## 1 Introduction  
The analytical computation for rock slope stability disturbed by large seismicity has traditionally been one of the challenges in the field of engineering. For slopes with poor-quality lithological media, prestressed anchor cables are commonly employed as a means of reinforcement [1; 2; 3; 4]. It can provide the resistance force acting on the structure to bear the external load and creates a compressive stress zone within the anchored rock layer, which allows the weak rock slope to resist heavy seismic effects [5; 6]. Moreover, there is a considerable amount of research on two-dimensional (2D) slopes reinforced with prestressed anchor cables in the previous literature, while slopes are indeed frequently in the three-dimensional (3D) status, which has received little attention [7; 8]. Currently, the safety assessment approaches of the 3D slope are primarily of the following three types: (1) limit equilibrium (LE), (2) limit analysis (LA), and (3) finite element (FE). Among these, the LA of plasticity ignores the elastic-plastic process during rock mass failure and directly analyzes the limit state of 3D slopes [9]. Since LA can readily obtain the exact analytical solution [10; 11] as well as avoid the irrational assumptions of LE and the time-consuming computations of FE [12], this method is utilized in this paper. Building the kinematically admissible failure mechanism is the main difficulty with utilizing LA to solve the stability solution, and there is a wealth of literature in this area of study [13; 14; 15]. For the first time, a 3D sliding mechanism composed of numerous logarithmic spirals was created in order to investigate the 3D stability of vertically tangential slopes at different angles [16]. A 3D integral sliding mechanism was constructed, and the effect of slope top foundation load on the overall and local stability of the slope was examined using this sliding mechanism [17]. Considering the volume deformation of sliding bodies for slopes, a horn-shaped rotating sliding mechanism for 3D stability analysis of slopes with soil or rock was proposed [18], and it was adopted in this paper. For rock media, the Hoek-Brown (H-B) yield criterion is one of the most frequently employed strength criteria [19]; it was proposed based on triaxial tests on hundreds of rock specimens and many statistical analyses for engineering field tests, combined with a large amount of previous rock failure theories in the 1980s [20]. In 1992, [PERSON] et al. [21] published, the generalized Hoek-Brown yield criterion based on the existing criterion by introducing the Geological Strength Index (_GSI_), which is applicable to the case of weak rock masses. In 2002, the perturbation factor \(D\) was introduced to consider the effects of blasting and stress relief on the stability of the rock masses [22]. Nevertheless, since the H-B yield criterion reflects the relationship between the maximum and minimum principal stresses when destruction occurs in rock structures, this is not easy to utilize directly in the structural stability analysis of rock engineering. In order to address this issue, the generalized tangent technique and the equivalent Mohr-Coulomb strength criterion (EMC) have been proposed by scholars, respectively, for incorporating the H-B yield criterion into rocky stability analysis [23; 24], in which the former is employed in the article. Recently, the impact of seismicity on the safety of slopes has been the subject of numerous study findings [25; 26; 27]. On the premise of the pseudo-static method, the seismic safety of 3D steep slopes was explored. The seismic safety of 3D steep slopes was investigated based on the pseudo-static approach's premise [28]. However, the pseudo-static method does not take into consideration the impact of seismic arousal characteristics on the stability of slopes and evaluates seismic effects in a very simple manner [29].