# Influence Law of Foundation Pit Excavation on Stress of Surrounding Tunnel Bolt
## 1 Introduction  
Given that many underground space projects are built in cities, the foundation pit excavation of surface engineering is often adjacent to existing tunnels [1]. With increasing excavation depth, due to the excavation unloading effect, the grouting on the foundation pit wall moves to the interior of the foundation pit [2, 3], thus causing the deformation or differential deformation of the surrounding underground tunnels to change with the construction process [4], as shown in Figure 1. Therefore, it is necessary to study the influence law of the foundation pit excavation on the deformation stability of existing tunnels [5]. At present, by focusing on the influence of excavation on nearby subway tunnels, some research has been conducted, but most results are according to practical engineering experience [6, 7]. Based on the field data, the semi-empirical and the semi-theoretical formula, the qualitative analysis of underground engineering was implemented [8]. [PERSON] and [PERSON] [9] proposed a new longitudinal structural model to consider the shearing dislocation between rings. Quantitative analysis and calculation are limited, and the simulation calculation of the construction process of the foundation pit cannot be carried out. For example, [PERSON] [10] found that the displacement of the side wall of the foundation pit, the deformation of the retaining structure of the foundation pit, and the settlement of the backfill soil of the foundation pit would lead to the horizontal displacement of theunderground pipeline. [PERSON] et al. [11] believed that the proximity of the foundation pit to the tunnel changes the transfer of surrounding rock displacement, which is mainly manifested as transverse deformation. [PERSON] et al. [12] found that the excavation of the foundation pit had an obvious influence on the adjacent tunnel, especially the horizontal displacement. [PERSON] and [PERSON] [13] studied the influence of rigid and flexible supporting foundation pits on the structural safety of neighboring buildings through the engineering case of adjacent building cracking by foundation pit excavation and explored the cracking causes and prevention measures. On the other hand, with the development of numerical calculation [14; 15; 16; 17], many scholars compiled numerical simulation software to study the interaction between foundation pit excavation and adjacent tunnels [18; 19]. [PERSON] [20] used a numerical simulation method to simulate the excavation process of the foundation pit above the tunnel, and the results were basically consistent with the field-measured data. [PERSON] and [PERSON] [21] studied the size effect and space effect of foundation pit excavation by numerical simulation. [PERSON] and [PERSON] [22] used Plaxis 3D software to establish a three-dimensional numerical calculation model to simulate the excavation effect of a deep foundation pit of a building, which was compared with the two-dimensional model. [PERSON] and [PERSON] [23] took the construction of the foundation pit adjacent to the Toronto subway as the background, simulated and predicted the additional displacement of the underground subway tunnel caused by different construction schemes. Based on the foundation pit project of Shanghai Agile Square, [PERSON] [24] established a three-dimensional finite element model with FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) and analyzed the effect of excavation with different reinforcement methods on reducing the vertical displacement of the subway below. [PERSON] et al. [25] used PLAXIS to analyze the influence of four different working conditions on the tunnel deformation based on the open excavation foundation pit. [PERSON] et al. [26] employed MIDAS/GTS to simulate the deformation characteristics of shield tunnel under different construction stages and pit-tunnel location relations. In summary, theoretical or numerical analysis methods have been widely used to study the effect of foundation pit excavation on adjacent subway tunnels [27; 28; 29].