“…On the one hand, after coupled loading, a descriptive analysis of the rock damage evolution process is performed by determining the properties such as failure strength, residual strength, cumulative plastic strain, and so on (Cai et al, 2020;Jin et al, 2014;Ma et al, 2004;Wang et al, 2010Wang et al, , 2013. However, when the initial stress of rocks is close to the instability strength (in the vicinity of the strength limit), a small disturbance not exceeding the peak value can also cause instability (Tang et al, 2014), and the strength-based criteria may become invalid. On the other hand, the instability process of rocks can be described by defining energy-related damage variables (Li et al, 2020;Yang et al, 2021), but most of the existing studies only define damage deterioration of rock materials by roughly analyzing the evolution law of dissipated energy, which also cannot reveal the energy conversion relationship in the vicinity of strength limit accurately.…”