## 4 Results and Discussion
### Vertical Stresses  
During the S and P tests, crown stresses (\(\sigma_{\rm crown}\)) were measured at L3 and L4, and invert stresses (\(\sigma_{\rm invert}\)) were measured at L1 and L2. Figure 6 compares these stress values with the results obtained from analysis. The analyses reveal that in the S test under localised loading conditions, stresses and displacements are distributed over a wider area from the bottom of the loading plate downwards. Different settlements with unclear boundaries occur between the central and adjacent soil prisms beneath the loading plate. The resulting Fv values from these distinct displacement conditions contribute to the arching to a limited extent in the S test. Conversely, in test P, using an HDPE pipe, which leads to more displacement than in the soil, enhances the Fv under boundary conditions with a width approximately equal to the pipe diameter. This positive effect improves the arching and reduces crown stresses. The vertical stresses acting on the pipe cause pipe deflection and arching. These stresses are transferred to the adjacent soil prism, clearly reducing the invert stresses (Figure 6b). The analyses indicated that the stiffness of the bottom of the pipe and the distribution of stresses over a larger area at the bottom of the pipe contribute to this result. Figure 5: The variation of measured and computed surface displacements with applied stress. Figure 6: The variation of measured and computed stresses for; (a) crown and (b) invert. The u\({}_{\rm pyv}\) component of the surface displacement in the P test functions in the same way as the trapdoor and is the most critical parameter influencing arching. When z = 0 and h = q are adopted in the differential solution of [PERSON]'s arching theory equation, Equation (2) is derived. The first part of the equation represents the stresses due to the soil pressure, and the second part represents the stresses due to the surcharge. \[\rm V=\frac{B(\gamma)}{Ktan(\phi)}(1-e^{-Ktan(\phi)h/B})\ +\ q_{sur}e^{-Ktan(\phi)h/B} \tag{2}\]  
where, V is the vertical stress after arching, B is the half-width of the moving segment, h is the soil height above the moving segment, q is surcharge stress. In [PERSON]'s arching theory, a clear understanding of the lateral earth pressure coefficient (K), describing the horizontal effect of V, is crucial. Equation (2) is employed to calculate the vertical stresses at the crown in the P test, with K becoming the sole variable. The study established the variation of \(\sigma_{\rm crown}\) using Equation (2) for test condi-tions. Figure 7 compares these stresses to the \(\sigma_{\rm crown}\) values derived from the analyses. Figure 7b shows that the stresses determined from the test and analysis correspond to different K values at various loading levels. In particular, K and \(\sigma_{\rm crown}\) were determined assuming that the frictional force occurs in vertical planes (Figure 1). The variation of K and \(\sigma_{\rm crown}\) can be studied under different assumptions regarding the formation, boundaries, and configuration of the arching in the central soil prism. The enhancement of arching due to the vertical deflection of the pipe increases the stresses transmitted from the central soil prism to the adjacent soil prisms. The shear planes in the soil-pipe friction also significantly aid in the transfer of vertical stresses to the sides of the pipe. This increased stress transfer to the adjacent soil prism results in higher stresses in the P test compared to the S test (Figure 8). The vertical stresses transmitted to the adjacent soil prism due to arching, as well as the vertical effect of the stresses applied from the surface, decrease from the pipe springline towards the tank wall. It is noted that the stresses at points L9 and L10 are approximately 45% lower than the stresses at points L7 and L8 (Figure 8). This rate of reduction particularly increases from the springline towards the tank walls.