## 1 Introduction
[20] employed a modified pseudo-dynamic method to study the seismic stability of nailed vertical cut, and a closed-form solution was derived to estimate the influence of the seismic inertial force. For non-homogeneous slopes, [PERSON] et al. [21] conducted a new pseudo-dynamic method to analyze a two-layered cohesive-friction soil slope, and the result was verified against finite element analysis. However, the pseudo-dynamic method was born with many congenital deficiencies, and an obvious one isthat the slip body is defined as a rigid body. This means that the deformation of the slope cannot be obtained in the whole process of earthquake. Therefore, the slope stability can only be explained by the single safety factor when applying the pseudo-dynamic method. The other calculation method for the safety factor, the finite element numerical method, which analyzes the failure mechanism between the structural plane and slip body in its entirety, is often conducted using commercial software [22]. Owing to consideration of the effects of the slope elastic-plastic deformation, this approach has the advantages of reasonably simulating the complex seismic dynamic process and interaction mechanics between the slip body and surrounding rock mass. In the finite element method, the slope stability problem can assume a plane strain condition in Mohr-Coulomb's strength theory. Hence, many researchers provided a variety of finite element methods and their analysis methods have been different from each other since the 1940s [23]. [PERSON] et al. [24] developed a shear strength reduction technique for slope stability analysis based on the finite element technique, and the centerpiece of that study was that the slope failure was defined according to the shear strain failure criterion. [PERSON] et al. [25] discussed the computation method for the safety factor and location of the critical slip surface in finite element slope stability in detail under the strength reduction framework, and the effectiveness of the proposed procedures were demonstrated by an actual case. Moreover, for definitions of the safety factor, including the strength reserving definition and overloading definition, [PERSON] et al. [26] provided some strategies for how to select the safety factor for different slope types when the finite element method was used for the slope stability analysis. Inrecent years, [PERSON] et al. [27] carried out the finite element lower bound and finite element upper bound approach to analyze the seismic stability of soil slope with the weak interlayer, and they determined the safety factor upper or lower limit. [PERSON] et al. [28] analyzed the influences of constitutive models such as the Mohr-Coulomb model and hardening soil model on slope stability by using the numerical simulation technique, and the results showed that the Mohr-Coulomb model was better suited for stability analysis of slope due to the concise input parameters. [PERSON] et al. [29] used the elastic finite element stress fields to analyze the slope stability, and a 2D rock slope problem involving a nonlinear failure model and a 3D shallow slope problem were adopted to validate the proposed method. [PERSON] et al. [30] introduced a surface layer method for slope stability based on the finite element technique, which aimed to stabilize the surface of the calculation model in the strength reduction approach, and they verified it by the 2D and 3D slope problems. The studies mentioned above are important references to determine the slope safety factor. Although there are many advantages for the finite element technique, an unavoidable problem is that professional numerical software is usually needed to analyze the more complex numerical model, and it takes a long time to calculate the safety factor. A quick and efficient approach to assess slope stability is often the center of attention for engineers.