A three-dimensional damage model was established combined with statistical mechanics to simulate failure process of heterogeneous rocks. The heterogeneities on mesoscopic scale were considered by assigning element mechanical properties randomly by following a certain statistical distribution function. It was assumed that each element kept elastic before reaching to the failure threshold, and it may fail in either in tensile failure mode or shear failure mode according to a shear failure criterion combined with a tension cut-off. Uniaxial compression test, uniaxial tension test, three bending test and conventional triaxial compression test are carried out to calibrate the model. The simulated crack initiation and propagation as well as the whole progressive fracture process are compared with the theoretical results, the experimental observations and other numerical simulation results. It can be found that heterogeneity plays an important role in rock failure process. Numerical tests for the typical mechanical experiments also indicate the developed damage model is a valuable numerical tool for research on the rock failure progressive fracture.


Analysis of a wide range of problems in rock mechanics and engineering requires knowledge of the failure process in rock. This includes tunnel design, rock slope design and other engineering applications as well as geophysical problems such as earthquake prediction. Though experimental observations have provided a great deal of insight into the complicated failure process, the mechanism of rock fracture under mechanical loading, the details of the failure mechanisms, including the microfracture initiation, propagation, and coalescence, is not fully understood. Rocks are non-transparent and it is difficult to trace the propagation of the rock fracture and fragmentation within the rock. The evolution of the fracture progressive process cannot be successively and visually shown in experimental observations. Besides, it is too expensive to conduct a large number of experiments. On one hand, real fracture processes are 3D and not 2D, and the problems encountered in rock mechanics and engineering are almost all three dimensional to some extent. On the other hand, the two-dimensional analysis is intrinsically limited. There are many loading cases which cannot be simulated in 2D (for instance biaxial loading cases which fail out of plane, or triaxial tests), and even for those which can, it would be desirable to evaluate the importance of the three-dimensional effect because, strictly speaking, 2D calculations would correspond to arrangements of aggregates or particles of prismatic shape in the third dimension [1]. Further, tension experiments on concrete have shown that the fracture process is rarely uniform in the third direction, since cracks generally propagate from one corner, rather than uniformly through the entire depth of a specimen [2]. In addition, neither in plane strain nor in axisymmetric triaxial loading conditions can the intermediate principal stress be taken into consideration. RFPA2D have been successfully used to model the failure of brittle materials and the associated microseismicities. The work presented in this paper is the further study of the work of RFPA2D. and the mesoscopic elastic damage model.

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