## 1 Introduction  
Loess soil covers about 10% of the Earth's land surface [1; 2], and it covers the north-eastern, northwestern, and middle of the Yellow River regions in China. The total area of loess in China is estimated to be as much as 630,000 km\({}^{2}\), accounting for 6.63% of the total land area [2]. Loess soil supports one sixth of the Chinese population and constitutes one fifth of China's arable land area, with over 700 important towns and cities distributed within loess soil [3; 4]. However, the loose structure of loess, the presence of numerous gullies on the surface of loess soil, and frequent rainstorms that cause severe erosion, make the region prone to frequent geohazards that pose a serious threat to engineering activities and the population in general [5; 6; 7; 8]. Loess areas are densely covered with hills and gullies, and the surface has a fragmented terrain [9; 10]. Therefore, many towns located in the Loess Plateau are constrained by limited space and geohazards, making further development difficult [11]. In recent years, various major projects have been carried out in the Loess Plateau to accelerate urbanization and improve the standards of living of residents [12; 13; 14], making it more critical than ever to understand how loess soil behaves under various engineering attempts to mitigate inevitable water erosion. For example, in order to mitigate the issue of erosion in the loess tabled area in Qingyang City, Gansu Province, a major project called \"Gully Stabilization and Table-land Protection\" was carried out; the project that involved the burial of 14,035 gullies in 42 large tabledands within the city area. In Yan'an City, Shaanxi Province, and Lanzhou City, Gansu Province, the \"Plain-to-Mountain Urban Construction\" project was launched to accelerate urbanization and expand the scale of urban areas [10; 12; 13; 14]. During the implementation of these projects, many high slopes were inevitably generated due to excavation and filling operations [10; 12; 13]. Consequently, these projects have resulted in various mitigation measures [15]. Although some slopes have merely been leveled without any protection, others have undergone drainage treatment. Nevertheless, the stability of such slopes remains uncertain, and the effectiveness of slope protection measures warrants evaluation. On-site field investigations have revealed severe erosion and damage to some slopes which with different protective measures (Figure 1). Hence, it is critical to study the stability of HLFSs under different protective measures, especially during rainfall. Accurate descriptions of the modes and mechanisms of slope instability, along with implementing corresponding geohazard prevention and mitigation measures, hold significant reference value for engineers [12; 15]. Extreme or prolonged periods of rainfall are the primary triggers of geohazards such as landslides and debris flows [11; 16; 17; 18]. The rainfall and water infiltration process increases the moisture content of the soil, thereby reducing the soil's matrix suction and shear strength, ultimately leading to slope instability and deformation [19; 20]. In the China's Loess Plateau, the unique loess landforms and the frequent occurrence of extreme rainfall  
Figure 1: Erosion due to precipitation in the Gully Stabilization and Highland Protection projects (**(a)** collapse in the toe of the slope which with a stepwise drainage channel mitigation; **(b)** collapse on the slope which with a stepwise drainage channel mitigation; **(c)** erosion along the slope surface which with a declining gradient mitigation). events have led to equally frequent geohazards [3; 21; 22; 23]. Moreover, water infiltration is also a leading cause of slope instability and destruction in various engineering projects, as exemplified by reported cases such as the Guangming New District landslide in Shenzhen, the Lvliang Airport landslide, and the Bai Lu Yuan Baqiao landslide in Xi'an [24; 25; 26; 27].