An improved Chebyshev semi-iterative method for simulating rainfall infiltration in unsaturated soils and its application to shallow landslides

Abstract

A Chebyshev semi-iterative method (CSIM) with preconditioner (P-CSIM) is proposed to simulate numerically unsteady flow in unsaturated soils. An exponential function was used to linearize Richards’ equation, which was discretized using a finite difference method to obtain the linear equations. For layered soils, the numerical discretization takes into account the continuity of the pressure head at the interface. Conventional iterative approaches, including the Jacobi and the Gauss–Seidel iterative methods, require more iterations to obtain numerical solutions. The CSIM incurs more computational cost per iteration. The improved P-CSIM by comparison solves the linear equations in fewer iterations, with higher computational efficiency, and better robustness. The results indicate that the proposed P-CSIM provides good computational acceleration; specifically, at least 50% more than the CSIM and the Gauss–Seidel and Jacobi iterative methods. To simulate shallow landslides, the stability analysis of infinite slopes was developed to incorporate the time-varying pressure head and soil–water characteristic curves of unsaturated soils. The results of the examples indicate that the solver is able also to represent the increase of pressure head which may lead to a landslide. As a result, the proposed method with high computational efficiency can be developed to effectively analyze rainfall-induced shallow landslides in unsaturated soils.