非饱和流固耦合物质点方法(CMPM)的原理及应用

Formulations and Applications of Coupled Material Point Method for Unsaturated Soils

基于连续介质力学的质量及动量守恒原理,考虑了固-液两相材料的水力耦合相互作用,推导并提出了基于速度场(v-w formulation)的耦合物质点方法(CMPM),可考虑水力耦合作用下,饱和/非饱和结构的大变形力学行为.同时,详细描述了耦合物质点方法的公式推导、矩阵离散过程以及数值实现步骤.随后,通过对比一维太沙基饱和土固结理论解,以及Liakopou⁃los非饱和砂土的入渗试验,初步验证了耦合物质点方法在水力耦合问题上的准确性.最后,结合某边坡在降雨作用下的失稳破坏全过程,分别模拟了持续降雨以及短暂降雨作用下,边坡的深层破坏及浅层剥蚀现象,进一步验证了方法在岩土流固全耦合大变形问题中的适用性.

Based on the mass and momentum conservations of the continuum,this paper presents a novel coupled material point method based on the v-w formulation,which fully considers the large deformation mechanics of saturate and unsaturated structures under the interactions between the solids and the fluids.For simplicity,the gas phase is neglected in the formulation,while an additional item,i.e.degree of saturation,is incorporated in the governing equations to simply study the saturated/unsaturated soils.The detailed derivation process of the governing equations,discretization process in the matrix forms and the computational cycles of CMPM is introduced.Via two benchmark examples,i.e.one-dimensional Terzaghi consolidation solution,and the Liakopoulos test,the validity of the CMPM is proven.In the end,a slope failure analysis due to the rainfall infiltration is presented,where both deep progressive and superficial slope failures are shown,further demonstrating that CMPM is a promising tool in simulating hydro-mechanical problems.