## 4 Results and Discussions
### Parametric Effects Discussions  
In accordance with the Equation (77), nonlinear properties of soil medium, geometric parameters of two-step slopes, and seismic parameters in the modified pseudo-dynamic analysis are all factors that affect the safety factor \(FS\) for 3D two-step slopes, the effects of which are depicted in Figures 5-8, respectively, with the corresponding basic parameters:  
Figure 6: The interactions between the nonlinear factors on the stability for 3D two-step slopes: (**a**) nonlinear coefficient \(m\) and initial cohesion \(c_{0}\); (**b**) nonlinear coefficient \(m\) and axial tensile strength \(\sigma_{t}\). Figure 7: Impacts of geometric factors on the stability for 3D two-step slopes: (**a**) step-width coefficient \(\lambda_{\alpha}\); (**b**) depth coefficient \(\xi_{1}\); (**c**) inclined angle \(\beta_{1}\); (**d**) inclined angle \(\beta_{2}\). As shown in Figure 5, the nonlinear coefficient \(m\) and axial tensile strength \(\sigma_{t}\) are inversely correlated with the safety factor \(FS\); i.e., the larger the nonlinear coefficient and axial tensile strength lead to the smaller \(FS\). Nonetheless, the initial cohesion \(c_{0}\) is positively connected with \(FS\), and the magnitude of the effect is stronger, as the \(FS\) varies from 0.4 to 2.3 corresponding to the initial cohesion value ranging from 12.5 to 32.5 kPa. Then, Figure 6 illustrates the interactions between the nonlinear parameters. It can be observed that the trend of \(FS\) remains constant with \(\sigma_{t}\) and \(c_{0}\), but when \(m\) is small, the slope stability changes dramatically. Moreover, when nonlinear parameters \(m\), \(\sigma_{t}\) and \(c_{0}\) are fixed, \(FS\) decreases as \(B/H\) rises. It means that the stability of 3D slopes is better compared with 2D slopes at the same other parameters. This also demonstrates that treating the 3D slope simply as the 2D case in real engineering is overly conservative. The effects of geometric parameters on slope stability are shown in Figure 7. It is obvious that the depth coefficient \(\xi_{1}\) and step-width coefficient \(\lambda_{a}\) are positively correlated with \(FS\), while the inclined angles \(\beta_{1}\) and \(\beta_{2}\) are negatively correlated with \(FS\). It is worth noting that the \(FS\) variation range corresponding to \(\beta_{2}\) is larger compared with \(\beta_{1}\) in the same range of 45-75\({}^{\circ}\), indicating that \(\beta_{2}\) has a stronger effect on slope stability. This has some significance for the design of two-step slopes. Furthermore, for the geometric parameters \(\xi_{1}\), \(\lambda_{a}\), \(\beta_{1}\), and \(\beta_{2}\), when the value of \(B/H\) is changed from 2 to 4, there is a significant drop in \(FS\). With a rising \(B/H\), the \(FS\) falls slowly and gravitates to 2D solutions. In Figure 8, the influence of pseudo-dynamic parameters varying with \(B/H\) on slope stability is described. The variation pattern of \(FS\) with \(B/H\) is consistent with the foregoing  
Figure 8: Impacts of seismic factors on the stability for 3D two-step slopes: (**a**) horizontal seismic coefficient \(k_{bi}\); (**b**) damping ratio \(D\); (**c**) period \(T\); (**d**) S-wave propagating velocity \(V_{s}\). conclusions; although, \(FS\) variations with the modified pseudo-dynamic parameters are all minor, not surpassing 5%. By comparing the results obtained by the original pseudo-dynamic method and the previous relevant research literature, the reliability of the proposed method has been verified, repeatedly. The results obtained from the sensitivity tests of geometric parameters, pseudo-dynamic parameters, and nonlinear parameters of soil have considerable significance for the design and safety evaluation of three-dimensional stepped slopes in current practical projects. The design mode of a two-order slope can resist the negative impacts of seismic events on slope stability to a certain extent.