## 1 Introduction
[33] divided the calculation of acceleration in one time step into two parts before spatial discretization, and proposed an explicit-implicit algorithm for the case of zero permeability assumption to effectively avoid the instability of the mixed formulations calculation. By introducing a parameter \(\delta\), [PERSON] et al. [34] gave an implicit-implicit algorithm of the \(\mathbf{u}\)-\(p\) formulation under zero permeability assumption, resulting in computational stability. [PERSON] et al. [35] proposed a fractional step algorithm based on velocity and pore pressure, allowing the shape functions of the same order for both displacement and pore pressure. To reduce computation and ensure computational stability in a relatively large time step, an iterative stabilized fractional algorithm [36] and an iterative pressure-stabilized fractional step algorithm [37] were proposed successively based on the algorithm of [PERSON] et al. [PERSON] and [PERSON] [38] proposed an FEM-based stable algorithm that combines multiple time steps, remeshing, and subiteration. [PERSON] et al. [39] divided the soil into solid and fluid subdomains and established an uncoupled model for each subdomain and solved each model separately. The dynamic equilibrium equation of the solid phase was calculated using the implicit Newmark method. For the liquid phase, a wave equation of pore pressure in scalar form was established by using its equilibrium equation and the fluid continuity equation, and it was calculated using the explicit Green-Newmark method. The coupling interaction between solid-fluid two phases, which had not yet been considered due to the use of uncoupled models, was achieved by applying interface forces on the two subdomains. This algorithm was finally proved unconditionally stable. By diagonalizing both mass and fluid compressibility matrices, [PERSON] et al. [40] proposed a fully explicit iterative integration method with high efficiency. Considering the low computational efficiency of using constant time step in the temporal computation of the FEM, [PERSON] et al. [41] used the mixed error of soil displacement and pore pressure as a criterion for adjusting the time step, and proposed an adaptive time-stepping method for calculating the fluid-solid coupling interaction or liquefaction problems based on the FEM-FDM method. In this paper, an explicit FEM for solving the \(\mathbf{u}\)-\(p\) equation of saturated porous media is proposed. In the space domain, a spatial discretization is employed that divides the whole computational domain into local node systems for all nodes, i.e., the dynamic responses of any node are related only to its surrounding nodes. In the time domain, combined with a fully explicit integration method for the \(\mathbf{u}\)-\(p\) equation [40], the displacement and pore pressure responses of the soil in any time step are directly calculated using the results from the previous two time steps. In addition, the proposed method is combined with the viscoelastic local artificial boundary [42] to establish an effective FEM with decoupling characteristics for solving the wave problem of saturated porous media. In the end, two examples are verified the proposed method, and the method is embedded into OpenSees software to analyze the seismic liquefaction of the saturated sand.