitahara, H., Sammori, T., & Kawanami, A. 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The effect of the earth pressure coefficients on the runout of granular material. Environmental Modelling & Software, 22(10), 1437–1454. → pages 109 Poisel, R., Preh, A., & Hungr, O. (2008). Run out of landslides - continuum mechanics versus discontinuum mechanics models. Geomechanik und Tunnelbau, 1(5), 358–366. → pages 100, 101 Pollet, N., & Schneider, J.-L. (2004). Dynamic disintegration processes accompanying transport of the Holocene Flims sturzstrom (Swiss Alps). Earth and Planetary Science Letters, 221(1-4), 433–448. → pages 9, 135 Potter, D. (1973). Computational physics. Wiley New York. Lagrangian reference frame. → pages 101 Prochaska, A. B., Santi, P. M., Higgins, J. D., & Cannon, S. H. (2008). A study of methods to estimate debris flow velocity. Landslides, 5, 431–444. → pages 13 Reznick, B. (1994). Some thoughts on writing for the putnam. Mathematical thinking and problem solving, (pp. 19–29). → pages 104 94  Rickenmann, D. (2005). 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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 models in how they treat scale, composition, internal deformation, coordinate systems, dimensionality, and continuity.  A.1 Scale Models must be used to investigate behaviours on scales equal to or greater than the representative 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). 1 See 2 An  Section A.3.2. 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 heterogeneous (“distributed state”) mass compositions. The failure mass may be homogeneous, with a non-varying rheological composition, reducing computational intensity at the expense of accuracy. The failure mass may instead be heterogeneous, with each element within a system separately described with spatially varying rheological composition, increasing 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 distinct 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 continuum 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 landslides as a single externally deformable mass that is not internally deformable. Mathematical solutions use finite-element and finite-difference techniques applied to mass and momentum 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 continuum models 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). 3 Another  technical use of “lumped”, not to be confused with “lumped mass” models. called “continuous mass” models, or, confusingly, “lumped mass models” for “lumping” the masselements together, in contradiction to the term’s use in describing point-mass models as described in Section 4.2.2. 4 Also  100  A.3.2  Discontinuum Models  Discontinuum models5 treat landslides as an assembly of interacting particles rolling, bouncing, 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 (Walton, 1993), but with variable element size, even very small topographic and structural details may be retained, reducing the danger of over-simplifying the model. Discontinuum models permit internal deformation, allowing for toe deformation (Evans et al., 1994), distinguishing between landslides where internal layout is preserved or deformed into a sheet of jumbled debris (Hs¨u, 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 between 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 example is the DAN3D application of smooth particle hydrodynamics, where a continuous body of individual mass-elements interacts through the application of hydrodynamic relationships7 .  A.4 Eulerian and Lagrangian Coordinate Systems The classes of mathematical solutions to the kinematic equations may use Eulerian or Lagrangian coordinate systems, and be 1-, 2-, or 3-dimensional solutions. Eulerian coordinates 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 reference 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 5 Also  called “discontinuous mass,” “discrete mass,” or “granular” models. called “coupled” models. 7 Please see Section C.5 for more details. 6 Also  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 depthaverage 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 hydrodynamics (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 displacements or deformations can excessively distort the mesh (Crosta et al., 2006) reducing accuracy of the output. Examples of continuous models utilizing mesh computational tech102  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 models 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. Although calibration of any tool is logical, software models are instead verified through crossvalidation. Cross-validation is a method of testing the hypothesis, “Inputing specific parameters 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 validation 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 verification 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 backanalysis 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 parameters. 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 statistical 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 parameters 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 parameter 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 possible 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 parameters. 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 verification 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 comparisons 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.  2 Although 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 hydrodynamics. 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 overriding 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 densities 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 velocity 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 consistent 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 exponential growth rate E, which may be determined through trial-and-error or a priori calculation: ∂b = Ehv ∂t where the bed erosion velocity  ∂b ∂t  (C.1)  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. Shallow 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 stressfree1 . 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). 1 See Hungr (2009) for a more in-depth discussion of the assumptions in determining internal stress conditions.  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 03-032009. 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 deformable blocks to calculate runout along a user-prescribed 2-dimensional3 flow path (Figure C.1). The analyses in this thesis are performed with DAN-W version 9.0 updated 0303-2009.  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 momentum loss. The user-input path and width are fixed, which does not truly reflect conditions 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 conditions 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  width depth  > 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 2 See  Pirulli, Bristeau, Mangeney, & Scavia (2007) for greater discussion on the importance of using the appropriate earth pressure equations. 3 Technically, a 2 1 - or quasi-3-dimensional as the model permits manually-input widths. 2  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 hydrodynamics to calculate runout along a user-prescribed 3-dimensional digital elevation model. The analyses in this thesis are performed with DAN3D beta version updated 06-132006. (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), Tozawagawa 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  -0.072 112  Table 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.  T-test on... Scheidegger Corominas Unobstructed Channelized Impact  p-values Except Tozawagawa Events since 1900 Intercept Slope Intercept Slope 0.02 0.43  0.00 0.74  0.08 0.94  0.13 0.55  0.25 0.29 0.29  0.80 0.48 0.83  0.38 0.36 0.50  0.67 0.49 0.61  Table D.2: P-values from t-testing the regression coefficient and intercept of my modified 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  Clusters for alpha N = 25  2000 1000  Within groups sum of squares  3000  !  ! !  !  0  !  2  4  !  !  6  !  8  !  !  10  !  !  12  !  !  !  14  Number of Clusters  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  5  Normal Q−Q  2  5! !  1  Standardized residuals  3  4  37 !  ! !! ! !  0  !  −1  ! ! ! !  !  !!  ! !!  ! !!! !!! ! ! ! !!! !!  !  !  !  !  ! 