## 1 Introduction  
As important foundation forms, piles are widely used in engineering to bear vertical loads. However, many studies have been limited to the analysis of the behavior of dissimilar piles under vertical loads. Research studies on the behavior of dissimilar piles under horizontal loads are very few in the literature [1]. Indeed, in addition to vertical loads, piles are often subjected to significant horizontal loads applied at the pile head or pile shaft caused by wind, earth pressure, tides, currents, ship impacts, mooring ropes, earthquakes [2], deep excavation [3], and tunnel construction [4]. Therefore, it is of great significance to study the bearing characteristics of piles and the pile-soil interaction mechanism under horizontal loads [5]. Compared with constant section piles, the bearing mechanism of piles with multiple branches has changed greatly. The branch increases the action range of the pile-soil interaction and improves the pile-side friction. The branch enhances the effect of the pile-soil interaction by making full use of the mechanical properties of each layer of soil between the branches. Hence, the bearing capacity of the single square concrete in the pile is significantly improved so as to save on costs and shorten the construction period [6]. Squeezed branch piles have been applied in domestic civil engineering, municipal, shipping, aviation, and highway settings, bringing about enormous social and economic benefits [7]. Many scholars have carried out research on the bearing characteristics of squeezed branch piles under vertical loads. [PERSON] [8] and [PERSON] [9] based their studies on the load transfer method, providing a theoretical expression of the load transfer coefficients of squeezed branch piles, which shows that this method is applicable for predicting the ultimate load in engineering applications. [PERSON] and [PERSON] [10] explored the effects of the branch position, spacing, number, and diameter on the bearing capacity of piles and investigated the soil failure patterns around the branches through field load testing, suggesting that the branch shares a significant proportion of the transferred load, which greatly improves the bearing capacity of squeezed branch piles. [PERSON] [11] performed a static load model test on squeezed branch piles, studied the stress changes and surface potential response characteristics, and established a loading system and a potential data acquisition system for squeezed branch piles under laboratory conditions, providing an important experimental basis for assessing concrete damage. [PERSON] [12] discussed the bearing performance of squeezed branch piles through a finite element model and analyzed the influence on the bearing performance of both the branch quantity and the ratio of the horizontal load to vertical load, proposing that within a certain range, increased branch quantities lead to increases in ultimate bearing capacity and decreases in vertical pile displacement. The above research proves the excellent bearing capacity and significant social and economic value of squeezed branch piles. In addition, due to the needs of various projects, the research on the lateral load of squeezed branch piles is increasing gradually. [PERSON] [13; 14; 15] used the testing method for small-scale half-section model piles with undisturbed soil to observe the whole process from soil loading to destruction and the influence of the bearing disc position, disc spacing, and disc number on the horizontal bearing capacity and soil failure state around the pile, providing a reference for the research and development of pile foundations in oceanographic engineering. [PERSON] [16] designed different slope angles for a model pile through computer simulations and used ANSYS 2020 software to analyze the effect of the bearing capacity of NT-CEP piles and the failure behavior.