## 1 Introduction  
Coal, as a fundamental energy source and industrial raw material, plays a dominant role in energy production and consumption. As China's economy continues to develop, the demand for coal resources is increasing. With the depletion of shallow coal reserves, mining operations are inevitably transiting to deeper deposits. However, this transition brings about significant changes in the mining environment, with increased mining depth. Due to the complex impacts of \"three highs and one disturbance\", the green, safe, and efficient production of deep coal is facing serious challenges [1, 2, 3, 4]. One of the critical aspects affected by these changes is the support design for large-section open-cut roadways in fully mechanized mining faces with large mining heights. The opening cut provides the necessary place for the installation of mining equipment and serves as the site for working face mining. The stability of opening cut support plays a crucial role in the smooth installation of mining equipment and subsequent mining operations. In recent years, with the improvement in coal mining technology, mining has been continuously developed towards larger-scale, intensive, heavy-duty, and intelligent operations, especially the wide application of large mining height technology. In addition, as mine depths increase, the dimension of the opening cut in fully mechanized mining working face is continually increased. This expansion in the height and width of the opening cut roadway has resulted in larger deformation and fracture zones in the surrounding rock, making support more challenging and leading to increased risks of roof caving, roof falls, and dynamic impacts [6; 7; 8; 9; 10]. In 1956, China's coal mines began to use anchoring rod support technology in rock roadway, with a history spanning over 60 years [11]. This technology has evolved from low strength to high strength, and further to high pre-stress and strong support [12; 13; 14; 15; 16]. In conditions of increased stresses, both vertical and horizontal, one of the best solutions for the support of large-size workings is cable anchors, which, thanks to their elasticity and flexibility, perfectly adapt to the deformation of rocks around the workings [17], and additionally demonstrate high dynamic load-bearing capacity [18]. Currently, anchoring rod support technology for coal mine roadway is being actively promoted and applied domestically, yielding favorable technical and economic benefits [19; 20; 21]. The large-section cut of a large mining height working face differs from the general thin and medium-thickness coal seam roadway, and features characteristics such as large section size, severe deformation of surrounding rock, rapid early-stage deformation, large total volume, long durations, and overall rock mass deformation [22; 23; 24; 25]. Inappropriate selection of support forms and parameters can lead to two extremes: excessive support strength resulting in material waste, or inadequate support strength resulting in roof falls [26; 27; 28; 29]. Therefore, the optimal selection of anchoring rod support parameters for the large-section opening cut holds paramount importance, and many experts and scholars have conducted extensive research in this aspect [30; 31; 32; 33; 34]. Mining causes disturbance of the coal rock body, resulting in the generation of joints, fissures, and other discontinuous surfaces, thereby changing the strength characteristics of the coal rock body [35; 36; 37; 38]. According to the three key factors determining roadway stability--the surrounding rock strength, surrounding rock stress, and support technology--research on the optimal anchoring rod support parameters for large-section open-cut hole has been carried out around these three aspects [39; 40; 41; 42]. This study is of significant importance to achieve stability in supporting surrounding rock in deep and large-section opening cuts.