Study On The Mechanical Behavior Of Granular Materials Based On Meso-structure And Meso-macro Homogenization Procedure

Granular materials,consisting of a large number of irregular particles and void spaces partially or fully filled with pore fluid,widely exist in nature,such as soil,rock-soil aggregate,geo-structure,etc.Granular materials are highly heterogeneous and discontinuous medium at the grain scale,the discrete nature of granular materials makes its behavior highly nonlinear,dissipative and intimately related to its meso-structure.At present,researchers and engineers commonly adopt continuum model,discrete particle model,and multi-scale model combined the merits of the above mentioned models to simulate the complex mechanical behavior of granular materials.The discrete element method(DEM)combined with different discrete particle models has become an increasing popular approach for studying the mechanical behavior of granular materials.However,as the study is only limited to modeling the contact law between two typical particles in contact at the micro-scale,or performing the overall mechanical analysis for a granular structure consisting of a huge number of particles with DEM solver at the macro-scale,one would be unable to reveal mesomechanical mechanisms of macroscopic failure phenomenon occurring in the granular structure.As a result,it's necessary to present a mechanical model to describe the meso-structure of granular materials.The damage factors and equivalent plastic strain of continuum model for granular materials to describe the damage and plastic mechanical behavior,respectively,are important indexes for engineers to measure the degree of material damage in granular structure.But their values depends on the macroscopic phenomenological criterion to govern thresholds of both damage and plastic processes and the evolution laws to govern their developments,when a macroscopic continuum model was adopted to simulate the damage and plastic mechanical behavior of granular structure,at the same time the evolution of meso-structure of granular materials can't been revealed in the damage and plastic processes of granular structure.Discrete element analysis could trace the evolution of meso-structure of granular materials,such as loss of contacts between contacting particles,force chain collapse,plastic sliding,etc.,but the internal state variables of continuum model,which are familiar to engineers,such as damage factors,equivalent plastic strain,etc.,couldn't be given in the numerical results of DEM solver.Hence,it's necessary to develop meso-structure of granular materials and its evolution informed macroscopic effective continuum model,and reveal mesomechanical mechanisms of macroscopic failxire phenomenon occurring in the granular structure.In summary,for granular materials without considering the effect of pore fluid,the Voronoi cell model to describe the meso-structure of granular materials is developed,and then anisotropic constitutive relation of effective Cosserat continuum for granular materials is proposed based on meso-structure and its evolution,after that macroscopic characterization method for damage-healing-plastic mechanical behavior of effective Cosserat continuum for granular materials is presented in the first part of this thesis.The developed Voronoi cell model involves not only the reference particle laid inside the Voronoi cell but also its intermediate neighboring particles around the reference particle.Distinguishing from the classical isotropic constitutive relation of Cosserat continuum,where the Cauchy stresses,couple stresses are just related to the strains and curvatures,respectively.The derived meso-mechanically informed constitutive relation of macroscopic effective Cosserat continuum reveals that the Cauchy stresses are not only constitutively related to the strains but also to the curvatures defined in Cosserat continuum,likewise,the couple stresses are not only constitutively related to the curvatures but also to the strains.In addition,it could quantitatively demonstrate the anisotropy of effective Cosserat continuum due to intrinsic characters and deformation-indruced evolutions of meso-structure of granular materials.As the isotropic case of the meso-structured Voronoi cell model is considered in the frame of homogenization,the derived meso-mechanically informed constitutive relation of macroscopic effective Cosserat continuum could degrade to the constitutive relation of classical isotropic Cosserat continuum,the rationality of the degraded form of the derived constitutive relation of effective Cosserat continuum is verified,at the same time the elastic constitutive parameters of isotropic Cosserat continuum,such as 'the characteristic length,Young's modulus,Poisson's ratio,etc.are obtained in terms of meso-structural parameters.Based on the proposed macroscopic characterization method for damage-healing-plastic mechanical behavior of granular materials,while neither macroscopic phenomenological damage-healing and plastic criterion nor their evolution laws are required,the mesomechanical mechanisms of macroscopic damage-healing-plastic phenomenon are revealed.The damage factors of anisotropic damage-healing