| Granular materials widely exist in many fields,such as natural environment,industrial production and daily life etc.They are usually composed of randomly distributed discrete solid particles and interstitial fluid and have the characteristics of high heterogeneity,nonlinearity and multi-field coupling,and their hydro-mechanical behavior is very complicated.The study of hydro-mechanical behavior of wet granular materials based on mesoscopic model composed of discrete solid particles and interstitial fluid has important engineering practical significance for the study of mesoscopic mechanisms of its macroscopic behavior and has attracted the attention of many researchers at home and abroad.The first part of the present work is devoted to the development of a concurrent secondorder computational homogenization method for saturated granular materials based on the saturated discrete particle assembly-saturated porous gradient Cosserat continuum model.It is roughly divided into four successive parts:(Ⅰ)to establish the downscaling rule from the macro-scale to the meso-scale(Downscaling);(Ⅱ)to develop the numerical method for the solution of the initial boundary value problem(IBVP)of hydro-mechanics on the mesoscopic scale;(III)to upscale the meso-hydro-mechanically informed macroscopic physical quantities(Upscaling);(IV)to develop the numerical method for the solution of the IBVP of hydromechanics on the macroscopic scale.Among them,the transfer and switching rules of physical quantities between mesoscopic saturated discrete particle assembly and macroscopic saturated porous continuum derived by(Ⅰ)and(III)are the key foundations for the proposed concurrent second-order computational homogenization method of saturated granular materials.(Ⅰ)In this paper,the classical average strain theorem of Cauchy continuum is extended to gradient Cosserat continuum,and the generalized Hill theorem is derived for the second-order computational homogenization of saturated granular materials.Based on the generalized Hill theorem,the downscaling rule from the macroscopic saturated porous gradient Cosserat continuum to the mesoscopic saturated discrete particle assembly is formulated.Hydromechanical boundary conditions prescribed by macroscopic physical quantities imposed on the mesoscopic RVE that satisfy the generalized Hill-Mandel energy condition is specified.(Ⅱ)At the mesoscopic scale,saturated granular materials are modeled as saturated discrete particle assembly.In this paper,the discrete-continuum model is adopted to solve for the nonlinear hydro-mechanical response of the mesoscopic RVE under the given coupled hydro-mechanical boundary conditions,and a DEM/FEM numerical solution scheme with a staggered and iterative manner is proposed for the model.It should be emphasized that,the hydro-mechanical coupling boundary conditions imposed on the RVE not only the boundary displacements and pressures prescribed by downscaled macroscopic strain variables and pore pressure from the local points of the macroscopic continuum,but also the periodic boundary conditions represented by constrained mesoscopic boundary displacement fluctuation and boundary force constraint,as well as constrained boundary pore fluid pressure fluctuation and boundary Darcy velocity constraint.In addition,a new scheme and associated algorithm for imposing periodic boundary conditions on the RVE of granular materials are proposed in the framework of the concurrent second-order computational homogenization method of granular materials,to improve the meso-hydro-mechanically informed macroscopic effective hydromechanical constitutive relations required to upscale to the local points of the macro continuum.(III)Based on the average field theory and the generalized Hill-Mandel energy condition derived from the established generalized Hill theorem,the meso-hydro-mechanically informed rate-type macroscopic hydro-mechanical constitutive relation is derived from evolving meso-structures of the RVE,which are obtained by numerical solutions of IBVPs of meso-structured RVE subjected to time-dependent hydro-mechanical boundary conditions,and upscaled to the macroscopic scale.(IV)At the macro scale,based on the continuum model for the coupled hydromechanical analysis of saturated porous media and the gradient-enhanced Cosserat continuum model for dry granular materials,the saturated porous gradient-enhanced Cosserat continuum model is established,the mixed finite element process is devised and the associated nonlinear u-p form finite element formula is derived.At last,aiming at the proposed second-order computational homogenization method for saturated granular materials,a FEM-(DEM/FEM)nested numerical solution scheme is designed and implemented in this paper to simulate and solve the initial and boundary value problem of the hydro-mechanical process of saturated granular materials within the framework of the second-order computational homogenization method.Numerical examples and results demonstrate the capability of the developed computational multi-scale method and its solution scheme to simulate the hydro-mechanical behavior(especially the strain localization behavior)of saturated granular materials.The second part of the present thesis is devoted to the study of the mesoscopic simulation of hydro-mechanical behavior in unsaturated granular materials at low saturation.A discrete particle-binary bond liquid bridge-liquid thin film model for unsaturated granular materials with low saturation was established,in which the discrete element model is used to simulate the solid-phase discrete particle assembly and the binary bond liquid bridgeliquid thin film model is used to simulate the mesoscopic structure of interstitial liquid.A wet discrete element method is developed to simulate the interstitial liquid migration process associated with the movement of solid particles and the "drainage" process or the process of“liquid uptake” for the RVE of unsaturated granular materials with low saturation under the given time-varying hydro-mechanical boundary conditions.In the developed wet discrete element method,given the initial uniform distribution saturation of the RVE of unsaturated granular materials,a scheme for constructing the initial meso-structure of binary bond liquid bridge-liquid thin film is proposed.An iterative process of updating capillary forces of binary bond liquid bridge between particles coupled with updated contact forces is devised to simulate evolutions of the mesoscopic structure of discrete particle-binary bond liquid bridge-liquid thin film system with respect to time.In the iterative process,the mechanisms governing the evolution of the liquid bridge – liquid thin film system coupled with the movement of discrete particles and the flow of interstitial liquid in the particle gaps are as follows:(1)rupture of the liquid bridges;(2)formation and/or re-formation of liquid bridges;(3)liquid transfer between each two neighboring liquid bridges.The meso-hydro-mechanically informed macroscopic hydraulic constitutive relation –SWCC(Soil Water Characteristic Curve)hysteresis curve at the local material point of the unsaturated porous continuum can be obtained from the numerical results of the "drainage" process or the process of “liquid uptake” for the RVE by using the developed wet discrete element method and the average field theory.The generalized effective stress – strain constitutive curves,including at their softening and post softening stages,are also provided by volume averages of the numerical results of the wet RVE subjected to hydro-mechanical boundary conditions.Those results demonstrate the effect of interstitial liquid on enhancing the bearing capacity of granular materials and reveal the mesoscopic mechanisms behind it. |
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