非均质饱和多孔介质弹性固结和动力学行为的多尺度分析方法

A multiscale method for the elastic consolidation and dynamics analysis of heterogeneous saturated porous media

为了准确高效地求解非均质饱和多孔介质弹性固结与动力学问题,提出了1种广义耦合多尺度有限元方法。多尺度数值基函数基于饱和多孔介质u-p形式控制方程离散后的单胞等效刚度阵进行构造,所获得的耦合基函数考虑了固相与液相之间的耦合效应及动力学效应,可以直接高效地双向传递粗尺度与细尺度之间的信息。对强非均质问题,利用多节点粗单元技术来获得高阶的数值基函数。最后通过固结与动力学分析算例,并与传统有限元进行比较,验证了所提出方法在处理非均质饱和多孔介质弹性固结与动力学问题时的有效性与高效性。

To solve the elastic consolidation and dynamics problems of heterogeneous saturated porous media effectively and accu- rately, a general coupling multiscale finite element method was proposed. The coupling multiscale base functions were obtained based on the equivalent stiffness matrix of the unit cell. Coupling effects between different phases and dynamics effects were con- sidered in the coupling base functions, which bridges effectively the coarse--scale and fine--scale meshes. Multi--node coarse el- ement technique was used to get the high--order numerical base functions for the heterogeneous problem. Several representative consolidation and dynamics examples were presented to validate the proposed method. Results demonstrate the high efficiency of the proposed method for the elastic consolidation and dynamics analysis of heterogeneous saturated porous media.