## 1 Introduction  
Many nations have constructed substantial road networks and residential communities in hilly and mountainous terrain as a result of the global population increasing and socioeconomic development. However, landslides occasionally occur in these regions, and they can be extremely dangerous for people and property, particularly in places with steep terrain and considerable rainfall [1; 2; 3]. Thus, geotechnical researchers have focused increasingly on slope stability assessments. [PERSON] [4] stated that finite element methods have been used to analyze a large number of dams, as well as other embankments and slopes. [PERSON] et al. [5] proposed a hybrid superposition integration method based on finite element analysis and field data to improve slope stability prediction. [PERSON] et al. [6] conducted a reliability analysis of stiffened soil's internal and external stability under static and seismic loads. [PERSON] et al. [7] proposed an example of numerical analysis of slope stability on a national expressway in Northern Taiwan (This article is a revised and expanded version of a paper entitled \"Case Studies on Numerical Analysis of Slope Stability of National Expressway in Northern Taiwan\", presented at ACEM22/Structures22, 16-19 Au-gust 2022, Seoul, Republic of Korea). [PERSON] et al. [8] engaged in a characterization and stability analysis of rock-mass discontinuities in layered slopes, taking the Fushun West Open-Pit Mine as an example.  
In mountainous regions, landslides rank among the most dangerous natural calamities [9; 10]. Taiwan's landscape is primarily made up of hills and mountains, which make up almost two-thirds of the island's overall area. As a result, safety in the event of landslides is a major concern for the appropriate government bodies. Since the construction of National Freeway 1, the demand for motorways has grown. The freeway segment between Keelung and Xizhi was constructed 46 years ago, and shotcrete has been used to cover the bedrock slope's surface. The shotcrete covering has been repaired and maintained, but aging has led to cracks and plant growth on the surface. On 13 January 2011, a severe landslide occurred on the slope of the southbound lane of Taiwan's Freeway 1, with a mileage of 4K + 820. It is worth noting that on National Freeway 5, several slopes are classified as high-risk according to the \"Freeway Maintenance Manual\" [11].  
Slope stability is an important and complex issue in road engineering which is related to soil properties, soil density, soil pore water pressure, excavation methods, load effects, etc. In view of the above, locations with a high risk of landslides on the slopes of Taiwan's Freeways 1 and 5 were selected in this work as case studies because severe landslides have occurred near these locations. The slope displacement and safety factor at normal and high groundwater levels were simulated using the PLAXIS 2D CE finite element analysis tool, and variations in acceleration, speed, and displacement in slope models were examined using pseudo-static analysis in seismic circumstances. In short, the aim of this study was to provide numerical simulation data to government departments as a reference for evaluating the effectiveness of freeway slope protection projects. In the future, the numerical simulation results might help prevent the collapse of freeway slopes when severe rains or other conditions impair their stability.