## 3 Three-Dimensional Finite Element Model Analyses
### Numerical Modeling Procedure  
The validated pile-soil 3D model has then been developed to analyze the change of loading capacity of remaining sand after stress relief during scouring. The sand is assumed to be normally consolidated before scouring.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Meaning of Parameters** & **Parameter** & **This Test** \\ \hline \multirow{3}{*}{Elastic parameters} & Elastic modulus & \(G_{0}\) & 50 \\  & Poisson’s ratio & \(v\) & 0.1 \\  & Stress ratio at the critical state & \(M\) & 1.25 \\ Critical state & Intercept of CSL in \(e-\left(\frac{p^{\prime}}{p_{s}}\right)^{\xi}\) or \(e-lnp^{\prime}\) plane & \(\varepsilon_{\text{T}}\) & 0.934 \\  & Slope of CSL in \(e-\left(\frac{p^{\prime}}{p_{s}}\right)^{\xi}\) or \(e-lnp^{\prime}\) plane & \(\xi\) & 0.019 \\ Dilatancy & Parameters of dilatancy function & \(d_{0}\) & 1 \\   parameters & Parameters of dilatancy function & \(m\) & 3.5 \\  & Hardening parameters & \(h_{1}\) & 3.15 \\  & Parameters of the hardening law & \(h_{2}\) & 3.05 \\  & & \(n\) & 1.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters of state-dependent saturated sand in [PERSON]’s test.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Meaning of Parameters** & **Parameter** & **This Test** \\ \hline \multirow{4}{*}{Basic parameters} & Mean particle size (mm) & \(D_{50}\) & 0.4 \\  & Specific gravity & \(G_{s}\) & 2.65 \\  & Maximum void ratio & \(e_{max}\) & 0.934 \\  & Minimum void ratio & \(e_{min}\) & 0.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Typical engineering properties of Toyoura sand in [PERSON]’s test.  
Figure 2: Validation of the numerical model against the centrifuge test reported by [PERSON] et al. [25], compared with (**a**) deflection; (**b**) moment of the pile.  
According to the conclusion of field investigation and scour model test, the local scour condition in Figure 3b forms a conical scour pit caused by the hydrodynamic loads from the no scour condition in Figure 3a. Aiming to analyze the soil horizon at each depth before and after scouring effectively, another type of scouring has been identified in Figure 3c as the general scour and the entire elevation of the soil surface is globally reduced by erosion. This scour pattern is only used to analyze the influence of the remaining overburden soil surrounding the pile on the bearing capacity of interfacial soil after scouring.  
The standard stipulated that the limit scour depth of the marine structure is 1.3 \(D\). Consequently, the scour depths are identified as \(S_{d1}=1\)\(D\)\((6\) m) and \(S_{d2}=1.5\)\(D\)\((9\) m) for the case considered in this paper in which the slope angle is 30\({}^{\circ}\) based on [PERSON] and [PERSON]'s test [9] and detailed procedures are as follows:  
1. Establishing the model in no scour condition (as shown in Figure 3a), then identifying the scour depth of each case;
2. Defining a special step for the formation of the scour pit. According to the depth of scour in this step, the scour soil is divided into many layers by 0.5 \(D\) of each horizon Then, the scour soil is slowly removed by means of adding the keywords in the ABAQUS input file, i.e., Model change, remove as shown in Figure 3b. This operation models the slow unloading process during scouring, and considers the influence of the stress relief;
3. Applying the displacement on the pile head. Making sure that the deflection of the pile-soil interaction is developed uninterruptedly;
4. Changing the depth of the scour pit base, and the same displacement is applied to the structure.