# Spatial Deformation Calculation and Parameter Analysis of Pile-Anchor Retaining Structure
## 1 Introduction  
As the urban population continues to grow, so does the demand for urban space. However, urban space is limited, prompting scholars to propose the concept of underground urban space. The goal of this concept is to alleviate the scarcity of urban space by developing underground space. Foundation pit engineering is considered the most significant underground space engineering in cities. Foundation pit engineering plays a crucial role in creating initial construction space for a variety of structures such as high-rise building foundations, subway stations, underground shopping malls, and underground parking lots. However, the excavation process of a foundation pit can potentially lead to alterations in the initial state of the surrounding soil, posing a risk of damage to nearby buildings and structures [1; 2; 3]. As a result, construction risks during foundation pit excavation have been a major topic of interest among scholars. The study of [PERSON] et al. [4] showcased the practicality of utilizing the random set finite element method (RS-FEM) and event tree analysis (ETA) to effectively evaluate the reliability and potential lethality risk associated with urban excavations; [PERSON] et al. [5] developed a risk assessment modelfor excavation systems; [PERSON] et al. [6] proposed a fuzzy hierarchical analysis (AHP)-based model for pit health assessment. In their work, [PERSON] and [PERSON] [7] integrated the uncertainty and correlation of evaluation indices with the fuzzy nature of expert evaluation. They devised an evaluation model grounded in fuzzy theory. The stability of a foundation pit can be directly inferred from the deformation characteristics exhibited by its retaining structure during excavation. Various research methods are employed to analyze such deformations, including numerical simulation, theoretical analysis, and indoor testing. In their study, [PERSON] et al. [8] introduced a combined structural model that incorporates an elastic roadbed beam and a continuous beam. They incorporated elastic springs to simulate the interaction between the piles and the basement wall. Finite difference equations and calculation methods were developed to accurately calculate the internal forces and displacements of the combined pile-wall structure. This approach enables precise calculation of excavation-induced internal forces and deformations of retaining piles during the excavation phase. [PERSON] et al. [9] used the PLAXIS 3D numerical simulation software to study the deformation characteristics of foundation pits under asymmetric loading. [PERSON] et al. [10] conducted a study on the deformation characteristics of a shaped foundation pit support structure using the deep foundation pit of Malian North Station on Xiamen Metro Line 2. They employed field observation and numerical simulation methods to analyze the deformations. On the other hand, [PERSON] et al. [11] designed and executed a large-scale model test of a pile-anchor-supported foundation pit with a geometric similarity ratio of 1:10. [PERSON] et al. [12] used the virtual image technique to calculate the soil displacement caused by the deformation of the support structure, and at the same time, introduced the rotational misalignment collaborative deformation model to analyze the longitudinal deformation of the tunnel and the maximum displacement equivalent field of the tunnel caused by different support structure deformation methods. The theoretical analysis method can provide designers with prediction values quickly using prediction formulas, significantly enhancing the efficiency of predicting construction risks. An improved support system known as cast-in-place pile and anchor cable (pole) support utilizes anchor bolts and anti-slide piles to provide anchoring and sliding resistance forces. This system effectively resists soil sliding behind the support structure. Due to its exceptional support effectiveness and stability, the cast-in-place pile and anchor cable support system is highly favored by designers and researchers.