## 1 Introduction  
In response to the call for carbon reduction, many countries have begun to vigorously develop new energy constructions. Renewable and clean energy sources, represented by solar and wind power, will occupy a dominant position in the future energy supply. Due to the significant variability of wind and solar energy, there is a substantial amount of energy waste. Large-scale energy storage technology can enhance the grid's peak-shaving capability, offering a solution to the issue of extensive energy discarding. Among these technologies, compressed air energy storage (CAES), with its large capacity, small footprint, and long lifespan, has become one of the mainstream energy storage technologies. The working principle involves using surplus electricity during low-demand periods to compress air and store it in storage facilities. During peak electricity demand, the compressed air is released to drive turbine generators. For large-scale compressed air storage systems, considering cost-effectiveness, underground storage caverns are generally chosen as the storage solution. The working principle of the system is illustrated in Figure 1. Based on the currently available surface process parameters, the typical maximum storage pressure for lined rock caverns used in compressed air energy storage is generally between 10 MPa to 18 MPa or higher. Underground air storage reservoirs can generally utilize geological cavities such as salt caverns, lined rock caverns (LRCs), abandoned mines, depleted oil and gas reservoirs, and aquifers [1; 2; 3]. Generally speaking, salt caverns are the best option for gas storage due to their excellent natural self-sealing properties [4; 5; 6]. However, not all locations requiring the construction of compressed air energy storage facilities have salt caverns. An LRC is a type of cavern that is artificially excavated in hard rock. Except for the LRC, geological limitations affect all other chambers, meaning that the proposed CAES site cannot guarantee a distribution of these geological formations. Therefore, LRCs stand out as the optimal choice for air storage. The main structural components of LRCs are as follows: sealing layer, concrete liner, and surrounding rock. The core concepts of the engineering design are (1) the sealing layer deforms flexibly in the annular direction and has only a sealing function; (2) the concrete liner is used to smooth the pressure and transfer the load to the surrounding rock; and (3) the surrounding rock restrains the deformation of the structure with its strength and stiffness and absorbs the internal pressure load. Therefore, the air pressure is completely transferred to the surrounding rock in a flexible form. Thus, the main air pressure is borne by the surrounding rock, while the lining and sealing layers are subjected to only negligible pressure. The LRC is usually subjected to high internal pressures, and thus also poses several geotechnical problems, the core of which are the overlying rock stability problem and the sealing structure stress problem [7], as shown in Figure 2. There are two main types of LRCs, the silo type and the tunnel type (Figure 3). Figure 1: The working principle of CAES. Figure 2: The key problems and main structure of an LRC. The minimum \"distance\" between the actual working state (or designed working state) and the damage state of a building is defined as the degree of safety, and the factor of safety is a numerical value that expresses this \"distance\". The depth of burial is an important parameter in the design of shallow LRCs and is directly related to the factor of safety. In general, the larger the safety factor, the safer and more reliable the design is. However, too large a safety factor corresponds to too deep a burial depth, which can lead to an increase in the cost and difficulty of the project, so it is important to analyze the stability of the overlying rock mass for the design of the project. In 1989, [PERSON] et al.