## 3 Numerical Model and Simulation Scheme of the Strain-Structural Plane
### Characteristics of Stress Information  
Figure 4 shows the distribution of the principal stress difference (\(\Delta\sigma=\sigma_{1}\)-\(\sigma_{3}\)) within the surrounding rock under different conditions. From Figure 4, the larger value of the \(\Delta\sigma\) is mainly distributed between the structural plane and tunnel, and some blocks exhibit obvious stress concentration at the arch foot. The \(\Delta\sigma\) distribution shows obvious differences with the variation of the structural plane geometric parameters. The distribution characteristics of the stress field are analyzed under different conditions, and the specific variation laws are as follows.  
Observing Figure 4a-c, the effect of \(\theta\) on the \(\Delta\sigma\) is reflected in two aspects: On the one hand, \(\theta\) controls the distribution range of the larger value of \(\Delta\sigma\), which gradually decreases as \(\theta\) increases. The value of \(\Delta\sigma\) near the structural plane at \(\theta=60^{\circ}\) is only 40-50 MPa; on the other hand, the \(\Delta\sigma\) distribution above the structural plane is also significantly affected by \(\theta\), where the larger value of \(\Delta\sigma\) above the structural plane likewise decreases as \(\theta\) increases. Observing Figure 4d-f), when \(L=6.5\) m, the structural plane has less influence on the \(\Delta\sigma\) distribution, and the stress field distribution is approximately symmetrical; When \(L=8.5\) m, the distribution range for the larger value of \(\Delta\sigma\) extends from structural plane to tunnel wall. When \(L=10.5\) m, the larger value of \(\Delta\sigma\) distribution below the structural plane  
Figure 4: The distribution of principal stress difference under different conditions (unit: Pa): (**a**) \(\theta=30^{\circ}\); (**b**) \(\theta=45^{\circ}\); (**c**) \(\theta=60^{\circ}\); (**d**) \(L=6.5\) m; (**e**) \(L=8.5\) m; (**f**) \(L=10.5\) m; (**g**) \(D=0\) m; (**h**) \(D=1.7\) m; (**i**) \(D=3.4\) m.  
extends further to the top of the right sidewall. As \(L\) increases, the stress concentration degree and distribution range of the surrounding rock increase. Observing Figure 4g-i, when \(D\) = 0 m, the peak value of \(\Delta\sigma\) was 70.7 MPa, and the \(\Delta\sigma\) values between the left spandrel, the vault, and the arch foot on both sides are all larger than 65 MPa, the \(\Delta\sigma\) value on the right sidewall is relatively small. The degree of stress concentration and distribution range is significantly affected by the structural plane. When \(D\) = 1.7 m, the peak value of \(\Delta\sigma\) is 162.7 MPa, and the larger values of \(\Delta\sigma\) are located in the vault, both sides of the spandrel and the arch foot, and the distribution range of \(\Delta\sigma\) on the right spandrel increases gradually. When \(D\) = 3.4 m, the peak value of \(\Delta\sigma\) is 149.8 MPa, and its distribution characteristics are similar to those of \(D\) = 1.7 m, the structural plane effect on the stress field is reduced. The peak value of \(\Delta\sigma\) at \(D\) = 0 m is much smaller than that when \(D\) is 1.7 m and 3.4 m, which indicates that when there is a certain distance between the structural plane and tunnel, the degree of stress concentration in the surrounding rock is more obvious, but the value of \(\Delta\sigma\) tends to decrease gradually with the further increase in \(D\).