# Fuzzy Synthetic Evaluation of the Long-Term Health of Tunnel Structures
## 4 Evaluation of Structural Health Status of Cang Ling Tunnel Based on Filed Data  
In order to accurately evaluate the current structural safety status, the value of each index in the evaluation model should be obtained. Through the investigation of the design data, construction data, and related research results of the Cang Ling Tunnel, the stress characteristic of the structure is obtained by the long-term monitoring sensors that were embedded during the construction. These data can be obtained by automatic inspection of the established long-term health monitoring network system. Due to the numerous data, this paper only takes the segment of K102+300-K102+365 on the right line as an example to illustrate. The surrounding rock in this segment is mainly granite-porphyry and the surrounding rock is classified as grade IV. The thickness of the secondary lining is 45 cm. The long-term monitoring sensors embedded in the section of K102+340 acquire the contact pressure and the stress of the secondary lining. The data of the vault are shown in Figure 10.  
As we can see from Figure 10, the contact pressure and the bending moment tend to gradually converge after about 700 days. The axial force tends to converge after about 750 days. This is because the data of the crown are stable after about 750 days and at this time the values of the crown almost reach the maximum. Therefore, the data at 2500 days are taken as stress indices to evaluate the safety of the structure. The value axial force is 1.52 \(\times\) 10\({}^{6}\) N, the bending moment is 3.68 \(\times\) 10\({}^{3}\) N\(\cdot\)m, and the contact pressure is 275 kPa. Through a series of analyses, the index values are set as: [275, 5.0, 52.5, 98.7, 0.52, 10, 0.7, 54.35, 4.5, 12.22, 0.65, 7.5, 0.75, 5]. Substituting the above index values into the membership functions, the fuzzy relationship matrix R of the index layer can be obtained. Figure 9: Figure of membership function for qualitative indices. Figure 10: Time-history curve of the contact pressure, axial force, and bending moment of the vault (K102+340 section). (**a**) Contact pressure; (**b**) Axial force; (**c**) Bending moment. It should be noted that in Figure 10, since the time span of the horizontal coordinate is pretty long, some parts of the time-history curve show a sudden increase. However, the actual variation time is still pretty long. Take the contact pressure of the vault (Figure 10a) for instance: the contact pressure began to increase significantly at day 665 and gradually converges after about 700 days. The increasing stage is about a month. However, compared with the total of 2496 days, this month looks just like a few days. In this paper, the fuzzy relationship matrix of the stress characteristics of the structure \(R_{1}\) is given as:  
\[R_{1}=\left[ \begin{array}{cccc}0.9997&0.053&0&0\\ 0.804&0.203&0&0\end{array} \right]. \tag{3}\]  
After obtaining the fuzzy relationship matrix \(R_{i}\), the \(U_{i}=W_{i}\times R_{i}\) is used to carry out the fuzzy operation (\(W_{i}\) means the weight matrix of the index layer). Then the fuzzy relationship matrices of the control layer \(U_{i}\) can be obtained:  
\[U_{1}=W_{1}\cdot R_{1}=\Big{[} \begin{array}{cccc}0.5&0.5\end{array} \Big{]} \cdot\left[ \begin{array}{cccc}0.9997&0.053&0&0\\ 0.804&0.203&0&0\end{array} \right]=\Big{[} \begin{array}{cccc}0.902&0.128&0& 0\end{array} \Big{]}. \tag{4}\]  
Similarly, the fuzzy relationship matrix \(V\) of the target layer is  
\[V=W_{i}\cdot U_{i}=\Big{[} \begin{array}{cccc}0.524&0.244&0.107&0.063&0.063 \end{array} \Big{]}\cdot\left[ \begin{array}{cccc}0.902&0.128&0&0\\ 0.114&0.553&0.321&0.046\\ 0.333&0&0.667&0\\ 0&0.556&0.444&0\\ 0.32&0.616&0.058&0.13\end{array} \right] \tag{5}\]  
According to the principle of maximum membership degree, it can be known that the current health status of the tunnel structure in segment K102+300-K102+365 is level I, which means this segment is safe. The health status of each segment of the Cang Ling tunnel can be evaluated as above.