## 3 Loads Caused by Dewatering
### Tunnel Load Caused by Groundwater Level Drop  
In an analysis of tunnel and soil-structure interaction, the weight of the soil mass above the tunnel has a significant impact [28]. The underground dewatering increases the effective stress of the soil above the tunnel, resulting in additional load on the tunnel. Depending on the relative position of the groundwater level and the calculation point, the effective stress induced by dewatering can be categorized into two distinct calculation scenarios. The increments in effective stress at points \(B_{1}\) and \(B_{2}\) in Figure 4, denoted as \(\Delta\sigma_{1}\) and \(\Delta\sigma_{2}\), respectively, are as follows:  
\[\Delta\sigma_{1}=h_{1}(\gamma-\gamma_{s}+\gamma_{w}) \tag{21a}\] \[\Delta\sigma_{2}=\big{(}H_{0}-h(r_{B_{2}})\big{)}(\gamma-\gamma_{s}+\gamma_{w}) \tag{21b}\]  
In the formula, \(h_{1}\) represents the height difference between point \(B_{1}\) and the initial water level, while \(h(r_{B2})\) is the groundwater level at point \(B_{2}\). \(\gamma\), \(\gamma_{s}\), and \(\gamma_{w}\) correspond to the unit weight of soil, the saturated unit weight of soil, and the unit weight of water, respectively. Therefore, based on the relative position of the groundwater level after dewatering in  
Figure 5: The scope of influence of dewatering. relation to the existing tunnel, the additional stress on the tunnel can be categorized into the following two distinct calculation scenarios. First, following dewatering, the groundwater level is situated above the tunnel, as depicted in Figure 6a. Second, following dewatering, part of the water level drops below the tunnel, as shown in Figure 6b. Scenario 1: The horizontal distance between point \(x\) on the tunnel and the dewatering well is given as: \(r=\sqrt{x^{2}+d^{2}}\). Taking the distance back to Equation (19) determines the groundwater level at the tunnel location after dewatering, which then can be used in Equation (21b) to obtain the additional tunnel stress as follows:  
\[q(x)=\left(H_{0}-\sqrt{\left(H_{0}^{2}-H_{t}^{2}\right)\frac{\ln\frac{R}{ \sqrt{x^{2}+d^{2}}}}{\ln\frac{R}{R_{0}}}}\right)\cdot\left(\gamma-\gamma_{s}+ \gamma_{w}\right) \tag{22}\]  
Scenario 2: In this scenario, the tunnel section above the water level experiences a uniform and constant additional stress, as detailed below:  
\[\sigma=h_{1}(\gamma-\gamma_{s}+\gamma_{w}) \tag{23}\]  
The calculation of additional stress on the tunnel section below the water level can be determined using Equation (22). When \(h\)(r)= \(H_{0}-h_{1}\), it precisely corresponds to the point of intersection between the water level and the tunnel. Therefore, the coordinates of this specific point can be derived as follows:  
\[x=\sqrt{\left(R\frac{\left(H_{0}-h_{1}\right)^{2}-h_{1}^{2}}{H_{0}^{2}-H_{t}^ {2}}\cdot R_{0}^{\frac{\left(2h_{0}h_{1}-h_{2}\right)}{H_{0}^{2}-H_{t}^{2}}} \right)^{2}-d^{2}} \tag{24}\]  
Overall, the formula for calculating the additional stress induced by foundation pit dewatering on an adjacent existing tunnel is as follows:  
\[q(x)=\left\{ \begin{array}{l}\left(H_{0}-\sqrt{H_{0}^{2}-\left(H_{0}^{2}-H_{ t}^{2}\right)\frac{\ln\frac{R}{\sqrt{x^{2}+d^{2}}}}{\ln\frac{R}{R_{0}}}} \right)\cdot\left(\gamma-\gamma_{s}+\gamma_{w}\right),x^{2}>\left(R\frac{ \left(H_{0}-h_{1}\right)^{2}-H_{t}^{2}}{H_{0}^{2}-H_{t}^{2}}\cdot R_{0}^{ \frac{\left(2h_{0}h_{1}-h_{2}\right)}{H_{0}^{2}-H_{t}^{2}}}\right)^{2}-d^{2}; \\ h_{1}(\gamma-\gamma_{s}+\gamma_{w}),x^{2}\leq\left(R\frac{\left(H_{0}-h_{1} \right)^{2}-H_{t}^{2}}{H_{0}^{2}-H_{t}^{2}}\cdot R_{0}^{\frac{\left(2h_{0}h_{ 1}-h_{2}\right)}{H_{0}^{2}-H_{t}^{2}}}\right)^{2}-d^{2}\end{array} \right. \tag{25}\]  
So far, we obtain the additional load on the tunnel caused by the change in groundwater level. Then, the settlement and bending moment of the tunnel can be calculated by substituting Equation (22) into Equations (16)-(18).