factor tensor and principal damage directions of effective Cosserat continuum for granular materials are obtained with the introduced nonorthogonal principal damage coordinate.Thermodynamic framework describing isothermal damage-healing and plastic processes of granular materials is presented,while equivalent plastic strain to describe the plastic dissipative energy of granular materials is defined.According to the non-negativity of the density of incremental net damage dissipative energy,which is defined to describe the damage-healing processes of granular materials,the damage and healing criterion of granular materials are presented.After that,the damage,healing variables to describe the anisotropic damage,healing mechanical behavior,respectively,and net damage variable to combine both material damage and healing effects of granular materials,are defined.The numerical results ver:ified the validity of the proposed definitions of meso-mechanically informed net damage,damage,healing variables and the proposed healing variable to heal the initial defects of material on the one hand,on the other hand,demonstrated that the proposed density of plastic and damage dissipative energy,and density of healing energy make effects of the damage-healing and plastic component processes on the material failure quantitatively comparable.Meanwhile,the numerical results demonstrated the proposed characterization method could capture the real weakened location and developing directions of the zones of strain localization(shear bands)in the failure process of granular structure characterized with strain localization phenomena and softening.There are more and more reports on geological disasters in recent years,such as landslide,debris flow,sand liquefaction,etc.It has been observed that to reveal mesomechanical mechanisms of coupled hydro-mechanical behavior is important way to explore the causes of macroscopic failure phenomenon of granular structure induced by wetting.At the same time,effective stress governing the mechanical behavior of solid skeleton of unsaturated porous media is a hot issue for researchers and engineers,but the definition of effective stress for unsaturated porous media proposed based on macroscopic phenomenological model is still debated.As a result,for unsaturated granular materials at low saturation as the pore liquid exists in the form of binary bond mode of liquid bridges,the computational model for binary bond mode of liquid bridge and DEM model taking into account the effect of liquid bridge are proposed,and then xneso-hydro-mechanmcally informed effective stress and effective pressure tensors of effective unsaturated Cosserat continuum for unsaturated granular materials at low saturation are defined in the second part of this thesis.The numerical procedure to compute the geometric eigenvalues and capillary force of liquid bridge in 2D is presented,as the distance between two neighboring particles and the volume of liquid are given.The relationship between the critical rupture distance of liquid bridge and the radii of particles is discussed,and then the fitting formula to determine the critical rupture distance of liquid bridge expressed in terms of radii of the two particles,the contact angle and the volume of liquid is obtained.The relationship between the capillary force of liquid bridge of binary contacting or non-contacting particles and the volume of liquid is presented.The numerical results obtained by simulating the suction effects of unsaturated granular materials with the proposed DEM model,demonstrated the capability of the proposed DEM model to capture the failxire modes characterized with strain localization phenomena in unsaturated discrete particle assembly.The anisotropic unsaturated Voronoi cell model to describe the anisotropic meso-structure of unsaturated granular materials at low saturation,consisting of three immiscible and interrelated(solid grains,pore liquid and gas)phases,is proposed.And then,based on tiie unsaturated meso-structured Voronoi cell model and meso-macro homogenization procedure,meso-hydro-mechanically informed effective stress and effective pressure tensors for unsaturated granular materials at low saturation are defined,while with no need to introduce any macroscopic phenomenological assumptions for the description of hydro-mechanical constitutive behavior.As the isotropic case of unsaturated meso-structured Voronoi cell model is considered in the frame of homogenization,meso-hydro-mechanically informed effective pressure is obtained as a scalar variable,which has the same form as that given in the theory of unsaturated porous continuum.At the same time the Bishop's parameter is expressed in terms of the saturation,the porosity and meso-structural parameters,while with no need to introduce any phenomenological assumptions.At last,for the purpose of self-completeness,some topics:intimately related to the contents of this thesis,such as basic theory of Cosserat continuum model and liquid bridge,discrete element method,efifective stress of unsaturated porous media,etc.are briefly introduced.Besides,the main modules,data structures,and flow charts of the developed computer program are provided.