## 1 Introduction  
The rock strength theory and deformation failure characteristics form the theoretical basis for research and analysis of rock engineering safety and stability. For years, rock strength and failure criteria based on classical elastic-plastic theory have been the basis for judging engineering failure [1]. However, rocks are typically nonuniform and discontinuous media that contain a large number of structurally discontinuous and irregularly shaped microcracks. The failure mechanism of rocks is closely related to the mode of action of the host environment, and the mechanical properties of rocks at failure show complex changes under different loading forms. Some strength theories and failure criteria make it difficult to effectively analyze the complex strength changes and failure behaviors of rocks. The thermodynamic theory states that material failure is a state instability phenomenon driven by energy, and the transfer of energy is the essence of material deformation and failure [2]. Therefore, studying and establishing the energy variation pattern during the rock failure process and its relationship with the strength and overall failure from an energy perspective will be more conducive to reflecting the essential characteristics of rock strength variation and overall failure under external loads. Recently, domestic and international scholars have conducted studies on the law of energy evolution during rock deformation. [PERSON] et al. [3] conducted uniaxial cyclic loading tests on sandy undstones and siststones, obtained damage variables based on the dissipated energy, and established a damage constitutive model that could describe the mechanical properties of rocks under cyclic loading according to the Lemaitre strain equivalence principle. [PERSON] et al. [4] showed that the dissipated energy generated under an external load damages the rock and reduces its strength and that the failure of the rock is caused by the sudden release of the internally accumulated strain energy. [PERSON] et al. [5] conducted conventional triaxial tests on fine-to-medium-grained granite under different confining pressures and loading and unloading stress paths to study their energy evolution and failure processes. [PERSON] and [PERSON] [6] found that the energy required to cause fractures increased rapidly with increasing amplitude and frequency in dynamic cyclic loading. [PERSON] et al. [7] demonstrated that under different loading rates, the distortion energy during rock expansion and failure follows a linear relationship with the average normal stress. [PERSON] et al. [8] experimentally studied the energy dissipation and release during coal failure under conventional triaxial compression and proposed two parameters (failure energy ratio and stress drop coefficient) to describe the failure mode of coal under different confining pressures. [PERSON] et al. [9] studied the damage and failure of coal and rock with bursting liability from the perspective of energy dissipation using the geophysical method of electromagnetic radiation and explored the energy dissipation characteristics during uniaxial compression and their main influencing factors. [PERSON] et al. [10] established an energy mutation failure criterion based on the evolution law of gravitational potential energy, elastic strain energy, and kinetic energy. The criterion has the advantages of clear physical meaning, strong integrity, and good applicability y, which can accurately predict the instability and failure of jointed slopes. [PERSON] et al. [11] conducted conventional triaxial compression tests on marbles and sandstones with different bedding plane dip angles under different confining pressures, obtained the influences of confining pressure on critical strain energy release rate and energy transformation of anisotropic intact rocks, and established a new critical strain energy release rate failure criterion. [PERSON] et al.