A stabilised semi-implicit double-point material point method for soil–water coupled problems

This paper presents a novel semi-implicit two-phase double-point Material Point Method (MPM) for modelling large deformation in geotechnical engineering problems. To overcome the computational limitations of explicit methods, we develop a semi-implicit approach that eliminates time step dependency in soil–water coupled problems. Unlike existing single-point methods that use one set of material points to represent soil–water mixtures, our approach employs two distinct sets of material points to model soil and water phases separately. To address MPM’s inherent stress oscillations, we introduce a stabilisation technique based on the modified F-bar method. Through validation against Terzaghi’s one-dimensional consolidation theory, one-dimensional large deformation consolidation, and large deformation slope stability studies, our method demonstrates superior performance. Further testing with the hyperelastic Nor-Sand constitutive model in landslide simulations reveals that the double-point approach produces significantly more reliable results than single-point methods, particularly for dilatant soils. Notably, while implementing two sets of material points, our method incurs less than 10% increase in computational cost while achieving markedly improved accuracy. These findings establish the double-point MPM as a robust and efficient approach for analysing large deformation geotechnical problems under fully saturated conditions.