Theoretical Study Of Instability Phenomena And Coupled Finite Element-Meshfree Method For Strain Localization In Saturated Porous Media

The study of instability phenomena occurring in saturated porous media,such as the subsidence of soil foundation,the collapse of pit walls in the pit construction or the excavation process of tunnels,the landslide of soil slopes and dikes subjected to earthquake or rainstorm loads,is of great significance in sciences and engineering.The present dissertation devotes to the failure phenomena and processes in the saturated(particularly fully saturated) porous media subjected to static and dynamic loads,i.e.stationary discontinuity,flutter instability and strain localization.The wave propagation problems have to be investigated while the high frequency modes of the loading pulse dominate the response of the porous media due to impact or explosive loading.A great number of engineering porous materials are classified as plastic strainsoftening materials.The stress and strain states at some local points where traveling waves through will first reach the limit load-carrying capability.Which follow to occur are strain localization characterized by intensely increasing inelastic deformation into narrow bands around the local points and a reduction of the load-carrying capability due to strain-softening.The present work is carried out on the basis of the non-linear coupled hydro-dynamic model named after the generalized Biot model for saturated and unsaturated porous media. The inertial coupling between the solid skeleton and pore fluid is incorporated into the model to account for the response to the excitation with high frequency modes.In what follows the non-associated Drucker-Prager criterion is particularly considered to simulate the pressure dependent elasto-plastic constitutive behavior in the media.With no consideration of compressibility of solid grains and the pore fluid,the discontinuity and instability of the wave propagation in saturated poro-elastoplastic media are analyzed for the plane strain problems in detail.The critical conditions for the stationary discontinuity and flutter instability to occur in the wave propagation in poro-elastoplastic media are derived and formulated.It is found that stationary discontinuity can be regarded as a result of material instability due to strain softening and does not necessarily mean that the media will entirely lose the ability to wave propagation passing through the surface of discontinuity.Flutter instability stems from non-associated plasticity used to simulate the non-linear constitutive behavior of the solid skeleton of the porous medium and may occur prior to the stationary discontinuity,i.e.at the plastic strain hardening stage.This phenomenon can only occur for saturated porous medium. In the solids even when non-associated plasticity is considered,no flutter instability may occur.The dispersivity of wave propagation implies that phase velocity of a single harmonic wave is a function of the angle frequency.This property of wave propagation is intrinsically related to a correct simulation of wave propagation in the zone where the strain localization due to strain softening occurs.Based on the coupled hydro-dynamic model mentioned above, the instability and dispersivity of wave propagation in inelastic saturated/unsaturated porous media in one dimensional problem are analyzed.The effects of the following factors on the instability and dispersivity are discussed.They are the viscous and inertial couplings between the solid and fluid phases,compressibility of the mixture composed of solid grains and pore fluid,degree of saturation,visco-plastic(rate dependent inelastic) constitutive behavior of the solid skeleton under high strain rate.The results and conclusions obtained by the present work will provide some bases and clues for overcoming the difficulties in numerical modeling of wave propagation in the media subjected to strong and shock loadings.It has been experimentally observed in many engineering materials such as in the clay that a shear band of intense plastic deformation caused by strain softening possesses a finite width.In addition,the threshold and evolution of the shear band until its final formation is a progressive failure process.To numerically simulate and reproduce the progressive process the gradient plasticity model is introduced as a regularization mechanism in the present work. A coupled finite element and meshfree method attributed to a solution procedure of linear complementary problem(LCP) for gradient plasticity continuum for both saturated porous medium and the solid is presented.The von-Mises criterion and non-associated Drucker-Prager criterion are respectively adopted to model elasto-plastic constitutive behaviors in the solid and the saturated porous medium.With the mesh-free(MF) method based on moving least-square approximation (MLS) procedure,the plastic multiplier field is assumed and approximately interpolated in terms of its discretized values defined at the integration points.Whereas the displacements and pore pressure fields are discretized in terms of their discretized values defined at the nodal points with finite element(FE) interpolation approximations.Hence,respective advantages of both FE and MF methods are exploited and their respective weak points are avoided.The weak form of the equilibrium equation along with the non-local constitutive equation and the non-local yield criterion locally enforced at each integration point are combined to mathematically educe a normal form of LCP solved by means of Lexico-Lemke algorithm.A consistent algorithm based on backward-Euler return mapping integration scheme with a global iterative procedure based on the Newton-Raphson method is devised to simultaneously satisfy at each iteration the discretized momentum conservation equation as well as the non-local constitutive equation and non-local yield criterion at each of local integration points.It is remarked that there is no need to derive non-local consistent tangent elasto-plastic modulus matrix in the proposed method while the second convergence rate for the solution of the boundary problem of gradient plasticity continuum is still retained. Moreover,the global generalized stiffness matrix for the LCP solver derived by the proposed method remains symmetric even for the non-associated plasticity model.The numerical results demonstrate the validity of the proposed model and numerical method in the simulation of progressive failure process characterized with the strain localization problem due to strain softening.