## 3 Case Study
### Collapse Risk Assessment Based on Instrument Monitoring Data  
The instrument monitoring data include surface settlement, vault settlement displacement and horizontal convergence displacement in the shallow buried section, which reflects the stability of the tunnel support after the initial lining. The effect of surface settlement for deep tunnels is often not considered, and only the vault settlement displacement and horizontal convergence displacement are selected for collapse risk analysis. According to the national standard for Technical Specification for Highway Tunnel Construction (JTG/T 3660-2020), and Technical Specification for Monitoring and Measurement of Highway Tunnels (DB 35/T 1067-2010), the daily change rate and cumulative deformation are taken as indicators. The farther the monitoring point is from the palm surface, the larger the accumulated displacement limit value is, so the cumulative displacement value needs to be multiplied by a factor \(\zeta\). These two judgment indicators are divided into four levels, as shown in Table 6. The accumulated displacement needs to be multiplied by a factor \(\zeta\) according to the distance between the measurement point and the palm surface. According to the Standard for Technical Specification for Monitoring and Measurement of Highway Tunnels (DB 35/T 1067-2010), the relationship between \(\zeta\) and D is shown in Table 7, where B is the span of the excavated tunnel. The instrument monitoring datasets have four types of risk levels, which are Level I, Level II, Level III and Level IV. The number of features for each risk level is 2, which are vault settlement displacement and horizontal convergence displacement. The inputs to the test set are the monitored values of vault settlement and horizontal convergence. The tunnel collapse level is the output of model. Then, according to the most unfavorable principle,  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**Probability**} & \multicolumn{2}{c  
the larger collapse risk level is used as the label. The output is the tunnel collapse failure probability value. The collapse level corresponding to the maximum value of collapse failure probability is the collapse level predicted by the model. The model prediction accuracy is obtained by comparing the model prediction values with the labeled values. A collapse risk assessment model is built based on the scikit-learn machine learning library. The number of features in the instrument monitoring datasets is 2. The test set sample is 60 tunnel cross-sections in Section 3.2. The supervised learning model is chosen because the samples need to be trained with labels. In this paper, a Support Vector Machine with the key parameters of kernel function, kernel function parameters and penalty parameters is selected. Based on the fact that both the number of features and the number of samples are small, and the number of features is much smaller than the number of samples, Radial Basis Function (RBF) is selected as the kernel function. The key parameters are the penalty parameter C and the kernel function parameter gamma. A grid search method to find the optimal hyperparameters (C, gamma). The parameter optimization range of C is 0.05, 0.1, 0.15 and 0.2. The parameter optimization range of gamma is 0.001, 0.002, 0.004 and 0.006. The classification probability distribution chart of tunnel collapse risk level is shown in Figure 5.  
Figure 5a shows the classification probability distribution chart when gamma is 0.004, and C are 0.05, 0.1, 0.15 and 0.2, respectively. The result shows the relationship between classification probability and color. The darker the color is, the lower the classification probability value is. It can be seen that there is a point where it has clearly deviated from the other points when C is 0.05, and the level is II. However, all points are gathered together when C is 0.1, 0.15, 0.2, and the level is II.