## 3 Application to the Shuangjiangkou Hydropower Station
### Characteristics of In Situ Stress around Underground Caverns  
The purpose of the in situ stress inversion is to investigate the distribution of in situ stress in the engineering area. By studying its distribution characteristics, it is possible to provide some references for the engineering's design, construction, and long-term stability. Hence, based on the boundary conditions obtained from the PSO-BP inversion, the distribution characteristics of the in situ stress in the Shuangjiangkou underground cavern area were computed.  
Figure 7 shows the stress distribution in the cross-section of the main powerhouse, while Figure 8 plots that in the longitudinal section direction. As can be seen, there is an increasing trend in the distribution of in situ stresses with the increase in rock burial depth. The shallow surface presents local stress relaxation with relatively low stress values in this area. This is followed by a stress transition zone, where the principal stress distribution gradually becomes horizontal with a progressive increase in stress. The deeper part of the rock has a higher stress level and a more stable stress state. The first principal stress ranges from 20 to 26 MPa, with some stress concentration occurring around the river valley. The third principal stress ranges from 14 to 18 MPa and is predominantly oriented in the vertical direction. Fault F1 and the lamrophyre notably influence the stress distribution in the main powerhouse area, resulting in a significant reduction in the stresses within 10 m.  
Figure 6: Comparison of inverted results with measured results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Test No.** & \(\sigma_{\textbf{v}}\)**/MPa** & \(\sigma_{\textbf{y}}\)**/MPa** & \(\sigma_{\textbf{z}}\)**/MPa** & \(\tau_{\textbf{xz}}\)**/MPa** & \(\tau_{\textbf{yz}}\)**/MPa** & \(\tau_{\textbf{xy}}\)**/MPa** \\ \hline
1 & 18.33 & 20.07 & 14.83 & 1.02 & \(-\)2.63 & 1.22 \\
2 & 18.08 & 20.91 & 14.45 & 1.12 & \(-\)2.18 & 1.27 \\
3 & 11.98 & 18.10 & 9.41 & 1.63 & \(-\)0.80 & 0.37 \\
4 & 17.72 & 22.48 & 14.02 & 1.69 & \(-\)2.34 & 0.73 \\
5 & 17.96 & 23.49 & 14.00 & 2.65 & \(-\)2.45 & 0.79 \\ \hline \end{tabular}
\end{table}
Table 5: Computational stress components at test points.  
The results of the in situ stress inversion indicate that weak structural planes may have the potential to significantly influence the stress state of an engineering area. As shown in Figure 9, all three stress components increase with the buried depth while remaining relatively consistent within the main powerhouse area at the same elevation. There is a sudden drop in stress values at the fault area, with the \(\sigma_{\rm x}\) falling to around 10-12 MPa, \(\sigma_{\rm y}\) about 17-20 MPa, and \(\sigma_{\rm z}\) about 8-10 MPa. However, the stress state around the tailrace surge chambers does not fluctuate since the fault and the lamrophyyre do not intersect with the tailrace surge chambers. Thus, faults and lamrophyyre could notably influence the in situ stress distribution, leading to a reduction in the in situ stress value of the surrounding rock.  
Figure 8: Stress distribution in the longitudinal section of the main powerhouse. (**a**) the first principal stress; and (**b**) the third principal stress.  
Figure 7: Stress distribution in the cross-section of the main powerhouse. (**a**) the first principal stress, (**b**) the third principal stress.