## 1 Introduction  
Pile foundations are a core technology in construction engineering, with load-bearing capacity and settlement characteristics being key research areas. Traditional optimization and construction methods for pile foundations are relatively mature [1, 2, 3], research primarily focuses on exploring the effects of pile shape, external load patterns, and subsurface lithology on pile-bearing capacity and pile-soil interaction. The research methodologies include theoretical analysis, field tests, and numerical simulations. Studies have shown that pile-pile interaction can be influenced by pile shape, external load patterns, and soil properties [4; 5; 6]. With the continuous development of urban construction, pile engineering is becoming increasingly complex [7], especially in renovation projects where numerous existing piles are left in place. When dealing with existing pile foundations, two common methods are considered: remove and reuse. However, removing existing piles not only increases construction costs but also significantly reduces soil stability [8; 9]. Therefore, the reuse of existing piles has become a new research direction in geotechnical engineering [10]. Researchers evaluate the load-bearing capacity of existing piles for reuse [11; 12], which greatly reduces environmental pollution and resource waste [13; 14]. Compared to existing structures, new bridges often require higher load demands, necessitating the addition of a specific number of supplementary piles in the foundation to ensure the safety of the new bridge. The existing pile foundations have been in the ground for many years, and the surrounding soil has consolidated or aged due to long-term loading [15; 16; 17]. Therefore, under the same applied load, uneven settlement may occur between new and existing piles due to differences in load history. Identifying these differences and implementing targeted improvements could effectively control potential engineering hazards caused by differential settlement. [PERSON] [18] found through theoretical research that existing piles are subjected to axial forces and bending moments due to the driving of adjacent piles, causing structural damage or tensile failure. [PERSON] and [PERSON] [19] proposed an analysis system based on load transfer and shear displacement methods to predict settlement interaction between new and existing piles. Some researchers have also conducted theoretical analyses on the installation process of new piles [20; 21; 22; 23]. In addition to theoretical research, [PERSON] and [PERSON] [24] found through centrifuge tests that the addition of new piles improved the performance of existing pile foundations. [PERSON] et al. [25] used vertical static load centrifuge tests to study the impact of existing piles on the vertical bearing capacity of new piles, showing that existing piles provide constraint to the surrounding soil, increasing the total shaft resistance of new piles. However, theoretical analyses and model tests have limitations in comparing a large number of working conditions, especially in complex geological conditions. Numerical simulations can quickly achieve different condition comparisons to overcome these limitations. For example, finite element analysis, as a continuum method, can automatically consider pile-soil coupling, which traditional load transfer methods cannot achieve [3]. [PERSON] et al. [26] used numerical experiments to study the impact of existing piles on new pile construction at different pile spacings. Additionally, [PERSON] et al. [27] analyzed the contribution of the fixed degree of existing pile heads to the lateral load response of new piles through numerical simulation and proposed a new pile design method considering the fixed degree of existing pile heads. [PERSON] [25] used finite element analysis to assess the influence of existing piles on the lateral resistance of new piles.