## 5 Conclusions  
The various internal and external loads acting on shallowly buried flexible pipe systems cause horizontal and vertical deflection of the pipe. These deflections and arching results stress distributions and lateral earth pressure coefficients that differ from the initial conditions in the buried pipe system. This study investigates the effects of pipe deflection and arching on stress distributions and lateral earth pressure coefficients through full-scale  
Figure 23: Variation of K for SP-1 (**a**) for different stress values (**b**) for different \(\tau_{\rm s}\). Figure 22: Variation of \(\sigma_{\rm crown}\) for different \(\tau_{\rm s}\). laboratory experiments, analysis and proposed empirical equations. The findings are presented below. 1. Pipe deflections are a key parameter defining the behaviour of the system, particularly in the crown and springline regions. The lateral earth pressure in the Ko condition tends towards Kp as the arching effect increases in the central soil prism, and towards Ka as the arching effect weakens. The correct estimation of K in the central soil prism in the final situation indicates that the stresses applied to the crown can be computed using [PERSON]'s arching theory. 2. The horizontal deflection of the pipe causes the backfill at the springline to move in the direction of the tank wall. As a result, the lateral earth pressure coefficient tends to convert from Ko to Kp, leading to an increase in horizontal stresses. This variation in K increases further towards the tank wall. In buried flexible pipe designs, where pipes are spaced and placed side by side, these horizontal effects will impose additional stresses on the neighbouring pipe. It is therefore essential that these effects are considered at the design stage. 3. The correlation between pipe deflections and stresses at the SP-1 was observed to be strong (R\({}^{2}\) = 0.99). This relationship indicated that both horizontal and vertical stresses in the pipe springline can be defined by estimating pipe deflections. 4. The presence of a rigid pavement in shallow flexible buried pipes provided a more homogeneous distribution of localised stresses over a wider area. This variation in stress distribution resulted in a reduction in stress and deflection of up to 84%. Additionally, the lateral earth pressure coefficient approached Ko beyond a distance of D/3. This transition occurred due to the significant reduction in horizontal stresses from the spring line to the tank wall. 5. Increasing the burial depth led to a significant reduction in stresses and pipe deflections. Specifically, the horizontal stresses at the springline decreased more than the vertical stresses, and the effect of these horizontal stresses extended to the tank wall. 6. The increase in pipe stiffness caused a noteworthy reduction in pipe deflections and horizontal stresses at the springline. In particular, the reduction in \(\sigma_{\text{v1}}\) was more pronounced than the reduction in \(\sigma_{\text{h1}}\) at the springline, and the gradual increase in Ep led to the establishment of the Ko condition along the sides of the pipe. 7. The increment in backfill stiffness considerably reduced both Ph and Pv, enhancing soil support and arching. However, there was no considerable variation in the lateral stresses transmitted from the pipe to the backfill, and in the influence distance of these stresses, as the pipe stiffness remained constant. The results obtained from the tests, analyses and empirical equations in this study are valid for shallow buried flexible HDPE pipes subjected to the surcharge stresses, test procedures, material parameters and local loading considered. To achieve a more comprehensive evaluation, further experimental studies are necessary. Conceptualization, M.G. and H.K. ; methodology, M.G. and H.K. ; software, M.G. and H.K. ; validation, M.G. and H.K. ; investigation, M.G. ; original draft preparation, M.G. ; review and editing, M.G. All authors have read and agreed to the published version of the manuscript.