Richards equation for the assessment of landslide hazards

In this study, we investigate numerical simulation models for water flow in variably saturated (unsaturated) soils. These models are crucial for addressing soil-related challenges and analyzing water-related risks, particularly in the context of water resource management, soil water-induced disasters, and the agricultural impacts of global environmental changes. The Richards equation is one of the most widely used models for simulating water flow in porous media, especially in unsaturated soils. However, as a highly nonlinear parabolic partial differential equation (PDE), it has limited analytic solutions, which often lack precision in practical scenarios. This necessitates the development of innovative and robust numerical methods for accurate simulations. We introduce a numerical procedure that linearizes the Richards equation using the Kirchhoff integral transformation, followed by discretization with various time-stepping schemes. This approach enables efficient and accurate modeling of water flow. To extend its application, we integrate the numerical solution with a hydrological infinite slope stability model to evaluate landslide hazards. Specifically, we calculate the factor of safety index based on an axisymmetric form of the Richards equation, which helps identify potential landslidenprone areas. Furthermore, our model provides a framework for predicting landslides by considering the interplay between water flow and the physical, geological, and topographical characteristics of a landscape. This integrated approach offers valuable insights for geohazard assessment and the mitigation of water-induced risks