16  −2  −1  0  1  Theoretical Quantiles lm(log10(tan(d2$alpha * (pi/180))) ~ log10(d2$volume_initial))  2  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: Charmon´etier (Section E.5), Las Colinas (Section E.16), and Tozawagawa (Section E.37).  115  5  Residuals vs Leverage  4  ! 37  2  0.5  5!  1  ! ! !  !  !  ! ! ! ! ! !! !! !! ! ! ! !  −1  !  !  !  0  Standardized residuals  3  1  ! !  !  ! !  ! ! !  ! !  !  !  16 !  −2  Cook's distance 0.00  0.02  0.04  0.06  0.08  0.10  0.12  Leverage lm(log10(tan(d2$alpha * (pi/180))) ~ log10(d2$volume_initial))  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 influence the regression strongly. Case numbering is alphabetical: Charmon´etier (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 associated 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  Width = 127 m  80 60 40 20 0  Height (m.a.s.l.)  100  120  horizontal length L = 442 m and dropped a vertical height H = 145 m, with a fahrb¨oschung Abbots Cliff angle α = 18◦ (Hutchinson, 2002).  0  100  200  300  Distance (m)  Figure E.1: Abbot’s Cliff profile. For back analyses, see Table F.1 and Table G.1.  118  400  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 fahrb¨oschung 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).  2000 1500 Width (m)  1200 1000  1000  800  500  600 400  Height (m.a.s.l.)  1400  2500  1600  Goldau  1000  2000  3000  4000  Distance (m)  Figure E.2: Arth-Goldau profile. For back analyses, see Table F.2 and Table G.2. 119  5000  6000  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 Rhˆone River. The mass travelled horizontal length L = 337 m and dropped a vertical height H =240 m, with a fahrb¨oschung 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  Width = 100 m  500 450 400  Height (m.a.s.l.)  550  600  infrastructure damage included destroyed sheds and a cable car, and damage to roads, a railway line, and water channel (Locat et al., Arvel 2006; Crosta et al., 2009).  100  200  300 Distance (m)  Figure E.3: Arvel profile. For back analyses, see Table F.3. 120  400  500  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 fahrb¨oschung 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  450 500 Width (m) 400  2200  350  2000  300  1800  Height (m.a.s.l.)  2400  550  600  2600  conical molards, with minor distal thickening to 5-8 m at the toe. The deposit diverted the Brazeau Lake creek from the southeast of the fan to the northwest (Cruden, 1982).  0  500  1000  1500  2000  Distance (m)  Figure E.4: Brazeau Lake profile. For back analyses, see Table F.4 and Table G.3.  121  2500  E.5  1987 Charmon´etier, Is`ere, 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  600 800 Width (m)  1000  400  900  200  800 700  Height (m.a.s.l.)  1100  1000  1200  1200  m, with a fahrb¨oschung angle α = 41◦ . The landslide left a talus cone deposit (Locat et al., Charmonetier 2006; Couture et al., 1997).  0  200  400 Distance (m)  Figure E.5: Charmon´etier profile. For back analyses, see Table F.5.  122  600  E.6  1442 Claps de Luc, Drˆome, 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  Width = 1050 m  800 700 600  Height (m.a.s.l.)  900  H = 370 m, with a fahrb¨oschung angle α = 25◦de (Locat Claps Lucet al., 2006; Couture et al., 1997).  0  200  400  600  Distance (m)  Figure E.6: Claps de Luc profile. For back analyses, see Table F.6.  123  800  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 V f = 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 fahrb¨oschung 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).  150 100 Width (m)  900 800  50  700 600  Height (m.a.s.l.)  1000  1100  200  Eagle Pass  200  400  600  800  Distance (m)  Figure E.7: Eagle Pass profile.  124  1000  1200  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 significant 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 fahrb¨oschung 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  300 350 Width (m)  1300 1200  250  1100  200  1000  Height (m.a.s.l.)  1400  400  1500  450  avalanche killed 115 people (Heim, 1932; Hs¨ u, 1978; Eisbacher & Clague, 1984). Elm  0  500  1000  1500  Distance (m)  Figure E.8: Elm profile.  126  2000  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 fahrb¨oschung 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;  1600 1200 1400 Width (m)  1800  800  1400  1000  1600  Height (m.a.s.l.)  2000  1800  Cruden & Hungr, 1986; Locat et al., 2006). Frank Slide  500  1000  1500  2000  2500  Distance (m)  Figure E.9: Frank Slide profile. For back analyses, see Table F.9. 128  3000  3500  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 fahrb¨oschung angle α = 13◦ (Hutchinson, 2002).  Width = 590 m  100 50  Height (m.a.s.l.)  150  200  Great Fall  0  200  400 Distance (m)  Figure E.10: Great Fall profile. For back analyses, see Table F.10 and Section G.6.  129  600  800  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.  Width = 23 m  10 5 0  Height (m.a.s.l.)  15  20  The mass dropped a vertical height H = 25 m with a fahrb¨oschung angle α = 11◦ (Wang Hiegaesi et al., 2002).  0  20  40  60 Distance (m)  Figure E.11: Hiegaesi profile. For back analyses, see Table F.11.  130  80  100  E.12  1965 Hope Slide, British Columbia, Canada  On 9 January 1965, V = 47.3 million m3 of metamorphic rock and snow failed from southwest 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 opposite 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 fahrb¨oschung 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  1000 Width (m)  1200  500  1000 800  Height (m.a.s.l.)  1400  1500  1600  2000  1800  4 fatalities (Bruce & Cruden, 1977; Mathews McTaggart, 1978). Hope&Slide  0  500  1000  1500  2000  Distance (m)  Figure E.12: Hope Slide profile.  131  2500  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 fahrb¨oschung 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 fahrb¨oschung 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). Jonas Creek (north)  650 600 550 Width (m)  2200  450  1800  0  500  1000  1500  2000  2500  3000  400  1600  1600  400  1800  500  2000  500 Width (m) Height (m.a.s.l.)  2200 2000  Height (m.a.s.l.)  600  2400  2400  700  700  2600  Jonas Creek (south)  500  Distance (m)  1000  1500  2000  Distance (m)  (a) (north)  (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 fahrb¨oschung angle α = 16◦ . The deposit dammed the river  500 400 Width (m) 300  1200  100  200  1000 800  Height (m.a.s.l.)  1400  600  1600  700  to an average thickness of 25-30 m (YilmazKuzulu et al., 2006; Ulusay et al., 2007).  0  500  1000  1500  2000  Distance (m)  Figure E.14: Kuzulu profile. For back analyses, see Table F.15. 134  2500  3000  E.15  La Madeleine, Savoie, France  Approximately 7,600 years ago, Vi 71 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 V f = 125 million m3 . The mass travelled horizontal length L = 4500 m and dropped a vertical height H = 1561 m, with a fahrb¨oschung 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;  Width = 600 m  2000 1500  Height (m.a.s.l.)  2500  3000  Pollet & Schneider, 2004; Locat et al., 2006). La Madeleine  0  1000  2000  3000  Distance (m)  Figure E.15: La Madeleine profile. For back analyses, see Table F.16.  135  4000  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 volcanic tephra from the northern flank of B´aslamo 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 entrained 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 V f = 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 fahrb¨oschung 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  120 80 100 Width (m) 40  950  60  1000  Height (m.a.s.l.)  1050  140  Colinas event resulted in 485 fatalities (Crosta etLas al., 2005).  0  200  400  600  Distance (m)  Figure E.16: Las Colinas profile. For back analyses, see Table F.17 and Section G.8. 136  800  1000  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 V f = 20 million m3 . The event flowed over the village and dammed at least four streams. The material ran out over D = 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  200 Width (m) 150  400  100  200 0  Height (m.a.s.l.)  600  250  800  (Lagmay et al., 2006; Catane et al., 2007; EvansSlide et al., 2007). Luzon  0  1000  2000  3000  Distance (m)  Figure E.17: Luzon Slide profile.  