# Inversion and Analysis of the Initial Ground Stress Field of the Deep-Buried Tunnel Area
## 3 Case Study
### The Inversion Results Analysis of Initial Ground Stress  
Using the calculation results of each stress component of different stress states in the 3D geological model, combined with the multiple linear regression equation, the ground stress nephograms at different depths of the longitudinal section along the tunnel in China are finally calculated, as shown in Figure 5. To explore the distribution of the initial ground stress field of the surrounding rock around the tunnel, the initial ground stress data of 500 m, 800 m, and 1100 m were extracted from the mileage section DK872-DK880 with \begin{table}
\begin{tabular}{c c c} \hline
**Coefficient Estimation** & \multicolumn{2}{c}{**Absolute Value of Mean**} & \\
**Method** & **Relative Error (AMRE)/\%** & **Number of AMRE \textgreater{} 10\%** \\ \hline OLS & 4.73 & 6 \\ RR & 4.99 & 7 \\ LR & 4.76 & 5 \\ \hline \end{tabular}
\end{table} 
Table 7: Error comparison of regression results of three coefficient estimation methods. Figure 4: Relative error between the regression value and the measured value of different measuring points. (**a**) OLS; (**b**) RR; (**c**) LR. coefficient in the direction of large horizontal principal stress with a buried depth of 500 m ranges from 1.5 to 1.8, and the lateral pressure coefficient in the direction of small horizontal principal stress ranges from 1.1 to 1.5; The lateral pressure coefficient in the direction of large horizontal principal stress with a buried-depth of 800 m ranges from 1.3 to 1.5, and the lateral pressure coefficient in the direction of small horizontal principal stress ranges from 1.1 to 1.3; The lateral pressure coefficient in the direction of horizontal large principal stress with a buried depth of 1100 m ranges from 1.2 to 1.3, and the lateral pressure coefficient in the direction of horizontal small principal stress ranges from 1.0 to 1.1. Further extracting the stress value, the relationship between the principal stress value and mileage at the tunnel axis is obtained, as shown in Figure 6.  
From Figures 5 and 6, it can be seen that the distribution characteristics of the stress field along the tunnel are closely related to the topographic. When the topographic relief increases, the stress isoline density increases, and the ground stress change gradient increases, which is consistent with the distribution characteristic of the actual ground stress field. The maximum vertical principal stress along the tunnel is 18.3 MPa, which is about at the mileage of DK874+000. The maximum value of the maximum horizontal principal stress is 26.8 MPa, which is about at the mileage of DK880+000; The maximum value of the minimum horizontal principal stress is 23.3 MPa, which is about at the mileage of DK880+000. The overall stress characteristics from large to small are as follows: the maximum horizontal principal stress, the minimum horizontal principal stress, and the vertical principal stress, which indicates that the horizontal tectonic stress is dominant in the tunnel area and the horizontal tectonic stress is significant. Compared with the uniaxial compressive strength of the rock mass in Table 4, the ratio of surrounding rock strength to the ground stress is less than 0.5, indicating that the ground stress is high and prone to large deformation [44]. There is F3 fault at the tunnel mileage of DK878+000. The horizontal tectonic stress is slightly released [32], and the ratio of horizontal principal stress to vertical principal stress is smaller than that of both sides. The reduction of the geo-tress at the fault makes the stress of the tunnel structure uneven, which is very disadvantageous to the tunnel structure. At this time, the structure needs to be strengthened, and the adaptive implementation of support becomes inevitable [46]. F2 fault also exists at the tunnel mileage of DK876+500, and the regional tectonic stress is partially released [32]. The ratio of horizontal principal stress to vertical principal stress of the adjacent area shows the same trend.