Modelling unsaturated soils with the Material Point Method. A discussion of the state-of-the-art

Many natural hazards involve large deformations of unsaturated soils, e.g. rainfall-induced landslides, embankment collapses due to wetting, seepage-induced instabilities of dams and levees, etc. The study of these phenomena requires accounting for the complex hydro-mechanical interactions between solid skeleton and pore fluids and modeling large deformations to predict the post-failure behaviour, which poses significant computational challenges. In recent years, several hydro-mechanical coupled MPM formulations were developed to model saturated and unsaturated soils. These approaches are slightly different in terms of governing equations, integration schemes and have been implemented in different MPM software; thus, they benefit from various computational features. The purpose of this paper is to present an overview of the available MPM approaches to model unsaturated soils discussing differences and similarities of the formulations and their impact on the results under different conditions in a range of geotechnical applications. In addition, the effect of partially saturated conditions on the critical time step in explicit numerical integration schemes is studied for the first time. Different analytical expressions are derived and compared with the numerical results.