137  4000  5000  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 fahrb¨oschung angle  800 Width (m)  2100  600  2000  400  1900  Height (m.a.s.l.)  2200  1000  2300  1200  α = 13◦ .The rock avalanche left a deposit 1500 m wide (Hungr, 1995; Trunk & Dent, 1986). Madison Canyon  0  500  1000 Distance (m)  Figure E.18: Madison Canyon profile.  139  1500  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  300 Width (m)  1300 1200  200  1100  100  1000  Height (m.a.s.l.)  400  1400  500  1500  glacial till in a 1.6 km long, thin distal deposit to a fahrb¨oschung angle α = 10◦ . (Evans McAuley Creek et al., 2003; McDougall, 2006).  0  500  1000  1500  Distance (m)  Figure E.19: McAuley Creek profile. For back analyses, see Table F.20.  141  2000  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 V f = 1.08 million m3 . The material reached a maximum velocity of 70 m/s. Superelevation indicates the material 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 fahrb¨oschung angle α = 19◦ (Evans et al., 2001; Hungr, 2006).  150 200 Width (m)  1200 1000  100  800 600  50  400  Height (m.a.s.l.)  1400  250  1600  300  Mount Cayley  0  1000  2000  3000  Distance (m)  Figure E.20: Mount Cayley profile. For back analyses, see Table F.21 and Section G.10. 142  4000  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 V f = 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  1500 Width (m)  2500  1000  2000 1000  500  1500  Height (m.a.s.l.)  3000  2000  3500  2500  velocity for the center of mass was 55 m/s, and Cook 60 m/s for the toe (McSaveney, 2002). Mount  0  2000  4000  6000  8000  Distance (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 from Mount 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 fahrb¨oschung 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  1500 2000 Width (m) 500  500  1000  1000  Height (m.a.s.l.)  1500  2500  3000  buried the town of St. Andr´e and possibly smaller hamlets, killing 1,500 to 5,000 people Mount Granier (Goguel & Pachoud, 1972; Cruden & Antoine, 1984; Eisbacher & Clague, 1984).  1000  2000  3000  4000  5000  6000  Distance (m)  Figure E.22: Mount Granier profile. For back analyses, see Table F.23 and Table G.15.  144  7000  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).  600 800 Width (m)  2200  200  400  2000  0  1800  Height (m.a.s.l.)  1000  2400  1200  1400  The mass ran out curvilinear distance D = 1.3 km, travelling horizontal length L = 400 Mount Ontake m.  0  1000  2000  3000  4000  Distance (m)  Figure E.23: Mount Ontake profile. For back analyses, see Table F.24.  145  5000  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 (although the maximum descent over the glacier was Hmax = 2160 m), with a fahrb¨oschung angle αdeposit = 18◦ . The rock avalanche ran out over a total area 3.66 km2 (Lipovsky et al., 2008).  1500 1000 Width (m)  3500 3000  500  2500  Height (m.a.s.l.)  4000  2000  4500  Mount Steele  0  2000  4000  6000  Distance (m)  Figure E.24: Mount Steele profile. 146  8000  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 presentday location of Highway 99. The material ran out over curvilinear distance D = 4 km with a fahrb¨oschung angle  800 900 Width (m)  1000  700  800  600  600  500  400  Height (m.a.s.l.)  1200  1000  1400  1100  1600  1200  α = 15◦ . The rock avalanche ran out over a total area of 1.2 km2 (Evans et al., 1994; Hungr Mystery Creek et al., 1999; Nichol et al., 2002).  0  1000  2000  3000  Distance (m)  Figure E.25: Mystery Creek profile. For back analyses, see Table F.26.  148  4000  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 V f = 0.66 million m3 . Superelevation indicates the material was traveling at 22.5 m/s at the first bend (at approximately 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 fahrb¨oschung angle α = 13.5◦ (Guthrie et al., 2003; Hungr & Evans, 2004).  150 200 Width (m)  600  100  500  0  50  400  Height (m.a.s.l.)  700  250  800  300  Nomash River  0  500  1000  1500  2000  Distance (m)  Figure E.26: Nomash River profile.  149  2500  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 fahrb¨oschung angle α = 13◦ . The deposit has distal  400 350 Width (m) 250  300  1500  200  1000  Height (m.a.s.l.)  2000  450  2500  500  thickening up to 20 m (Evans & Hungr, 1989). Pandemonium Creek  0  2000  4000  6000  8000  Distance (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 V f = 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 fahrb¨oschung 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  250 200 Width (m)  300 200  150  100 0  Height (m.a.s.l.)  400  500  300  a forestry road (Geertsema et al., 2006).Pink Mountain  0  500  1000  1500  Distance (m)  Figure E.28: Pink Mountain profile.  152  2000  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  Width = 500 m  2200 2000 1800  Height (m.a.s.l.)  2400  2600  and dam a lake. The mass travelled horizontal length L = 2645 m and dropped a vertical Queen Elizabeth height H = 950 m, for a calculated fahrb¨ oschung angle α = 20◦ (Locat et al., 2006).  0  500  1000  1500  Distance (m)  Figure E.29: Queen Elizabeth profile. For back analyses see Table F.30.  154  2000  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. Runup 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 fahrb¨oschung 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).  1500 Width (m)  800  1000  600  500  400  Height (m.a.s.l.)  1000  2000  1200  2500  The event is modelled as a block forRockslide the first 4.5 km. Pass  0  1000  2000  3000  4000  5000  Distance (m)  Figure E.30: Rockslide Pass profile. For back analyses see Table F.31 and Table G.18. 155  6000  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 height H = 1060 m, with a fahrb¨oschung angle α = 13◦ . The rock avalanche ran out over a total area 1.1 km2 , leaving a deposit 3.5 m long and 200350 m wide thickening up to 15 m. The event eventually led to a court ruling barring  1010 Width (m)  600  1005  400 0  1000  200  Height (m.a.s.l.)  800  1000  1015  residential development in the area (Moore et al., 1978; Hungr et al., 1999). Rubble Creek  0  1000  2000  3000  4000  Distance (m)  Figure E.31: Rubble Creek profile. For back analyses see Table F.32 and Table G.19. 156  5000  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 fahrb¨oschung angle α = 11◦ . The flow slide ran out over a total  800 600 Width (m)  2150  400  2100  200  2050  0  2000  Height (m.a.s.l.)  2200  2250  1000  area 1.3 km2 to an average thickness of 24 m. The deposit has proximal thickening up to Sale Mountain 70 m (Zhang et al., 2002).  0  500  1000 Distance (m)  Figure E.32: Sale Mountain profile. For back analyses, see Table F.33 and Table G.20. 157  1500  E.33  1850 Seaford, England  In 1850, an artificial blast triggered the failure of Vi = 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.  Width = 135 m  50 40 30 20  Height (m.a.s.l.)  60  70  80  The mass traveled horizontal length L = 121 m and dropped a vertical height H = 68 m, Seaford with a fahrb¨oschung angle α = 28◦ (Hutchinson, 2002).  50  100  150 Distance (m)  Figure E.33: Seaford profile. For back analyses see Table F.34 and Table G.21.  158  200  250  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 distance D = 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 fahrb¨oschung 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,  1500 Width (m) 500  400  1000  600  Height (m.a.s.l.)  800  2000  1000  2500  1966; Bull & Marangunic, 1966; McSaveney, Sherman1978). Glacier  0  1000  2000  3000  4000  5000  Distance (m)  Figure E.34: Sherman Glacier profile. For back analyses see Table F.35 and Table G.22. 159  6000  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 fahrb¨oschung angle α = 16◦ , and left a deposit 2000 m long and 400 m wide (Hungr & McDougall, 2009). Six de Eaux Froids (right)  400 Width (m) 300  400  200 Width (m) Height (m.a.s.l.)  300  200  0  500  1000  1500  0  0  100  200  100  150  200  Height (m.a.s.l.)  400  600  250  500  500  600  800  Six de Eaux Froids (left)  0  Distance (m)  500  1000  1500  2000  2500  Distance (m)  (a) (west)  (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 Section 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 height H = 420 m, for a calculated fahrb¨oschung angle α = 14.5◦ . The rock avalanche ran 120 m up a gentle  Width = 500 m  1900 1800 1700 1600  Height (m.a.s.l.)  2000  incline before damming the Fiddle River with a deposit area 1.3 km2 to an average depth of Slide Mountain 25 m (Locat et al., 2006).  