循环荷载饱和土动力学问题稳定有限元解法

Stabilized finite elements for dynamic problems of saturated soil subjected to cyclic loading

使用等阶近似插值函数的常规有限元方法,在求解渗透系数较小且孔隙水压缩性可以忽略不计的饱和土动力学u–p形式时存在数值上的困难。首先讨论分别基于交叉时域解法和对孔隙水流动守恒方程直接修正的两类稳定方法。然后将着重分析这两种方法所得到的稳态形式,根据它们的稳态形式,讨论了关键的单元稳定参数的选取,从而使孔压的计算精度得到大大的提高。最后,给出了两个关于饱和土体受到表面循环荷载的计算实例来说明所提出有限元技术的有效性。

Conventional finite element procedures with equal order interpolations for dynamic u-p formulation of saturated soils have been experiencing numerical difficulties for the problems concerning with small permeability and neglectable compressibility of pore-fluid. This paper discusses the stabilization techniques based on the staggered implicit-implicit algorithm and direct α-method to overcome the above mentioned difficulties. Attentions will be paid to the steady state formulations resulted from both approaches. Based on the steady state formulations, the paper will then discuss the determination of the local stabilization parameters, with which a significant improvement for the obtained solutions of pore-pressure can be achieved. Finally, two numerical examples regarding saturated soils subject to a surface cyclic loading are presented to illustrate the effectiveness of the proposed techniques.