## 4 Numerical Analyses Result and Discussion
### Pipe Material (HDPE-PVC) Effects  
To examine the effects of HDPE and PVC material on stresses for 0.762 m diameter thermoplastic pipes, the analyses conducted on the C-type HDPE pipe and the B-type PVC pipe shown in Table 3 were compared. The stresses around the pipe are shown for the ITI model in Figure 11 and for the ETI model in Figure 12. The left side of the graphic shows the HDPE pipe, and the right side shows the PVC pipe. Table 9 presents the calculated stresses on the pipe crown, invert, and spring line for a 30 m embankment. Figure 9: In the ITI model, stresses in PS-650 and PS-302 pipes for 30 m embankment. Figure 10: In the ETI model, stresses in PS-650 and PS-302 pipes for 30 m embankment. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**HDPE (C Type)**} & \multicolumn{3}{c}{**PVC (B Type)**} \\ \cline{3-8}  & & **Crown** & **Spring Line** & **Invert** & **Crown** & **Spring Line** & **Invert** \\ \hline \multirow{3}{*}{Reference} & Cr. R & 267 & 235 & 209 & 307 & 269 & 247 \\ \cline{2-8}  & Sand & 316 & 254 & 256 & 341 & 271 & 281 \\ \cline{2-8}  & Clay & 379 & 297 & 338 & 392 & 294 & 348 \\ \hline \multirow{3}{*}{ITI model} & Cr. R & 156 & 154 & 178 & 158 & 168 & 197 \\ \cline{2-8}  & Sand & 176 & 185 & 224 & 178 & 192 & 236 \\ \cline{2-8}  & Clay & 237 & 257 & 301 & 235 & 252 & 298 \\ \hline \multirow{3}{*}{ETI model} & Cr. R & 138 & 97 & 121 & 138 & 103 & 122 \\ \cline{2-8}  & Sand & 153 & 113 & 136 & 152 & 116 & 135 \\ \cline{2-8}  & Clay & 206 & 193 & 207 & 194 & 179 & 185 \\ \hline \end{tabular}
\end{table} 
Table 9: Stress on HDPE and PVC pipes with 0.762 m diameter for the 30 m embankment (in kPa). It can be seen from Figures 11 and 12 that the stresses acting on the PVC pipe at the crown, spring line, and invert of the pipe are higher in the reference than in the HDPE pipe. Similar results were obtained in the study of [84], in which HDPE and PVC pipes were examined. When the stresses presented in Table 9 were considered, it was determined that there was a difference of 15 to 18% at the pipe crown, 7 to 10% at the pipe spring line, and about 3% at the invert level of the pipe in the ITI and ETI models, respectively. This is because the stiffness of the HDPE pipe is lower than the PVC pipe. The HDPE pipe deflects more, causing further development of positive arching. As a result, less stress affects the HDPE pipe. In the ITI and ETI models, it was seen that the stresses acting on the crown of the HDPE and PVC pipe were very close to each other, depending on the backfill type (Table 9). The stresses affecting the different parts of the pipe are approximately similar. In the ITI and ETI models, the most significant difference between the stresses acting on both pipes was around 10%. Thus, if EPS is used with a pipe with lower rigidity, it shows the expected performance of a rigid pipe. Especially in the ETI model, approximately uniform stress distribution around the pipe (crown, spring line, and invert) was obtained using EPS. Figure 11: In the ITI model, stresses on the HDPE and PVC pipes for the 30 m embankment. Numerical analyses were conducted for the thermoplastic pipe buried using EPS in the ITI and ETI models by considering the diameter, stiffness, and material type (HDPE and PVC). In the analysis, the effects of the backfill material (crushed stone, sand, and clay) on the stresses around the pipe were determined (Figures 7-12). As can be seen, the lowest stress affecting the pipes due to diameter, stiffness, and thermoplastic material type (HDPE and PVC) effects were calculated for crushed stone, sand, and clay backfills, respectively. As expected, the highest stress values occurred in the clay backfill. It has been stated in many studies investigating the effects of backfill material stiffness that this changes the pipe behavior [10; 26; 36; 49]. It is known that loads acting on thermoplastic pipes are a function of soil-structure interaction and depend on the relative stiffness of the soil. Under soil load, vertical deflection occurs in the pipe.