0  500  1000 Distance (m)  Figure E.36: Slide Mountain profile. For back analyses see Table F.38.  161  1500  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 fahrb¨oschung angle α = 66◦ . The deposit dammed the  140 120 Width (m)  400  100  350 300  80  250  Height (m.a.s.l.)  450  500  160  Tozawaga River, with a deposit maximum width of 35 m and depth of 15-20 m (Yamagishi Tozawagawa et al., 2004; Sassa, 2005).  0  100  200  300  Distance (m)  Figure E.37: Tozawagawa profile. For back analyses see Table F.39 and Table G.24.  162  400  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 with V f = 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 fahrb¨oschung 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  Width (m) 500  2500  0  2000  Height (m.a.s.l.)  3000  1000  3500  destroyed a lot of cheese (Grove, 2004).Triolet Glacier  0  2000  4000  6000  Distance (m)  Figure E.38: Triolet Glacier profile. For back analyses see Table F.40 and Table G.25. 163  8000  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 tributary 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 V f = 1.4 million m3 .  The material reached a maximum velocity of 34 m/s. Superelevation indicates the material was traveling at 26 m/s at the first major curve of the path. The mass ran out to a fahrb¨oschung 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 Pacific Northern Gas pipeline (Schwab et al., 2003; Boultbee et al., 2006; McDougall, 2006).  200 150 Width (m)  800  100  600  50  400  0  200  Height (m.a.s.l.)  1000  250  1200  1400  300  Zymoetz River  0  1000  2000  3000  Distance (m)  Figure E.39: Zymoetz River profile. 164  4000  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 forwardprediction 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 observation 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 L  Le  α  442 m  210 m  18◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  72 28 -5 -14 -24 -35 -41 -48 -55 -63 13 43 43 69 61 -3 32 43 45 52 -13 15 23 24 30 -22 0 7 8 12  185 67 -6 -25 -46 -68 -80 -94 -109 -124 32 105 104 175 152 -1 76 105 109 129 -24 37 56 58 72 -41 5 20 22 29  -57.8 -25.9 2.2 11.9 24.6 42.2 54.1 69.8 90.2 117.9 -13.8 -37.2 -37.0 -55.5 -49.7 -0.2 -28.8 -37.2 -38.2 -43.7 11.3 -15.7 -22.4 -22.9 -27.4 21.2 -3.2 -9.2 -10.0 -13.0  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.1: Mathematically-selected parameters for Abbot’s Cliff. For case description, see Section E.1. For back analyses with user-selected parameters, see Table G.1.  167  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●● ●  ●● ● ●  10  ●  10  ●  ● ●  ●  ● ●  ●  ● ● ●  ● ●  200  300  400  ●●  ●  ● ●  500  ● ●  600  ● ●●  ●  ●  ●  ●  ●  ● ●  700  ●  ●  ● ●  ●  ●  10  15  20  35  40  ●  40  ●  40  30  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●● ●  ● ●  ●  ●  ● ●  ●  300  400  500  ● ●● ● ●  600  ●  ●● ●  ● ●  ●  ●  10  ●  10  friction angle  25  700  ●  ● ●  ●● ●  ●  ● ●● ●  800  10  (c) D  15  20  25  ● ● ● ● ●●  30  35  ● ●  40  (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 L  Le  α  6025 m  4001 m  12◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  13 -16 -31 -40 -61 -70 -71 -71 -72 -72 -28 -25 -25 -7 85 -33 -23 -23 -18 -14 -36 -27 -22 -20 -23 -38 -32 -27 -25 -24  -0 -12 -43 -55 -76 -85 -85 -85 -86 -86 -37 -33 -32 1 -643 -46 -28 -27 -17 -8 -50 -36 -26 -21 -27 -53 -44 -36 -32 -29  20.2 -9.9 30.3 46.1 69.8 84.9 86.5 87.0 87.8 88.1 22.5 16.8 15.2 -18.2 412.3 34.2 10.1 9.6 -4.5 -13.8 39.6 21.0 7.1 0.2 9.6 43.3 32.1 22.0 15.5 12.1  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  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  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●●● ● ●  10  ● ●●●  10  ●  ● ●  ●●● ●  ● ● ● ●● ●  2000  ●  ● ● ●● ●  4000  ●● ●  ● ●  ●  6000  8000  ●  10000  ●  ● ●  ● ●●  ●  10  20  30  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  ●  20  30  60  ●  40  40  ●  ●  ●  ● ●  ●  ● ●  ●  ● ●● ●●  ●  ● ●●● ● ●  ● ● ●●  10  ●●●● ●  10  friction angle  50  (b) α  (a) L  20  40  ●  ●  5000  ● ●  ●  10000  15000  20000  ●  ●  25000  0  (c) D  20  40  ● ●  ●  ● ●  60  ● ● ●  80  ● ●  ●  100  120  (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 Observed  Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  ξ  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  L  Le  α  363 m  -21 m  35.5◦  ∆L  ∆Le  ∆α  -67 100 100 100 100 59 26 9 -7 -19 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100  839 16265 3722 3098 1519 -771 -531 -258 13 331 9878 21049 19075 4055 19112 3130 19707 4953 24221 9760 1600 8750 11455 6049 -27 74 6600 2671 3881 4830  66.0 88.1 38.4 33.1 16.2 -28.8 -25.1 -16.1 -4.8 10.6 71.1 96.3 93.2 41.0 93.3 33.4 94.2 47.4 100.4 70.7 17.2 66.9 76.3 54.1 -8.3 -6.3 57.0 29.0 39.7 46.6  vmax  Table F.3: Mathematically-selected parameters for Arvel. For case description, see Section E.3.  171  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ● ●  ●  ● ●  ●  ●  ● ●  ●  ●  ● ●  200  400  600  800  1000  ●  ●  ●  ●  ●  ● ●  1200  ● ●  1400  30  40  50  ●  ●  ● ●  ●  ●  ● ●  60  ●  70  (b) α  ●  40  40  ● ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ● ●  ●  ●  ●  ●  ● ●  ●  ●  ● ●  ●  ● ●  ●  ●  ● ●  ●  ●  ●  1000  ● ●  ●  2000  ● ●  ●  ●  ●  3000  ● ●● ●  10  ●  10  friction angle  ●  ●  ●  (a) L  0  ●  10  ●  10  ●  ●  ●●● ●  ● ●  ●  ●●  4000  50  (c) D  ●  ● ● ●  ●  ● ●  100  150  200  (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 θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Le  α  2700 m  18◦  ξ  ∆L  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  29 15 6 -3 -16 -35 -56 -84 -89 -90 -6 -1 -1 16 3 -11 -4 -1 11 -5 -34 -11 -0 5 1 -40 -21 -8 -2 1  -69.8 -35.3 -17.5 -5.6 8.8 28.7 61.8 76.6 84.5 88.6 -1.7 -7.6 -8.6 -37.4 -14.1 3.6 -4.1 -8.6 -27.2 -2.9 28.1 3.9 -8.8 -16.9 -11.4 35.9 13.2 0.7 -6.3 -11.5  Observed Rheology  L  vmax  Table F.4: Mathematically-selected parameters for Brazeau Lake. For case description, see Section E.4. For back analyses with user-selected parameters, see Table G.3.  173  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●  ● ●  ● ●  10  ●  10  ●  ● ●  ● ●  500  1000  1500  2000  ● ●●  ●● ● ●  ●  ●  ●● ●  2500  ●  ●  ●  3000  3500  5  ●  ● ●●  10  15  ●  ●  ●  20  25  30  35  (b) α  ●  40  ●  40  ● ●  ● ●●  ●  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ● ●  ● ●  ●  ● ●  ●  500  1000  1500  2000  2500  ●● ●  3000  ●  ●● ●  ●● ● ●● ●  ●  10  ●  10  friction angle  ●  ●  ●● ●  ● ●  ● ●  ● ●  ●  3500  20  (c) D  ● ●  40  ● ●  60  ●● ● ● ●  80  ● ●  ●  100  (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 Charmon´etier, Is`ere, France L  Le  α  600 m  -232 m  40.9◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  51 51 53 54 57 63 75 8 -54 -67 18 22 27 30 33 17 21 17 28 30 16 20 21 17 24 15 18 22 20 20  -348 -344 -384 -409 -459 -575 -896 -15 -46 -50 -45 -60 -87 -113 -133 -41 -56 -40 -98 -113 -38 -51 -59 -42 -71 -33 -46 -63 -54 -51  -68.7 -68.0 -75.6 -80.4 -89.8 -111.2 -162.1 -4.3 3.5 9.0 -11.0 -14.1 -19.3 -24.2 -27.9 -10.1 -13.2 -10.0 -21.3 -24.1 -9.4 -12.2 -13.8 -10.4 -16.2 -8.5 -11.1 -14.6 -12.8 -12.3  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.5: Mathematically-selected parameters for Charmon’etier. For case description, see Section E.5.  175  40  ●  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ●  ●  ●  10  ●● ●●●  10  ● ●● ●● ●  ●  ●●●● ● ● ●  ●●●● ● ●●  ●  ●●  ●  ● ● ● ●●  200  400  600  800  1000  −20  −10  0  20  30  40  ●  40  ●  40  10  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ●  ●  ●  ●● ●●●  ●  ●  ● ●● ●●  ●  ●  ●  ●● ● ●●  500  1000  ● ●●  10  ●●● ● ●  10  friction angle  ●●  ● ● ● ●●  ●  ●  1500  2000  ● ●●  ●  ● ●● ●  50  (c) D  ●  ● ●●  100  150  200  (d) vmax  Figure F.5: Raw output data for models of Charmon´etier 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, Drˆome, France L  Le  α  800 m  208 m  25◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  29 45 23 11 1 -15 -31 -45 -64 -76 35 61 73 57 63 30 59 58 58 55 13 56 55 56 52 -23 55 52 48 54  -469 -1173 -296 -83 -9 -29 -73 -115 -143 -136 -701 -2272 -2268 -1997 -2474 -498 -2125 -2070 -2065 -1833 -115 -1909 -1851 -1879 -1642 -44 -1799 -1615 -1359 -1761  89.9 145.2 65.9 23.9 2.4 4.2 17.2 35.1 56.7 64.8 113.7 181.8 177.7 175.3 186.0 93.3 178.5 177.2 177.0 170.8 31.4 173.0 171.3 172.1 164.8 7.7 169.8 163.9 154.0 168.6  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.6: Mathematically-selected parameters for Claps de Luc. For case description, see Section E.6.  