Numerical Analysis And Constitutive Simulation Of Anisotropic Granular Materials Considering Fabric Evolution

For sand and the other typical granular materials in civil engineering,the influence of anisotropic micro-structure(i.e.fabric)on the mechanical characteristics,such as strength and deformation,is obvious.According to the causes,the anisotropy can be divided into the inherent anisotropy and the stress induced anisotropy.In classical failure criteria(for instance,the Mohr-Coulomb criterion and the Lade-Duncan criterion)and flow rules(Cam-clay constitutive model and Rowe's stress-dilatancy relation),the anisotropy of granular materials is not considered.In recent years,some scholars have considered the inherent anisotropy in their constitutive models.However,there would be more space for further researches on the fabric evolution equation of granular materials,and the mechanism of the effect of stress induced anisotropy on strength,deformation characteristics.To study the evolution of micro-structure in granular materials and the mechanism of its influence on mechanical characteristics,for instance,the failure criterion,the stress-strain and stress-dilatancy relation,numerous true triaxial tests of granular materials under different shear modes are performed by discrete element method(DEM).The mechanical properties at the critical state,the development of fabric and the non-coaxiality between stress tensor and fabric tensor are studied through the simulations.Based on the derivation of micro-mechanics,by introducing the concept of "true stress tensor",the evolution equation of anisotropic fabric is derived,the anisotropic failure criterion and stress-dilatancy relationship for general granular materials is proposed.The proposed theories are applied to sand,the typical engineering granular material.Then an elastoplastic constitutive model for sand considering the inherent anisotropy and stress-induced anisotropy is established in the framework of critical state theory.The main research content and conclusions include:(1)The discrete element method(DEM)was used to simulate the true triaxial tests of granular materials under different shear modes and stress paths.The mechanical characteristics at critical state,the evolution equation of anisotropic fabric,and the non-coaxiality between stress tensor and fabric tensor of granular materials under complex stress states were studied.The researches indicated that the fabric of isotropic samples evolved under anisotropic loading,and obvious anisotropic fabric at peak state and critical state were observed.The stress ratio at both peak and critical state decreased with an increasing Bishop parameter b,however,the critical anisotropic fabric increased with b.The anisotropic loading with 0<b<1 would result in a non-coaxiality between stress and fabric.The main causes of non-coaxiality were the shear contact force and the uneven normal contact force.The critical state line in e-p' plane was non-unique,and was related to the intermediate principal stress.(2)Based on the fabric-stress-strain relationship of numerical simulation,a fabric evolution equation of granular materials was derived.Through theoretical analysis and numerical simulations,the state parameter was introduced into the evolution equation,and the determination theory of fabric evolution parameter through the concept of "critical particle friction angle" was proposed.The parameters of revised fabric evolution equation had clear physical meaning,and revealed the mechanism of fabric evolution in the view of microscopic.The proposed evolution equation predicted the fabric evolution of numerical samples under complex stress states with different initial density well.(3)Through the micro-mechanics analysis,by introducing the concept of true stress tensor and the direction of sliding surface,the anisotropic strength characteristics of granular materials under complex stress states were studied in particle scale.The macro and micro energy conservations in representative volume element were proved through tensor analysis.Through the derivation of average contact force and average contact displacement,anisotropic failure criterion and stress-dilatancy relationship of granular materials were built.The failure criterion and stress-dilatancy relationship implied the fabric evolution equation,and reflected the influence of fabric evolution on the strength and deformation characteristic of granular materials.(4)In the framework of critical state theory,for the typical engineering granular material,an anisotropic elastoplastic constitutive model considering the fabric evolution of sand was established,and the calibration theory of model parameters was proposed.The researches indicated that in view of micro-mechanism,the constitutive model analyzed the yield and deformation characteristics of sand in particle scale,and predicted the stress-strain relationship of anisotropic sand reasonably based on laboratory experiments.