Material Point Method For Dynamic Analysis Of Saturated Porous Media

In the recent years,more and more attention has been paid on the research ofmultiphase porous media,like geomaterials,which play important role in landslide related to the failure of soil foundation,land subsidence in petroleum extraction and the interaction between soil and underground structure in the geotechnical engineering.Saturated porous medium,as a kind of soils,is considered particularly in the dissertation.Because saturated porous medium is composed of solid skeleton and pore fluid,its simulation is more difficult than that of single-phase materials.A variety of the Finite Element Methods(FEMs) have been developed for such problem in the past decades;but they may have some disadvantages in some special cases,like mesh distortion in large strain or strain localization.To overcome the disadvantages of the FEM,some new numerical techniques,like meshless method,have been developed.The Material Point Method(MPM) is the representative one of meshless methods, which is proposed to predict the time-dependent problems of single-phase material in the previous works.The MPM is extended in the dissertation to predict the coupling responses of saturated porous media.The new MPMs are applied to simulate the strain localization of saturated porous media and the dynamic contact between saturated porous media and solid bodies.The chapters of the dissertation are organized as follows.The first chapter introduces the background of the research,and reviews the development of geomechanics.Several meshless methods,like SPH and EFG,are also surveyed briefly.At the end of the chapter,the contents of the dissertation are outlined.Chapter 2 provides the physical description of saturated porous media,which is modeled as the solid-fluid mixture.Saturated porous medium has heterogeneous structures in space in the mireo-scale.To model the heterogeneous two-phase material as a continuum in the macro-scale,a fundamental assumption of every phase filling the entire domain is made, which means that all the phases are superposed at any material point.Under the assumption, the mathematical model of saturated porous media is obtained,which consists of a set of coupled partial differential equations:the momentum balance of the whole system,the transportation equation of pore fluid,Darcy's equation,and the mass balance of pore fluid.In Chapter 3,the original MPM is reviewed,which has been used to solve some history-dependent problems,like contact/impact and penetration/perforation,in the solid mechanics without invoking any master/slave relationship as required in the conventional FEM.The discrete formula and the numerical algorithm of the MPM are provided explicitly.Based on the u-p form governing equations of saturated porous media,the coupling MPM is proposed to predict dynamic responses of saturated porous media in Chapter 4.The material point refers to the mixture of saturated porous media in the coupling MPM.In the coupling MPM,the solving scheme is proposed for the Darcy's equation for the first time, and the treatments on the boundary conditions in the pore pressure field are described.The prescribed pressure boundary is imposed approximately with the use of the pressure boundary layer.The validity of the approach developed here is demonstrated in the comparison with the results of the FEM.It can be found that the interaction between solid skeleton and pore fluid in saturated porous media is successfully simulated.In chapter 5,the two-phase MPM is developed to simulate the solid-fluid coupling in saturated porous media with the use of the u-U form governing eqatuions of saturated porous media.In the two-phase MPM,two sets of material points are invoked to represent the deformation of solid skeleton and the pore fluid flow.In this chapter,the numerical implementation of the two-hase MPM is provided explicitly,and the vadility of the two-phase is shown in the numerical examples.The strategy for the dynamic contact between saturated porous media and solid bodies is proposed in the frame work of the MPM in chapter 6,in which the responses of saturated porous media and solids are predicted by the coupling MPM and the original MPM respectively.The link between these two kinds of MPMs is the contact algorithm proposed in the current chapter,in which the slip between saturated porous media and solid bodies is allowed following Coulomb friction law,and the inter-penetration between saturated porous media and solid bodies is forbidden.The results of numerical calculations demonstrate the validity of the proposed strategy which shines a light of modeling the problems of soil-structure interaction in a new and effective way.Stain localization is one of the most frequently found mechanisms leading to progressive failure of materials.To simulate the strain localization of saturated porous media,a modified strong decohesion model is developed in Chapter 7,in which the solid-fluid coupling in saturated porous media is considered with bringing the effect of pore pressure into the traction on the decohesion surface.In the frame scheme of the two-phase MPM,the modified strong decohesion model is coupled with the bifurcation analysis of the stress-strain field,whose stress state is updated with the corresponding return mapping algorithm developed here. Objective and mesh-independent results are obtained in the representative examples.The main contributions of the dissertation are summarized and the further works are suggested in chapter 8. Appendix A introduces the code of Geo-MPM which is developed to predict the dynamic responses of saturated porous media.In Geo-MPM,three kinds of MPMs,the original MPM,the two-phase MPM and the coupling MPM,are implemented.Geo-MPM can simulate the ealstoplastic behaviour and strain localization of both saturated porous media and solids,and contact among solid bodies and between saturated porous media and solid bodies.