## 5 Discussion on the Coupling of In Situ Stress and Blasting  
In the process of calculating the range of the loose zone using the stress and work-energy relationship methods, the quantitative analysis of the coupling effect of the in situ stress and blasting on the formation of the final loose zone has always been a difficulty. Here, taking the stress method as an example, the coupling effect between the stress loose zone and the blasting-expansion loose zone is discussed through the comparison of the theoretically calculated values for both loose zones. First, the calculation effect of the stress relaxation circle was analyzed through numerical simulations, and the three-dimensional numerical model was established by FLAC3D. The rock, soil, and tunnel body were modeled by solid elements, and the initial support was modeled by shell element simulations. The model size was 30 m (Y) \(\times\) 12 m (Y) \(\times\) 40 m (Z). The formation calculation parameters taken by the model are shown in Table 2, and the model diagram and calculation results are shown in Figure 13.  
The calculation and numerical simulation results for the range of the stress relaxation zone using the Fenner solution under low ground stresses are shown in Table 4. The calculation results of the stress loose zone thickness \(L_{BI}\) under different working conditions are shown in Figure 14.  
The above analysis showed that when using the Fenner solution to find the stress loose zone, the calculated results were consistent with the numerical simulation results, which were quite different from the measured values. This showed that when using the Fenner solution to calculate the loose zone, the results only considered the loose zone caused by the stress release after the chamber excavation while ignoring the loose zone formed in the blasting process. The stress loose zone only accounted for a small part of the final loose zone. The main part was the loose zone produced by blasting crack propagation. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Working Condition**} & \multirow{2}{*}{**Stress Method (m)**} & \multicolumn{2}{c}{**Work–Energy Relationship Method 1**} & \multicolumn{1}{c}{\multirow{2}{*}{**Work–Energy Relationship Method 2**}} & \multirow{2}{*}{**Measured Value (m)**} \\  & & & **(m)** & \\ \hline
1 & 1.36 & 1.47 & 1.43 & 1.2–1.4 \\
2 & 2.47 & 2.73 & 2.66 & 1.8–2.6 \\
3 & 1.17 & 1.51 & 1.21 & 0.6–1.5 \\ \hline \end{tabular}
\end{table} 
Table 3: Theoretical calculation results and measured values of the loose zone range under different operating modes. Figure 13: Cont. In the above derivation and analysis, it was found that the final calculated value was smaller than the measured value after adding the thickness of the stress loose zone, and the blasting extended the loose zone directly. This was because, in the actual chamber excavation process, the formation of the loose zone under the action of in situ stress and the formation of the blasting stress wave, which extended the loose zone, did not occur independently but had a coupling effect. The calculation results and coupling coefficients of the stress loose zone and blasting-expansion loose zone are discussed below. The calculation results are shown in Table 5, where \(L_{b1}\) is the thickness of the stress loose zone, \(L_{b2}\) is the thickness of the blasting-expansion loose zone, \(L_{b}\) is the thickness of the final loose zone, and \(m\) and \(n\) are the coupling coefficients. As discussed above, the higher the grade of the surrounding rock, the smaller the values of \(m\) and \(n\), approaching 1.0. The lower the grade of the surrounding rock, the larger the values of \(m\) and \(n\). In comparison, the variation range of \(m\) was larger, which showed that in the process of the loose zone formation, although the range of the loose zone under the influence of the in situ stress was small after chamber excavation, the influence of the in situ stress on the final loose zone formation was large.