177  40  ●  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●  ● ●  400  600  800  ●  1000  ● ●●  1200  ●  1400  30  40  50  ●● ● ●  60  70  (b) α  ●  40  40  ● ● ● ● ●●  ●  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ● ●  ● ●  ●  ●  ●  ●●  10  ●  10  ● ● ●  ● ● ●  ●●●  2000  ●● ●  3000  ● ● ● ● ● ● ● ● ●  ● ●  1000  ●  ●  20  30  ●  ●  (a) L  friction angle  ●  ●● ● ●  ● ●●  ●  ●● ● ● ● ●  200  ●  10  ● ●● ●  10  ●  ● ● ● ● ● ● ●  4000  ●  ● ●  5000  0  (c) D  ●  2000  4000  6000  8000  10000  (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  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  31◦  Observed Rheology  α  ξ  ∆α -52.3 -45.6 -27.3 -19.1 -17.9 -5.7 7.6 15.3 27.3 38.8 4.4 -0.4 2.5 -13.6 -19.4 7.7 1.5 -0.3 -6.8 -16.4 8.9 3.4 -3.3 0.4 -13.5 9.6 5.0 -1.8 -1.6 -0.2  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  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  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●●  ● ●●  10  ●  10  ●  ● ●  ● ● ●  ●  ●●  ●  200  400  600  800  ●  ●  ●● ●  ●  ●  1200  15  20  ●  ●●  ● ●  ● ●●  30  35  40  (b) α  ●  40  ●  40  ●  ● ●  ●  25  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●●  ● ●  ● ●  ●●● ●● ●● ●  200  400  600  800  1000  ●  ●  ●  ●  ●  ● ●  1200  ●  ●  ● ●  ● ●  ●  10  ●  10  friction angle  ●  ●  ●  ● ●  1000  ●  ●  ●  ●  1400  20  (c) D  ● ●  ● ●  ●  40  ● ●  ●  ● ●  60  ● ●  80  (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  2000 m  2017 m  1036 m  16◦  84 m/s  ξ  ∆D  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  49 51 24 8 -9 -27 -38 -46 -51 -58 19 49 58 66 70 -1 42 51 58 57 -11 29 42 48 51 -18 12 26 33 36  36 38 12 -5 -21 -38 -50 -57 -63 -69 7 36 45 52 55 -13 29 38 45 44 -23 17 29 35 38 -29 0 14 20 24  83 90 29 -1 -32 -66 -89 -102 -112 -122 19 84 109 134 145 -17 66 90 109 107 -35 38 66 80 89 -48 7 33 46 54  -32.1 -34.7 -10.4 1.9 20.2 50.3 80.4 103.8 126.1 152.6 -6.4 -32.2 -42.9 -53.5 -58.3 10.5 -25.1 -34.9 -42.9 -42.0 22.6 -13.7 -24.9 -30.8 -34.4 33.1 -1.7 -11.9 -16.9 -20.0  8 -2 -9 -12 -17 -26 -36 -48 -63 -68 -14 1 3 6 8 -20 -4 -2 -0 2 -26 -10 -8 -7 -6 -31 -16 -13 -13 -11  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.8: Mathematically-selected parameters for Elm. For case description, see Section E.8. For back analyses with user-selected parameters, see Table G.5.  181  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ● ●  ●● ●  10  ●  10  ●  ● ●  ●  ●  ●  ● ●  1000  1500  ●  ●  ●  2000  2500  ●● ● ●● ●  ●  ●  ●  ● ● ● ● ● ● ●  ●  ●  ● ●  ●●  ●  3000  ●  ●  ●  10  15  20  35  40  ●  40  ●  40  30  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ● ●  ● ●  ●  ● ● ●  1000  1500  2000  ●  ● ●  ●  ●  ● ●  2500  ● ●● ●  10  ●  10  friction angle  25  ● ●  ●● ●  ● ●●● ●  ●● ●●  ● ●  ●  3000  30  (c) D  40  50  60  70  ● ●  80  ● ● ●  90  (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: purple, ξ = 1000: blue, ξ = 1500: cyan, and ξ = 2000: green).  182  F.9  1903 Frank Slide, Alberta, Canada L  Le  α  vmax  3500 m  2284 m  14◦  45 m/s  ξ  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  3 -8 -12 -18 -29 -46 -54 -60 -74 -83 -30 -15 -18 1 -19 -40 -15 -14 -4 -15 -46 -23 -13 -10 -12 -49 -29 -20 -15 -13  23 -10 -21 -33 -53 -78 -91 -102 -108 -111 -54 -28 -33 16 -35 -69 -28 -25 2 -28 -77 -41 -23 -14 -21 -81 -52 -36 -27 -22  -44.1 -9.4 3.1 16.1 38.6 74.5 104.9 133.4 163.7 200.3 40.4 10.9 16.1 -37.1 18.0 59.9 10.9 7.6 -22.3 11.4 73.2 24.8 5.8 -4.8 3.4 81.9 37.3 19.7 10.0 4.8  173 142 115 105 90 64 31 -15 -43 -73 33 114 138 149 155 28 103 126 136 143 23 92 114 124 130 17 81 101 111 117  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.9: Mathematically-selected parameters for Frank Slide. For case description, see Section E.9.  183  40  ●  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ●●  ●●  10  ●  10  ●  ● ●  ● ●  ● ●● ●  500  1000  1500  2000  ● ●● ●  ●● ●  2500  ●  ●  ●  ●  ●  3000  ●  ●  ●  ●● ●  ●  ●● ●  ●  3500  ● ●  ● ●●  10  15  ●  20  30  35  40  (b) α  (a) L  40  ●  40  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ●●  ● ●  ●  ● ● ●  1000  1500  2000  2500  3000  ● ●  ●● ●  ● ●  ● ●  3500  ●  ● ● ●  ●● ● ● ●●  ●  10  ●  10  friction angle  25  ●  4000  20  (c) D  40  ●  ● ●  ●  60  ● ●  80  100  ● ● ●  ● ● ●  120  (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 L  Le  α  628 m  388 m  13◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  30 51 13 3 -8 -20 -27 -33 -45 -51 30 37 35 70 33 4 44 49 59 47 -5 27 38 44 48 -12 10 20 25 28  27 75 -2 -20 -40 -61 -74 -86 -100 -108 26 41 36 133 33 -18 55 69 95 63 -34 21 44 57 65 -46 -8 8 17 22  7.7 -22.0 24.6 37.9 56.5 81.3 99.6 120.5 145.8 165.1 8.2 -0.8 2.0 -58.2 3.9 36.0 -9.5 -18.5 -34.7 -14.5 51.0 10.8 -2.5 -10.8 -15.6 63.3 28.2 18.5 13.5 10.6  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table 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  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ●●  ●● ●  10  ●  10  ●  ● ●  ● ●  ●  ●●  ● ●●  ●  ●  ● ●● ●  400  600  ● ●  800  ●  ●● ●  ● ●  ●●● ●  5  10  15  20  ●  35  ●  ●  30  ●  friction angle  20  ●  ●  ●  ●  20  ●  ●  ●  ● ●  ●  ●  ●●  ● ●  ●  ● ●  ●  ● ● ●● ●  400  600  800  ●  ●  ● ●  ● ● ● ●●  ●  10  ●  10  ●  200  30  ●  40  40  ●  30  25  (b) α  (a) L  friction angle  ●  ●  ●  ●  1000  ●  ●  ● ●  ● ●  ● ●  ●  ● ●  ●  1000  25  (c) D  ● ● ●  ● ● ●  30  35  ● ●  ● ●  40  (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 L  Le  α  67 m  27 m  11◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  51 46 3 -8 -27 -49 -62 -62 -62 -63 15 51 52 52 52 8 48 52 52 51 3 19 30 45 46 -5 9 13 15 16  166 146 44 14 -26 -62 -86 -87 -88 -88 77 168 171 172 171 59 153 174 174 168 44 92 115 142 146 24 62 74 79 82  -7.3 3.1 38.6 57.9 84.2 115.5 155.7 157.5 159.5 160.4 20.4 -7.9 -9.6 -10.3 -10.0 30.5 -0.4 -11.5 -11.3 -8.1 38.4 12.2 6.4 4.6 3.1 50.4 28.6 22.1 19.6 18.1  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.11: Mathematically-selected parameters for Hiegaesi. For case description, see Section E.11.  187  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●●●  ●●●  10  ●  10  ●  ● ●  ●  ●  40  60  80  ●●● ● ● ●● ●  ●● ●  ● ● ●  ● ●●  100  10  ●  ●  ●  ●●  ●  ● ●  ●  ● ●  15  20  (b) α  (a) L  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ● ●●●  ● ●  ●  ●  ●  60  ● ● ●● ●  ●  40  ●  ●●  ●  80  ●● ●●  10  ●  10  friction angle  25  ● ●  ●● ●  ● ●● ●  ● ●●  ●  100  2  (c) D  4  6  8  ●  10  ● ●  ●●  12  (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 L  Le  α  4240 m  2288 m  16◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  -40 -40 -39 -38 -39 -43 -58 -61 -65 -65 -40 -40 -39 -39 -39 -40 -39 -40 -40 -40 -40 -40 -39 -40 -40 -40 -40 -40 -40 -40  -66 -67 -63 -60 -62 -76 -94 -97 -96 -96 -65 -65 -64 -64 -65 -65 -64 -66 -66 -65 -66 -65 -65 -65 -66 -67 -66 -65 -65 -65  46.6 48.6 42.8 37.5 40.4 60.7 88.2 94.2 90.8 90.5 45.6 45.4 43.2 44.2 44.9 45.8 44.6 46.1 47.1 45.8 46.2 45.6 45.1 45.8 46.4 48.7 46.6 45.7 45.6 45.9  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table 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  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ● ●  ●  ●  ● ● ●●  ● ● ●  ●● ●● ●  ●●● ●  ● ●● ● ●  ● ● ● ●  1600  1800  2000  2200  2400  ● ●  10  10  ●● ● ●  ● ●●● ●  2600  22  24  26  ●  40  ●  40  30  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ●  ● ●  3200  3400  3600  3800  ● ●  ● ● ●●  3000  ● ●● ●  ● ● ● ● ●● ●● ●  2800  ●  10  ●● ● ● ●  10  friction angle  28  ●  4000  0  (c) D  20  40  ● ●● ●  ● ●  60  80  ●●  ●  ● ● ●  100  120  (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 L  Le  α  3250 m  1842 m  17.1◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  7 2 -7 -9 -18 -34 -50 -83 -83 -83 -10 -9 -10 -7 -8 -11 -9 -9 -10 -10 -31 -10 -7 -8 -9 -37 -19 -8 -6 -6  48 16 -22 -28 -48 -71 -93 -103 -103 -103 -33 -30 -32 -23 -28 -37 -30 -30 -31 -33 -67 -34 -24 -27 -29 -75 -48 -27 -21 -21  -54.4 -27.2 6.4 11.9 27.0 46.4 75.7 102.7 102.7 102.7 15.7 13.2 15.3 7.6 11.5 19.2 13.7 13.9 14.6 15.8 43.0 17.0 8.6 10.9 12.8 51.2 27.4 11.1 5.5 5.8  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.13: Mathematically-selected parameters for Jonas Creek (north). For case description, see Section E.13.  