Coupling Material Point Method For Dynamic Analysis Of Unsaturated Porous Media

In the recent years,multiphase porous media,like soil,have been one of the research focuses in he geotechnical engineering,which plays an important role in landslide related to the failure of soils,land subsidence in petroleum extraction.A variety of the Finite Element Methods(FEMs) have been developed for such problem in the past decades,but the FEM has some disadvantages,like mesh distortion in large strain or strain localization.To overcome the disadvantages of the FEM,meshless methods are developed.The Material Point Method (MPM),as the representative one of meshless methods,is proposed to predict the mechanical problems of single-phase material.In the geotechnical engineering,the Coupling MPM (CMPM),as the extension of the original MPM,is proposed to simulate the dynamic responses of the saturated porous media.The goal of the dissertation is to extend the CMPM for the dynamic analysis of the unsaturated porous media.The porous media are non-homogeneous and discontinuous in the microscopic level.To model the non-homogeneous multiphase system as a porous-continuum in the macroscopic level,a fundamental assumption of every phase filling the entire domain is made,which means that all phases are superposed at any material point.Under the assumption,the mathematical model of the unsaturated porous media consists of a set of coupled partial differential equations: the mass balance equation,the linear momentum balance equation and Darcy's equation.In the current research,the governing equations of unsaturated porous media are provided based on the cavitation model,in which the gas pressure is assumed to be constant.Using the cavitation model of unsaturated porous media,the CMPM is extended to simulate the dynamic responses of unsaturated porous media in the current work.The discrete forms of the governing equations are given explicitly.The validity of the developed method is demonstrated with the comparison between the CMPM and the conventional FEM.It can be found that the coupling in unsaturated porous media is successfully simulated.