Theoretical Study on the Failure of Rocks with Preexisting Cracks Considering the Extension of the Crack Tip Plastic Zone

Rock failure, which causes instability in rock engineering, is an engineering accident that generally occurs through the coalescence of the preexisting cracks in rocks. Therefore, it is very important to research the coalescence of rock cracks to prevent rock engineering accidents. Based on the mechanical theories of elastoplastic mechanics and fracture mechanics (the generalized Drucker–Prager (D-P) yield criterion and the core concept of the Kachanov method), the propagation of the plastic zones at rock crack tips affected by far-field uniform pressures is theoretically researched considering the interaction of two collinear cracks of unequal length. Moreover, for two cases of two cracks of equal length and unequal length in rocks, the basic laws of crack coalescence by the propagation of the plastic zones at rock crack tips are first studied, and the suggested threshold values of crack spacing for crack coalescence in rocks are provided. The results show that, for equal-length cracks, as the crack spacing decreases, the cracks propagate by a quadratic polynomial function, and the threshold is 0.2 of the ratio of crack spacing to crack length. Moreover, for unequal-length cracks, as the crack spacing decreases, the cracks propagate by a linear function, and the threshold is 0.3 of the ratio of crack spacing to secondary crack length. Finally, using the numerical simulation of a rock slope including equal-length and unequal-length cracks, and a laboratory test with a rock-like material specimen including unequal-length cracks, the main conclusions of the abovementioned theoretical studies have been verified. In this study, although the basic law of crack coalescence is first studied and the threshold value of crack coalescence is suggested first, the researched crack morphology and rock properties are relatively simple.