Hydro-mechanical Model for Slope Stability Assessment A Polygonal Stabilization-free Discretization

Jul 16, 2026

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Rainfall-induced landslides result from the coupled action of subsurface water flow and soil mechanics, requiring reliable numerical simulation of variably saturated porous media. The study formulates a semi-coupled hydro-mechanical model using Richards’ equation and linear elasticity, then discretizes it with a stabilization-free Virtual Element Method on general polygonal meshes. The framework avoids problem-dependent stabilization terms, uses mass lumping for the storage term, and applies Nitsche’s method to weakly impose infiltration and seepage-face boundary conditions with automatic Neumann/Dirichlet switching. Backward Euler time stepping and Picard iterations handle nonlinearities, and experiments confirm stability for rainfall infiltration and slope stability via the Local Factor of Safety.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages26

Reading Time1 h 6 min

Introduction

Hydro-mechanical processes in rainfall-triggered landslides

Slope stability via Local Factor of Safety (LFS)

Numerical methods: FEM and its limitations

Virtual Element Method (VEM) and stabilization challenges

Stabilization-free VEM framework for the proposed model

arXiv :2607 .04778v1 [math .NA] 6 Jul 2026 HYDRO-MECHANICAL MODEL FOR SLOPE STABILITY ASSESSMENT: A POLYGONAL STABILIZATION-FREE DISCRETIZATION A PREPRINT Stefano Berrone Dipartimento di Scienze Matematiche“G. L. Lagrange” Politecnico di Torino, Italy stefano .berrone@polito .it Francesca Marcon Dipartimento di Scienze Matematiche“G. L. Lagrange” Politecnico di Torino, Italy francesca .marcon@polito .it Gioana Teora Dipartimento di Scienze Matematiche “G. L. Lagrange” Politecnico di Torino, Italy gioana.teora@polito.it July 7, 2026 ABSTRACT Rainfall-induced landslides are governed by the interaction between subsurface water flow and soil mechanics, requiring robust numerical methods for the simulation of variably saturated porous media. In this work, we consider a semi-coupled hydro-mechanical model based on Richards’equation and linear elasticity and propose a numerical framework based on a stabilization-free Virtual Element Method for its spatial discretization. The proposed approach naturally accommodates general polygonal meshes while avoiding problem-dependent stabilization terms, whose design may become challenging when heterogeneous and strongly non-linear coefficients are involved. The approach is combined with a mass-lumping technique to improve stability in the treatment of the storage term and with Nitsche’s method to weakly impose seepage-face and infiltration boundary conditions, allowing for the automatic switching between Neumann and Dirichlet conditions. Time integration is performed using the backward Euler scheme, while non-linearities are handled through a Picard iteration. Numerical experiments demonstrate the stability and robustness of the proposed methodology and show its effectiveness in simulating rainfall infiltration and evaluating slope stability through the Local Factor of Safety. Keywords Polygonal mesh; stabilization-free; infiltration; seepage; soil-stability 1 Introduction Landslides are geological processes involving the downslope movement of soil and rock masses, often triggered by intense or prolonged rainfall events that increase soil saturation and reduce slope stability [1] . Rainwater infiltration modifies both the unit weight of the soil and the pore water pressure, thereby altering the stress distribution within hill-slopes and reducing the available shear strength [2] . In particular, an increase in pore water pressure decreases matric suction and effective stress, leading to a reduction in soil cohesion and, consequently, to a higher susceptibility to slope failure [3] . To investigate these processes, hydro-mechanical multi-physics models are commonly employed, coupling subsurface flow and soil mechanics [4, 3] . Since soils are generally unsaturated or partially saturated, water flow is modelled using Richards’ equation, which combines Darcy’s law, mass conservation, and constitutive relationships linking saturation and permeability to the pressure-head [1, 3] . The mechanical behaviour is described by the linear momentum equilibrium equation together with a linear elasticity constitutive relation. The resulting mathematical model describes the quasi-static consolidation of variably saturated porous media, commonly referred to as unsaturated poro-elasticity [5] . Slope stability is commonly assessed through the Local Factor of Safety (LFS), a Coulomb stress-field-based indicator defined as the ratio between the Coulomb stress for the potential failure state and the Coulomb stress for the current state of stress under the Mohr-Coulomb criterion [4] . The LFS is evaluated pointwise throughout the computational domain and depends on the effective stress tensor, soil cohesion, and internal friction angle. Unlike traditional limit-equilibrium approaches, the LFS does not require prior assumptions regarding the geometry or location of the failure surface. Consequently, it can be naturally computed on unstructured meshes, providing detailed

FAQs

What physical processes does the proposed model capture for rainfall-triggered landslides?

It couples subsurface water flow with soil mechanics, modeling variably saturated porous media under rainfall infiltration using Richards’ equation and linear elasticity.

Why does the method emphasize a stabilization-free Virtual Element Method (SFVEM)?

Standard VEM formulations often need problem-dependent stabilization to regain coercivity, which becomes difficult for strongly non-linear problems such as Richards’ equation; SFVEM avoids these stabilization terms.

How are infiltration and seepage-face boundary conditions handled?

Nitsche’s method is used to weakly impose infiltration and seepage-face boundary conditions, enabling automatic switching between Neumann and Dirichlet conditions.

Jul 16, 2026

Upload by Violet