## 4 Results and Discussion
### Results of the Parametric Study
#### 4.6.2 Effect of Burial Depth  
Elevating the burial depth (h) increases the \(\rm u_{\rm ys}\) component and decreases the \(\rm u_{\rm pyv}\) component as a consequence of lowering the stresses acting on the pipe. Although the change in \(S_{\rm d}\) in the final state was minor, the proportion of \(\rm u_{\rm pyv}\) in \(S_{\rm d}\) had a considerable effect on the arching.  
As a result of the decrease in locally applied stress from the surface soil with increasing burial depth, remarkable variations in the stresses acting on the pipe or culvert were observed depending on, the burial depth [13; 21; 28]. Stress concentration in the crown region and the corresponding Pv tend to direct particle movement within the central soil prism from the Ko state to the Ka state. Figure 15 illustrates the variation of stresses determined from Equation (2) and the analysis for the crown.  
Figure 14: The variation of stress and deformation for rigid pavement; (a) \(r_{\rm vd}\) (b) \(r_{\rm vs}\).  
The analyses revealed that when h was 0.5D, both Pv and arching indicated local arching in the crown, leading to a significant reduction in stresses within the crown region. This resulted in the maximum stress occurring at a certain distance from the crown. However, Equation (2) does not take into account this specific behaviour of shallow buried flexible pipes, making the data incompatible at a burial depth of 0.5D.  
The stress variation at the crown of the pipe significantly affects both flexing and arching. The values of \(\mathrm{r_{vs}}\) and \(\mathrm{r_{vd}}\) were determined for burial depths ranging from 0.5D to 3D, with reference to a burial depth of 1D (Figure 16). These \(\mathrm{r_{vs}}\) and \(\mathrm{r_{vd}}\) remained approximately the same for different loading levels at a constant burial depth, allowing comparisons to be made by averaging these values for a general assessment.  
Increasing the burial depth resulted in a decrease in \(\mathrm{\sigma_{h1}}\), but did not significantly alter the distance over which \(\mathrm{\sigma_{h1}}\) was effective. Similarly, Pv and stress transfer to the sides of the pipe decreased as the burial depth increased. The decrease in \(\mathrm{\sigma_{h1}}\) was more pronounced than the decrease in \(\mathrm{\sigma_{v1}}\). Therefore, the lateral soil pressure coefficient at SP-1 decreased with increasing burial depth.  
Figure 16: Stress and deformation variation ratios for different h values (**a**) \(\mathrm{r_{vd}}\) (**b**) \(\mathrm{r_{vs}}\).  
Figure 15: Comparison of stresses obtained from Equation (2) and analysis for crown.  
The increase in burial depth positively affected the d\({}_{\rm r}\) values, which ranged from a mean of 0.74 to 0.83. The values for c\({}_{1}\) at different burial depths were 0.845, 0.891, 0.90, 0.915, 0.875, and 0.845. Figure 17a demonstrates the variation of K for different loading levels and burial depths. Figure 17b shows the K obtained from Equation (7) using c\({}_{1}\) and the mean d\({}_{\rm r}\), as well as the change in K computed from the \(\sigma_{\rm v1}/\sigma_{\rm h1}\) ratio for the analyses.