## 3 Theoretical Derivation of Surface Deformation Around Foundation Pit Excavation  
In the framework of elastic theory, the foundation can be regarded as a composite system composed of several elastic layers with finite thickness and a semi-infinite elastic medium at the bottom layer. The homogenous rock and soil layer in the foundation pit excavation region may be thought of as a semi-infinite space elastic body, provided that the terrain is free of noticeable undulations and that the rock and soil layers are uniformly dispersed across a large area. As seen in Figure 7, the excavation depth, design angle, and width of the foundation pit are represented by \(H\), \(\alpha\), and \(2A_{p}\), respectively, while the elastic modulus and Poisson's ratio of the rock and soil layer are indicated by \(E\) and \(\mu\). In the foundation pit excavation problem, by applying the equilibrium differential equation [23], strain compatibility relationship [24], and Hooke's law [25] in the rectangular coordinate system and introducing the stress function \(\varphi=\varphi(x,y)\), the stress expression of the element body can be derived as follows:  
\[\left. \begin{array}{l}\widetilde{\sigma}_{x}^{c}=-\varsigma^{2}\overline{ \varphi},\\ \widetilde{\sigma}_{y}^{c}=\frac{\partial^{2}}{\partial x^{2}}\overline{ \varphi},\\ \widetilde{\tau}_{xy}^{c}=\varsigma\partial\overline{\varphi}/\partial x, \end{array} \right\}, \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name of Vertical** & **Pearson Correlation** & **Average Pearson** \\
**Transmission Tower** & **Coefficient** & **Correlation Coefficient** \\ \hline DX1 & 0.9923 & \\ DX2 & 0.9826 & 0.9754 \\ DX3 & 0.9514 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pearson correlation coefficient results of each group of curves. Figure 5: The relationship between the surrounding surface settlement displacement \(V_{r}\) and the distance from the slope top. Figure 6: Comparison curve graphs of monitoring displacement data and numerical simulation results. \(\varphi=\varphi(x,y)\) should satisfy the biharmonic formula. Performing Fourier cosine integral transformation on the variable y that satisfies the biharmonic equation can obtain:  
\[\int_{0}^{\infty}\
abla^{4}\varphi\cos(\bar{z}v)dy=0, \tag{2}\]  
Equation (2)'s general solution is then:  
\[\overset{-c}{\varphi}=(A+BH)ch(\bar{\zeta}H)+(C+DH)sh(\bar{\zeta}H), \tag{3}\]  
In the equation, \(A\), \(B\), \(C\), and \(D\) are integration constants; \(ch(\bar{\zeta}H)\) is the hyperbolic cosine function; \(ch(\bar{\zeta}H)=(e^{\bar{\zeta}H}+e^{-\bar{\zeta}H})/2\); \(sh(\bar{\zeta}H)\) is the hyperbolic sine function; and \(sh(\bar{\zeta}H)=(e^{\bar{\zeta}H}-e^{-\bar{\zeta}H})/2\). According to the general solution result of Equation (3), the Fourier integral transformation expression of stress and displacement of a homogeneous foundation pit can be obtained. \[\left\{ \begin{array}{l}\overset{-c}{\sigma}_{x}^{c}=-\xi\left[\begin{array} []{l}Ach(\bar{\zeta}H)+B\xi Hch(\xi H)\\ +Csh(\bar{\zeta}H)+D\xi Hsh(\xi H)\end{array}\right],\\ \overset{-c}{\sigma}_{y}^{c}=\xi\left[\begin{array}{l}Ach(\xi H)+Csh(\xi H )\\ +2 Bsh(\xi H)+BHch(\xi H)\\ +2 Dch\xi H+DHs(\xi H)\end{array}\right],\\ \overset{-c}{\tau}_{xy}^{s}=\xi\left[\begin{array}{l}Ash(\xi H)+Ch(\xi H)+ \\ Bch(\xi H)+BHsh(\xi H)\\ +Dsh(\xi H)+DHch(\xi H)\end{array}\right],\\ \overset{-c}{u}=\frac{1+\mu}{\bar{\epsilon}}\left[\begin{array}{l}-Ash(\xi H )-Ch(\xi H)\\ +B(1-2v)ch(\xi H)-BHsh(\xi H)\\ +D(1-2v)sh(\xi H)-DHch(\xi H)\\ \overset{-c}{v}=\frac{1+\mu}{\bar{\epsilon}}\left[\begin{array}{l}Ach(\xi H )+Csh(\xi H)\\ +2B(1-v)sh(\xi H)+BHch(\xi H)\\ +2D(1-v)ch(\xi H)+DHsh(\xi H)\end{array}\right],\end{array}\right.\end{array} \right.