A Fully Explicit–Explicit Staggered Algorithm for the Dynamic Response of Fluid-Saturated Porous Media

The analysis of the dynamic response of fluid-saturated porous media under stress waves is of great practical value in the fields of geotechnical engineering, geophysics, earthquake engineering and marine engineering. In this research, a new fully explicit finite element algorithm for solving the coupled soil-pore fluid dynamic problem is developed based on the u–p formulation. The proposed method is a staggered algorithm that is realized with the central difference method used to solve the displacement u and the improved Euler method used to solve the fluid pressure p, it has a second-order theoretical accuracy since both the central difference method and the improved Euler method are second-order methods. The correctness and efficiency of the proposed method are investigated through two numerical examples. The computational results of the one-dimensional soil column model shows that the numerical solution of the proposed algorithm agree well with the theoretical analytical solution. The differences of the computational accuracy and efficiency between the proposed method and the other existing methods are also discussed in the numerical examples, and the results show that the proposed explicit method is higher in calculation efficiency than the implicit algorithm, and its accuracy is higher than that of the existing first-order explicit method.