Coupling Material Point Method For Three Dimensional Non-linear Dynamics Analysis Of Saturated Porous Media

The disasters in earthquakes, such as landslide, ground subsidence and house collapse, usually cause giant lose for people. Thus, more and more attention has been paid to the study on reducing the destruction of geological disasters and the dynamic analysis of soil is one of the most fundamental tasks. Many types of soil could be modeled as Saturated Porous Media (SPM). Compared to single phase materials, usually it is harder to get the analytic solution of the governing equations and only the numerical solution is available for SPM.The Finite Element Method (FEM) has been successfully used in the numerical simulation. Many special problems, like solid-fluid interaction, contact and penetration, however, could not be handled precisely by FEM due to mesh distortion and difficulties in preprocessing. Other numerical methods based on mesh, like finite difference method, boundary element method, have similar problems, which could be effectively treated by meshless methods. Material Point Method (MPM), among meshless methods, has many significant advantages bacause it has two types of mesh, which makes both the mesh distortion of Lagrangian mesh and the nonlinear convection term of Eulerian mesh disapear.This thesis focuses on the three dimensional elastoplastic dynamic analysis of SPM with Coupling MPM (CMPM). Firstly, the discrete formulation of u-p equations is derived. Secondly, the treatment by CMPM of the boundary pressure and the boundary flux is depicted. Thirdly, return mapping algorithm of Drucker-Prager Elastoplastic Model is discussed in detail. Finally, the above functions are incorporated into the Geo-MPM program, by wich Some examples are designed for verification of stability, precision and efficiency, and the influence of mesh density is probed.Examples show that CMPM gets smaller displacement, smaller strain, smaller effective stress and lager pore pressure compared with FEM, and CMPM delays the elements to generate plasticity, while refined mesh reduces the difference between the two methods. Good agreement between the 3D results with the previous 2D results and FEM results demonstrates the high precision, stability and efficiency of the proposed algorithm. The present work fills the Geo-MPM program with more functions and makes it more applicable to simulate engineering problems like 3D elastoplastic dynamic problems, consolidation and seepage phenomenon.