A 3D numerical meso-mechanical model is proposed to describe the deformation and fracturing of brittle rock under various loading. The model accounts for rock material heterogeneity and local material degradation. The model introduces the concept of a mesoscopic renormalization to capture the co-operative interaction between microcracks and describes the temporal and spatial evolution of acoustic emissions in the rock by recording the counts of failed elements. The model simulates the damage and fracturing process of rocks under various loading. The model reproduces the mechanical behaviour observed in laboratory tests. and shows the complex macroscopic mechanical behaviour by the small-scale interaction of elements.


The initiation and growth of microcracks in rock as well as their impact on properties of rock has been widely studied. However, the emphasis is mainly attributed to material damage induced by compressive stress. Indeed, because of the stress redistribution during the damage process, both compressive and tensile stress are distributed in the rock. In particular, because the rock is less resistant to tensile stress, tensile cracks are more easily initiated and propagated, and are often observed in stressed rock. Furthermore, the induced damage under tensile stress condition is essentially related to the opened cracks, which is especially unfavorable to the safety and stability of the rock mass.

The tensile strength of rock is commonly determined by Brazilian test due to its easy sample preparation and simplicity of working and Brazilian test has been suggested as a standard test for determining the tensile strength of rock by the International Society for Rock Mechanics (ISRM 1978). It is also considered a method to determine the fracture toughness of rock in many references(Tang 1997, Tang and Kou 1998). Many efforts about laboratory testing and theoretical analysis have been done to study the tensile strength or fracture toughness of rock. Cho, Ogata et al. (2003) performed dynamic tensile tests on Inada granite, and analyzed the fracture processes under various loading conditions to verify the differences between the dynamic and static tensile strengths. Liu, Xu et al. (2011) carried out the direct and indirect tensile tests on salt rock, and concluded that the tensile strength of salt rock determined by direct tensile test was more precise than by indirect tensile test. Mishra and Basu (2012) used the block punch test to predict the Brazilian tensile strength of granite and concluded that prediction by the block punch index is more precise than by the point load strength. Through numerical, John, Antoun et al. (1992) found that the stress distribution in the Brazilian test was similar to the static test, therefore, they found that the dynamic Brazilian test was an effective method to measure the tensile properties.

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