Numerical investigation on determining the optimal heterogeneity index and compressive–tensile ratio of granite using a damage-based numerical manifold method

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The heterogeneity of rock at the mesoscopic level and the compressive–tensile ratio affect the macroscopical mechanic behavior and failure mode of rocks. In this study, a damage-based numerical manifold method was used to examine the optimal heterogeneity index and the compressive–tensile ratio of Lac du Bonnet granite. This study examined the numerical manifold method and damage theory, as well as the Weibull distribution. The uniaxial compression test and the Brazilian splitting test on granite were simulated to calibrate the basic input parameters, including the uniaxial compressive strength, Young’s modulus, and Poisson’s ratio. The uniaxial compressive tests on model specimens with different heterogeneity indices and the Brazilian splitting tests on model specimens with different compressive–tensile ratios were conducted using the damage-based numerical manifold method (NMM) program. The simulation of the macroscopic mechanical behavior and the failure mode of model specimens showed good agreement with granite in the laboratory. The relationship among the heterogeneity index, compressive–tensile ratio, macroscopic mechanical behavior, and failure mode were examined. The numerical results indicated that the heterogeneity index had the most significant effect on the crack initiation stress and the peak strength of granite, while the compressive–tensile ratio affects the failure mode the most. Finally, the optimal heterogeneity index and compressive–tensile ratio of Lac du Bonnet granite are proposed. A comparison of the results showed that the optimal heterogeneity index and compressive–tensile ratio could model the cracking behavior of rocks more precisely.