## 1 Introduction  
China is situated on the eastern edge of the Eurasian Plate, adjacent to both the Pacific and Indian Plates, and strong tectonic interactions make it highly prone to earthquakes [1]. Data show that, between 1993 and 2017, a total of 299 significant earthquakes occurred across Chinese mainland, resulting in over 7400 fatalities, 474,000 injuries, and approximately CNT 1.1 trillion in direct economic losses [2]. Frequent seismic activities have triggered a range of geological disasters, which have significantly impacted China's economic development and posed severe risks to lives and property [2, 3, 4]. Among these, earthquake-induced landslide is a major component. For instance, the Wenchuan earthquake led to more than 15,000 landslides, collapses, and debris flows, causing about 20,000 fatalities [5].  
In the seismic stability assessment (\(SSA\)) of slopes, the pseudo-static method (\(PS\)) [6] and pseudo-dynamic method (\(PD\)) [7] estimate the slope safety factor (\(F_{S}\)) by simplifyingseismic forces. However, even if the slope \(F_{S}\) briefly falls below 1 during an earthquake, it may still maintain overall stability. Consequently, the Newmark sliding block method (\(N\)_NBM_) is often applied to assess seismic stability of slope based on permanent displacement. Small displacement indicates an overall stable slope, while increasing displacement leads to partial failure, culminating in total sliding. The critical threshold of displacement is generally considered to range from 5 cm to 15 cm [8; 9; 10].  
The permanent displacement of an earthquake-induced landslide depends on factors such as ground motion energy, static slope stability, and duration of ground motion. For a specific slope, its permanent displacement can be derived through double integration of ground motion data exceeding the yield acceleration. However, accurately predicting the ground motion time-history curve is challenging in practice. Thus, the empirical model (_EM_) is commonly used in \(SSA\). Numerous scholars [11; 12; 13; 14; 15] have proposed _EM_s, which provide a theoretical foundation for continued research. However, few studies have proposed _EM_s for permanent displacement of seismic slopes in China.  
In recent research, some scholars [16; 17; 18; 19; 20; 21] enhanced model accuracy by optimizing calculation methods, increasing model parameters, and expanding ground motion datasets. [PERSON] et al. [8; 22; 23; 24; 25] improved model accuracy by refining fitting parameters. Additionally, [PERSON] and [PERSON] [26] employed a logic tree method to account for experimental or methodological errors, which enhanced regional landslide risk assessment accuracy. [PERSON] and [PERSON] [27] examined the impact of vertical seismic force on permanent displacement values, compared results with and without vertical force, and found that including vertical seismic force typically increases permanent displacement by a factor between 1 and 1.1. _EM_s enable the rapid calculation of slope deformations under different earthquake intensities, providing an efficient means of assessing slope stability during seismic events [28]. Moreover, the development of such models is highly valuable for the regional evaluation of seismic landslide stability [29; 30; 31].  
Numerous studies have explored the \(N\)_NBM_ and _EM_; however, few _EM_s are based specifically on ground motion data from China. This study employs \(N\)_NBM_ and regression analysis to propose _EM_s for predicting permanent displacement. These models provide a critical foundation for advancing the understanding of earthquake-induced landslide mechanisms and enhancing emergency response strategies for geological hazards.