## 1 Introduction  
After the completion of a fully mechanized mining face, the equipment needs to be retracted to the next working face, during which the stability of the RR is crucial for ensuring the safe and rapid retracement of this equipment. The pre-driven longwall single retracement roadway (PLSRR) technique is commonly employed in the northern Shaanxi mining areas to retract the equipment from the working face during the end-miningstage [1]. After the excavation of the RR, anchored mesh cables are commonly used as an initial support, while hydraulic checks are employed for secondary support as the working face enters the end-mining stage. However, during the end-mining and connection process, issues such as large-scale hydraulic support crushing accidents or support failures in the RR often arise due to unclear stress distribution patterns in the coal pillars at the working face. For instance, support crushing accidents occurred during the retracement of the N14201 working face at Zhangjianao Coal Mine [2], the 15,205 working face at Hongliulin Coal Mine [3], and the 12,211 working face at Shangwan Coal Mine [4]. Numerous researchers worldwide have conducted extensive studies on this topic. [PERSON] et al. [5] improved the initial support force by using full cable bolts for roof support and a combination of cable bolts and mesh for coal wall support to ensure the smooth withdrawal of working face equipment. [PERSON] et al. [6] found that the support resistance increases gradually as the coal pillar width between the working face and the empty roadway decreases. [PERSON] et al. [7] employed a numerical simulation to examine the stress distribution and displacement characteristics of a mine roof when the working face passed through an abandoned roadway, pre-splitting the roof in advance. [PERSON] et al. [8] analyzed the limit width of coal pillars and the supporting force required by an abandoned roadway in the working face, and put forward the supporting technology combining anchor cables and pumping pillars. [PERSON] [9] studied the variation law of the abutment pressure of the working face when the working face was at different positions from the abandoned roadway, and provided the basis for the working face to determine the range of advanced support and to take the position of strengthening support. [PERSON] et al. [10] proposed a method for longwall working faces to pass through parallel abandoned roadways by employing cutting techniques. [PERSON] et al. [11,12] applied hydraulic fracturing technology to pre-fracture and relieve pressure on the roof strata, thereby reducing roof pressure intensity during the end-mining stage. [PERSON] et al. [13] studied the deformation characteristics and reasonable location design of the RR under the action of different superimposed stress conditions in closely-spaced coal seams. [PERSON] et al. [14] analyzed the impact of superimposed benefits of advanced support pressure and lateral support pressure on the stability of the RR during the final extraction stage. [PERSON] et al. [15] explored the spatial relationship between the RR of soft roofs and thin coal seams and the basic roof fracture subsidence, analyzed the relationship between the support resistance and the rotation angle of the immediate roof, and determined the reasonable time for the RR layout. [PERSON] et al. [16] used a numerical simulation to study the roof pressure relief technology of pre-excavated RRs by hydraulic fracturing. [PERSON] et al. [17] studied the impact of the superimposed effects of roadway support pressure and roof instability stress on the stability of RR-surrounding rock during the final extraction of the large mining height working face in the Jinjitan Coal Mine, and proposed a surrounding rock control strategy involving \"blasting of the roof and constant resistance anchor cable support\". [PERSON] et al. [18] demonstrated that the lateral support pressure of the working face during the final extraction stage affected the stability of RR-surrounding rock. [PERSON] et al.