## 4 Numerical Results
### The Analysis of the Remaining Sand Horizon
When the volume of soil is increased by dilation, the remaining interface soil can withstand more growth of the normal stress and thus the failure of the soil structural occurs earlier. The volume enlargement is also not obvious in lower soil. In the same ultimate displacement on the pile head, the depth below \(1\,D\) is a pure compression zone where the relative depth of dilatancy is shallower than that in the scour condition without slope angle. Compared with the state development in no scour and general scour conditions, interface soil at the same relative depth in local scour conditions can sustain more stress aggregation when the void ratio changes simultaneously. This phenomenon is similar to the result of the simulation proposed by [PERSON] et al. [18] which can be attributed to the inhibition of the remaining overburden soil surrounding the pile to dilatancy and the structural failure. In the process of soil extrusion from the pile displacement, the shallow horizon of interface soil is sheared but the surrounding soil limits the volume change of sand. The shallow interface sand in the center of the scour pit can release more thoroughly without any damage and the expanding surface sand will compress the underlying sand horizon at the same time, boosting its strength. Normal stress increases in that the dilation restrained by the surrounding soil is crucial to the lateral soil resistance. In the entire  
Figure 8: Modified data and theoretical fitting of the CSL (critical state line) in e-p’ space for Toyoura sand in (**a**) no scour condition; (**b**) general scour condition; (**c**) local scour condition. remaining pile-soil interface, the lateral soil resistance is eventually reduced at the shallow horizon while it increases at the underlying horizon. To visualize the stress distribution of the interface and the surrounding soil under extrusion, the effective normal stress contour from the axial compression side in no scour and local scour conditions are extracted in this study. The displacement inflicted on the pile head is the limit in the standard of 0.2 \(D\) (1.2 m) and the stress contour of 525 kPa at the depth of the strengthening soil interface of local scour intensity is highlighted in Figure 10. From the distribution of normal stress in no scour condition in Figure 10a, the normal stress concentration is in the absolute depth region of 1 \(D\)-3 \(D\), and the lateral influence range is 0.5 \(D\). The decline of normal stress in shallow horizon leads to the reduction in lateral resistance, which is positively related to the stress relief resulted from scouring. The concentration depth of the normal stress in the local scour condition turns to 1.5 \(D\)-4 \(D\) region and the lateral influence range enlarges into 1 \(D\) in Figure 10b. The regional evolution range of stress increase presents that lateral soil resistance is strengthening. According to studies by [PERSON] et al. [28], responses of a given pile-soil interface are governed by the state of the interface soil including relative density and normal stress. Dilation or contraction of the interface soil induces variation in normal stress, which in turn influences the shear stress mobilized at the interface. Figure 10a,b examines the effect of surrounding sand on compression and deformation inhibition of lower soil interface. While the lateral resistance of the surface interface soil after the stress relief cannot carry the displacement of the pile, which explains the reduced carrying capacity of the shallow horizon of the remaining soil. Figure 9: Dilatancy of shallow horizon of the remaining interface soil in local scour condition.