## 4 Numerical Results
### The Analysis of the Remaining Sand Horizon  
In the shallow scour depth of \(S_{d1}\) in local scour conditions, the whole horizon of the remaining interface soil changes stiffer. Differently, in the scour depth of \(S_{d2}\), the remaining sand can be divided into two characteristics in local scour condition:  
1. The shallow sand horizon is softened and is subjected to scour obviously when the lateral sand resistance is lower than that at the same depth under original soil. 2. The deeper depth is 10-20% hardener than that at the same horizon before. For variation 1, a similar phenomenon of lateral sand resistance reduction after scouring was found in [PERSON]'s centrifuge test [9] while variation 2 was found in [PERSON]'s experiment and simulation [17,18] accordingly. The simulation in this research observes a combination of both phenomena simultaneously, which is related to the state-dependency dilatancy of the interface soil. In the analysis of lateral soil resistance after soil excavation, [PERSON] et al. [27] highlights the effect of stress relief on soil strength during the soil removal and the scour can also be regarded as a slow removal process of the shallow horizon, even for the slow removal process of shallow horizon under scouring. The shallow horizon undergoes stress relief, the interaction between the changed soil particles. Therefore, the change of lateral soil resistance can be analyzed by the stress state of the soil interface. Based on the existing sand model, the state variation curve of the remaining sand in e-p' space is sorted out to investigate the stress-strain development characteristics in different scour conditions. To analyze the characteristics of remaining soil in different scour conditions better, the simulation makes a comparison of three types of soil conditions in Figure 3. This research captures the variation of the stress state of interface soil on the axial compression side. Thus, the research defines the depth calculated from the mudline as the absolute depth \(z\), and the depth calculated from the top of the remaining soil as the relative depth \(z\prime\). Comparison in different states of sand at the same relative depth can be used to evaluate the characteristics of soil development. The model simulates the lateral loading process of piles in different scour conditions, and then extracts the void ratio and the effective stress at the compressive interface of the pile-soil in e-p' space in Figure 8. The critical state line (CSL) is collated from the total of 17 shear loading tests accomplished by Verdugo & Ishihara and the critical-state framework is also verified by [PERSON]'s state-dependent dilatancy [15] which can be used in the  
Figure 7: Load displacement characteristics of piles at different depths in \(S_{d2}=1.5\)\(D\) (9 m) condition. constitutive study of Toyoura sand. In e-p's space, no matter what the initial state of the sand is, it will eventually develop to the critical state line. Figure 8: _Cont._  
Figure 8a,b displays the state variation of the interface soil in each relative depths during pile displacement in the no scour and the general scour condition respectively. In the analysis of the variation of interfacial soils at the compression side of the scour pit base in each horizon, the curve in the same relative depth in the general scour condition is similar to that in the no scour condition. The dilatancy on the surface of the remaining sand becomes more obvious after the upper soil layer has been scoured away. The lateral soil resistance is stronger than that of lower void ratio and denser soil. In the local scour condition in Figure 8c, the variation of stress state in the same effective depth differs entirely from that of the other two conditions. The surface of the remaining sand center has a slower dilatancy characteristic, as shown in Figure 9. The dilation of the shear band surrounding the pile plays a decisive role in the resistance of piles in sand.