## 1 Introduction  
With the large-scale exploitation of shallow mineral resources in the earth, numbers are approaching exhaustion, and mineral exploitation is expanding deeper. The deep high-stress occurrence of this environment makes the rock have a mechanical behavior that is different from that of shallower depths. Traditional rock mechanics theories and methods may fail [1; 2; 3; 4]. Moreover, with the construction of tunnels, the excavation of underground chambers and other deep underground projects, rock in its original equilibrium state is disturbed. As a result of repeated loading, the internal energy of the rock accumulates and releases, damage accumulates and the stability of the engineering of the rock is affected, thus causing a sequence of safety accidents, including rock burst and collapse. Therefore, studying the mechanical properties of deep rock during cyclic loading at different stress grades can contribute to disaster prediction and prevention.  
At present, experts have conducted much research on the mechanical characteristics of rock damage and have achieved many results. There are two main methods of studying the mechanical characteristics of the rock. One is to explore the microscopic damage mechanism, and the other is to describe the macroscopic deformation behavior [5; 6; 7; 8; 9]. [PERSON] al. [10] constructed an intrinsic equation that can describe the whole stage of rock damage under the new concept of the void strain ratio, describing the relationship between rock deformation and void and skeleton deformation. [PERSON] et al. [11] found that the Weibull probability distribution ontological model is more reasonable and superior in the plastic stage by establishing two constitutive models of rock micro-element strength, satisfying the power function distribution and Weibull probability distribution, respectively. [PERSON] et al. [12] established an elastoplastic damage intrinsic equation considering different damages under tension and compression-shear conditions. [PERSON] et al. [13] constructed a piecewise constitutive model based on the relationship between strain, void deformation and skeleton deformation. They believe that the rock strain before the rock yield can be composed of void strain and skeleton strain.  
According to the laws of thermodynamics, material destruction is accompanied by energy transformation [14; 15]. [PERSON] et al. [16] investigated the energy properties of limestone under different confining pressures. [PERSON] et al. [17] established a nonlinear relationship between different energy characteristics of granite and cycle amplitude and cycle times. [PERSON] et al. [18] performed comparative research of rock energy under different moisture contents.  
In summary, it is hard to represent rock changes under complex stress states by using the damage intrinsic relation of conventional M-C and D-P theory. Based on this, a damage intrinsic model considering the effect of intermediate principal stress can be established. The strength of the rock micro-units satisfies the Mogi-Coulomb strength criterion, and the micro-units failure follows the Weibull probability formula. The constitutive model with fewer parameters can be combined with the nonlinear fitting function of the Origin software to obtain the model parameters quickly. It is more suitable to analyze internal changes in the deep underground surrounding rock. In this paper, the model verification and model parameter analysis were carried out through a cyclic loading test on sandstone. The law of mechanical parameters and the energy in the course of cyclic loading are explored, and the damage properties of sandstone under high-stress cyclic loading were revealed, which provides some theoretical support for underground engineering.