Theory And Numerical Realization Of Multi-scale Soil Membrane Constitutive Model

Soil is a multiphase medium composed of macro-meso-micro grains with multiple scales.Particles of different scales have different effects on the macro-mechanical properties of the medium;for example,tiny particles such as powder particles and clay mainly express the effect of inter-particle cohesion,while coarse particles such as sand and gravel mainly express the friction between inter-particles.By arranging or aggregating in different proportions,differentsize particles form different fabrics,which gifts soil with complex mechanical characteristics.To describe the stress-strain relationship of soil across the macro-meso-micro scale,the influence of soil granularity and fabrics can be considered,which can be called the multi-scale constitutive theory.However,most of the scale constitutive theories of early time used but new size parameters to consider the scale characteristics of the medium under the framework of the classical continuum mechanics theory;since the introduced parameters lacked reasonable physical and mechanical bases,the description of the scale effect of granular media is not well consistent with the media’s true nature.The cell body model,which has a clear physical basis,can consider the mechanical properties of the soil when the fine particles filled around the coarse particles with a certain thickness;while it cannot express the mechanical characteristics of the soil when the fine particles are only enough to form a reticular membrane structure around the coarse particles.To overcome the shortcomings of traditional theories and existing scale theories,the membrane model constitutive theory was adopted to conduct theoretical and numerical research on the soil.The membrane model uses the energy scale to divide the soil particles into matrix particles that mainly exhibit cohesive properties and reinforcement particles that mainly exhibit friction effects,which are described by different micro-mechanical resistance models;considering the different arrangements and probability distribution of the particles,and eventually reflect the micromechanical behavior to the macroscopic stress and strain expression via the virtual work principle;the model is built for the particle media that composed of pure matrix membrane contacts or pure the direct contact of reinforcing particles or the contact forms mixed by the above two.The main works carried out in this paper and the main research conclusions obtained are listed below:(1)Based on the membrane model theoretical framework and its system equations,this paper first used the Cosserat elastoplastic to describe the resistance of the matrix and a generalized Hertz contact proposed herein to describe the direct contact resistance of the reinforcement particles;then realized a specific derivation of the static constitutive relationship on membrane model,which can degenerate into the Cosserat model and the classical elastoplastic(CEP)model,reflecting the good compatibility between the membrane model theory with the classical theory and the Cosserat theory.(2)This paper realized the finite element numerical calculation of the membrane model constitutive via secondary development.In the process of the numerical realization,this paper formed a "hybrid return mapping algorithm" out of the radial return mapping algorithm and the midpoint incremental algorithm for the stress update of the membrane model,which effectively enhanced the iteration accuracy and calculation stability and reduced the dependence on the step size setting of the model calculation.(3)In this paper,the membrane model constitutive theory was applied to conduct numerical calculations for indoor tests and engineering examples,such as the triaxial compression,the centrifuge experiments,and the instability of foundations and slopes.The results showed that the membrane model can reasonably simulate the asymmetric deformation localization phenomenon caused by the granular and structural characteristics of the soil;under the same stress condition,the centrifuge model numerical simulation results changed with the model size,indicating that compared with the Cosserat model and the CEP model,the membrane model can consider the intrinsic asymmetry and size effect of the granular media;while the calculation results of the foundation and slope failure analysis consistent with the CEP model further verified the engineering practicability of the membrane model.