Statistical probability model for mesoscopic mechanical parameters of rock material under elastoplastic strain-softening framework

The inherent heterogeneity of rocks is an essential reason for the complexity of its mechanical behaviors.In order to explore the strength-deformation characteristics and trans-scale fracture behaviors of rocks, a numerical model based on statistical distribution functions was proposed in the framework of continuum mechanics.The normal distribution, log-normal distribution and Weibull distribution were introduced to describe the spatial variability of elastic modulus and uniaxial compressive strength in each mesoscopic element which exhibits elastoplastic strain-softening mechanical response.Based on the definition of non-uniform indices under different distributions, various numerical uniaxial compressive tests were first carried out to analyze the stress-strain curves, strength and failure modes of specimens with different heterogeneities.Then the numerical Brazilian tests of homogenous and heterogenous specimens were performed respectively to study the effect of mesoscopic tension to compression strength ratio on the positions of crack initiation points and failure modes.The results show that under uniaxial tests, with the decrease of uniformity, the macroscopic peak strength and elastic modulus of numerical samples are gradually reduced, and the peak strength is more sensitive to the change of uniformity, the nonlinear characteristics of stress-strain curves are progressively enhanced.Moreover, the failure modes of numerical specimens change from tensile failure to shear failure and further to plastic flow failure.Significant tensile stress can be produced in heterogeneous rock under compressive loading.With Brazilian tests, the failure mode of numerical disc is affected by the ratio of tensile strength to uniaxial compressive strength of the specimen.As the ratio increases, the initial fracture point will change from the center to the loading points of the disc.Only when the initial fracture point is located at the disc center, the tensile strength calculated from the peak load is effective.For disc samples with crack initiation points near the loading ends, the tensile strength calculated from the peak load will be lower than the true tensile strength of the samples. © 2020, Editorial Office of Journal of China Coal Society. All right reserved.