## 6 Discussion and Conclusions  
In this study, a database was developed using 312 time-history records from 19 strong earthquake events (\(M_{S}\)5.2-8.0) in China. Permanent displacements induced by these earthquakes were calculated using the _NSBM_. The main conclusions are as follows:  
1. Based on the J07 and R&S08 Models, empirical models (Model 1 and Model 2) for predicting the permanent displacements of earthquake-induced landslide in Chinawere developed through regression analysis. The standard deviation of \(\log(u)\) of Model 1 is 0.540, with an \(R^{2}\) of 0.866. The standard deviation of \(\log(u)\) and \(R^{2}\) of Model 2 are 0.410 and 0.923, respectively, indicating a better fitness than Model 1.
2. The residuals of permanent displacement in Model 1 display an approximate normal distribution with Arias intensity and show a nonlinear relationship with the yield acceleration ratio. This nonlinearity can be effectively mitigated by including higher-order terms for the yield acceleration ratio, as seen in Model 2.
3. Comparisons between Model 1, Model 2, and other classical models (Equations (3)-(7)) reveal that both Model 1 and Model 2 predictions lie within the ranges of the remaining models, demonstrating strong applicability.  
However, it is important to note that this study employs the _NSBM_ to calculate the permanent displacement of slopes, which may have certain limitations when applied to deep landslides or large-scale rockslides. Additionally, the shear resistance parameters of the material are assumed to remain constant throughout the deformation process. Therefore, from a conservative perspective, we recommend using the residual shear resistance parameters. Furthermore, since the models' dataset is derived from the historical earthquake events in China, its applicability to other regions requires further investigation.  
In summary, Model 2 provides a superior fit compared to Model 1. Using time-history records from China, Models 1 and 2 assess earthquake-induced landslide stability via permanent displacement, offering valuable insights and guidance for SSA evaluation and seismic slope design in China. Moreover, combining the findings of this study with geographic information system (GIS) technologies can contribute to early warning systems for seismic landslides and regional landslide stability assessments.  
Conceptualization, M.Z. and J.L.; methodology, F.Q. and Y.D.; software, F.Q.; validation, F.L. and H.L.; formal analysis, F.L.; J.L. and C.G.; investigation, F.Q. and J.L.; resources, J.L.; data curation, F.L. and F.Q.; writing--original draft preparation, F.L. and F.Q.; writing--review and editing, F.L., F.Q., M.Z. and J.L.; visualization, F.L., F.Q. and C.G.; supervision, M.Z. and Y.D.; project administration, M.Z.; funding acquisition, M.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (grant number 2018 YFC1504700) and the National Natural Science Foundation of China (grant numbers: 41530640 and 42107209).  
The time-history records used in this paper were downloaded from the National Earthquake Data Center of China ([[http://data.earthquake.cn](http://data.earthquake.cn)]([http://data.earthquake.cn](http://data.earthquake.cn))) and PEER Ground Motion Database ([[https://ngawest2.berkeley.edu](https://ngawest2.berkeley.edu)]([https://ngawest2.berkeley.edu](https://ngawest2.berkeley.edu))). The author was not allowed to share these records. The calculation procedures and the calculated displacements are available from the corresponding author with a reasonable request.  
Acknowledgment for the data support from \"China Earthquake Networks Center, National Earthquake Data Center ([[http://data.earthquake.cn](http://data.earthquake.cn)]([http://data.earthquake.cn](http://data.earthquake.cn)))\".  
The authors declare no conflicts of interest.