## 2 Methodology for Structural Stability Evaluation
### Procedure of Local Damage Detection  
There is no doubt that in-site detection is an irreplaceable method of evaluating structural status and preventing abnormal conditions. The existing research shows that NDT methods have developed into a reliable technology for field detection [20; 21]. In recent years, tunnel accidents caused by the leakage of grouting holes have attracted attention, e.g., the leakage accident that occurred in the Nanjing Yangtze River tunnel on 24 May 2018. Unlike previous applications, we used multiple NDT equipment methods--a ground Penetrating Radar (GPR) and a thermal infrared camera--to work synergistically to detect the status of the grouting holes. This is because conditions that filled with water but did not leak out cannot be determined if only IR is used. Inversely, it is difficult to determine whether water has overflowed and whether to take supporting measures if only GPR is used. Therefore, both of these methods are indispensable. The detection procedure was formalized as shown in Figure 2. First, GPR is adopted to invert the internal conditions of grouting holes. The launcher receiver moves across the surface of a fire-proof plate from left to right. According to the differences in the filling medium in the holes, the inversion results are classified into three categories to reflect the typical conditions in the field--empty, filled with water, and filled with grout. Empty holes are defined as safe and no further testing and analysis is required. Infrared cameras locate damage by determining whether there is water leaking in holes.  
Figure 1: The workflow of the developed methodology.  
The GPR is an instrument used to detect the boundaries of different mediums through electromagnetic waves [22]. The type of GPR used in the present experiment and field detection is a Zond-12e, produced by Latvia. The electromagnetic wave spreads in the semi-infinite space with a spherical surface. The practical detection zone is an ellipse, and the detection zone is related to relative permittivity, which is expressed as follows:  
\[\left\{\begin{array}{rl}a&=&\frac{\lambda}{4}+\frac{d}{\sqrt{c_{r}-1}}\\ &b&=&0.5a\end{array}\right. \tag{1}\]  
where \(a\) and \(b\) are the semi-major axis and semi-minor axis of the ellipse, respectively; \(d\) is detection depth; \(\lambda\) is the wavelength of electromagnetic wave; and \(\varepsilon_{r}\) is the relative permittivity.  
The thermal infrared camera is used to determine the leakage position through the difference in infrared energy between water and the structure [23; 24]. The type of GPR used in our study is an Inf-Rec R500, developed by Nippon Avionics company in Yokohama, Japan. The radiant energy is turned into an electrical signal and identified by the detector, calculated as follows:  
\[\left\{\begin{array}{rl}L_{\lambda}&=&L_{\lambda 1}+L_{\lambda 2}\\ L_{\lambda 1}&=&\zeta_{\lambda}L_{b\lambda}(T_{o})\\ L_{\lambda 2}&=&\rho_{\lambda}L_{b\lambda}(T_{u})\end{array}\right. \tag{2}\]  
where \(L_{\lambda 1}\) is the radiance of the object and \(L_{\lambda 2}\) is the radiation emitted by the surroundings and reflected by the object. \(T_{u}\) and \(T_{o}\) are the temperature of the environment and on the surface of the object, respectively. \(\zeta_{\lambda}\) is surface emissivity. \(\rho_{\lambda}\) is surface albedo.  
If the hole is leaking, the leaking water would lower the temperature around the hole. Thus, infrared thermography would express a clear lower temperature boundary. On the contrary, if it is not leaking, the temperature distribution expressed in infrared thermography is uniform.