A compressive damage model for a rock considering the microcrack mechanical behavior

The contributions of the microcrack sliding and propagation to the rock total deformation, the mixed propagation criterion of the microcrack, and the influence of the rock damage degree on the number of the activated microcracks are not completely considered in the existing rock compressive damage model. Thus, the microcrack sliding and propagation mechanism under uniaxial compression was studied with the mesoscopic mechanics. Firstly, the uniaxial compression stress-strain relationship was developed according to the microcrack sliding model and energy balance which assumed the microcracks being Weibull distribution. Then the mixed fracture propagation length of the wing-crack was solved with the strain energy density criterion as the microcrack propagation criterion and iteration method. The damage evolution equation was obtained with the wing-crack propagation length. A new damage model for the rock under uniaxial compression was proposed and verified. Finally, the parametric sensitivity analysis was adopted to study the effects of the microcrack length, friction coefficient, and rock fracture toughness on the rock mechanical properties. The results show that the rock climax strength from the proposed model is consistent with the corresponding test result, indicating that the proposed model is reasonable. The uniaxial compression climax strength and strain both decrease with the increase of the microcrack length and the decrease of the microcrack friction coefficient. When the microcrack length increases from 60 μm to 120 μm, the uniaxial compression climax strength almost decreases linearly. When the microcrack friction coefficient increases from 0.5 to 0.8 and the rock fracture toughness increases from 0.3 MPa·m^1/2 to 0.6 MPa·m^1/2, the uniaxial compression climax strength increases slowly and then rapidly. This study provides new insight into the establishment of the rock damage constitutive model under compression.