A theoretical approach to quantify the effect of random cracks on rock deformation in uniaxial compression

Cracks have a significant effect on the uniaxial compression of rocks. Thus, a theoretically analytical approach was proposed to assess the effects of randomly distributed cracks on the effective Young's modulus during the uniaxial compression of rocks. Each stage of the rock failure during uniaxial compression was analyzed and classified. The analytical approach for the effective Young's modulus of a rock with only a single crack was derived while considering the three crack states under stress, namely, opening, closure-sliding, and closure-nonsliding. The rock was then assumed to have many cracks with randomly distributed direction, and the effect of crack shape and number during each stage of the uniaxial compression on the effective Young's modulus was considered. Thus, the approach for the effective Young's modulus was used to obtain the whole stress-strain process of uniaxial compression. Afterward, the proposed approach was employed to analyze the effects of related parameters on the whole stress-stain curve. The proposed approach was eventually compared with some existing rock tests to validate its applicability and feasibility. The proposed approach has clear physical meaning and shows favorable agreement with the rock test results.