## 1 Introduction
[8] used continuous and discontinuous models to analyze the deformation of LRC buried at a depth of 50-100 m. They verified the feasibility of the LRC concept and suggested that good geological conditions and sufficient burial depth are the key factors for LRC. In 2001, [PERSON] et al. [9] introduced two limit equilibrium models, the rigid cone model, and the log spiral model, as evaluation criteria for stability in assessing the safety of silo-type LRCs against ground uplift. The rigid cone model assumes that the failure surface is an inclined straight line with a vertical inclination of 30\({}^{\circ}\) to 45\({}^{\circ}\), the lower cone angle is suitable for loose or weathered rock mass, and the strength of the rock mass is not taken into account. The log spiral model is based on the ultimate pullout resistance of single vertical anchors, presented by [PERSON] et al. [10] in 1994, which takes into account the friction at the failure surface of the rock mass, and the failure surface shape is a logarithmic spiral function with respect to the internal friction angle; however, [PERSON] [11], in 1988, found that the shape of the spiral is also sensitive to the horizontal geopathic stress and that lower horizontal geopathic stresses produce a narrower and steeper spiral curve. In 2012, [PERSON] et al. [12] proposed a model in which the cracking surface is a vertical surface and gave a calculation method for the safety factor of two types of LRCs, which considered parameters such as ground stress coefficient and rock strength, etc. The advantage is that the calculation is simple, but the results of their calculations are on the conservative and safe side, and the assumed cracking surface is not reasonable. These three models can be seen in Figure 4. Regarding the issue of uncertainty in fracture surfaces, various scholars have initiated research into the morphology of fracture surfaces in overlying rock masses. [PERSON] and [PERSON] et al. [13; 14; 15; 16] combined numerical methods and physical model experiments to study the cracking patterns of overlying rock masses in tunnel and large cavern LRCs, providing the crack initiation pressure, the location of crack initiation points, and the  
Figure 3: The key problems and main structure of an LRC. morphology of the failure surface under different geostress coefficients, offering significant references for engineering design. [PERSON] et al. (2017), based on physical model tests and numerical analyses, primarily focused on the impact of the strength characteristics of the rock on the mode of failure. Their analysis indicated that the failure mode of silo-type LRCs strongly depends on the strength properties of the rock, independent of the initial geostress conditions; the initiation location of fractures, on the other hand, was influenced by both the rock strength and the initial geostress. [PERSON] (2018) used the upper bound theorem of limit analysis to assess the geometry of the failure surface. The effects of geometrical and geotechnical parameters on uplift pressure are analyzed systematically. [PERSON] et al. (2019) proposed a failure mechanism for tunnel-type LRCs overlying a single rock layer and multiple rock layers, considered the effects of ground loads and arbitrary tunnel profiles and derived an analytical solution for the critical uplift pressure and the corresponding failure surfaces based on the limit analysis and the variational principle. [PERSON] et al. (2020) investigated, by stress analyses performed on a continuum model as well as by comparative limit equilibrium computations, the uplift failure of sealed CAES tunnels crossing weak rock at relatively small depths of cover. Currently, most scholars are less likely to compare the analysis of the two types of LRCs. For the silo-type LRC, studies usually focus on the crack morphology and damage modes, while there is a relative lack of exploration of its ultimate pressure and stability. In contrast, studies on tunnel-type LRCs are more comprehensive.