## 4 Numerical Analyses Result and Discussion
### Vertical and Horizontal Deflections  
In Figures 15 and 16, vertical and horizontal deflections are presented for 0.762 m diameter PVC and 1.524 m diameter HDPE pipes, respectively. In the reference, the highest deflection was obtained with clay, sand, and crushed stone backfill, respectively. In Figure 15, the lowest deflections were obtained with the 0.762 m diameter PVC pipe in the ITI model compared to the reference. Horizontal deflection decreased from 3.9 to 1.4%, from 5.7 to 1.5%, and from 7.5 to 0.2%, respectively, for crushed stone, sand, and clay  
Figure 13: Arching factors for 0.762 m diameter PVC pipe. (**a**) Vertical arching factor (VAF). (**b**) Horizontal arching factor (HAF). backfills. The vertical deflections decreased from \(-4.5\) to \(-1.4\)%, from \(-6.2\) to \(-1.5\)%, and from \(-8.1\) to \(-0.3\)%. The deflections obtained in the ETI model were greater than in the ITI model. In Figure 16, the lowest deflections were obtained with the 1.524 m diameter HDPE pipe with the ITI model compared to the reference. Horizontal deflections decreased from 2.62 to 0.70%, from 4.40 to 0.92%, and from 6.85 to 1.00%, respectively, for crushed stone, sand, and clay backfills. The vertical deflection values decreased from \(-4.77\) to \(-1.7\)%, from \(-6.7\) to \(-1.88\)%, and from \(-9.32\) to \(-0.25\)%. The deflections obtained in the ETI model were greater than in the ITI model. As shown in Figures 15 and 16, vertical and horizontal deflections due to the increase in embankment height are considerably higher in the reference than in the ITI and ETI models. When the thermoplastic pipe is buried according to the ETI model, active soil wedges at the sides of the pipe are induced, leading to a significant reduction in horizontal stresses that act on the pipe spring line. Contrary to the stresses, horizontal and vertical deflections in clay backfill are smaller than in crushed stone and sand backfill. This is because the EPS Geofoam material on the sidewall of the pipe is more compressed in the clay than in the sand and crushed stone (the greater horizontal stress has been transferred onto the clay backfill). As a result of this interaction, the pipe showed peaking behavior. Figure 14: Arching factors for 1.524 m diameter HDPE pipe. (**a**) Vertical arching factor (VAF). (**b**) Horizontal arching factor (HAF). Reduction in horizontal stress in the pipe spring line is controlled by compression of the EPS zone that covers the side of the pipe. Various institutions and standards or codes have presented recommendations for the deflection limit of thermoplastic pipes. The German Code recommends the limiting value for pipe deflection to be 6% [86], AASHTO to be 6.15% [87], and both CCPA and PPI recommend it to be 7.5% [88; 89]. It is seen that the deflections in the ITI and ETI models, corresponding to the reference model stress for a 30-m-high embankment, were much smaller than the allowable design limits (Figures 15 and 16). [PERSON] et al. [17] conducted field experiments to examine the effect of the degree of compaction of the backfill material on the mechanical behavior of HDPE pipes. As a result of the experiments, they stated that the backfill density in the haunch region of the pipe has the most significant effect on the deflections of the pipe. In HDPE pipes in a well-compacted fill, the most critical area of the outer pipe wall is the spring line. In loose soil placement around the pipe, deformations are concentrated in the crown or invert regions. They emphasized that the pipe's response to loose backfill is related to the size of the loose-backfill region and the region's location and that the area of the loose-backfill region is more critical than the size. Figure 15: The 0.762 m diameter PVC pipe deflections. (**a**) Horizontal. (**b**) Vertical. According to experimental and numerical analyses conducted to examine the mechanical behavior of HDPE pipes under different loading conditions by [18], pipe properties (diameter, stiffness, etc.) affected the response of the pipe to the backfill material.