191  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●●  ● ●  10  ●  10  ●  ● ●  ●  1500  2000  2500  ● ●●● ●  3000  3500  10  15  25  30  35  ●  40  ●  40  20  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ● ●  ● ●  ●●  ● ● ● ●  10  ●  ● ●  ● ●●●  ●● ●  ●● ● ●  ●● ● ●  ●  ●●●●  1000  1500  2000  2500  3000  ●  ●  10  ●  ●  ●  20  30  ●  friction angle  ●  ● ●● ●  ●  ●●●●  1000  ●  ●●● ●  ●● ● ●  500  ●  ●  ● ●●●  ● ● ●  3500  4000  0  (c) D  ● ●  1000  ●  2000  3000  4000  5000  (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 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).  192  F.14  Jonas Creek (south), Alberta, Canada L  Le  α  2500 m  1028 m  26.5◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  36 17 9 13 6 -20 -45 -80 -84 -84 -0 1 1 -0 4 -3 -2 4 8 12 -6 -5 1 5 7 -20 -11 -4 1 6  181 58 25 40 13 -48 -88 -101 -100 -100 -7 -2 -3 -5 7 -14 -11 6 21 35 -20 -19 -3 10 18 -47 -32 -15 -3 14  -80.0 -41.3 -30.9 -35.7 -27.2 -7.2 11.7 23.5 21.9 21.9 -20.8 -22.1 -22.1 -21.1 -25.2 -18.5 -19.5 -24.8 -29.6 -34.2 -16.4 -16.8 -21.9 -26.0 -28.6 -7.4 -12.7 -18.1 -22.0 -27.4  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.14: Mathematically-selected parameters for Jonas Creek (south). For case description, see Section E.13.  193  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ●  ●  ●  ●  ●  ●  10  ●  10  ●  ● ● ● ●●  ●  ● ●  ●  ●  ●  ● ●  ●  ●  ●  ●  ●  ●● ●● ●  500  1000  1500  2000  2500  3000  3500  5  ●  ●●  10  15  20  25  30  (b) α  ●  40  ●  40  ●  ● ●  ● ●● ●  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ●  ● ●  ●  ●  ● ●  ● ●  ●  ● ● ●  1000  1500  2000  2500  ●  ●  ●  ● ●● ●  500  ●  3500  4000  0  (c) D  20  ● ●  ●  3000  ●  ● ●  ● ●● ●●  ●  10  ●  10  friction angle  ●  ●  ● ●●  ●  40  ● ●  60  ● ● ●  ● ●  80  ● ●  100  (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 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).  194  F.15  2005 Kuzulu, Turkey D  L  Le  α  vmax  2300 m  3300 m  1780 m  16◦  14 m/s  ξ  ∆D  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  350 118 43 26 -51 -76 -76 -76 -76 -76 143 264 283 297 309 86 47 192 226 244 76 88 101 110 118 46 53 57 60 62  100 47 -6 -18 -69 -85 -85 -85 -85 -85 64 100 100 100 100 24 -3 98 100 100 17 26 34 41 46 -4 1 4 6 7  384 89 -5 -25 -74 -86 -86 -86 -86 -86 117 256 280 300 318 51 1 170 209 230 39 54 69 80 89 -1 9 14 18 21  -66.4 -32.7 -1.4 9.9 16.7 9.7 9.7 9.7 9.7 9.7 -36.5 -49.6 -52.4 -54.8 -57.1 -24.4 -4.5 -41.6 -44.9 -46.9 -20.9 -25.4 -28.8 -31.1 -32.7 -3.4 -8.4 -10.9 -12.5 -13.8  597 482 273 145 19 5 -2 -11 -20 -29 328 530 586 608 620 249 420 482 506 522 153 325 383 414 434 91 211 271 305 331  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.15: Mathematically-selected parameters for Kuzulu. For case description, see Section E.14.  195  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  10  ●● ● ●  10  ● ●●● ● ●  ●  ● ● ● ●● ●  ●● ●  ●  ●  ●  ●  ●  2000  ● ●  4000  6000  ● ●  ●  ● ● ●  8000  10000  ●  ● ● ● ●  ●  8  10  6  40  40  ●  12  14  16  18  ●  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  ●  20  30  ●  (b) α  ●  ●  ●  ● ●  ●  ● ●  ●  ●  ● ●  2000  4000  ●  ●  ● ●  ● ● ● ●● ●  ●  10  ● ●●● ●  10  friction angle  ● ●  (a) L  20  ●  6000  ●  ●  ● ●  ● ●  8000  ● ● ●  ●  ● ● ●  ●  ●  10000  20  (c) D  40  60  ● ● ●  80  ● ● ●●  100  (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 L  Le  α  4500 m  2002 m  19◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  66 59 37 47 43 -34 -43 -50 -58 -67 18 44 54 22 62 14 45 46 49 51 0 20 35 38 42 8 8 79 19 21  210 173 89 124 110 -76 -92 -102 -115 -121 35 110 153 45 190 24 114 120 131 140 -5 40 80 91 103 12 12 287 38 42  -67.9 -56.1 -28.3 -39.9 -35.2 44.9 59.7 71.1 88.6 103.5 -10.1 -35.4 -49.5 -13.4 -61.7 -6.2 -36.5 -38.7 -42.4 -45.2 4.8 -11.7 -25.2 -28.9 -33.1 -1.7 -1.9 -92.3 -10.9 -12.5  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.16: Mathematically-selected parameters for La Madeleine. For case description, see Section E.15.  197  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ●  ●  ●  ●  ●  ● ●  ●  ● ●  3000  4000  ● ●● ●● ●●  5000  ●  ● ●  6000  ●  8000  ●  0  ●  10  ●●  30  40  (b) α  ●  40  ●  40  ● ●  20  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ●  ●●  ●  ● ●  ● ●  ●  1000  2000  3000  ●● ●● ●●  ● ●  4000  ●  5000  6000  ●● ●  ●● ● ●  ● ●  ●  ●● ● ●  7000  0  (c) D  ●  ●  ●● ●  ●  ●  10  ●  10  friction angle  ●  ●● ●●  ●  ●  7000  ●  ●  ● ● ●  ●  2000  ●●  10  ●●  10  ●  ●  ●  ●  500  1000  1500  2000  2500  3000  (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  8000 m  715 m  459 m  12.6◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  -86 -89 -92 -93 -95 -96 -97 -99 -99 -99 -92 -88 -86 -86 -86 -93 -91 -89 -87 -87 -94 -92 -91 -90 -90 -95 -93 -93 -92 -92  36 7 -34 -46 -61 -77 -85 -101 -102 -102 -24 14 38 41 34 -42 -16 8 22 30 -52 -34 -18 -8 -2 -61 -45 -36 -30 -25  63 17 -44 -60 -77 -92 -97 -101 -101 -101 -30 26 67 74 59 -54 -17 17 39 52 -67 -44 -20 -6 3 -77 -58 -46 -37 -31  -35.2 -15.3 24.6 42.7 67.6 104.4 128.3 102.1 100.5 100.6 12.3 -19.3 -36.7 -40.2 -33.0 36.0 3.1 -15.7 -24.3 -29.6 52.0 24.4 5.5 -4.0 -9.2 67.6 39.8 26.9 18.7 13.7  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table 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  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ● ●  ● ●  10  ●  10  ●  ● ●  ●  ●  ●  ●  ●  ● ● ●  ●  0  200  400  ●  ●  ●  600  ●  ●  ● ● ●  800  ●●●  1000  ● ●  ●  ●  ● ●  ●  ●  ● ●  10  15  20  25  (b) α  ●  40  ●  40  ●  ●  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ● ●  ● ●  ●  ●  ●  ●  ●  ●  200  400  600  ● ● ●  800  ● ●● ●  ● ●  ●  ●  10  ●  10  friction angle  ●  ●  ●  ●  ● ●  ● ● ● ●  ● ●● ●  ●  1000  0  (c) D  10  20  ● ●  30  ●● ●  ● ● ●  40  (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  4100 m  3800 m  2504 m  12◦  130 m/s  ξ  ∆D  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  28 5 -38 -53 -64 -84 -85 -85 -85 -85 -20 -9 3 11 11 -25 -17 -8 -1 3 -36 -23 -16 -12 -9 -49 -34 -29 -25 -23  33 9 -38 -53 -65 -85 -86 -86 -86 -86 -18 -7 7 15 15 -24 -15 -5 2 7 -36 -22 -14 -9 -6 -49 -34 -28 -24 -21  65 16 -54 -69 -81 -93 -95 -95 -95 -95 -25 -8 13 26 27 -34 -20 -5 5 12 -51 -31 -19 -12 -7 -65 -47 -39 -33 -29  -45.0 -12.3 47.6 62.2 83.1 100.8 113.2 113.2 113.2 113.2 15.9 2.0 -10.3 -19.3 -19.7 23.7 11.2 0.6 -5.5 -9.9 43.0 21.0 10.5 4.8 1.7 57.2 38.4 28.6 23.3 19.8  -35 -51 -63 -67 -76 -87 -94 -98 -100 -100 -70 -54 -48 -45 -42 -73 -59 -54 -51 -49 -77 -64 -60 -58 -57 -81 -70 -66 -65 -64  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.18: Mathematically-selected parameters for Luzon Slide. For case description, see Section E.17.  201  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ●●  ●● ●  10  ●  10  ●  ● ●  ●  ●  ●  ● ●  1000  2000  ●  ●● ●  ●  ●  ●  3000  ● ●  ●  ● ●  4000  ● ●  5000  ●  ●  ●  ●  ● ●  10  15  25  ●  40  40  20  (b) α  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ● ●  ●  (a) L  ●  ●  ● ●  ●  ●  ● ●●  ● ●  ●  ●  ●  ●  ● ●  1000  2000  3000  ● ●  ●  ● ●  4000  ● ●● ●  ● ● ●  ●  10  ●  10  friction angle  ●  ●  ● ●  ●  ●  ● ●  ● ● ●  ● ●  5000  0  (c) D  20  ● ●●  40  ● ●  60  ● ●  ● ●  ●  ●  80  (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  1280 m  1300 m  756 m  13◦  50 m/s  ξ  ∆D  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  8 12 10 2 -7 -19 -32 -45 -45 -45 8 15 22 21 11 11 18 15 21 1 8 14 10 19 9 2 15 18 20 21  -3 1 -1 -9 -17 -29 -42 -54 -54 -54 -3 3 10 9 -0 0 6 3 9 -10 -3 2 -1 7 -2 -8 4 7 8 9  1 10 4 -14 -34 -60 -81 -90 -90 -90 1 18 35 34 8 8 26 17 34 -16 1 15 7 29 2 -12 19 27 31 32  6.8 -1.2 3.7 20.8 42.8 75.3 107.0 119.6 119.6 119.6 6.9 -8.1 -22.6 -22.1 0.8 0.1 -14.9 -7.8 -22.0 23.0 6.9 -5.5 1.8 -17.7 5.8 19.0 -9.6 -15.9 -19.5 -20.5  21 2 -14 -22 -33 -55 -84 -100 -100 -100 -15 13 19 21 22 -20 6 11 12 13 -26 -2 2 3 4 -31 -10 -7 -5 -5  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.19: Mathematically-selected parameters for Madison Canyon. For case description, see Section E.18. For back analyses with user-selected parameters, see Table G.11.  203  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ● ●●  ●● ●  ● ●● ● ●  600  800  1000  ●  ● ●  ●  ●  ●  ●  ●  ● ●  ●  10  ●  10  ●  1200  ●  ● ●  ●  ● ●  ● ●  1400  10  ● ●  ● ●●  ●  ●  ●  ●  ●  ● ●  15  20  (b) α  (a) L  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ● ●●  ●  ● ●● ● ●  ● ●  800  1000  1200  ● ●● ●  10  ●  10  friction angle  25  ●  ●  ●  ●  ●  ●  ●  ●  ● ●  ● ●● ● ●  ● ●  ● ●  1400  0  (c) D  10  20  30  40  ●●● ●  50  ● ●●●  60  (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 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  F.20  2002 McAuley Creek, British Columbia, Canada D  L  Le  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  10◦  Observed Rheology  α  ξ  ∆α 16.2 -8.2 59.2 75.4 101.5 140.9 174.9 318.6 256.1 256.1 -25.8 -30.7 -2.9 -91.8 -14.1 38.2 -22.9 -14.1 -37.4 -46.8 63.8 8.9 -8.6 -15.2 -20.7 83.8 46.3 37.1 31.8 28.0  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  Table F.20: Mathematically-selected parameters for McAuley Creek. For case description, see Section E.19.  