A Phenomenological Model of Brittle Rocks under Uniaxial Compression

A quantitative model was recently proposed by Peng et al (2015) to characterize the crack closure behavior of rocks. The model can simulate the initial nonlinearity of stress–strain curves in uniaxial and triaxial compressions. However, the crack propagation behavior near peak and in the post-peak deformation stage cannot be captured by the model. This paper extends the model to simulate the complete stress–strain curves of rocks under uniaxial compression. A phenomenological damage model, which uses a logistic function to describe the damage evolution, is adopted to model the pre-peak and post-peak deformation stages beyond the crack closure stage. Combining the crack closure model and the damage model yields a new phenomenological model. A uniform continuity condition is used to ensure that the stress–strain curve is smooth and continuous at the junction point of the crack closure model and the damage model. The proposed model has four model parameters, which can be calibrated using laboratory test data. The uniaxial compression tests of the Carrara marble under different heating cycles are simulated to verify the proposed model. The simulated stress–strain curves agree well with the test data, from initial crack closure to near peak and post peak, suggesting that the model can be used for simulating the entire deformation stage of brittle rocks with different degrees of initial microcrack damage.