## 1 Introduction  
The existence of the structural plane destroys the continuity of rock mass. For engineering rock mass, the rock mass structure will change relative to changes in engineering scale and size. When a cavern span is small, there will be relatively few structural planes in the surrounding rock, and the strength of the rock mass will be close to the overall rock strength; when a cavern span is large, there will be more structural planes in the surrounding rock, and the strength of the rock mass will be close to the strength of the structural plane. In this context, the failure mode of the surrounding rock is predominantly part of the controlled failure of the rock mass structure. Therefore, under the same surrounding rock conditions, for the large-span cavern project, the strength of the rock mass will be lower, the degree of fragmentation will be higher, and progressive collapse will happen more easily. The mechanical mechanism of the rock mass and the stability analysis method of the project are different for different structures of engineering rock mass [1, 2]. Therefore, it is of great theoretical significance and practical value to carry out in-depth research on the progressive collapse mechanism of the surrounding rock of large-span caverns.  
Scholars both at home and abroad have studied the collapse mechanism of surrounding rock by using the nonlinear Hoek-Brown failure criterion and the upper limit analysis theorem. [PERSON] et al. [3, 4, 5] proposed a combination of plasticity theory and the Hoek-Browncriterion to analyze the collapse profile of cavern excavation and obtain the analytical solution of the collapse curve of a vault of circular and rectangular tunnels. The research results have also been expanded upon and applied by many scholars. [PERSON] et al. [6; 7; 8; 9] studied the tunnel collapse failure mechanisms of circular, rectangular, and layered soil. [PERSON] et al. [10] derived the three-dimensional failure mechanism of deep soil tunnels based on the Mohr-Coulomb criterion, studied the influence of various parameters on the collapse range, and obtained the exact solution of the collapse curve. [PERSON] et al. [11] established a three-dimensional progressive collapse mechanism for deep-buried tunnels and compared it with the actual tunnel engineering situation, verifying the applicability of the theoretical calculation results to predict the progressive collapse range of tunnel vaults. In underground mining, particularly with room and pillar methods, excavations are often expanded to residual dimensions during the pillar recovery phase. This approach aims to minimize operational losses [12] and optimize waste storage [13].  
The collapse of the surrounding rock of the cavern is not formed in a single instance. With the gradual weakening of the mechanical parameters of the surrounding rock of the cavern during excavation, a short-term stable collapse arch will be formed within the loosening range of the surrounding rock for each collapse failure, until the minimum residual strength of the surrounding rock is reached, when, finally, a stable collapse will be formed. The progressive collapse phenomenon of rock surrounding a cavern has been confirmed many times [14; 15; 16]. At the same time, according to the statistical results of underground engineering collapse accidents [17], among 50 underground engineering collapse accidents, 44% had two or more collapses. Among them, the instances of three or more collapses accounted for 26%.  
By reviewing the relevant literature, it is apparent that research on the collapse of rock surrounding an arch mainly focuses on the final failure mode, with research lacking on progressive collapse incubation and evolution mechanisms. This paper will use the Hoek-Brown failure criterion and the upper limit theorem to study the progressive collapse characteristics of the surrounding rock of long-span caverns through theoretical analysis and model experiments.