SPH implementation of a critical state-based hypoplastic model for granular materials in large-deformation problems

Abstract

In this work, an advanced hypoplastic model incorporating the critical state is integrated into smoothed particle hydrodynamics (SPH) for numerical investigation of problems with large deformation. This numerical method performs well in cases of element tests such as oedometer test, simple shear test and plain strain compression test, which usually own regular velocity fields. However, the standard SPH implementation will generate significant stress drift away from the failure surface in more complex geotechnical problems featured with dramatically-varying velocity field. This unrealistic stress state may deteriorate the stress state with a further step. As a result, a vicious circle takes place, which could give rise to a calculation failure. With this regard, a return mapping strategy is proposed to regulate the stress state locating beyond the failure surface. To this end, a closed-form solution to predicting the failure surface implicitly incorporated in the hypoplastic model is derived. Finally, the capability of the proposed numerical method is examined with two classical benchmark problems for granular materials, including the sand column collapse and rigid footing by comparing the numerical results with those from experiments and theoretical solutions.