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3 | (18) |
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3 | (2) |
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5 | (4) |
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9 | (12) |
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15 | (6) |
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Part II A Topography-Fitted Coordinate System and Related Issues |
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2 A Topography-Fitted Coordinate System |
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21 | (30) |
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2.1 Basics of the Geometry and Kinematics of a Surface |
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21 | (5) |
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2.1.1 Basics of the Geometry of a Surface |
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21 | (4) |
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2.1.2 Basics of a Moving Surface |
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25 | (1) |
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2.2 Mathematical Description of the Topographic Surface |
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26 | (9) |
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2.2.1 Topographic Surface as a Stationary Surface |
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27 | (5) |
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2.2.2 Topographic Surface as a Moving Surface |
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32 | (3) |
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2.3 Topography-Fitted Coordinates |
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35 | (11) |
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2.3.1 Coordinates Fitted to a Stationary Topographic Surface |
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35 | (5) |
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2.3.2 On the Components of Vectors and Tensors |
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40 | (2) |
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2.3.3 Coordinates Fitted to a Moving Topographic Surface |
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42 | (4) |
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2.4 The Topography-Fitted Coordinates in the Context of the Unified Coordinates (UC) Approach |
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46 | (5) |
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49 | (2) |
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3 Differential Operators and Balance Laws in the Topography-Fitted Coordinates |
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51 | (26) |
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3.1 Differential Operators in the Topography-Fitted Coordinates |
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51 | (11) |
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3.1.1 Differential Operators in Curvilinear Coordinates |
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51 | (2) |
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3.1.2 Gradient and Divergence in the Topography-Fitted Coordinates |
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53 | (7) |
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3.1.3 Time Derivative in the Topography-Fitted Coordinates |
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60 | (2) |
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3.2 Strain-Rate and Surface Strain-Rate in the Topography-Fitted Coordinates |
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62 | (4) |
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3.3 Balance Laws in the Topography-Fitted Coordinates |
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66 | (11) |
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66 | (5) |
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3.3.2 Non-conventional Route |
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71 | (2) |
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73 | (4) |
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Part III Model Equations for Shallow Geophysical Mass Flows down Arbitrary Topographies |
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4 Depth-Averaged Modelling Equations for Single-Phase Material Flows |
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77 | (44) |
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4.1 Physical Background and Intrinsic 3D Modelling Equations |
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78 | (4) |
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4.2 3D Modelling Equations in the Topography-Fitted Coordinates |
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82 | (4) |
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4.2.1 Boundary Conditions in the Conventional Route |
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82 | (3) |
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4.2.2 Boundary Conditions in the Non-conventional Route |
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85 | (1) |
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4.3 Dimensionless 3D Modelling Equations in the Topography-Fitted Coordinates |
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86 | (5) |
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4.3.1 Dimensionless 3D Model Equations in the Conventional Route |
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87 | (3) |
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4.3.2 Dimensionless 3D Model Equations in the Non-conventional Route |
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90 | (1) |
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4.4 Depth-Averaging Approach |
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91 | (2) |
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4.5 Depth-Averaged Model Equations in the Conventional Route |
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93 | (20) |
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4.5.1 Depth-Averaging in the Conventional Route |
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93 | (6) |
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4.5.2 Thin-Layer Approximations |
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99 | (6) |
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4.5.3 Depth-Averaged Modelling Equations |
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105 | (4) |
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4.5.4 A Hierarchy of Depth-Averaged Modelling Equations |
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109 | (2) |
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4.5.5 Depth-Averaged Modelling Equations for Flows On Slightly Curved Topographies |
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111 | (2) |
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4.6 Depth-Averaged Modelling Equations in the Non-conventional Route |
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113 | (8) |
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119 | (2) |
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5 Closure Relations for the Depth-Averaged Modelling Equations |
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121 | (36) |
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121 | (4) |
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5.2 Constitutive Models for the Thin Material Layer |
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125 | (16) |
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5.2.1 Avalanching Mass as a Newtonian/Non-Newtonian Viscous Fluid |
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125 | (8) |
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5.2.2 Avalanching Mass as a Mohr-Coulomb Type Material |
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133 | (8) |
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5.3 Erosion/Deposition Rate Law |
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141 | (4) |
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5.4 Example-One-Dimensional Thin Flow on a Slightly Curved Surface |
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145 | (12) |
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155 | (2) |
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6 Conclusions and Discussions |
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157 | (8) |
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151 | (14) |
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Part IV Numerical Implementation, Simulations and Applications |
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7 Numerical Implementation of the Model Equations |
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165 | (12) |
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7.1 Brief Overview of the NOC Scheme |
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165 | (7) |
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7.1.1 One-Dimensional NOC Scheme |
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165 | (2) |
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7.1.2 Two-Dimensional NOC Scheme |
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167 | (5) |
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7.2 Numerical Implementation of Thin Flow Models on a Slightly Curved Surface |
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172 | (5) |
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176 | (1) |
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8 Numerical Tests and Simulations of Granular Avalanches |
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177 | (26) |
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8.1 One-Dimensional Benchmark Problem-Finite Granular Mass Flowing down an Inclined Plane Chute onto The Horizontal Plane |
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178 | (6) |
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8.1.1 Effects of the Deposition Heap |
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181 | (2) |
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8.1.2 Effects of the Earth Pressure Coefficient |
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183 | (1) |
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8.2 Two-Dimensional Benchmark Problem-Finite Granular Mass Glowing down an Inclined Plane Chute onto The Horizontal Plane |
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184 | (9) |
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8.2.1 Effects of the Velocity Ratio Xb and the Velocity Profile |
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188 | (5) |
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8.3 Comparison between Theoretical Prediction and Experiments |
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193 | (8) |
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8.3.1 Experimental Setup and Material Preparation |
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193 | (2) |
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8.3.2 Development of the Deposition Heap |
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195 | (1) |
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8.3.3 Comparison of Theoretical Results with Experiments |
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196 | (5) |
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201 | (2) |
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202 | (1) |
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9 Applications to Avalanching Landslides in Taiwan |
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203 | (48) |
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203 | (3) |
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206 | (17) |
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9.2.1 Statistical Empirical Scaling Laws of Friction |
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212 | (1) |
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9.2.2 Calibration of Rheological Parameters |
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213 | (3) |
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216 | (3) |
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9.2.4 Landslide Induced Co-seismic Ground Motion |
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219 | (3) |
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222 | (1) |
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223 | (16) |
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9.3.1 Simulation Setup and Parameter Calibration |
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226 | (3) |
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229 | (3) |
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9.3.3 Associated Seismic Motion |
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232 | (2) |
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9.3.4 Near-Surface Magnetic Survey and Flow in the Village |
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234 | (3) |
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237 | (2) |
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239 | (12) |
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9.4.1 Rotary Shearing Tests for Hsiaolin Landslide |
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241 | (1) |
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9.4.2 Rotary Shearing Tests for Tsaoling Landslide |
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242 | (4) |
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246 | (5) |
Appendix A Some Proofs |
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251 | (22) |
Solutions |
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273 | (4) |
Glossary |
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277 | (2) |
Index |
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279 | |