## 1 Introduction  
With the rapid advancement of civil aviation airport construction in China, the number of high-slope projects in mountainous areas has significantly increased. Simultaneously, the frequent occurrence of global extreme weather events [1], such as typhoons, tornadoes, and heavy rainfall, has posed severe challenges to urban infrastructure and transportation systems [2; 3]. Figure 1 shows the No. 12 landslide at Panzhihua Airport, which was located in the upper part of a wide and gentle valley area on the east side of the northern section of the airport. It was caused by the instability of the filled body and the reactivation of the old Yujiaoping landslide below. The maximum filling height of the filled body was approximately 128 m, and the maximum width was approximately 433 m (perpendicular to the airport runway direction). At 15:00 on 3 October 2009, the filled body slid, triggering the reactivation of the old landslide. The elevation of the landslide front was 1550 m, and the elevation of the rear edge was 1980 m (the elevation of the airport soil surface area). The height difference between the front and rear edges was approximately 430 m. The landslide was 1600 m long in the longitudinal direction, with a total volume of approximately 5.1 million m\({}^{3}\). After the landslide occurred, a huge gap formed in the soil surface area. The horizontal distance from the landslide scarp to the centerline of the runway was only 75 m, and it continued to deform and collapse. Some residential houses and farmland water conservancy facilities below were damaged, and operations at Panzhihua Airport were suspended for a period [3]. Against this backdrop, stability management and disaster prevention in slope engineering have become critical issues for ensuring the safe operation of airports and the sustainable development of regions. Geotechnical reinforcement techniques are now widely used in geotechnical engineering, especially in foundation works. This technology can fully exploit geotechnical energy in order to improve the self-stabilizing ability and reduce the self-weight of a structure and preserve the material, which has significant economic and social benefits [4]. Figure 1: A large-scale landslide that occurred on the slope of Panzhihua Airport [3]. Owing to the wide range of fields involved in geotechnical engineering, it is a highly comprehensive discipline. It includes geotechnical engineering investigation, soil mechanics, foundation and foundation engineering, the mechanics of materials, structural mechanics, and other multidisciplinary topics. The soil nailing support structure was developed in the 1970s, and its application has grown extensively over the years. However, the theory behind soil nail supports still lags far behind the engineering reality. Although our country has issued several design regulations and norms on soil nail supports [5; 6; 7], in general, soil nailing support design and calculation methods are not perfect, and many scholars have conducted research on this problem. [PERSON] [8] conducted theoretical analysis and suggested that after soil nails are installed in the soil, the stress state in the soil body will change and the direction of the principal stress will be deflected. The sliding crack surface of the soil will also change accordingly. [PERSON] et al. [9] assumed that the sliding surface had a parabolic shape and established a search model for the most critical sliding surface using geometric relations and an integral method. [PERSON] et al. [10] proposed a new method to determine the potential fracture surface of soil nailing walls based on the relationship between the residual sliding force of soil at the potential fracture surface and the nailing force in the sliding zone. [PERSON] et al. [11], based on the cantilever beam model, compared the critical instability height of the rock layer with the height of the preset failure surface, dividing the rock layer on the failure surface into stable, active toppling, and passive toppling zones.