## 1 Introduction  
Recently, with the establishment of the regional economy and growth in urbanization, land for urban construction has become increasingly scarce, and developing and utilizing higher terrace, ridge, and hill areas around cities has become an important way to alleviate this issue, leading to increased foundation depth and difficulty in loess areas [1]. Raising the level of science and technology in professional domains via theoretical research and constructing a high-quality infrastructure with the aid of science and technology are currently key challenges for engineers and technicians. The deep foundation of a large collapsible loess foundation consists primarily of a pile foundation, particularly bored piles. However, at the pile-soil interface, a layer of paste-like soil mud is created due to the influence of construction technology, which reduces the pile side friction. Additionally, the presence of sediment at the pile's base reduces pile end resistance, and the bearing capacity of a single pile is limited [2]. However, at collapsible loess sites, pile foundations must penetrate the collapsible soil layer and are typically extremely long. Under normal loading conditions, most of the bearing capacity of pile foundations is supported by the pile's side friction resistance. Consequently, increasing the side friction resistance is an excellent method for enhancing the bearing capacity of pile foundations in collapsible loess foundations [3; 4; 5]. A bored pile is a completely extruded type of pile. It drives a bidirectional thread-closed extruded drill bit with a high-torque drill, extrudes all soil in the pile hole into the soil surrounding the pile, and then pours concrete into the pile hole through the hollow pipe of the drill tool to produce a totally extruded cylindrical pile. By utilizing the extrusion and expansion action of the drill bit and the positive compaction effect during pile formation, the soil density around the pile is enhanced, and the compactness of the surrounding soil and friction resistance of the pile are substantially increased [6; 7; 8; 9; 10; 11]. Compared to continuous flight auger piles (CFAs), the bearing capacity of pile foundations can be significantly enhanced, and pile side mud and pile bottom silt are not produced, leading to distinct technical and economic benefits [4]. After the 1990s, bored piles became popular in dozens of nations, including Europe, the United States, and Australia. [PERSON] et al. used bored piles to treat soft soil foundations and discovered that soil displacement was primarily focused on a circular area six times the pile diameter [8]. [PERSON] et al. used bored piles and CFA piles to treat Australian railway roadbeds and discovered that compared to CFA piles with the same bearing capacity, bored piles had a smaller pile diameter and could avoid the problem of soil disposal, resulting in better technical and economic benefits [9]. [PERSON] et al. used bored piles to treat sandy soil and silty soil foundations and discovered that bored piles could enhance the density of the soil around the pile and boost the side friction resistance and ultimate bearing capacity of the pile via the squeezing effect that occurs during pile formation [10; 11; 12]. [PERSON] and [PERSON] et al. discovered that, in comparison to non-extruded piles, bored piles have a greater bearing capacity and lower compressibility, and their construction technology is dependable, noiseless, and vibration free [13; 14]. Through field experiments, [PERSON] et al. determined that the bearing capacity of bored piles in porous red soil foundations is double that of bored piles of the same diameter [15]. [PERSON] et al. investigated the impact of drilling settings on the compaction effect during bored pile development [16]. Tests conducted by [PERSON] and [PERSON] et al. revealed that bored piles exhibit excellent bearing performance in soft-to-hard clay and loose-to-medium-dense sandy soil foundations [17; 18]. [PERSON] et al.