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

1st ed.

Cham

2016

282 S.

60 illus., 4 illus. in color

Monographie

Advances in Geophysical and Environmental Mechanics and Mathematics

978-3-319-02627-5

201819

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.
Earth sciences; Geology; Geology ; Statistical methods; Natural disasters; Engineering geology; Engineering ; Geology; Foundations; Hydraulics
Part I Introduction; Introduction ; The Subject ; Outline ; Miscellanea ; References ; Part II A Topography-Fitted Coordinate System and Related Issues; A Topography-Fitted Coordinate System ; Basics of the Geometry and Kinematics of a Surface ; Basics of the Geometry of a Surface ; Basics of a Moving Surface ; Mathematical Description of the Topographic Surface ; Topographic Surface as a Stationary Surface ; Topographic Surface as a Moving Surface ; Topography-Fitted Coordinates ; Coordinates Fitted to a Stationary Topographic Surface ; On the Components of Vectors and Tensors ; Coordinates Fitted to a Moving Topographic Surface ; The Topography-Fitted Coordinates in the Context of the Unified Coordinates (UC) Approach ; References ; Differential Operators and Balance Laws in the Topography-Fitted; Coordinates ; Differential Operators in the Topography-Fitted Coordinates ; Differential Operators in Curvilinear Coordinates ; Gradient and Divergence in the Topography-Fitted Coordinates ; Time Derivative in the Topography-Fitted Coordinates ; Strain-Rate and Surface Strain-Rate in the Topography-Fitted Coordinates ; Balance Laws in the Topography-Fitted Coordinates ; Conventional Route ; Non-conventional ; Part III Model Equations for Shallow Geophysical Mass Flows down; Arbitrary Topographies; Depth-Averaged Modelling Equations for Single-Phase Material Flows. ; Physical Background and Intrinsic 3D Modelling Equations ; 3D Modelling Equations in the Topography-Fitted Coordinates. ; Boundary Conditions in the Conventional Route ; Boundary Conditions in the Non-conventional Route ; Dimensionless 3D Modelling Equations in the Topography-Fitted Coordinates. ; Dimensionless 3D Model Equations in the Conventional Route ; Dimensionless 3D Model Equations in the Non-conventional Route ; Depth-Averaging Approach. ; Depth-Averaged Model Equations in the Conventional Route ; Depth-Averaging in the Conventional Route ; Thin-Layer Approximations ; Depth-Averaged Modelling Equations ; A Hierarchy of Depth-Averaged Modelling Equations ; Depth-Averaged Modelling Equations for Flows ; On Slightly Curved Topographies ; Depth-Averaged Modelling Equations in the Non-conventional Route ; Closure Relations for the Depth-Averaged Modelling Equations. ; Bed Friction Law. ; Constitutive Models for the Thin Material Layer ; Avalanching Mass as a Newtonian/Non-Newtonian Viscous Fluid ; Avalanching Mass as a Mohr-Coulomb Type Material ; Erosion/Deposition Rate Law ; Example—One-Dimensional Thin Flow on a Slightly Curved; Part IV Numerical Implementation, Simulations and Applications; Numerical Implementation of the Model Equations ; Brief Overview of the NOC Scheme ; One-Dimensional NOC Scheme ; Two-Dimensional NOC Scheme ; Numerical Implementation of Thin Flow Models on a Slightly Curved Surface ; Numerical Tests and Simulations of Granular Avalanches ; One-Dimensional Benchmark Problem—Finite Granular Mass Flowing down an Inclined Plane Chute onto The Horizontal Plane ; Effects of the Deposition Heap ; Effects of the Earth Pressure Coefficient ; Two-Dimensional Benchmark Problem—Finite Granular Mass Glowing down an Inclined Plane Chute onto; The Horizontal Plane ; Effects of the Velocity Ratio ~χb and the Velocity Profile ; Comparison between Theoretical Prediction and Experiments ; Experimental Setup and Material Preparation ; Development of the Deposition Heap. ; Comparison of Theoretical Results with Experiments ; Concluding Remarks ; Applications to Avalanching Landslides in Taiwan ; Tsaoling Landslide ; Statistical Empirical Scaling Laws of Friction ; Calibration of Rheological Parameters ; Landslide Motion ; Landslide Induced Co-seismic Ground Motion ; Hsiaoling Landslide ; Simulation Setup and Parameter Calibration ; Landslide Motion ; Associated Seismic ; Near-Surface Magnetic Survey and Flow in the Village ; Rotary Shearing Test ; Rotary Shearing Tests for Hsiaolin Landslide ; Rotary Shearing Tests for Tsaoling Landslide ; Appendix A: Some Proofs ; Solutions