A Elastoplastic Damage Model Of Rock Basd On Micromechanics

The deformation and failure process of rock-like materials is non-uniform andnon-continuous, the initiation, propagation and convergence of micro-cracks,micro-holes and other microscopic defects in rock induced by external loading resultin weakening the mechanical properties of rock and engineering stability significantly.However, the macro-plasticity of rock matrix and damage evolution based onmicro-crack propagation and micromechanics are critical for the rock constitutivemodels and engineering applications.This plastic yield criterion is used simultaneously with the damage criteria tosimulate the physical behavior of rock-like materials in this paper. The topics of thepaper mainly include:1. Rock’s yield function, macroscopic plastic potential function,plastic hardening function, micro-crack growth law and density distribution wereemployed based on plastic mechanics, damage mechanics as well as fracturemechanics.2. The elastoplastic damage model with its implicit integration algorithmis proposed, and the code of elastoplastic damage model is embedded into subroutineUSERMAT in finite element code ANSYS by using the Fortran language.3. Theplastic properties of the rock and macro-plastic behaviors were analyzed from therespects of micro-crack parameters, like initial crack length, micro-crack density,friction coefficient, and confining pressures; the proposed model will be comparedwith the experimental tests. The conclusions are as the following aspects:(1) Compared with the elastic-plastic hardening/softening model under uniaxialcompression, the proposed constitutive model can describe the plastic dilation, thebehaviors of damage softening and plastic softening properties of the rock material.The plastic hardening segment was not manifested in the curves of rock elastoplasticdamage model under uniaxial tension, and the proposed elastoplastic damageconstitutive model can characterize the nonlinear elastic properties of the rock-likematerials during uniaxial tension, and the different performances of initial yieldstrength f0and yield limit fubetween the uniaxial tensile and compressive loadings.(2) For the mixed mode plastic zone of crack tip under small scale yielding, thedimensionless function of the plastic zone diameter based on Drucker-Prager criterion is derived. The plastic zone models of mode I, mode II and mixed-mode (I+II) arecompared with plastic zones obtained from Mises criterion and the influences ofdifferent Poisson’s ratios for mixed-mode plastic zones of crack tip are studied. It isshown that the mode I and mixed-mode plastic zones of Drucker-Prager criterion arelager than that of Mises criterion, and its mode II and mixed-mode plastic zones arenot continuous between the upper and lower surfaces of crack.(3) The elastoplastic damage model based on microscopic mechanics can bettermanifest that the rock damage is often induced by micro-crack propagation andsliding in rock-like materials; the damage is lagging behind and the damage evolutionrate slows with reducing the length of micro-cracks. With the high confining pressure,the corresponding stress is large during the whole process of strain increases. Theconfining pressure has little effect on the initial macroscopic damage, however, thedamage evolution rate relatively slows with confining pressure increases.(4) A mechanism-based constitutive model is presented for the inelasticdeformation, energy dissipation and fracture of rock. The proposed model identifiesthe anisotropic properties of cracked rock, the micro-crack propagation and theaccompanying plastic deformation of rock matrix, as well as the influence betweenthem. The rock damage tensor D_c, derived from energy theory induced by micro-crackpropagation, is represented by the initial micro-crack length, micro-crack density N,crack propagation length l, and friction coefficient μ. When the axial stress reaches theyield limit, the smaller initial micro-cracks corresponds to the shorter wing crackpropagation length, and the different initial micro-cracks length has little effect oninitial plastic deformation.