# Influence of Loess-Mudstone Strata Structure on Slope Seismic Stability of Loess Plateau in China
## 2 Materials and Methods
### Methods  
The pseudostatic method, Newmark method, and time-history analysis method are the three main methods used for analyzing the seismic stability of slopes. Since the Haiyuan earthquake occurred many years ago, the complete seismic wave was not recorded, and the magnitude was too large. The pseudostatic method was used to simplify the seismic  
Figure 6: Sampling: (**a**) drilling; (**b**) samples. Figure 7: Geotechnical test: (**a**) consolidation test; (**b**) direct shear test. load in this paper. The influence mechanism and model of the strata structure on the loess slope seismic stability were studied. The pseudostatic method was first introduced into the slope seismic stability analysis by [PERSON] [40]. Due to its clear concept, simplicity, and applicability, researchers have widely adopted it and incorporated it into corresponding specifications [41; 42]. Its basic principle is to simplify the instantaneous seismic load to equivalent static load and put it on the centroid of each slice in a way that is not conducive to slope stability; then, the calculated safety factor calculated using the limit equilibrium method is used as the evaluation index to measure the slope stability under earthquakes. Due to the fact that the vertical seismic load affects both the antisliding force and the sliding force of sliding bodies, and has a small impact on the safety factor, it is usually ignored in the pseudostatic method. The equivalent static load is defined as:  
\[F\ =\ \frac{aW}{g}\ =\ K_{c}W_{i} \tag{1}\]  
where \(a\) is the pseudostatic acceleration, \(W_{i}\) is the weight of slice \(i\), \(g\) is the gravitational acceleration constant, and \(K_{c}\) is the seismic coefficient. The key lies in determining the seismic coefficient \(K_{c}\). At present, there are many ways to calculate the seismic coefficient \(K_{c}\). For example, in the Chinese specification, \(K_{c}\) is a constant related to the antiseismic fortification intensity [43]; in the U.S., \(K_{c}\) is a function of the magnitude and the epicenter distance [44]. [PERSON] et al. [45] argued that \(K_{c}\) should be 50% of the peak acceleration of bedrock. Since the Haiyuan earthquake had a magnitude of 8.5, a suggestion of [PERSON] et al. [46] was adopted in this paper when the magnitude was 8.5. The seismic coefficient should be set at 0.15 and the allowable stability safety factor should be 1.15. The Morgenstern-Price method was used to calculate the critical sliding surface and its corresponding safety factor. This method belongs to the classical limit equilibrium method, and its advantage is that the solution process is rigorous and accurate. However, compared to the global method, there may be problems of local convergence or nonconvergence during the iteration process [47]. The safety factor \(F_{S}\) can be calculated iteratively with Equation (2), according to the force balance of the slice [48]:  
\[\left(N_{i}{}^{\prime}\tan\varphi_{i}{}^{\prime}+c_{i}{}^{\prime}b_{i}\sec \alpha_{i}\right)/F_{S}=\left(W_{i}+\lambda f_{i-1}E_{i-1}-\lambda f_{i}E_{  
According to the statistics and analysis of the above investigation data, four influencing factors, i.e., slope height, slope angle, loess cover thickness, and mudstone dip angle, were determined for evaluating the seismic stability of loess slopes. Two models of a pure loess slope and a loess-mudstone slope was constructed (since the slope angle was not completely the same as the mudstone dip angle, and the effect of the slope shape was ignored, the shape of the mudstone topography and the slope shape were linear; the thickness at half the slope height was taken as the loess cover thickness). The slope geometric model is shown in Figure 9. Using the pseudostatic method, the stability of two slope models with different slope angles and slope heights was calculated. The influence of the existence of the underlying mudstone layer on the loess slope stability was comparatively studied. The loess parameters are shown in Table 1. The underlying mudstone layer was set as the bedrock.