## 3 Materials and Methods
### Methods  
(1) Indoor test  
The test loading unit employs a C64.106/1000 kN electro-hydraulic servo universal testing machine (Shanghai Sukyo Industrial Technology Co., Ltd., Shanghai, China), while the control unit utilizes Test Expert. In this study, the uniaxial compression test is conducted using a displacement control mode with a loading rate of 0.2 mm/min, as illustrated in Figure 3f. The electronic universal testing machine (China Machine Testing Equipment Corporation, Beijing, China) is also employed for the variable angle shear test, which is performed at three different angles: 55\({}^{\circ}\), 60\({}^{\circ}\), and 65\({}^{\circ}\), maintaining the same loading speed of 0.2 mm/min, as shown in Figure 3g. The test continues until the rock sample fails, resulting in a rapid reduction in strength, at which point the testing machine automatically ceases loading. The entire testing process is recorded using a high-speed camera operating at 50 frames per minute, while the strain of the rock samples is monitored with a TS3890N static resistive strain gauge (Langfang Zhongyi Science & Technology Co., Ltd., Langfang, China). The procedures for rock sample preparation and loading are depicted in Figure 3h.  
(2) Numerical simulation  
FLAC 3D numerical simulation software (version 5.0, Itasca Consulting, Inc., Minneapolis, MN, USA) was employed to analyze the stress evolution characteristics of the irregular ground surface at the 51,102 working face during the mining period. This analysis aimed to clarify the stress environment of the surrounding rock in the roadway.  
(1) Model parameters and mechanical parameters  
The model has dimensions of 300 m \(\times\) 370 m \(\times\) 82 m, with the cross-section of the two roadways being a rectangular shape measuring 4.5 m in width and 2.8 m in height. Protective coal pillars, measuring 45.5 m, are reserved on both sides, while 50 m of protective coal pillars are allocated in front of and behind the 51,102 working face. A pressure of 1.8 MPa is applied to the roof, with lateral pressure coefficients of 0.82 and 0.91, respectively. Given that the ground at the 51,102 working face exhibits a \"T\"-type configuration, the model simulates the impact of the combined effects of the irregular surface and mining stress on the stability of the surrounding rock in the two roadways of the 51,102 return airway. The boundary conditions for the model are as follows: the boundaries surrounding the model are constrained to prevent horizontal displacement, the bottom boundary is restricted from vertical displacement, and the roof boundary remains free. A diagram of the numerical calculation model is presented in Figure 4.  
The yielding deformation of the surrounding rock following the excavation of the coal mine occurs due to the combined effects of roof water infiltration and surrounding rock stress. The selection of parameters for numerical simulation involves continuously adjusting these parameters to ensure that the stress-strain curve and failure mode observed in the numerical simulations closely resemble those of physical experiments [37; 38]. Taking into account the flow-solid coupling effect [39; 40; 41; 42; 43] and the specific underground geological  
Figure 4: Numerical calculation model: (**a**) the dimensions and parameters, (**b**) the boundary conditions and constraints.  
conditions, the strength of the surrounding rock under conditions of gushing water can be estimated to be approximately 70% of that in a water-free environment (as illustrated in Figure 5), and is simulated using FLAC3D software (version 5.0, Itasca Consulting, Inc., Minneapolis, MN, USA). The physical and mechanical parameters for each rock layer are detailed in Table 1.