# Numerical Analysis of Cyclic Impact Damage Evolution of Rock Materials under Confining Pressure
## 1 Introduction  
In recent years, due to the rapid economic development and increasing demand for mineral resources, rock engineering involved in tunneling, mining resources exploitation, and underground space utilization has extended into deep environments [1; 2; 3]. Moreover, during rock excavation in deep environments, the dynamic disturbance induced by blasting or rock burst has a significant influence on the stability of rock engineering [4; 5; 6]. In fact, the instability of surrounding rock in deep rock engineering is not typically attributed to a single impact event but cumulative damage induced by cyclic loads [7; 8; 9]. Cumulative damage induced by cyclic loads leads to crack generation and propagation, fracture, and eventually instability [10; 11; 12; 13]. Therefore, investigating the dynamic damage evolution of rock materials under confining pressure holds significant engineering application value and is crucial for the protection of underground projects. The damage evolution of rock materials under cyclic impact conditions has been investigated by analyzing elastic modulus, acoustic emission, energy dissipation, wave impedance, and other parameters. [PERSON] [14] and [PERSON] [15] identified three stages in the damage evolution of rocks under cyclic impact, namely the initial stage, low-speed stage, and accelerated stage. Rock specimens experience significant impact damage at the initial stage, then the cumulative damage gradually increases at the low-speed stage, and finally,the damage accelerates rapidly, resulting in rock failure. Based on the results of cyclic impact tests, [PERSON] et al. (2016); [PERSON] et al. (2016) employed wave impedance to define the damage variable of rocks and revealed that the wave impedance method provides a more accurate depiction of the damage evolution characteristics of rocks than other commonly used methods for defining damage variables. [PERSON] et al. (2018) performed cyclic impact tests on sandstone using split Hopkinson pressure bar apparatus and analyzed the damage evolution based on the Weibull distribution statistical damage model. [PERSON] et al. (2019) conducted cyclic impact tests on sandstone specimens under various confining pressures and observed that the confining pressure restricts the accumulation of damage, namely a significant confining pressure effect. In the uniaxial cyclic impact test of rock, [PERSON] et al. (2019) employed the static crack initiation stress in a static stress-strain curve to estimate the dynamic crack initiation stress. By conducting constant amplitude cyclic impacts on granite, [PERSON] et al. (2019) found that the number of cyclic impacts initially increases and then decreases with the rise in axial pressure, which implies a strengthening effect when the pre-axial pressure is lower than the rock's crack initiation stress. Under the combined action of pre-axial compression and cyclic impact, [PERSON] et al. (2020) observed that the stress-strain curve of rocks under various axial pressures exhibits two distinct features, namely rebound and non-rebound, and the fragmentation of rocks is intensified as the axial pressure rises. [PERSON] et al. (2020) investigated the dynamic mechanical properties of rocks subjected to cyclic impacts under confining pressure and observed that the confining pressure can enhance the rock's resistance to cyclic loading. [PERSON] et al. (2021) performed cyclic impact tests on rocks using a SHPB apparatus with a confining pressure device and discovered a power function relationship between rock damage variables and average strain rate. Through three-dimensional coupled static-cyclic impact tests, [PERSON] et al. (2016); [PERSON] et al. (2016) found that axial pressure and confining pressure are negatively correlated and positively correlated with the total number of cyclic impacts, respectively. Therefore, reducing the axial pressure or increasing the confining pressure can improve the impact resistance of rock. By analyzing the energy dissipation and damage of rock under cyclic impact, [PERSON] et al.