# Numerical Investigations of Pile Group Foundations under Different Pile Length Conditions
## 1 Introduction  
Pile foundations are widely used in various infrastructure engineering fields due to their numerous advantages, including high vertical bearing capacity, stability, and adaptability to different site conditions. In many building foundations, the pile group-cap system is commonly adopted, where both the piles and the cap work together to support the loads from the superstructure and soil deformation. In the southwest region of China, where railroad lines often need to cross steep slopes and deep valleys, a considerable number of bridge group pile foundations are constructed. However, the challenging terrain, geological conditions, and alignment selection in these areas increase the risk of landslides caused by factors such as heavy rain, earthquakes, and human activities. These landslides can result in soil deformation and overall sliding, endangering the safety of the bridge structure. Therefore, it is crucial to fully consider the stability of the group pile foundation under the influence of the slope when constructing such foundations. Numerous scholars have conducted in-depth analyses and studies on group pile foundations on steep slopes, with a significant focus on studying group piles under verticalloads [1; 2; 3; 4; 5]. For instance, [PERSON] [6] found that changing the load direction can significantly reduce the peak displacement of the pile group. [PERSON] [7] established a database of simplified models to predict the non-linear pile interaction within vertically loaded pile groups. [PERSON] [8] evaluated the effects of pile geometry and inclination on soil-structure interaction. [PERSON] [9] proposed a method for evaluating the reliability of pile foundations in limit states. When it comes to physical tests, model tests are often preferred as they can more accurately simulate real field environments. [PERSON] [10], through quasi-static tests on specific group pile foundation models, revealed that the ultimate lateral force of the pile group is not solely determined by the yielding force of individual piles. [PERSON] [11] characterized the bearing capacities and deformation behavior of inclined pile foundations subjected to vertical and horizontal loads in pile-modeled tests. [PERSON] [12] reported results from multiple shaking table tests, focusing on the transverse response of pile group foundations. [PERSON] [13] conducted shaking table tests, which indicated that the inclusion of a drainage structure significantly improved the stability and safety of the bridge system. [PERSON] [14] studied the interaction effects between a scaled bridge model, abutments, foundation piles, and backfill soil. [PERSON] [15], through physical model tests, indicated that the ultimate bearing capacity of the piled raft foundation is considerably higher than that of a free-standing pile group with the same number of piles. Numerical simulation is a highly effective approach for conducting comparative analyses under different working conditions and parameter situations, compensating for the limitations of physical model testing methods. Among various numerical simulation methods, finite element analysis stands out as it can overcome the constraints of irregular slope geometries and material inhomogeneity. It offers a rigorous theoretical foundation and calculation results that fully satisfy static permits, strain coordination, and stress-strain ontological relationships. Consequently, this method is widely applied in analyzing various complex and large-scale engineering scenarios. For example, [PERSON] [16] investigated the distribution of pile forces in a group pile foundation under vertical loads and large moments using numerical simulation methods. [PERSON] [17] confirmed through numerical simulations that pile foundations with high-rise pile caps can better resist seismic loads than those with low-rise pile caps.