A stabilized Fractional Step, Runge–Kutta Taylor SPH algorithm for coupled problems in geomechanics

Failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering. Many finite element formulations for coupled problems present difficulties such as overestimating failure loads, or mesh alignment dependence resulting on spurious failure mechanisms. Moreover, the spaces where field variables are approximated have to fulfill additional requirements ensuring stability. Stress-velocity-pore pressure formulations in FE analysis provide accurate results for wave propagation and failure analysis. However, finite elements present important limitations when deformations are large. The purpose of this paper is to present a stabilized Fractional Step, SPH algorithm which combines the advantages of the SPH method for large deformation problems with those of the Taylor Galerkin algorithm used within the finite element framework.