## 1 Introduction  
Underground engineering construction will inevitably change the stress state of surrounding strata, which will force a negative impact on the surrounding environment, even leading to the large deformation and damage of some adjacent structures. With the vigorous development of metro construction in China, safety issues in the construction of underground engineering have received widespread attention, and the deformation of strata during excavation is the most direct and significant issue. Tunnels are an important component of urban subway systems. Many studies on site deformation induced by the excavation of tunnels were published. [PERSON] [1] analyzed a large number of measured data on tunnel engineering and found that the ground settlement trough perpendicular to tunneling can be described by a normal distribution curve, i.e., a Gauss distribution curve. By assuming that the volume of ground settlement trough generated by tunneling approximately equals the amount of ground loss during excavation, he proposed a mathematical expression to describe ground settlement trough, known as the Peck formula, which has become a classical formula for predicting ground settlement trough in tunneling. Subsequently, many scholars [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12] carried out a lot of research on the applicability of the Peck formula. [PERSON] et al. [13] developed a random forest (RF) model based on the Peck formula to predict ground settlements above tunnels, in which tunnel geometry, geological properties, and construction parameters were investigated as input variables to utilize in RF modeling. There are many other studies on ground settlement induced by the excavation of tunnels. For example, [PERSON] and [PERSON] [14] treated soil as a linear elastic material and provided an analytical solution for ground settlement causedby tunnel excavation. [PERSON] et al. [15; 16] developed a numerical model to simulate the excavation procedure with earth pressure balance (EPB), taking into account the full excavation sequence. [PERSON] et al. [17] developed a three-dimensional numerical model for the simulation of the complete tunnel excavation process by EPB machines, and compared the influence of the linear elastic constitutive model, Mohr-Coulomb constitutive model, and modified Cam-Clay model on the calculation results. [PERSON] et al. [18] developed an analytical approach to predict ground movement induced by a non-uniformly deforming circular tunnel in an elastic half-plane. [PERSON] et al. [19] investigated the deformation behavior of natural loess-experiencing complex stress paths around a shield tunnel. [PERSON] et al. [20] studied the displacement characteristics of a \"\(\pi\)\"-shaped double cross-duct excavated via the cross-diaphragm (CRD) method. [PERSON] et al. [21] constructed the distribution density function of two random parameters, analyzed the sensitivity of parameters using the Monte Carlo method, and obtained the relationship curve of failure probability. [PERSON] et al. [22] suggested a simplified method for calculating the stresses and displacements of the surrounding rock and tunnel lining with time. [PERSON] et al. [23] proposed an inverse method for improving the prediction of tunnel displacements during adjacent excavation. [PERSON] et al. [24] proposed a hybrid regional model for predicting ground deformation induced by large-section tunnel excavation. The works of [PERSON] and [PERSON] [25] indicate that site deformation induced by tunnel excavation is controlled by the geological conditions of the site, the construction process, and the design scheme. With the rapid development of cities, the environment of subway construction is more and more complex, and the shield construction method has become an important means of tunneling. Therefore, it is very important to study the site deformation characteristics induced by shield tunneling under different ground conditions, explore the influence scope, and propose prevention measures.