The material point method for unsaturated soils

The paper describes a three-phase single-point material point method formulation of coupled flow (water and air) for hydro-mechanical analysis of geotechnical problems involving unsaturated soils. The governing balance and dynamic momentum equations are discretised and adapted to material point method characteristics: an Eulerian computational mesh and a Lagrangian analysis of material points. General mathematical expressions for the terms of the set of governing equations are given. A suction-dependent elastoplastic Mohr–Coulomb model, expressed in terms of net stress and suction variables is implemented. The instability of a slope subjected to rain infiltration, inspired from a real case, is solved and discussed. The model shows the development of the initial failure surface in a region of deviatoric strain localisation, the evolution of stress and suction states in some characteristic locations, the progressive large strain deformation of the slope and the dynamics of the motion characterised by the history of displacement, velocity and acceleration of the unstable mass.