Coupling Dual Domain Material Point Method For Dynamic Analysis Of Saturated Porous Media

Saturated porous media exist widely in real life and the numerical analysis of the dynamic behaviors of these materials provides insights for many important problems in biomechanics and geotechnical engineering. Until now, many numerical methods have been developed and applied to the dynamic analysis of saturated porous media, among which the finite element method (FEM) is the most widely used one. However, FEM will confront numerical difficulties such as mesh distortion when solving large deformation problems. As one of the meshless and meshfree methods, the material point method (MPM) could avoid such problems effectively because the material information does not depend on the mesh distortion in MPM. In recent years, based on the original MPM, the coupling material point method (CMPM) has been proposed and successfully applied to the dynamic analysis of saturated porous media. However, the original MPM may encounter numerical errors when material points across grid boundaries. To overcome this problem, many improved versions have been developed and the dual domain material point method (DDMP) becomes one of the most promising version. In this work, based on the u-p form governing equation of saturated porous media, the coupling dual domain material point method for the dynamic analysis of saturated porous media is proposed, which improves the performance of the CMPM when dealing with large deformation problems.This thesis is organized as following,In the first chapter, the background and motivation of the current work will be presented and some related theories and numerical methods will be briefly introduced.In the second chapter, the continuum model and the effective stress principle of porous media will be discussed first. Then, based on the introduction of the mass and momentum conservation equations of continuum mechanics and the Darcy’s equation of pore fluid seepage, the macroscopic governing equations of saturated porous media are presented.In the third chapter, the discretization scheme and the algorithm flow of MPM will be briefly introduced. Then the comparison between the standard MPM and other three improved forms of MPM (including GIMP, CDPI and DDMP) will be presented. The graphical representation of the shape function of the four methods mentioned above are discussed and compared with each other for two-dimensional cases. The fourth chapter is the main part of this article, in which the idea of the DDMP will be applied to the dynamic analysis of saturated porous media. Based on the u-p form governing equation of saturated porous media, the coupling dual domain material point method (CDDMP) for dynamic analysis of saturated porous media will be proposed and the corresponding algorithm process will be given. The accuracy of CDDMP will then be verified in the dynamic analysis of small deformation problems, in both single-phase and saturated porous media problems. Then the CDDMP will be applied to solve large deformation dynamic problems and compared with the coupling convected particle domain interpolation based material point method (CCPDI). Some discussions on the accuracy and further improvements regards to the developed CDDMP will be given at the end..