## 2 Research Methodology
### Procedure  
An experimental plan was developed for this study (Table 5). First, all the three boxes were filled with air-dried dune sand (with 2% moisture content) and the first set of data was collected. Consequently, the following sets of data were collected by increasing the moisture content of the dune sand in all the three boxes. Experiments were conducted with a temperature ranging from 25 \({}^{\circ}\)C to 40 \({}^{\circ}\)C.  
After the experimental setup was prepared, water was pumped through the setup. Then, the three equipment devices were tested on each pipe in the same sequence for all the tests (GPR was run first, then Exemplar LS Spectrometer, and finally FLIR T420 IR Camera). A reference reading was taken at the beginning of the experiment of the undamaged pipe to represent the condition of pipes without leaks.  
Figure 7: (**a**) GPR; (**b**) Exemplar LS Spectrometer; and (**c**) FLIR T420.  
Each of the three NDTs mentioned above had a different survey plan. GPR was a line form of testing where the GPR was run along the length of the pipe, spectrometers employed a point-form of testing where data was collected from the established test points, and the IR camera covered large areas. Figure 8 illustrates the survey plan for each equipment device. A 3 mm wooden sheet was placed on the compacted soil to run the GPR along the four pipes. Three GPR scans were conducted for each pipe (along the pipe length, to the left, and to right of the pipe), as shown in Figure 8a. The data was collected every hour and the total duration of the experimentation was three hours. Hence, a total of three readings per pipe were taken. The direction in which the GPR was utilized on the pipes has been depicted using a blue arrow in Figure 8a. The following procedure was followed to process the GPR images.  
The dielectric constant of the dry sand was determined utilizing a metal plate which was placed at a known depth (bottom of the test box).  
In addition to the visual inspection of the images, Equations (2) and (3) were used to calculate the travel time of the pulse and confirm the existence of potential leakage.  
\[\text{V}=\text{C}/\text{Cr}\,\,\text{\text{\text{\text{1}}}} \tag{2}\]  
Figure 8: Survey plan for the experiments: (**a**) GPR; (**b**) spectrometer; and (**c**) IR camera.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sequence of Tests**} & \multirow{2}{*}{**Moisture Content**} & \multicolumn{3}{c}{**Pipe Material**} \\ \cline{3-5}  & & **PVC** & **PE** & **PPR** \\ \hline Round 1 & 2\% & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline Round 2 & 5\% & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline Round 3 & 10\% & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental plan.  
where V = velocity in the medium (m/s), C = velocity in free space (3 \(\times\) 10\({}^{8}\) m/s), and Cr = the relative dielectric constant. Additionally,  
\[\text{Cr}=\text{\text{\textcopy}}/\text{\textcopy}0 \tag{3}\]  
where \(\text{\textcopy}=\) the dielectric constant of the material (F/m) and \(\text{\textcopy}0=\) the dielectric constant of air, which is 8.85 \(\times\) 10\({}^{-12}\) (F/m).  
A similar procedure was followed by the authors and others [15; 46; 47; 48; 49; 50].  
Furthermore, for each spectrometer, it was tested at two locations (L = left and R = right) for each pipe, as shown in Figure 8b. Finally, IR images were taken for each pipe, as illustrated in Figure 8c.  
For processing of the IR images for leak detection, the region-growing algorithm (RGA) was used. RGA is a simple image segmentation method initiated from a seed pixel.