## 1 Introduction  
The increasing demand for urban development and the limited availability of space have resulted in buildings being constructed in close proximity to, or even directly above, metro tunnels [1]. These construction activities inevitably affect nearby metro systems, and excessive deformation can cause damage such as cracks, leakage, and other structural issues, which may disrupt metro operations and pose safety risks [2, 3]. In response, isolation piles are commonly used in engineering practice to create a barrier between excavation sites and tunnels and reduce the impact of excavation-induced movements [4]. This protective measure is essential for safeguarding existing tunnel structures. Consequently, investigating the effectiveness of isolation piles in mitigating these impacts holds significant practical and research value, as it enables the optimization of their design and implementation [5]. In recent years, substantial research has been conducted to explore the effects of isolation piles on tunnel deformation through a variety of approaches, including numerical simulations [6, 7], field monitoring [1, 8], theoretical analysis [9, 10], and indoor model tests [11; 12]. Despite significant advancements in understanding the role of isolation piles in controlling tunnel deformation, several controversial conclusions persist. These debates primarily focus on key factors such as pile head depth, pile length, and pile-to-tunnel distance. A summary of the relevant conclusions and analytical details is provided in Table 1. Specifically, regarding the influence of pile head depth, [PERSON] et al. [13] identified a complex relationship between pile head depth and tunnel horizontal deformation, where the deformation initially increases, then decreases, and later increases again before ultimately decreasing, based on two-dimensional numerical simulations. In contrast, [PERSON] et al. [1] and [PERSON] et al. [14] observed a more straightforward trend, with horizontal displacement initially decreasing and then increasing as pile head depth increased, based on three-dimensional simulations. [PERSON] et al. [15] reported that tunnel horizontal deformation decreased as pile head depth increased when the isolation pile was placed at the center of the foundation pit, based on indoor model tests. As for the influence of pile length, through a three-dimensional finite element analysis, [PERSON] et al. [5] identified two distinct zones in the soil surrounding the foundation pit: a displacement-affected zone (traction effect) and an anchorage zone (isolation effect). They observed that as the isolation pile length increased, the traction effect became more pronounced, leading to an increase in horizontal displacement. However, once the isolation pile entered the anchorage zone, the horizontal displacement decreased as the pile length increased. In contrast, [PERSON] et al. [16] found that tunnel deformation decreased as the pile length increased using three-dimensional numerical simulations. Likewise, by employing numerical simulations, [PERSON] [17] found that the tunnel deformation initially decreased, then increased, and later decreased again with increasing pile length. Based on a theoretical analysis, [PERSON] et al. [10] found that tunnel deformation initially decreased and then increased as the isolation pile length increased. The distance between the isolation pile and tunnel also influenced horizontal displacement, with [PERSON] et al. [17] noting a trend of increasing displacement. [PERSON] et al. [10], on the other hand, found that horizontal displacement decreased as the distance increased. These findings indicate that there is considerable controversy regarding the effects of pile head depth, pile length, and pile-to-tunnel distance on tunnel deformation, and a unified mechanism that systematically explains these phenomena is still lacking. Moreover, previous studies have mainly focused on either horizontal or vertical displacements independently.