205  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ●●  ●●● ●  10  ●  10  ●  ● ●  ● ●  ● ● ●●  500  1000  1500  2000  ●● ●  ● ● ●●  ●  2500  ●● ●  ●  3000  ●  ●  ●●●  ●  ●●  ●  ●  ●  ●● ● ●  0  10  20  ●  40  40  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  40  (b) α  (a) L  ●  ●  ● ●  ●  ●  ● ●●  ● ●  ●  ● ●  ●  1000  1500  2000  2500  ●  ●● ●●  3000  ●● ● ●  ●●●  ● ● ●●  ●  10  ●  10  friction angle  30  ●  ● ●●  ● ●  ● ●  3500  0  (c) D  20  40  ●  ● ● ●  60  ● ●  ● ●  80  (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 L  Le  α  vmax  3460 m  1572 m  19◦  70 m/s  ξ  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  62 46 24 10 -27 -49 -63 -75 -88 -90 21 24 27 32 28 15 18 23 26 29 -39 -22 15 20 23 -43 -38 -25 8 14  201 122 51 18 -34 -72 -91 -103 -106 -106 43 50 59 73 62 29 36 47 57 65 -55 -26 30 40 49 -62 -54 -31 14 26  -70.6 -43.0 -17.8 -6.7 7.1 32.1 52.7 76.4 98.3 101.9 -15.2 -17.6 -20.6 -25.5 -21.6 -10.5 -12.6 -16.4 -20.1 -22.6 18.5 3.2 -10.5 -14.2 -17.2 24.5 17.6 5.3 -5.3 -9.4  62 26 5 -3 -15 -35 -50 -67 -91 -97 -32 5 19 25 29 -34 -0 12 18 21 -38 -5 6 11 13 -41 -11 -1 2 5  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.21: Mathematically-selected parameters for Mount Cayley. For case description, see Section E.20. For back analyses with user-selected parameters, see Section G.10.  207  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●  ●  ● ●  10  ●  10  ● ●  ● ●  ●  ●● ●  ● ● ● ●●  ●  2000  3000  4000  ●  5000  5  10  15  20  ●  35  ●  ●  30  ●  friction angle  20  ●  ●  ●  ●  20  ●  ●  ●  ● ●  ●  ●  ●  ● ●  ●  ●  ●  3000  4000  ● ●  ●  ●● ●● ●  2000  ● ●● ●  ● ●● ●● ● ●●  1000  ●  10  ●  10  ● ●  0  30  ●  40  40  25  (b) α  ●  30  ●  ●  ●● ● ●●  (a) L  friction angle  ●  ●● ● ●●  ●  ● ● ●● ●  1000  ●  ●  ● ●●  ●  5000  0  (c) D  20  40  ● ●● ●  ●  ●●  ●  60  ●  80  ● ● ●  100  (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 Observed  Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  L  Le  α  vmax  7500 m ξ  ∆D  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  57 87 4 5 -3 -50 -59 -65 -73 -76 -1 3 4 4 4 -7 -5 -2 4 4 -10 -9 -6 -2 3 -60 -14 -9 -5 -2  Table F.22: Mathematically-selected parameters for Mount Cook. For case description, see Section E.21. For back analyses with user-selected parameters, see Table G.14.  209  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  ●  ● ●  ● ● ●  ●● ●  2000  4000  ●  ● ●  ●  ●● ● ●  6000  ●  ● ●  ●  ●● ●  ●  10  ●  10  ●  ● ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ● ●●  ●  ●  ● ●●  ● ●●  ●  ● ●● ●  8000  25  30  45  ●  40  ●  40  40  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ●  ● ● ●●  ● ●  ●  ● ●● ● ● ●●●  ●  ● ●  4000  6000  8000  ● ●●●  ●  ●  ● ●●  2000  ● ●●●  10  ●  10  friction angle  35  ●  10000  12000  14000  50  (c) D  ● ● ●● ●  ●  ● ●●  100  150  200  250  300  (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  7500 m  7690 m  5257 m  12◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  -3 -20 -56 -61 -66 -70 -71 -72 -76 -77 -5 -1 -4 3 -7 -16 -7 -2 -0 1 -37 -19 -14 -12 -11 -46 -41 -39 -38 -38  -8 -24 -58 -63 -68 -72 -73 -73 -77 -79 -10 -5 -8 -2 -11 -20 -11 -7 -5 -4 -40 -23 -18 -16 -15 -49 -44 -42 -41 -41  6 -21 -60 -66 -71 -75 -77 -77 -81 -83 2 11 5 19 -1 -15 -0 8 12 14 -37 -19 -12 -9 -7 -48 -42 -39 -39 -38  -35.8 -15.0 2.8 8.0 13.2 17.7 19.6 19.8 26.3 29.0 -32.7 -40.6 -34.9 -49.0 -30.5 -19.9 -30.6 -37.7 -41.8 -44.0 -17.3 -16.7 -22.2 -24.7 -26.2 -7.7 -13.4 -15.4 -16.1 -16.4  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.23: Mathematically-selected parameters for Mount Granier. For case description, see Section E.22. For back analyses with user-selected parameters, see Table G.15.  211  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ●  ●  ● ●● ●  ●● ● ●  ● ●● ●  ● ●●  2000  3000  4000  5000  ● ●● ● ●  10  ● ●● ●  10  ●  6000  ●  ● ● ●  ●  7000  ●  ●  ●  ●  ●● ●  ● ● ●  6  8  10  14  ●  40  40  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  12  (b) α  (a) L  ●  ●  ● ●  ●  ● ●● ●  ● ●  ●  ●  ● ●  ● ●● ●  ● ●●  3000  4000  5000  6000  ●  ● ●● ●  2000  ●●● ●  10  ●  10  friction angle  ●  ●  ●  ●●●  ● ●  ●  ● ●●  ●  7000  20  (c) D  40  ● ●  60  ●  ●  ●  80  (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 L  1300 m  400 m  32 m/s  ξ  ∆D  ∆L  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  287 100 39 31 27 20 19 19 19 19 258 341 360 373 381 127 178 182 189 194 78 87 99 101 104 49 53 55 55 56  100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100  41 5 -25 -42 -48 -53 -57 -67 -85 -87 5 27 32 42 48 -5 20 11 12 12 -17 -10 -8 -5 -3 -29 -22 -19 -17 -14  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Le  α  D  vmax  Table F.24: Mathematically-selected parameters for Mount Ontake. For case description, see Section E.23.  213  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  10  ● ● ●● ●  10  ●● ● ● ●  ●  ● ● ●●●  ●●● ● ●  ●● ●●  ●  ●  ●  2000  3000  ●  4000  ●● ●●  ●  5000  ●●  ●●● ●  6000  ●  10  15  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  ●  20  30  25  ●  40  40  ●  ●  ●  ● ●  ●  ● ●  ●  ● ● ●●●  ● ●  ●● ●●  3000  4000  ●  5000  ●● ● ● ●  ● ●  2000  ● ● ●●  10  ●● ● ●  10  friction angle  20  (b) α  (a) L  20  ●  ●  ●  ●●  ●● ● ●  6000  10  (c) D  20  30  ●  ● ●  ●  ●  ●  40  (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  7000 m  5760 m  2783 m  18◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  38 28 19 -11 -18 -28 -38 -50 -59 -72 -27 -18 12 20 20 -31 -21 -15 13 19 -33 -23 -17 -13 10 -35 -25 -19 -16 -14  42 37 29 -4 -13 -25 -38 -51 -62 -76 -23 -13 20 30 31 -28 -16 -10 23 29 -31 -19 -11 -7 18 -34 -22 -14 -11 -8  116 67 26 -16 -37 -66 -91 -110 -123 -124 -63 -37 6 29 32 -73 -46 -29 11 26 -79 -53 -32 -20 2 -84 -60 -42 -30 -24  -48.1 -20.6 1.4 9.9 23.0 44.8 67.8 91.2 116.7 137.6 42.1 23.2 9.4 0.2 -1.2 49.9 29.7 16.9 7.7 1.7 55.6 34.6 19.3 11.8 11.1 60.8 39.7 26.2 18.2 14.0  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.25: Mathematically-selected parameters for Mount Steele. For case description, see Section E.24.  215  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ● ●●  ●●  10  ●  10  ●  ● ●  ●  ●  ●  ● ●  2000  3000  ●  4000  ● ●  ●  ●  ●  ●  5000  6000  ●  ●  ●●  8000  10  15  ● ●  ● ●  20  25  30  ●  40  ●  ●  30  ●  friction angle  20  ●  ●  ●  ●  20  ●  ●  ●  ● ●  ●  ● ●●  ● ●  ●  ● ● ●  4000  ● ● ● ●  6000  ● ●  ●  ●  ● ●● ●  ●  ●  ●  10  ●  10  ●  2000  35  ●  40  40  ●  (b) α  ●  30  ●  ●  ●  ●  (a) L  friction angle  ●  ●  ● ●  ●  ● ●  7000  ●  ●  ●  ● ●  ●  ● ●  ● ●● ●  ●  8000  40  (c) D  60  80  ● ●● ●  100  120  ●  ● ●●  140  160  (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  4000 m  4000 m  2000 m  15◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  76 43 11 1 -12 -25 -35 -54 -71 -78 -26 26 36 57 43 -26 13 32 41 46 -27 1 18 25 30 -28 -9 5 12 15  64 33 2 -9 -22 -35 -44 -62 -77 -83 -35 17 26 46 33 -36 3 22 31 36 -37 -9 8 16 20 -38 -19 -5 2 6  181 86 13 -8 -34 -61 -85 -103 -106 -112 -62 46 69 124 88 -64 17 59 81 95 -67 -9 27 44 55 -69 -29 -0 14 22  -66.0 -29.5 3.5 15.3 32.3 57.7 89.9 119.7 133.9 168.4 59.4 -12.5 -22.5 -44.2 -30.1 61.3 1.5 -18.3 -27.5 -32.9 64.4 15.5 -3.7 -11.6 -16.5 67.3 28.3 10.5 2.9 -1.2  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.26: Mathematically-selected parameters for Mystery Creek. For case description, see Section E.25.  