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E-raamat: Shallow Geophysical Mass Flows down Arbitrary Topography: Model Equations in Topography-fitted Coordinates, Numerical Simulation and Back-calculations of Disastrous Events

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Geophysical mass flows, such as landslides, avalanches or debris flows, are frequent mass movement processes in mountain areas and often cause disastrous damage. This book lays a foundation for formulating the depth-averaged equations describing the shallow geophysical mass flows over non-trivial topography. It consists of the detailed derivation of the model equations. The stimulating numerical examples demonstrate how the proposed models are applied. All this make this book accessible to a wide variety of readers, especially senior undergraduate and graduate students of fluid mechanics, civil engineering, applied mathematics, engineering geology, geophysics or engineers who are responsible for hazard management.

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