## 4 Field Monitoring and Stress Analysis
### Stress Propagation Law and Comparative Analysis  
Based on the data in Table 6, the average damage factors and stress values at monitoring points 1-5 over five blasting cycles are summarized Table 7. To further examine the stress propagation behavior in the surrounding rock of the adjacent tunnel with respect to distance from the blast center, Figure 24 was generated using the data in Table 7. As shown in Figure 24, radial, axial, and hoop stresses all decrease with increasing distance, with radial stress showing the fastest attenuation rate, followed by axial and hoop stresses.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Blasting Times**} & \multirow{2}{*}{**Damage Factor D**} & \multirow{2}{*}{**Measure Point**} & \multicolumn{3}{c}{**Peak Voltage (mV)**} & \multicolumn{3}{c}{**Peak Stress (MPa)**} \\ \cline{3-10}  & & & **Radial** & **Axial** & **Hoop** & **Radial** & **Axial** & **Hoop** \\ \hline \multirow{5}{*}{\(1\)} & 0.20 & 1 & 5.77 & 3.19 & 2.72 & 0.89 & 0.49 & 0.42 \\  & 0.18 & 2 & 6.27 & 3.57 & 2.94 & 0.96 & 0.55 & 0.46 \\  & 0.14 &  
The mean relative error (MRE) between measured and theoretical stress values is defined as follows:  
\[\text{MRE}_{(i)}=\left|\frac{\overline{\sigma}_{\text{measured}}^{(i)}-\sigma_{ \text{theoretical}}^{(i)}}{\sigma_{\text{theoretical}}^{(i)}}\right|\times 100\% \tag{28}\]  
\[\overline{\sigma}_{\text{measured}}^{(i)}=\frac{1}{n}\sum_{j=1}^{n}\sigma_{ij} \tag{29}\]  
where \(\overline{\sigma}_{\text{measured}}^{(i)}\) is the mean measured stress at the \(i\)-th monitoring point, \(\sigma_{\text{theoretical}}^{(i)}\) is the theoretical stress at the \(i\)-th monitoring point, \(n\) is the number of blast events, and \(\sigma_{ij}\) is the measured stress at the \(i\)-th monitoring point during the \(j\)-th blast.  
And the average error (AE) of all measuring points is defined as follows:  
\[\text{AE}=\frac{1}{k}\sum_{i=1}^{k}\text{MRE}_{(i)} \tag{30}\]  
where \(k\) is the number of measuring points.  
A comparison between measured and theoretical stress values is presented in Figure 25. The results show that the measured stresses are slightly lower than theoretical predictions, with average errors of 7.02% for radial stress, 7.56% for axial stress, and 7.05% for hoop stress.  
Analysis of discrepancies: According to Reference [41], borehole stemming can improve explosive energy utilization by approximately 7.5%. In this test, however, the cut holes were unstemmed, leading to energy loss. Additionally, signal attenuation occurred due to excessive cable lengths at the signal receivers. According to reference [40], the voltage drop (\(\Delta U\)) along the cable is calculated as follows [42]:  
\[\Delta U=\Delta U_{0}\%\times I\times L \tag{31}\]  
where \(\Delta U_{0}\%\) is the percentage voltage drop per kilometer of cable, \(I\) is the load current (A), and \(L\) is the cable length (km). Based on data from reference [42], \(\Delta U_{0}\%\) was taken as 0.766%. With a measured load current of \(I\) = 0.52 A and cable length \(L\) = 0.1 km, the voltage drop calculated using Equation (31) is 0.3983 mV. This voltage drop reduced the peak voltage during measurements, resulting in values lower than theoretical predictions and contributing to the previously noted error, further lowering the reduced measured stress values. These factors collectively explain the observed discrepancies.  
Figure 24: Propagation law of measured stress with the distance from the blast center.  
Despite these minor deviations, the measured and theoretical values align well, with errors within acceptable limits (\(\leq\)8%), confirming the reliability of the analytical stress field solutions developed in this study. In tunnel engineering, the MRE between theoretical and measured stress values typically remains below 10%, a range acceptable for meeting project reliability requirements [43; 44].