## 4 Discussion
### Influence of Load Characteristics on Settlement Curve
In order to fit the stratigraphic conditions in Beijing, Equations (1)-(3) were modified according to the correction coefficient proposed by [PERSON] [31] et al., who considered that the maximum surface subsidence (\(S_{max}\), Equation (3)) correction coefficient \(\alpha\) should be  
Figure 9: Actual earth pressure distribution of the soil under the foundation pit. 0.6-0.9 in the stratum present in Beijing and that Equation (2) should be corrected by \(\beta\), the value of which was supposed to be 0.5 to 0.9. Therefore, the subsidence curve in the Beijing area should be expressed as in Equation (4). \[S_{(x)}=\alpha\cdot S_{max}\cdot\exp\{-\frac{x^{2}}{2\left(\beta\cdot i\right)^{ 2}}\} \tag{4}\]  
Taking the bottom plane of the foundation pit as the surface, the surface settlement curve is drawn according to Equation (4), as shown in Figure 9(a). Similarly, the settlement curve is drawn by the prediction formula of the double track parallel tunnel proposed by [PERSON] et al. (2018), shown in Figure 9(b). Combined with the correction coefficient, the prediction formula of the double track parallel tunnel proposed by [PERSON] et al. (2018) can be expressed as in Equation (5). \[S_{(x)}=\alpha_{l}\cdot S_{max}\cdot\exp\left\{-\frac{\left(x+0.5L\right)^{2}} {2\left(\beta_{l}\cdot i\right)^{2}}\right\}+\alpha_{r}\cdot S_{max}\cdot\exp \left\{-\frac{\left(x-0.5L\right)^{2}}{2\left(\beta_{r}\cdot i\right)^{2}}\right\} \tag{5}\]  
In Equation (5), \(\alpha_{l}\left(\alpha_{r}\right)\) is the correction coefficient for \(S_{max}\) of the left (right) tunnel and \(L\) is the distance between the center points of the twin tunnel. The strengthening effect on soil from the piles and the deviation of the settlement curve caused by asymmetric horizontal loading is clearly expressed in Figure 10. In order to better determine the magnitude of these two impacts, the curve of Case 2 was analyzed. The approximate expression is shown in Equations (6) and (7). \[S_{(x)}=\gamma\alpha\cdot S_{max}\cdot\exp\{-\frac{\left(x\pm\mu B\right)^{2} }{2\left(\beta\cdot i\right)^{2}}\} \tag{6}\]  
Figure 8:0  
In Equations (6) and (7), \(\gamma\) is the correction coefficient considering the strengthening effect on soil induced by piles, \(\mu\) is the correction coefficient considering the deviation of the settlement curve caused by asymmetric horizontal loading, and \(B\) is the width of the foundation pit. The positive and negative values are related to the unloading direction of the horizontal load. In this research, the values of \(\mu\) and \(\gamma\) can be obtained according to the curve data in Figure 8:1 The corrected settlement curve is shown in Figure 8:2  
Figure 8:3 Comparison between empirical formula and numerical model. It can be seen from Figure 11 that the correction factors \(\gamma\) and \(\mu\) well reflect the changes in the settlement curve under the influence of the load characteristics of the practical project. When the shield tunnel passes through the foundation pit with pile raft foundation, the reinforcement effect of the piles on the soil can be considered through the correction factors \(\gamma\). When there is asymmetric horizontal loading of the soil under the foundation pit, the settlement curve can be corrected by the correction factor \(\mu\).