## 1 Introduction  
In recent years, more and more deep excavations adjacent to existing tunnels have emerged [1; 2; 3; 4]. The excavation can inevitably destroy the original stress and displacement fields and then lead to the displacement of the tunnel in the soil. To guarantee the safety of the tunnel, it is important to predict the possible displacement of the tunnel and take some control measures before excavation. Generally, the commonly used prediction methods for tunnel displacement include empirical formulas, theoretical analysis, and numerical simulation. In terms of empirical formula, [PERSON] et al. [5] put forward an empirical prediction formula for horizontal displacement of tunnel induced by adjacent deep excavation based on 11 case histories. However, the proposed formula only considers the single factor of the clear distance between the tunnel and deep excavation, and it is obtained based on the limited cases in Shanghai soft soil. Considering the above shortcomings, [PERSON] et al. [6] supplemented the factor of excavation width along the tunnel axis to reflect the stress release degree of deep excavation and put forward a new prediction formula for horizontal displacement of the tunnel. [PERSON] et al. [7] put forward empirical prediction formulas for excavation-induced tunnel displacement in three different soil types based on 42 case histories. In terms of theoretical analysis, [PERSON] et al. [8; 9] proposed a two-stage method for predicting the longitudinal displacement of the tunnel induced by adjacent deep excavation; that is, the excavation-induced unloading stress at the existing tunnel location is estimated firstly using the Mindlin solution [10], and then the displacement response of tunnel is calculated using the Galerkin method regarding the tunnel as an Euler-Bernoulli beam locating on the Winkler foundation model. Considering the Euler-Bernoulli beam ignores the shear displacement of the jointed tunnel segments, and the Winkler foundation model is unable to consider the interaction of soil springs, [PERSON] et al. [11; 12] and [PERSON] et al. [13] used the Timoshenko beam to simulate the tunnel response with joints and used the Pasternak foundation model to consider tunnel-soil interaction. However, during the establishment and derivation of the above theoretical solutions, many simplifications and assumptions were made, and the values of some parameters have a significant effect on the accuracy of the results. In terms of numerical simulation, some scholars [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26] predicted the excavation-induced tunnel displacement and evaluated the control effect of some measures based on specific projects. However, the credibility of numerical simulation results depends on the constitutive model and parameters, boundary conditions, the simulation process, etc. The above-mentioned prediction methods for tunnel displacement, especially theoretical solutions and numerical simulations, are relatively complex and require high professional skills for users. To realize a simple prediction of excavation-induced tunnel displacement, [PERSON] et al. [27] took a deep excavation adjacent to an existing tunnel as the background and studied the excavation-induced tunnel displacement behaviors considering the different deformation modes and magnitudes of the retaining wall. Then, through an analysis of tunnel displacement isolines, the influenced zone of deep excavation was determined, and the tunnel displacement was predicted according to the actually influenced zone where it locates. This method considers the effects of the deformation mode and magnitude of the retaining wall, and the relationship between the influenced zone and tunnel displacement control standards is established, which is scientific and reasonable in theory. The tunnel displacement can be predicted just according to the actually influenced zone where it locates, which is simple in application.