A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite

A micromechanics-based continuum damage model for brittle failure of rock is proposed to provide a numerical tool for analyzing not only the macro-scale mechanical responses of rock under compression such as strength, but also microscopic events, which take place in association with inelastic deformation. Special emphasis is placed on predicting numerically the changes in crack length and crack density during inelastic deformation terminating in brittle failure. Only two parameters, typical size and fracture toughness, are involved in the present model. These can be determined by reading the stress at an initial damage point C′ on a stress–volumetric strain curve. The present model seriously underestimates the dilatational volumetric strains observed experimentally in triaxial tests of Inada granite. This is probably because a new micromechanism starts working in the final stage. The peak (failure) stress obtained numerically is in good accordance with the one observed in triaxial compression tests under a confining pressure higher than, say, 10 MPa. In the case of uniaxial tests in particular, the numerical model seriously overestimates the uniaxial strength. A major tension crack grows through the sample parallel to the axial direction in uniaxial tests, once the crack attains a critical length, while failure occurs in triaxial tests under confining pressures higher than 10 MPa only when the microcrack density is high enough. The overestimation probably reflects such a difference in the micromechanism leading to failure (peak stress). In spite of these difficulties, it can still be said that the proposed model has a chance of providing a sound basis for predicting crack growth, such as crack length and crack density, with sufficient accuracy. To improve the model, we must take into account the real micromechanism of crack growth effective in the final stage and the change in the number density of microcracks ρ during the loading process.

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