## 3 Bearing Capacity of Foundation
### Numerical Analysis
Values of \(z=s/\sqrt{2}\) and \(z=(s-a)/\sqrt{2}\) are also indicated in the figure, corresponding to the outer and inner radius of a three-dimensional soil arch as proposed by [PERSON] and [PERSON] [29], where \(z\) is the height above the base of the embankment. It has been found that when the bearing capacity of the subsoil ranges from 150 to 200 kPa, \(K\) tends to approach the static earth pressure coefficient (\(K_{0}\)) at the top of the embankment. As the depth of the embankment increases,  
Figure 9: Variation in vertical stress with embankment height for different bearing capacities of subsoil. rapidly increases, reaches a peak value, and then monotonically decreases along the depth of the embankment. It shows the presence of soil arching in the embankment, but the arching is not fully developed and falls within the category of rigid floating piles. When the bearing capacity reaches 280 kPa, the peak value of \(K\) exceeds the passive earth pressure coefficient (\(K_{\mathrm{p}}\)), indicating the occurrence of plastic failure within the embankment. It suggests the complete manifestation of the soil arching, placing it under the category of end-bearing piles. However, when the bearing capacity of the subsoil is less than 150 kPa, \(K\) decreases monotonically with the depth of the embankment, indicating the absence of soil arching and falling into the category of flexible floating piles. With the increasing bearing capacity of the subsoil, the peak value of \(K\) at the bottom of the embankment gradually increases. For a bearing capacity of 200 kPa, \(K\) increases from 1.70 (\(q_{\mathrm{u}}\) = 150 kPa) to 2.49 and further reaches 3.34 when the bearing capacity is 280 kPa, after which it tends to stabilize. It implies that the soil arching effect becomes increasingly prominent, obtaining its full manifestation when the bearing capacity reaches 280 kPa. Figure 11 presents the settlement distribution above the subsoil and pile top in an embankment on soil strata with different bearing capacities. It has been found that the settlement above the piles in the upper portion of the embankment is equal to the settlement in the overlying subsoil. With the increasing depth of the embankment, the settlement above the subsoil beneath the equal settlement plane increases, while the settlement above the pile top decreases, reaching maximum and minimum values at the bottom of the embankment, respectively. However, when the bearing capacity is 100 kPa, the settlement in the subsoil and above the piles is equal due to the smaller bearing capacity, which prevents differential settlement between the piles and soil. When the bearing capacity of the subsoil exceeds 280 kPa, the settlement at the pile top tends towards 0 mm due to the higher end-bearing capacity and the larger elastic modulus of the piles, resulting in minimal deformation under the embankment load. Figure 10: Variation in earth pressure coefficient with embankment height for different bearing capacities of subsoil. As the bearing capacity of the subsoil decreases, the settlement at the embankment surface gradually increases, from 74 mm at 315 kPa to 172 mm at 100 kPa, representing a 132% increase. The settlement at the surface of the subsoil increases from 100 mm at 315 kPa to 169 mm. The settlement at the pile top also increases with decreasing bearing capacity, but the differential settlement between the piles and soil initially increases and then decreases. It cannot be assumed that the increase in differential settlement and the weakening of the soil arching are directly related because the arching effect is essentially caused by differential settlement. It has been found that when the bearing capacity of the subsoil reaches 280 kPa, the settlement distribution within the embankment becomes stable, and the settlement at the pile top tends towards 0 mm, indicating that the piles in this scenario are considered end-bearing piles.