Implicit integration with a substepping scheme of the zero-elastic range SANISAND-Z model for sand

Abstract

The SANISAND-Z model is a zero-elastic range boundary surface model. The zero-elastic range makes the model incrementally nonlinear, and consequently, the system of ordinary differential equations of the model formulation is intrinsically implicit. Considering that the calculation results are heavily dependent on the integration step size when the backward Euler method is used to integrate the model, a two-stage diagonally implicit Runge-Kutta algorithm with a substepping scheme is proposed in this study. The substepping scheme is achieved by an embedded local integration error estimate. Based on the user-defined material subroutine interface UMAT of ABAQUS software, the SANISAND-Z model is numerically implemented with the proposed numerical integration algorithm. By monotonic and cyclic element tests and the case of strip footing loading, the performance of the proposed numerical integration algorithm is thoroughly investigated. The results show that the proposed algorithm is more accurate and efficient than the backward Euler method.