## 1 Introduction  
With the rapid advancement of urban construction, more and more foundation pit projects are located above or on both sides of existing subway tunnels. This leads to a significant impact on the complex underground pipeline network caused by the construction of nearby deep foundation pits [1]. As a result, the impact of construction on adjacent existing subway tunnels has gradually become a concern. The construction of foundation pits near existing operating subway tunnels can alter the displacement and stress fields of the surrounding soil [2, 3]. The soil is affected by the stress changes caused by excavation and the displacement of surrounding soil, resulting in the corresponding local deformation of adjacent subway tunnels. At the same time, some rock, soil, and underground engineering structures, including deep foundation pit engineering and shield tunneling, can be considered as low toughness structures [4]. Once additional unexpected events occur, the risk of large-scale damage or even a continuous collapse caused by local damage is relatively high. Therefore, solving the problem of existing tunnel deformation caused by excavation is of great significance for ensuring the safety and reliability of urban subway traffic operation. In recent decades, numerous scholars have accumulated valuable insights into the deformation of existing tunnels resulting from pit excavation. [PERSON] [5] discovered through numerical analysis that the deformation of the nearby tunnel and ground settlement both reach their maximum values when the excavation of the pit reaches the bottom, with the overall deformation of the tunnel presenting a \"horizontal oval\" shape directed towards the excavation. [PERSON] et al. [6] have shown that the excavation of the pit has a greater impact on the lateral deformation and convergence of the tunnel, with the deformation increasing closer to the retaining structure at point H. Additionally, the technique of subway tunnel grouting for deviation correction was found to effectively control the development of deformation. [PERSON] et al. [7] found that the impact zone of deformation on nearby existing tunnels caused by pit excavation is related to geological conditions, pit conditions, and tunnel conditions, while the mechanism of impact on the tunnels lying beneath is much simpler than that on lateral tunnels. [PERSON] et al. [8] used three levels of deformation control standards for tunnel maximum deformation at 20 mm, 10 mm, and 5 mm, and found that the deformation impact zone on underlying tunnels could be divided into the main impact zone, secondary impact zone, general impact zone, and minor impact zone. [PERSON] et al. [9] discovered through measured data that the maximum uplift deformation of the subway structure caused by the excavation of pits on both sides occurs near the connection between the station and the tunnel; as the load intensity increases, the amount of uplift of the subway structure decreases, and when it exceeds a certain intensity, some sections of the interval tunnel will settle. In the context of advancing urbanization, research on the excavation of foundation pit groups has emerged. [PERSON] et al. [10] used the finite element method to study the mutual influence of adjacent foundation pit simultaneous construction. The results showed that the simultaneous construction of two foundation pits caused significant horizontal deformation in the existing subway station, while the vertical settlement was relatively small. The overall impact of simultaneous construction on the deformation of existing nearby subway structures is roughly equal to the superposition of the effects of the excavation of the two foundation pits separately. [PERSON] et al. [11] analyzed the measured data of double foundation pit excavation and found that the excavation process of the foundation pit directly affects the deformation of the existing line foundation, and the impact of double foundation pit excavation on the deformation of the existing line foundation is superimposed.