## 3 Materials and Methods  
### Newmark Displacement Model  
The Newmark displacement model is based on the limit equilibrium theory and is used to calculate the cumulative displacement of landslides. The principle (Figure 3) is that the landslide along the sliding surface produces transient displacement and continuous accumulation under the effect of earthquake acceleration. When the earthquake acceleration along the slope is greater than the critical load acceleration, a landslide is produced,  
Figure 2: Geological conditions of the study area: (**a**) lithology; (**b**) fault; (**c**) DEM; (**d**) slope. and according to the theory of calculation, the second-order integral of the difference between the two accelerations is calculated, and the permanent displacement value is finally obtained [21]. The Newmark displacement parameters include the static factor of safety (\(F\)s), critical acceleration (\(a_{c}\)), and cumulative displacement (\(D\)). The formula is used to calculate the static factor of safety (\(F\)s) of landslides and calculate the critical acceleration (\(a_{c}\)) by gravity, the slope, and the static factor of safety (\(F\)s). Then, the second-order integral of the difference between the peak ground acceleration (\(a\)) and the critical acceleration (\(a_{c}\)) is calculated so that the cumulative displacement (\(D\)) can be obtained. The workflow of the calculation is shown below (Figure 4). (1) Calculate the simplified critical acceleration (\(a_{c}\))  
The commonly static factor of safety (\(F\)s) for an infinite-slope model is computed as follows:  
\[F\;s\;=\;\frac{c^{\prime}}{\gamma\;z\sin\beta}+\frac{\tan\varphi^{\prime}}{ \tan\beta}+\frac{m\gamma_{w}\tan\varphi^{\prime}}{\gamma\tan\beta}, \tag{1}\]  
where \(c^{\prime}\) represents effective cohesion; \(\gamma\) represents the weight of rock-soil mass; \(z\) represents the depth of the failure surface; \(\beta\) represents the degree of the slope; \(\varphi^{\prime}\) represents the internal friction angle; \(m\) represents the degree of slope saturation; \(\gamma_{w}\) represents the weight of underground water; and \(F\)s represents the static factor of safety. Considering the environmental conditions in which the study area is located, a region with little or no rainfall, the effect of groundwater is not considered [10]. The equations are simplified as follows:  
Figure 4: Flowchart of the calculations in the Newmark displacement model. Figure 3: Schematic diagram of the principle of the Newmark displacement calculation. \(a_{c}\)—critical acceleration; \(a\)—peak ground acceleration; \(\beta\)—slope; \(D\)—Newmark displacement. \[Fs\ =\ \frac{c^{\prime}+\gamma z\ \cos^{2}\beta\ \tan\varphi^{\prime}}{\gamma z \sin\beta\cos\beta}, \tag{2}\]  
where \(z\) is the depth of the failure surface, in m; \(\gamma\) is the weight of the rock-soil mass, in N/m\({}^{3}\); \(c^{\prime}\) is the effective cohesion, in Pa = N/m\({}^{2}\); \(\beta\) is the degree of slope, in \({}^{\circ}\); \(\varphi^{\prime}\) is the internal friction angle, in \({}^{\circ}\); and \(Fs\) is the static factor of safety, which is nondimensional. The critical acceleration (\(a_{c}\)) is calculated by assuming an infinite slope condition, and the equation is as follows:  
\[a_{c}\ =\ (Fs-1)g\sin\beta, \tag{3}\]  
where \(a_{c}\) is the critical acceleration, in m/s\({}^{2}\); \(g\) is the acceleration of gravity, which is 9.8 m/s\({}^{2}\); and \(Fs\) is the static factor of safety, which is nondimensional. (2) Calculate the displacement (\(D\))  
In this study, the [PERSON] [21] empirical regression equation is utilized to calculate the Newmark displacement (\(D\)), which involves two regional seismic parameters, namely, the peak ground acceleration (\(a\)) and moment magnitude (\(M_{w}\)). The earthquake magnitude will influence peak ground acceleration (\(a\)) which is crucial for seismic landslide hazard assessments, and the \(M_{w}\) is calculated from the surface wave magnitude (\(M_{s}\)) via the empirical formula.