A novel completely explicit algorithm to solve dynamic u-p equations of saturated soil

Abstract

A new completely explicit algorithm is developed to solve the dynamic u-p formation of fluid-saturated porous media. The mass matrix and the fluid compressibility matrix are diagonalized in the spatial domain. The central difference method, Lagrange quadratic interpolation and Taylor-series method are employed to solve the u-p formed equations in the time domain. The analysis for the theoretical accuracy and stability of the proposed method indicates that the new algorithm has second-order accuracy and is conditionally stable. Four examples are given to demonstrate the effectiveness of the proposed algorithm by comparing the solutions with those obtained by the analytical method, the explicit-implicit method developed by Zienkiewicz et al. and the explicit-explicit method developed by Xu et al. The comparison results indicate that the present method is accurate, also allow larger time step than that of Xu et al.