## 3 Materials and Method
### Verification of the Numerical Model  
Numerical analyses were performed for all pipes shown in the plan in Figure 2 [78]. However, for verification analysis within the scope of the article, only the results for Pipe 4 (A-A\({}^{\prime}\) section) and Pipe 14 (B-B\({}^{\prime}\) section) were compared with field measurements and presented in Figure 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Local Soil-Backfill** & **Pipe-Backfill** & **Pipe-EPS** & **EPS-Backfill** \\ \hline \(\varphi_{\text{inter}}\) (\({}^{\circ}\)) & 24 & 20 (\({}^{1}\)) & 14 (\({}^{2}\)) & \textgreater{}30 (\({}^{3}\)) \\ \hline R\({}_{\text{inter}}\) (-) & 1.00 & 0.67 & 1.00 & 1.00 \\ \hline \(\varphi_{\text{inter}}\) angle of interface strength; R\({}_{\text{inter}}\) interface strength reduction factor (\({}^{1}\)) [75], (\({}^{2}\)) [76], (\({}^{3}\)) [77]. & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of interface strength and corresponding interface reduction factors. Figure 4: _Cont._In the field test, after the pipe was placed in the trench, it was compacted by placing a backfill layer around it. To consider the effect of the compaction process on the pipe in the numerical analysis, the loads indicated in Table 5 were applied laterally to the pipe sidewall (Figure 3b). Thus, the deflection of the pipes during the backfill phase could be modeled more realistically. The magnitude of the point loads was determined by trial and error, considering the relative compaction values. Since the 6.1 m and 12.2 m embankment fills built over the negatively projected pipes were also placed by compaction, the embankment fill construction was modeled by applying a distributed load of 6 kN/m in the first fill layer and 12.5 kN/m in the other fill layers. After the trench backfill was completed in 11 steps, the 6.1 m- and 12.2 m-thick embankment was constructed in 15 and 22 steps, respectively. The values up to zero shown on the horizontal axis in Figure 4 show the trench backfill of the pipe placed with negative projection and then the backfill construction (6.1 m or 12.2 m). Figure 4: Field test and numerical analyses. (**a**) Vertical stress on the pipe crown and horizontal stress on the pipe spring line in Pipe 4. (**b**) Horizontal and vertical deflection in Pipe 4. (**c**)Vertical stress on the pipe crown and horizontal stress on the pipe spring line in Pipe 14. (**d**) Horizontal and vertical deflection in Pipe 14. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Layer 1** & **Layer 2** & **Layer 3** & **Layer 4** & **Layer 5** & **Layer 6** \\ \hline Pipe 4 & 1.0 & 0.9 & 1.4 & 1.0 & - & - \\ \hline Pipe14 & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 & 1.5 \\ \hline \end{tabular}
\end{table} 
Table 5: Loads acting on the pipe sidewall (Loads are in kN units). It was seen that the calculated deflection for both pipes was in approximate agreement with the field measurements, but the horizontal and vertical stresses were greater than those measured. In Figure 4a, there was a difference of roughly 25 kPa in stresses between numerical analysis and field measurement for Pipe 4. In comparison, a difference of 17 kPa in vertical stresses and 45 kPa in horizontal stresses occurred in Pipe 14 in Figure 4c, and the horizontal stress exceeded the vertical stress after 8.5 m of fill. In addition, it was seen that the measured vertical and horizontal stresses are quite close to each other. The vertical and horizontal stresses calculated from the analyses are close. Under the applied stress, positive arching occurred with vertical deflection of the pipe. As a result of the decrease in the vertical stresses, an increase in the horizontal stresses occurred. In the verification analysis, approximately similar pipe deflections were considered. In Figure 4b, the vertical deflection was more compatible with the measurements, while the horizontal deflection was slightly higher. In Figure 4d, both the vertical and horizontal deflection values were more consistent with the measurements.