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Rock crack evolution and propagation have an adverse effect on rock mass deformation and strength, so studying the crack evolution process is significant to rock engineering stability and safety. Tri-axial compression tests were carried out on granite from the Shuangjiangkou underground powerhouse to study the five stages of the crack evolution process, namely, the crack closure, elastic, stable crack growth, unstable crack growth, and post-peak stages. Rd, defined as the deviatoric stress to peak strength ratio, is introduced to analyze the test data. The confining pressure can influence the crack threshold stress, elastic modulus, and Poisson’s ratio. The crack closure ratio has a consistent exponential relationship with Rd under different confining pressures, and a unified constitutive model is proposed by introducing quasi-viscous, plastic, and elastic elements. This model can simultaneously and satisfactorily describe the whole axial and lateral crack evolution process and overcomes the shortcomings of previous models. In particular, the model can conveniently describe the post-peak stage behavior, revealing that the lateral deformation is notably greater than the axial deformation at the failure stage. Moreover, the model clarifies the rock mass macroscopic failure mechanism and has good application prospects in underground excavation damage research. [ABSTRACT FROM AUTHOR]