Two Dimensional Micromechanical Damage Models For Granite Based On The Microcrack Evolvement

As a kind of crude geological material,rocks often contain nunmerous microcracks,and the deformation of microcracks play important roles in their constitutive behavior and should be considerredin the description of deformation of materials.Therefore,it is of important theoretical and practical application significance to establish a detailed damage model which are able to describethe changes of microcracks in the rock material.Therefore,this paper considers the evolution of the microcracks within granite and establish a detailed damage model.First,the penetrating microcracks are placed in an infinite elastic matrix subjected to tensile stresses of the far field.Local Coordinate system for the crack surface and Global Coordinate system are established respectively.Considering the deformation and extension of penetration microcracks,Secondly,the strain caused by single crack with arbitrary spatial orientation is derived,and then the strain caused by all microcracks can be derived by employing the Taylor's scheme and an appropriate probability density function.Finally,the present model is verified by a uniaxial tensile experiment.Besides,the deformation and growth of microcracks under far-field compressive stress are considered,and the micromechanical damage model is established.The additional compliance strain induced by single closed penetrating microcrack is derived.A simplified method to calculate the kinked deformation of the closed microcrack is presented.The strain caused by all microcracks under far-field compressive stress is derived by employing the Taylor's scheme and an appropriate probability density function.Then the present model is verified by a uniaxial compression experiment and a triaxial compression experiment.Finally,a crack-containing plate under compressive stress is simulated by employing commercially finite element software ABAQUS.The propagation direction of the closed microcrack can be calculate by the maximum circumferential stress criterion,then the crack propagation path can be obtained.It is found that the crack propagation direction at final stage is almost vertical to the crack original faces.Then the additional compliance strain induced by this crack is derived,and compared this results with the theoretical results.