## 1 Introduction  
With the continuous construction and development of urban rail transit, conducting ultra-deep foundation excavation near operating traffic line is necessary. The excavation of a deep foundation pit is accompanied by ground settlement, causing varying degrees of damage to surrounding structures. Especially in the reclaimed stratum near the sea, the damage to the foundation soil will seriously affect the normal use of structures. The lateral displacement of the soil caused by excavation leads to additional deflection and bending moment of the viaduct pile foundation. Moreover, the vertical displacement of soil caused by excavation leads to negative friction of the viaduct pile foundation, resulting in uneven settlement of piles and deformation of superstructure. Therefore, it is of great significance to explore the deformation and stress distribution of adjacent viaduct foundation piles caused by the excavation of deep foundation in urban area. Previous research on soil deformation of foundation excavation, and its influence on adjacent structures, started in the early 1920s. [PERSON] et al. [1] proposed a method, called the total stress method, to estimate the supporting force of the envelope structure and the stability of foundation excavation. This method was continuously improved and modified in later development, and has been commonly applied. [PERSON] [2] calculated a set of empirical relationship curves of the surface settlement and settlement range behind the diaphragm wall, which was related to the soil properties and excavation depth, using an empirical estimation method that is still widely used. [PERSON] and [PERSON] [3] adopted an empirical analysis method to study and analyze the deformation law of the foundation pit envelope and the surrounding surface during the construction of a deep foundation pit. The surface settlement pattern behind the wall depended on the deformation pattern of the retaining wall. The soil deformation behind the wall was generally a triangular groove shape. [PERSON] et al. [4] believed that uneven surface settlement caused by deep foundation pit construction was the main cause of damage to the adjacent buildings. A method for predicting the degree of damage to buildings, called the KJHH simplified evaluation method, was proposed. This method was used to evaluate the settlement form and the range of settlement around the foundation pit. [PERSON] et al. [5] established governing differential equations of a single pile and the pile group by considering the coupling effects of longitudinal and transverse deformations. A new theoretical method was proposed to estimate the displacement of soil with a constant field caused by foundation excavation using the modified method as the basic calculation data of the envelope deflection curve. Based on this, a two-stage analysis method was proposed to study the influence of foundation movement caused by excavation on the performance of the pile foundation. The effectiveness of the method was verified by comparing the calculated results with centrifuge test results. The empirical formula method also plays a crucial role in studying the surface deformation of foundation pits and predicting the deformation of adjacent structures [6; 7]. For example, pile-soil interaction properties are widely studied using \(p\)-\(y\) curves, particularly in the clay soil [8; 9]. However, the complexity of stratigraphic conditions limits the theoretical solution methods. With the continuous development of technologies, the finite element method has gradually gained increasing interest because it can consider various factors to simulate the construction [10; 11]. [PERSON] et al. adopted a finite element method to study deep excavations and damage to adjacent buildings, and they proposed and validated allowable horizontal displacements of retaining wall based on limited settlements of adjacent building with shallow foundations [12; 13]. [PERSON] et al.