## 1 Introduction  
With economic development, more and more underground spaces are being developed and utilized. In order to facilitate public travel and reduce traffic congestion, many cities have opened underground rail transit lines. After the subway is completed, for the purpose of improving the intensive utilization of underground space, many foundation pit projects are adjacent to the existing subway lines. Excavation of foundation pits will cause stress relief around the soil mass, which leads to excessive deformation of subway tunnels. Excessive tunnel deformation will result in water leakage in the tunnel, local crushing of concrete, and even serious train accidents [1]. Therefore, how to predict the influence of foundation pit excavation on the deformation of adjacent subway tunnels has become the focus of many scholars in recent years [2]. [PERSON] et al. [3, 4] proposed a simplified algorithm for the influence of foundation pit excavation on the deformation of adjacent tunnels, and applied the Mindlin solution to predict the soil disturbance effect of foundation pit excavation. [PERSON] et al. [5] proposed a semi-analytical prediction method for the deformation of adjacent existing tunnels caused by new tunnels. The viscoelastic model was used to simulate the rheological deformation of soil, and the deformation laws of existing tunnels under different working conditions were analyzed. Taking into account the bending and shearing effects of the tunnel, [PERSON] et al. [6] regarded the tunnel as a Timoshenko beam on the Pasternak foundation, and analyzed the effect of the interaction between the tunnel and the soil on tunnel deformation. [PERSON] al. [7] regarded the existing tunnel as a Timoshenko beam on the Winkler foundation, and analyzed the effects of tunnel shear stiffness, tunnel spacing and soil mechanical parameters on tunnel deformations. [PERSON] [8] took an existing tunnel over a foundation pit in Prague as a background project, and carried out numerical calculations by establishing a two-dimensional finite element model. The results are consistent with the later monitoring data. [PERSON] et al. [9] took the foundation pit project of a nearby tunnel in Singapore as the background, used the GRISP finite element method to calculate the influence of foundation pit excavation on the tunnel deformation, and analyzed the influence of the tunnel flexural stiffness on the force and deformation. [PERSON] et al. [10] established a three-dimensional finite element model to predict the displacement of the tunnel and soil, and simulated the deformations of the existing tunnel and soil under different working conditions, such as foundation pit support structure, foundation pit dewatering, cement-soil mixing pile, and partition excavation. [PERSON] [11] and [PERSON] et al. [12] used MIDAS/GTS for numerical simulation, and analyzed the influence of the width of the foundation pit, the excavation depth, the excavation area of the foundation pit, the distance between the tunnel and the foundation pit and the hydrogeological conditions on the deformation of the adjacent tunnels. [PERSON] et al. [13,14] used finite element numerical simulation methods to study the influence of foundation pit shape, sand density, tunnel flexural stiffness and other factors on the vertical deformation of the tunnel, and proposed a method suitable for foundation pit excavation. [PERSON] et al. [15] used ABAQUS to establish a three-dimensional numerical model to simulate the construction of the dam above the tunnel, compared different construction schemes, studied the parameters, and finally proposed optimization suggestions for the construction scheme. Based on the H-S soil constitutive model, [PERSON] et al. [16] simulated the influence of foundation pit construction in soft soil areas on the uplift deformation of adjacent existing tunnels, and analyzed the relationship between the maximum uplift of the tunnel and the distance from the top of the tunnel to the base.