The establishment of a rock constitutive model considering microcrack propagation characteristics is an important channel to reflect the progressive damage and failure of rocks. The prepeak crack strain evolution curve of rock is divided into three stages based on the triaxial compression test results of granite and the definition of crack strain. According to the nonlinear variation characteristics of crack strain in the stage of rock crack stable propagation, rock deformation is expressed as the sum of matrix strain and crack strain. Then, the exponential constitutive relationship of rock crack stable propagation is deduced. The axial crack strains of the rock sample and its longitudinal section are equal. Thus, the longitudinal symmetry plane of the rock sample is abstracted as a model containing sliding crack structure in an elastic body, and the evolution equation of crack geometric parameters in the process of stable crack propagation is obtained. Compared with the experimental data, results show that the rock crack stable propagation model based on crack strain can adequately describe the evolution law of crack strain and wing crack length. In addition, the wing crack propagates easily when the elastic body with small width contains an initial crack with a large length and an axial dip angle of 45° under compressive load. This study provides a new idea for the analysis of the stable propagation characteristics and laws of rock cracks under compressive load.

Stress arching effect during the excavation of broken surrounding rock in underground engineering has an important influence on the stability of surrounding rock after underground excavation. To determine the stress arching effect in horizontally layered jointed rock mass, the stress arching characteristics of surrounding rock mass after excavation is analyzed in this study by using a series of numerical tests. The formation mechanism of stress arch is revealed through a comparison of the stress characteristics of a voussoir beam structure and theoretical analysis of multi-block mechanical relationship of jointed rock mass. The method for determining the boundaries of a stress arching zone is proposed, and the influence of various factors on a stress arch is further discussed. Results show that after the excavation of horizontally layered jointed rock mass, the stress arch bunch (SAB) is formed in the lower strata above the cavern, and the global stress arch (GSA) is formed in the higher strata, both of which are symmetrical arch stress patterns. The SAB is the mechanical manifestation of the voussoir beam structure formed by several low-level sandstone layers, and the GSA is caused by the uneven displacement between blocks. Compared with the GSA, the SAB is more sensitive to various influencing factors. The extent of stress arching zone decreases with the increase of an internal friction angle of the joint, lateral pressure coefficient, and overburden depth. In addition, the joint spacing of rock strata is conducive to the development of a stress arch. Results can provide technical support for deformation control and the stability analysis of broken surrounding rock in underground engineering.