## 1 Introduction
Many scholars have carried out a lot of research on the mechanical strength properties of deep rock under complex stress conditions such as cyclic loading and unloading by means of laboratory tests, theoretical analysis, field observations, numerical simulation, etc. [PERSON] et al. [14] investigated the acoustic emission properties of sandstone samples under uniaxial cyclic unloading and investigated the deformation and damage process of rock materials under cyclic loading and the effect of the loading and unloading rate on the strength of rock by exploring the acoustic emission properties of sandstone specimens under uniaxial cyclic unloading. The effect of the loading and unloading rate on the strength of the rock was investigated. [PERSON] et al. [15] explored the damage characteristics and the form of instability of rocks in the static loading and fatigue loading phases through triaxial cyclic loading and unloading tests and also investigated the internal fracture expansion law of the rock. [PERSON] et al. [16] found that the volumetric strain of the rock has a certain effect on the susceptibility of the rock to fracture extension by cyclic loading tests at different surrounding pressures. By increasing the surrounding pressure, the irreversible strain in axial and radial directions can be changed so that the change process of rock strain increases. In the research on the energy evolution characteristics of loaded rocks, [PERSON] et al. [17] analysed the energy characteristics of the pre-peak phase of rocks based on conventional uniaxial and triaxial rock compression tests. [PERSON] et al. [18] analysed the law of influence of surrounding pressure on the energy dissipation and energy release characteristics of rock damage crack extension and revealed the energy mechanism of the crack extension during the damage of rock samples under different triaxial stresses. [PERSON] et al. [19] analysed the characteristics of the energy transformation of the absorbed strain energy, dissipated strain energy, and elastic strain energy storage and release of the rock samples based on the marble peak-front unloading surrounding pressure test and the energy principle, revealing the strain energy transformation mechanism of the damage rupture evolution of the rock samples. [PERSON] et al. [20] analysed the energy evolution characteristics of marble under triaxial loading and unloading conditions and revealed the influence laws of the surrounding pressure and unloading rate on the energy accumulation and dissipation of rock samples. In the research on rock energy damage criteria, [PERSON] et al. [21] proposed that when the shape alteration energy of a material reaches its limit value, then the unit begins to break down and the continuous accumulation of the total strain energy is a necessary condition that leads to the destruction of the material. In summary, although there is much research on the mechanical properties of cyclic loading and unloading of different rocks, most of it focuses on lower-strength rocks. There is still some space for targeted research on deep, high-strength sandstone. Therefore, the research on the mechanical properties and energy evolution characteristics of high-strength hard sandstone under different peripheral pressure triaxial cyclic loading is an important demand for the current deep geotechnical engineering construction. In this research, conventional triaxial loading and triaxial multistage cyclic loading and unloading tests were carried out on high-strength sandstones under different surrounding pressures by a multi-field coupled triaxial tester. The stress-strain response characteristics of high-strength sandstones under different stress conditions, the strength properties, and the strain distribution law in cyclic loading and unloading were investigated. The energy evolution law and damage characteristics of high-strength sandstone under triaxial cyclic loading and unloading conditions were also analysed.