Abstract This paper presents a finite element scheme for analyzing the dynamic response of the saturated poroelastic media. The proposed scheme employs the standard finite element method for space domain discretization of the dynamic u-p equation system. We introduce the precise time step integration method as an explicit, direct integration algorithm for handling the time derivatives. The spectral radius analysis, the error and convergence analysis show that the proposed scheme is unconditionally stable as well as convergent with numerical solutions that are of any order accuracy to exact solutions. Compared with the Newmark scheme, the advantages of the proposed scheme are demonstrated by simulating five examples in both one- and two-dimensions. The proposed scheme yields high-precision results and exhibits good adaptability under large time step size, which remarkably outperforms the Newmark scheme.

中文翻译：

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一种用于饱和多孔弹性介质动态分析的无条件稳定高精度有限元方案

摘要 本文提出了一种分析饱和多孔弹性介质动态响应的有限元方案。所提出的方案采用标准有限元方法对动态上方程系统进行空间域离散化。我们引入精确时间步长积分方法作为处理时间导数的显式、直接积分算法。谱半径分析、误差和收敛性分析表明，所提出的方案是无条件稳定的，并且收敛于任何阶精度到精确解的数值解。与Newmark方案相比，通过一维和二维仿真五个例子，证明了所提出方案的优点。