An explicit stabilised material point method for coupled hydromechanical problems in two-phase porous media

This paper presents a single-point Material Point Method (MPM) for large deformation problems in two-phase porous media such as soils. Many MPM formulations are known to produce numerical oscillations and inaccuracies in the simulated results, largely due to numerical integration and stress recovery performed at non-ideal locations, cell crossing errors, and mass moving from one background grid cell to another. The same drawbacks lead to even worse consequences in the presence of an interstitial fluid phase, especially when undrained/incompressible conditions are approached. In this study, an explicit stabilised MPM, based on the Generalised Interpolation Material Point (GIMP) method with Selective Reduced Integration (SRI), is proposed to mitigate typical numerical oscillations in (nearly) incompressible coupled problems. It includes two additional features to improve stress and pore pressure recovery, namely (i) patch recovery of pore pressure increments based on a Moving Least Squares Approximation, and (ii) two-phase extension of the Composite Material Point Method for effective stress recovery. The combination of components leads to a new method named GC-SRI-patch. After a detailed description of the approach, its effectiveness is verified through analysing various consolidation problems, with emphasis on the representation of pore pressures in time and space.