## 1 Introduction  
Anchor cables are a common technical means for the reinforcement of deep roadways that has been widely used in many fields, such as underground mine roadways, open-pit slopes, and foundation pits [1, 2, 3]. With the increase in mining depth, complex and variable geological structures and stress environment result in a separated roof, roof collapse accidents, and a high repair rate of anchor cables. The ejection phenomenon of broken anchor cables is common [4, 5]. In addition to the influence of load and sudden external factors, the anchoring structure of anchor cables is also subject to damage accumulation, which results in bond failure, pull or shear failure of anchor parts, and other forms of anchorage system failure [6, 7, 8, 9]. Traditional anchor cable design methods have limitations in deep roadway support [10, 11]. Usually, only the axial bearing capacity of the anchor cable is considered, and the interaction of cable-surrounding rock is ignored. Therefore, a reasonable anchor cable design is of considerable significance in controlling the deformation of surrounding rock and improve safety [12, 13]. At present, scholars at home and abroad mainly focus on the mechanical effect of anchor cables but ignore the influence of surrounding rock and the relative relationship between the anchor cable and surrounding rock [14]. A large number of studies show that the deformation and failure of surrounding rocks in deep roadways are gradual [15; 16; 17; 18; 19]. Previous studies do not reflect the influence of the progressive failure behavior of surrounding rock and mechanical characteristics of cable wells, and the internal load transfer behavior and mechanism of anchor cable still cannot be explained quantitatively and evaluated correctly. Ordinary anchor cables are not adopted to high-deformation environments of surrounding rock. In view of the limitation of traditional anchor cables with respect to mechanical properties and severe engineering environments, new anchor cables with extraordinary mechanical properties should be developed. Existing NPR anchor cables have solved the deformation problem of deep, soft rock roadways [20; 21]. The deformation capacity increases to 3000-4000 mm, and the maximum constant resistance is 567.7-800 kN [22]. Some scholars have studied the failure mechanism of anchor cable systems using numerical software, achieving remarkable results. Through theoretical analysis and simulation verification, the mechanical properties of anchor cables under tension-torsion coupling action have been explored, and the tension-torsion coupling coefficient has been proposed and determined [23]. The surrounding rock characteristics of steel arch supports and NPR anchor cable supports are compared with 3 DEC software [24]. Bird's nest anchor cables are a new type of anchor cable. Compared with ordinary anchor cables, they has higher anchor force and elongation. The synergistic principle and evaluation method of rock surrounding bird's nest anchor cables are still in the research stage, and the failure process and the mechanisms of anchor structures are not clearly understood. The influence of different anchor cable supporting parameters on the stress diffusion of surrounding rock is studied by FLAC3D, and optimal parameters are proposed [25]. An anchor cable and C tube withstand transverse shear force are developed, and the new scheme can effectively control surface convergence and plastic zone expansion by FLAC3D [26]. Lagging theoretical research results in some accidents during construction or after completion [27; 28]. Designers do not have a clear understanding of its action mechanism to deal with the design and application of bird's nest anchor cables. The failure process of rock surrounding bird's nest anchor cables is analyzed and compared with theoretical analysis as well as pull-out tests and PFC simulation tests.