## 4 Results and Discussion
### Results of the Parametric Study
#### 4.6.1 Effect of Rigid Pavement  
In shallow buried pipe systems exposed to localised surface loading, the stiffness of the pavement and its presence are two critical factors affecting pipe performance and serviceability. The distribution of stresses applied from the surface is significantly influenced by the stiffness of the pavement under load [13]. To investigate this effect, an infinitely thin and weightless rigid plate was defined along the soil surface under load, without altering the height of the backfill, the magnitude of the applied stresses or the impact area. The results of the analyses with and without pavement were compared using the stress variation ratio (\(\mathrm{r_{vs}}\)) in Equation (8) and the deformation variation ratio (\(\mathrm{r_{vd}}\)) in Equation (9) (Figure 14). The terms \(\mathrm{di}\) and \(\mathrm{d_{f}}\) in the equations refer to displacement or deflection, while the terms \(\mathrm{\sigma_{i}}\) and \(\mathrm{\sigma_{f}}\) represent stresses. To compute the rates of variation, the values of \(\mathrm{\sigma_{i}}\) and \(\mathrm{d_{i}}\) were used for the test condition and the values of \(\mathrm{\sigma_{f}}\) and \(\mathrm{d_{f}}\) were used for a rigid pavement. Measurement points L7 and L8, specifically to investigate the change in horizontal and vertical stresses from the springline to the tank walls, are referred to as SP-2. For this region, vertical stresses are expressed as \(\mathrm{\sigma_{v2}}\) and horizontal stresses as \(\mathrm{\sigma_{h2}}\).  
\[\mathrm{r_{vs}}(\%)=\frac{\mathrm{\sigma_{i}}-\mathrm{\sigma_{f}}}{\mathrm{ \sigma_{i}}} \tag{8}\]  
\[\mathrm{r_{vd}}(\%)=\frac{\mathrm{d_{i}}-\mathrm{d_{f}}}{\mathrm{d_{i}}} \tag{9}\]  
The presence of a rigid plate allowed the surface stresses to be distributed over a larger and more uniform area. Due to this circumstance, maintaining the applied load constant while increasing the impact area resulted in significant changes in the measurements. These changes led to a reduction of 80% in the stresses, 84% in the \(\mathrm{S_{d}}\) and 82% in the Pv and Ph. In particular, the reduction in the Pv, which is one of the main causes of arching, significantly reduced the transfer of load from the central prism to the adjacent prisms.  
The rigid plate provided a stress distribution close to a uniformly distributed load condition. The stress and stress distribution varies slightly with depth, resulting in surface stresses acting on the crown. This behaviour renders [PERSON]'s arching theory dysfunctional in Equation (2).  
The 82% reduction in horizontal pipe deflection significantly reduces \(\sigma_{\rm h1}\) and the horizontal incident distances of this value. When there is no rigid plate, \(\sigma_{\rm h1}\) decreases by about 30% close to the tank wall, while in the case of a rigid plate, its effect diminishes after 0.5D from the springline. As it approaches the tank wall from the SP-1 point, the lateral stresses lose their effect, causing K to tend towards Ko. In the final situation, the changes in Ph and Pv in Figure 14a are parallel to the changes in \(\sigma_{\rm v1}\) and \(\sigma_{\rm h1}\) in Figure 14b.  
The variation in the values of \(\sigma_{\rm h1}\) and \(\sigma_{\rm v1}\), determining K, is similar as seen in Figure 14b. Therefore, the value of K in SP-1 for the pavement use case exhibited significantly less variation at different loading levels compared to Figure 13. Furthermore, changes in \(c_{\rm 1}\) and \(d_{\rm r}\) in Equation (7) were observed when a rigid plate was present on the soil surface. The \(d_{\rm r}\) decreased compared to the condition without a plate and showed a limited change in the range of 0.69-0.72. The \(c_{\rm 1}\) increased to reach 1.07. Thus, the increase in one component of K and the decrease in the other component did not lead to considerable changes in the K values.