## 1 Introduction  
In coal mine safety, the deformation and failure of roadway surrounding rock have been hot topics of research; the control of the plastic zone expansion of roadway surrounding rock is a problem that needs to be urgently solved. Ground stress is the main factor leading to the failure of roadway surrounding rock, and the original rock stress field is the basis for analyzing the stress redistribution of roadway surrounding rock. It is critical to study the roadway orientation under different stress fields for the stability of roadway surrounding rock [1, 2]. Many in-depth studies have been conducted on the deformation mechanism and deformation characteristics of roadway surrounding rock [3, 4, 5, 6, 7]. [PERSON] et al. deduced the boundary equation of the plastic zone of the surrounding rock of a circular roadway and established a two-dimensional numerical simulation model. The radius of the plastic zone was measured and analyzed by applying 13 stress states, helping to verify the theoretical analysis [8]. [PERSON] et al. put forward the pressure relief method of slotting in the roof and floor of a roadway and studied the release effect of the slotting depth on the plastic zone by the Mohr-Coulomb criterion [9]. [PERSON] et al. proposed the reasonable use of primary support and secondary support to achieve long-term stability of the roadway in view of floor heave and creep in the control of the surrounding rock of a deep roadway [10]. [PERSON] et al. systematically used the two-dimensional distribution stress solution and Mohr-Coulomb strength theory in elastic-plastic mechanics to obtain the formula of deviatoric stress and the plastic zone radius of circular roadway surrounding rock under a non-uniform stress field and studied the distribution law of deviatoric stress and the plastic zone, providing a reasonable theoretical basis for roadway support optimization [11]. [PERSON] et al. systematically studied the deformation and failure characteristics of deep roadway surrounding rock and obtained the surrounding rock mechanics and strata behavior characteristics of a deep mining roadway [12]. [PERSON] et al. studied the influence of horizontal stress on the stability of roadway surrounding rock [13]. Based on the space-time relationship of plastic zone expansion during repeated mining, [PERSON] et al. revealed the mechanical mechanism of the space-time relationship of the plastic zone with the expansion of roadway surrounding rock and put forward the method of graded reinforcement [14]. Based on the plane strain problem, [PERSON] et al. proposed the butterfly failure theory of roadway surrounding rock; they clarified that roadway surrounding rock failure has three basic forms, circular, elliptical, and butterfly, and explained the physical phenomena of asymmetric large deformation and roof fall of the roadway [15]. [PERSON] et al. proposed the concept of the shape coefficient of the plastic zone, deduced the formula of the shape coefficient, and used its size to distinguish the shape characteristics of the plastic zone, significant for roadway stability analysis and support design [16]. According to the maximum horizontal stress theory proposed by Australian scholars, roadway surrounding rock is most stable when the roadway axial direction is parallel to the maximum horizontal stress direction [17]. However, this theory has some problems. According to the butterfly failure theory of roadway surrounding rock, the principal stress ratio \(\eta\) of the regional stress field influences the stability of roadway surrounding rock. When the confining pressure ratio is large, a large stress deviation occurs in two directions, forming a high-deviatoric-stress environment, which creates conditions for the formation of a butterfly plastic zone. Once formed, this zone causes the large-scale destruction of roadway surrounding rock. At the same time, the failure zone is sensitive to stress change, which can easily cause dynamic disasters, such as floor heave, roof fall, large deformation, and rock burst [18].