## 5 Analysis of Numerical Simulation Results
### Ground Settlement Prediction for Pipe Jacking in the Soil-Rock Composite Stratum  
According to the results comparison between on-site monitoring and Peck formula calculation [7; 19; 22; 23; 24], the estimation formula of lateral land subsidence distribution in Peck is as follows:  
\[S(x)\ =\ \frac{V_{1}}{\sqrt{2\pi i}}\exp\biggl{(}-\frac{x^{2}}{2i^{2}}\biggr{)}, \tag{1}\]  
\[i\ =\ z/\left[\sqrt{2\pi}\tan\left(45^{\circ}-\varphi/2\right)\right], \tag{2}\]  
where \(S(x)\) is the land surface settlement (mm); \(x\) is the distance (m) from a point on the surface to the center line; \(V_{1}\) is the formation loss per unit length (m\({}^{3}\)/m); \(i\) is the width coefficient of settling tank (m); \(z\) is the distance between the pipe jacking axis and the ground; and \(\varphi\) is the internal friction Angle (\({}^{\circ}\)) of the soil. According to the construction site situation, assuming that the stratum loss rate is 0.5%, the maximum ground settlement \(S(x)\) = 2.7 mm, after the completion of the lower pipe jacking construction is calculated, which is significantly different from the field data of 0.8 mm. Therefore, the applicability of the Peck formula used for predicted settlement is poor when the pipe jacking in the soil-rock composite layer. The peck formula is widely used in the prediction of land surface subsidence in various projects due to its simple calculation. However, due to the differences in geological characteristics in different areas, there is a certain gap between the predicted value of the peck formula and the measured data. Many scholars have adapted the peck formula for different strata [8; 9; 25; 26; 27]. There is still a lack of modified peck formulas for sore-rock composite strata in many studies. Therefore, referring to the modification method  
Figure 12: Comparison of ground settlement at different vertical clear spacing. (**a**) Vertical arrangement of pipe; (**b**) ground settlement. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **0.5 D/mm** & **1 D/mm** & **2 D/mm** \\ \hline Lower pipe jacking (S\({}_{\text{L}}\)) & 2.64 & 0.75 & 0.09 \\ Upper pipe jacking (S\({}_{\text{U}}\)) & 4.00 & 2.21 & 1.59 \\ Total ground settlement (S\({}_{\text{T}}\)) & 6.64 & 2.96 & 1.68 \\ \(S_{\text{L}}/S_{\text{T}}\) & 39.8\% & 25.3\% & 5.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ground settlements at different vertical clear distances. of previous scholars, the compensation formula is adaptively modified for this project. According to the numerical results, with the increase in the vertical pipe jacking spacing, the depth of the lower pipe jacking embedded in the rock layer gradually increases, and the surface settlement caused by the lower pipe jacking construction gradually decreases. Therefore, the main reason for this difference is the depth of the pipe jacking embedded in the rock layer. In order to better study the specific relationship between such differences, the thickness of the pipe jacking embedded in the rock layer is represented by \(h\), and the influence of the surface settlement on the change of h is shown in Figure 13.  
It can be seen from Figure 13 that the surface subsidence is obviously affected by the change of \(h\). In order to further study the relationship between surface subsidence and h, the parameter \(k(h)\) is introduced to modify the peck formula. \(k(h)\) varies with the depth \(h\) of the pipeline embedded in the rock stratum. Through a large number of formula trial calculations and inversions, the relationship between \(k(h)\) and \(h\) is finally obtained, as shown in Equation (4). Therefore, the modified calculation formula is shown in Equations (3) and (4), as shown in the equation: \(S^{\prime}(x)\) is the land surface settlement after correction (mm), \(D\) is the outer diameter of pipe jacking, \(h\) is the distance from the bottom of the jacking pipe to the soil and rock strata interface, which is the thickness of the rock layer the pipe is embedded in the buried depth in the rock layer.