## 1 Introduction  
Based on the resource endowment conditions of having a relatively rich coal reserve, a poor oil reserve, and a limited natural gas reserve, it is expected that coal will continue to play a dominant role in China's energy system in the near future [1]. The stability of coal roadways poses numerous complex and challenging issues, particularly in high-stress areas that are subjected to repeated mining activities. However, due to the substantial increase in coal production, many mining locations are experiencing a rise in coal mining intensity. Consequently, the surrounding rock of the coal roadways often undergoes significant deformation and failure, which is a frequent problem. Therefore, it is crucial to conduct relevant research on the deformation characteristics of coal roadways and develop effective control strategies. When it came to the stability control of roadway surrounding rock, prior literature mainly concentrated on complex production geological conditions, such as deep high stress, large sections, geological structures (such as faults), extra thick coal seams, thick mudstone composite roofs, and proposed control countermeasures under various circumstances [2; 3; 4; 5]. The adoption of support modification pressure relief collaborative control technology was suggested by [PERSON] et al. [6]. He and his collaborators [7] advocated using anchor control technology with substantial deformation and steady resistance. A square steel (steel tube) concrete support is suggested in light of the deep, high-stress, dynamic-pressure roadway [8; 9; 10; 11]. Utilizing a truss control system was suggested by [PERSON] et al. [12]. The zoning joint control technology was proposed by [PERSON] et al. [13]. The application of prestressed synergistic support technology was suggested by [PERSON] et al. [14]. Long anchors, stiff long rebar bolts, anchor nets, \(W\) steel belts, and shotcrete were suggested by [PERSON] et al. [15] as the major body of a comprehensive control technology that can be attached to long anchors to strengthen the roof plate. According to [PERSON] et al. 's [16] proposal, the surrounding rock of the roadway was supported in zoning on the basis of drilling and depressurizing it. [PERSON] et al. 's [17] stepwise reinforcement and support approach was based on the expansion of the spatio-temporal relationship of the plastic zone in the recurrent mining operation. However, the majority of coal roadways are situated in areas with high levels of mining stress. This means that when the roadway is excavated, the surrounding rock becomes damaged. If the correct support technology is not used, this can result in significant deformation of the roof plate, leading to accidents such as roof destabilization and collapse. The initial excavation and repair of these roadways is particularly challenging and time-consuming because they often require frequent fixes, sometimes even in the same location. This circumstance makes it difficult to ensure the safety of coal mine production during the excavation process and requires personnel to regularly repair the considerable deformation risk zone in the surrounding rock. Numerous numerical simulations have been constructed and used recently to analyze the mechanism of roadway instability. Numerical approaches to research have the benefits of being inexpensive, very effective, and highly reproducible. Numerous case studies and numerical techniques for various applications confirm that modeling the failure mechanism is feasible. [PERSON] et al. [18] suggested the UDEC Trigon technique and simulated the evolution features of the surrounding roadway deformation, including crack development, roof displacement, damaged coal side zones, etc. Stability analysis of surrounding rock in a mining roadway. In order to analyze the primary influencing factors of the mining-induced vertical and horizontal stresses as multiple coal seams advanced sequentially, [PERSON] et al. [19] and [PERSON] et al. [20] conducted a numerical simulation.