217  ●  40  40  ●  ●  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  30  ●  ●  ●  ● ●  ●  ●  ● ●  ●● ●  10  ●  10  ●  ● ●  ●  ●  ●  ●  1000  ●  2000  3000  ●● ●  ●  ●  4000  ● ●  ● ●  5000  ●  ● ●  ●  ●  ●  6000  ●  5  ● ●  10  ●  ●  ●  ●  ●  ●  ●  15  20  30  35  40  ●  40  ●  40  25  (b) α  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ● ●  ● ●  ●  ●  ● ●  1000  2000  3000  ●  ●  4000  ●  ●  5000  ● ● ●  ● ●● ●  ● ●  ●  ●  10  ●  10  friction angle  ●  ●  ● ●  ●  ● ●  6000  ● ●  ●  ●  7000  20  (c) D  40  60  ● ●  ●  ● ●  80  100  ●● ● ●  ● ●  120  (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 L  Le  α  2270 m  1374 m  13.5◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  89 25 -30 -41 -53 -64 -70 -74 -80 -87 -56 -19 3 18 30 -67 -50 -34 -20 -5 -69 -57 -45 -36 -29 -71 -61 -52 -46 -41  169 45 -42 -58 -76 -93 -103 -109 -114 -114 -82 -24 9 34 54 -98 -71 -47 -25 -3 -101 -82 -64 -51 -39 -103 -88 -74 -65 -58  -63.2 -21.9 27.0 45.8 73.2 114.4 148.4 175.5 206.0 236.4 84.8 12.8 -7.0 -17.9 -25.1 128.4 65.0 32.0 13.5 -0.2 141.6 85.5 53.3 36.4 24.6 150.5 100.5 70.4 55.2 45.6  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.27: Mathematically-selected parameters for Nomash River. For case description, see Section E.26. For back analyses with user-selected parameters, see Table G.16.  219  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ● ●  ● ●  10  ●  10  ●  ● ●  ●  ●  ●  ●  ●  ●  ● ●  ●  ●  ●  1000  ● ●  ●  2000  ●  ●  ●  3000  ● ●  4000  ●  ●  ●  ●  ●  ●  ●  20  30  40  (b) α  ●  40  40  ● ●  ●  10  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ● ●  ●  (a) L  ●  ●  ● ●  ●  ●  ● ● ●  ● ●  ●  ●  ●  ● ●  ●  1000  ● ●  ●  ●  ● ●  ●  ●  ●  2000  ●  ●  3000  ● ●  ● ●  ● ●●  10  ●  10  friction angle  ●  ●  ●  ● ●  ●  4000  30  (c) D  ●  ●  ● ●  40  50  ● ●  60  ●  ● ●  ●  70  80  (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  9000 m  7800 m  4639 m  13◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  54 19 -23 -40 -52 -79 -86 -89 -93 -94 -9 -1 1 3 7 -45 -32 -11 -11 -8 -53 -49 -36 -33 -22 -57 -54 -49 -46 -41  72 33 -16 -35 -49 -79 -86 -89 -93 -95 -0 9 12 14 18 -41 -27 -3 -2 1 -50 -46 -31 -27 -14 -55 -51 -45 -42 -36  145 58 -23 -48 -67 -90 -96 -100 -102 -103 1 16 21 24 31 -55 -37 -3 -2 4 -68 -62 -42 -37 -21 -74 -70 -62 -57 -49  -58.1 -19.7 21.8 38.5 61.2 87.3 111.2 149.3 182.8 201.4 7.4 -0.5 -2.6 -4.5 -7.6 45.1 29.6 10.2 9.1 5.8 62.7 54.7 34.3 29.8 20.2 73.2 65.4 54.2 47.2 39.6  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  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  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ● ●  10  ●  10  ●● ●●  ● ● ●  ●● ●  ●  ●  ●● ● ●  0  2000  4000  6000  ●  ●●  ●● ●  ●  ●●● ●  8000  ●  10000  12000  5  10  15  20  25  30  ●  40  ●  ●  30  ●  friction angle  20  ●  ●  ●  ●  20  ●  ●  ●  ● ●  ●  ● ●  ● ●  ●● ●  4000  6000  ● ●● ●  8000  ●  ●  ● ●●● ●  10000  ●  ● ●  ●  ●  ●  2000  ● ●  10  ●  10  ●● ●●  0  35  ●  40  40  ●  (b) α  ●  30  ● ●  ●●●● ●  (a) L  friction angle  ● ●  ●  ●  ●  12000  14000  0  (c) D  ● ●  ●  ●  ● ●  50  ● ●  ● ●  100  ● ●  150  (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 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).  222  F.29  2002 Pink Mountain, British Columbia, Canada D  L  Le  α  2000 m  1950 m  1230 m  11.6◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  71 34 -7 -24 -54 -85 -87 -87 -87 -87 -1 12 25 33 34 -8 0 12 21 26 -12 -7 1 7 12 -16 -13 -8 -4 -1  70 34 -9 -26 -56 -86 -88 -88 -88 -88 -3 10 24 32 33 -10 -1 11 20 26 -14 -8 -1 6 11 -18 -15 -10 -6 -3  134 54 -17 -41 -71 -94 -95 -95 -95 -95 -7 14 36 52 53 -17 -5 15 29 39 -24 -16 -3 7 15 -30 -25 -18 -12 -7  -59.7 -16.5 27.2 48.1 73.8 107.0 114.7 114.7 114.7 114.7 19.7 6.3 -6.7 -15.3 -16.2 27.8 17.9 5.5 -2.7 -8.4 33.6 26.3 17.2 10.4 5.6 38.4 34.4 28.3 23.4 19.7  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.29: Mathematically-selected parameters for Pink Mountain. For case description, see Section E.28.  223  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  10  ●● ●  10  ●● ● ●● ● ●  ●  ●  ●  ●  ●  ●  500  1000  1500  ●  ●  ● ●  2000  ●  ● ●  ●  ●●  2500  ● ●  3000  5  ●  ● ●  ●  ●  ●  ●  ●  ●  15  20  25  ●  40  40  ●  (b) α  ●  ●  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  10  (a) L  ●  ●  ● ●  ●  ● ●  ●  ● ●  ●  ● ●  ●  ●  ●  500  1000  1500  2000  ●  ●  ● ●  ●  ● ●  2500  ● ● ●  10  ●● ● ●●  10  friction angle  ● ●  ●  ● ●  ● ●  ● ●●  ●  3000  3500  0  (c) D  20  ●  ●  ●  ● ●  ●  40  ● ●  ●  ● ●  ●  60  (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 L  Le  α  2645 m  1125 m  20◦  ξ  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  -1 -10 -19 -22 -31 -34 -37 -44 -65 -65 -35 -14 -15 -3 -15 -35 -14 -12 1 -13 -34 -18 -14 -2 -12 -36 -22 -8 -7 -16  62 11 -21 -32 -48 -60 -70 -104 -114 -114 -62 -7 -8 48 -10 -61 -7 2 74 -1 -60 -19 -6 53 4 -64 -30 20 23 -11  -45.7 -17.0 0.4 6.9 14.8 24.2 32.7 63.7 81.2 81.2 25.7 -7.1 -6.3 -38.0 -5.2 25.1 -7.2 -12.1 -52.5 -10.6 24.2 -0.5 -7.9 -40.7 -13.5 27.4 5.9 -22.5 -24.1 -4.8  D Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.30: Mathematically-selected parameters for Queen Elizabeth. For case description, see Section E.29.  225  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ●●  ●●  10  ●  10  ●  ● ●  ●  ●  ●  1500  ●  ●  ●●●  ●  ●  ●  2000  ●  10  ● ●  15  ●  20  25  30  35  (b) α  ●  40  ●  40  ●  ●  ●●●  (a) L  ●  ●  30  ●  friction angle  ●  20  ●  ●  ●  ●  20  30  ●  ●  ●  ● ●  ●  ●  ●  ●●  ●  ● ●  ●  ●  2000  ●  ●● ●  2500  ● ●● ●  ●  ● ●●  ●  1500  ●  ●  10  ●  10  friction angle  ●  ●● ●  ● ●  2500  ●  ●  ●  ● ●●  ●  1000  ●  ●  ●  ●  ●  ● ●  ●  ●  3000  0  (c) D  20  40  ● ●● ●  60  ● ●  80  ●  ● ● ●●  100  (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 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  Rockslide Pass, Northwest Territories, Canada D  L  Le  α  vmax  3000 m  6330 m  4730 m  8.5◦  70 m/s  ξ  ∆D  ∆L  ∆Le  ∆α  ∆vmax  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  -9 -38 -50 -54 -57 -59 -59 -59 -59 -59 -8 116 133 142 148 -28 -21 -20 -19 -19 -36 -34 -34 -33 -33 -42 -41 -41 -41 -41  -65 -78 -84 -86 -88 -88 -88 -88 -88 -88 -64 -6 3 7 9 -74 -71 -70 -70 -70 -78 -77 -77 -76 -76 -81 -80 -80 -80 -80  -79 -96 -104 -106 -108 -109 -109 -109 -109 -109 -78 -5 6 11 15 -90 -86 -85 -85 -85 -95 -94 -94 -93 -93 -99 -98 -98 -98 -98  121.9 232.8 328.4 367.5 400.9 422.0 422.0 422.0 422.0 422.0 119.6 4.6 -3.6 -7.9 -10.5 185.4 160.1 154.7 152.7 151.6 222.9 212.5 210.9 210.4 210.1 262.6 256.5 255.6 255.3 255.2  -52 -70 -86 -90 -95 -100 -100 -100 -100 -100 -52 -46 -45 -45 -45 -60 -56 -56 -55 -55 -68 -66 -66 -65 -65 -76 -75 -75 -75 -75  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  Table F.31: Mathematically-selected parameters for Rockslide Pass. For case description, see Section E.30. For back analyses with user-selected parameters, see Table G.18.  227  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ● ●●  10  10  ● ● ●  ●  ●● ●  ● ● ● ● ●● ●  ●  ●  ●  1000  2000  ●  3000  4000  5000  ●  6000  ● ●  ●●● ●  7000  10  20  40  40  ●  30 friction angle  ●  ●  ●  ●  20  30  ●  ●  ●  ●  ●  ● ●  ●  ●● ●  10  ● ● ●  ●  ●● ●  ● ● ●● ●  2000  3000  ●● ● ●  ● ●  1000  40  ●  ●  friction angle  30  (b) α  ●  20  ●  ●  (a) L  10  ● ● ●●  ●  4000  5000  6000  ●  ●● ●  ● ●  ● ●  7000  0  (c) D  10  20  30  ●●● ●  40  (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  6900 m  4500 m  2804 m  13◦  ξ  ∆D  ∆L  ∆Le  ∆α  100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000 100 500 1000 1500 2000  194 5 -46 -54 -64 -73 -79 -82 -86 -88 -32 -28 -12 6 281 -38 -33 -28 -25 -14 -53 -42 -34 -30 -29 -64 -52 -46 -41 -38  100 44 -23 -36 -51 -64 -72 -78 -83 -87 -1 4 28 45 100 -10 -3 5 8 26 -34 -17 -5 1 4 -51 -33 -23 -15 -11  -607 12 -34 -52 -70 -86 -94 -100 -103 -108 -2 7 35 10 -921 -18 -5 9 17 35 -50 -27 -8 1 6 -70 -48 -34 -25 -19  342.2 37.3 26.1 42.6 63.8 95.4 118.6 143.9 168.8 209.4 3.5 -3.1 -7.1 40.2 392.2 15.2 5.2 -5.0 -11.8 -9.9 40.1 21.0 7.7 1.7 -2.4 63.6 38.3 26.1 19.8 16.1  Observed Rheology  θb  Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Frictional Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy Voellmy  5 10 15 17 20 25 30 35 40 45  f  0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.2 0.2 0.2 0.2 0.2  vmax  Table F.32: Mathematically-selected parameters for Rubble Creek. For case description, see Section E.31. For back analyses with user-selected parameters, see Table G.19.  229  ●  40  40  ●  ●  ●  30  ●  friction angle  ●  ●  ●  ●  20  ●  20  friction angle  30  ●  ●  ●  ● ●  ●  ●  ●● ●  ●  ●  ● ●● ●  ●  ●●● ●  ●●  ●  ● ●  2000  ●●● ● ●  10  ●  10  ●  ●  4000  6000  ● ●● ● ●  ● ●  ●  8000  ●  ●  ●  ●● ●  10000  ●  10  ●  20  ●  30  ●  friction angle  ●  ●  ●  ●  ●  20  30  60  ●  ●  ●  ●  ● ●  ●  ● ●●● ●  10  ● ● ●●●  10  friction angle  50  ●  40  40  ●  20  40  (b) α  (a) L  ●  ●  ● ● ●● ●  ● ●●● ●  ●●●● ● ●●  0  30  ●  5000  ●  ● ●  ●  10000  15000  20000  ●  25000  0  (c) D  ● ●● ●  ●  ● ●● ●  100  200  300  400  500  (d) vmax  Figure F.32: Raw out