Hydraulic hysteresis effects on the coupled flow–deformation processes in unsaturated soils: Numerical formulation and slope stability analysis

Abstract

• A coupled flow–deformation numerical method with hydraulic hysteresis is proposed. • A return mapping algorithm is developed to implement the hydraulic hysteresis. • The performance and convergence of the numerical formulation is improved. • The significant effects of hydraulic hysteresis on slope stability is demonstrated. The hysteresis of water retention curve has a profound influence on the coupled hydro-mechanical behaviors in unsaturated soils, but numerical implementation with consideration of this property was rarely reported due to the difficulties in the integration of the coupled constitutive models. In this study, a numerical formulation is proposed for modeling the coupled flow–deformation processes with hydraulic hysteresis. A return mapping scheme is developed to integrate the water retention curve model with hydraulic hysteresis and the elasto-plastic model simultaneously within a time step, and the deformation-dependent nature of the water retention curve is considered rigorously by modifying the coefficient matrices in the discretized governing equations. The performance and efficiency of the proposed numerical formulation is validated by two existing laboratory tests and a computational example, demonstrating better performance and convergence of the proposed formulation. The proposed procedure is then applied for modeling the coupled flow–deformation processes in a soil slope under rain infiltration. The simulated results reveal the significant effects of hydraulic hysteresis on the coupled water–air two-phase flow and elasto-plastic deformation processes. The solid deformation and the evolution of the shear band would be remarkably overestimated, and the slope failure would be early predicted when neglecting hydraulic hysteresis.