This is an open access book. The aim of this book is to provide a thorough grounding in rainfall-induced landslides from three aspects: the coupling effect of hydraulic and mechanic; the analytical, numerical, and physical simulation methods, and the controlling factors underlying the problem of rainfall-induced landslides. The improved numerical methods, nonlinear, and linear iterative methods which can be used to address the related unsaturated infiltration problems are also presented. This book is an essential reading for researchers and graduate students who are interested in rainfall infiltration, landslides, slope stability, and geohazards in fields of civil engineering, engineering geology, and earth science. The book is written to guide professional engineers and practitioners in slope engineering and geohazard management. This book can enhance their understanding of rainfall-induced landslides, help them analyze a specific problem, prevent landslides, and design engineering slopes according to the local soil and climate conditions.
Author(s): Lizhou Wu, Jianting Zhou
Series: SpringerBriefs in Applied Sciences and Technology
Publisher: Springer
Year: 2023
Language: English
Pages: 139
City: Singapore
Foreword by Jianbing Peng
Foreword by Huiming Tang
Foreword by Limin Zhang
Preface
Contents
1 Background
1.1 Rainfall Infiltration Equation
1.2 Infiltration Equation for Unsaturated Slopes
1.3 Linearized Richards’ Equation
1.4 Unsaturated Soil Slope Stability Under Rainfall
References
2 Analytical Solution to Unsaturated Infiltration
2.1 Introduction
2.2 1D Analytical Solutions for Unsaturated Seepage
2.2.1 No Coupling
2.2.2 Hydro-mechanical Coupling
2.3 2D Analytical Solutions of Rainfall Infiltration in Unsaturated Soils
2.4 Analytical Solution of Water Infiltration of Vegetated Slope Considering the Coupling Effects
2.4.1 Governing Equations of Rooted Unsaturated Soils
2.4.2 Analytical Solutions
2.4.3 Comparison of Analytical and Numerical Solutions
2.4.4 Parametric Analyses
2.5 Discussions and Conclusions
2.5.1 Discussions
2.5.2 Conclusions
References
3 Numerical Solutions to Infiltration Equation
3.1 Introduction
3.2 Numerical Solutions
3.2.1 Finite Difference Method
3.2.2 Finite Volume Method
3.2.3 Finite Element Method
3.2.4 Numerical Approximation to the Fractional-Time Richards’ Equation
3.3 An Improved Method for Non-uniform Spatial Grid
3.3.1 Validation Example
3.3.2 Unsaturated Infiltration in Layered Soils
3.4 Application of Chebyshev Spectral Method to Richards’ Equation
3.4.1 Chebyshev Spectral Method
3.4.2 Validation Example
3.5 Conclusions
References
4 Improved Linear and Nonlinear Iterative Methods for Rainfall Infiltration Simulation
4.1 Introduction
4.2 A Chebyshev Semi-iterative Method with Preconditioner
4.2.1 Numerical Tests
4.3 Improved Gauss–Seidel Method
4.3.1 Integral Correction Method
4.3.2 Multistep Preconditioner Method
4.3.3 Mixed Method
4.3.4 Numerical Tests
4.4 Nonlinear Iterative Methods and Improvements
4.4.1 Newton and Picard Methods
4.4.2 Improved Picard Method
4.4.3 Numerical Tests—1D Transient Unsaturated Infiltration
4.5 Conclusions
References
5 Slope Stability Analysis Based on Analytical and Numerical Solutions
5.1 Introduction
5.2 Application of Unsaturated Soil Slope Stability Under Rainfall
5.2.1 Application of Chebyshev Spectral Method in Slope Stability Analysis
5.2.2 Application of P-CSIM in the Stability Analysis of Shallow Rainfall Slope
5.2.3 Application of Improved Picard Method into Unsaturated Slopes
5.2.4 Parameter Sensitivity Analysis of Slope Stability Under Rainfall
5.3 Rainfall Landslide Case Study—Tung Chung Landslide
5.4 Conclusions
References
