# Hypoplastic Modeling of Soil-Structure Contact Surface Considering Initial Anisotropy and Roughness
## 4 Finite Element Implementation of the Interface Constitutive Model
### Results Analysis  
Based on the numerical model shown in Figure 12, direct shear tests were conducted under different roughness and initial deposition angle conditions to verify the correctness of the FRIC subroutine and the rationality and superiority of the proposed hypoplasticity model for contact surfaces. The test results are presented in Figures 13-15. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Initial Parameters** & \( \begin{array}{c}\varphi_{c}/^{\circ}\end{array} \) & \( \begin{array}{c}h_{s}/\text{MPa}\\ 31\end{array} \) & \( \begin{array}{c}n\end{array} \) & \( \begin{array}{c}e_{a0}\end{array} \) & \( \begin{array}{c}e_{a0}\end{array} \) & \( \begin{array}{c}e_{a0}\end{array} \) & \( \begin{array}{c}\alpha\end{array} \) & \( \begin{array}{c}\beta\end{array} \) \\ 31\end{array}\) & \( \begin{array}{c}1000\end{array} \) & \( \begin{array}{c}0.29\end{array} \) & \( \begin{array}{c}0.61\end{array} \) & \( \begin{array}{c}0.96\end{array} \) & \( \begin{array}{c}1.09\end{array} \) & \( \begin{array}{c}0.13\end{array} \) & \( \begin{array}{c}2.0\end{array} \) \\ **Anisotropic** & \( \begin{array}{c}b_{1}\end{array} \) & \( \begin{array}{c}b_{2}\end{array} \) & \( \begin{array}{c}b_{3}\end{array} \) & \( \begin{array}{c}m\end{array} \) & \( \begin{array}{c}\text{\bf Roughness}\\ \text{\bf Parameters}\end{array} \) & \( \begin{array}{c}R\end{array} \) \\ 1.15 & \( \begin{array}{c}-0.28\end{array} \) & \( \begin{array}{c}42^{2}\end{array} \) & \( \begin{array}{c}2\end{array} \) & \(\begin{array}{c}\text{\bf Parameters}\) & \( \begin{array}{c}0.3\end{array} \)-\( \begin{array}{c}1.5\end{array} \) \\ \hline \hline \end{tabFigure 13 presents a comparison of the numerical calculation results from the hypoplastic model for contact surfaces with the theoretical analytical results under various initial void ratio conditions. It is evident that the stress levels derived from numerical calculations are marginally lower than those predicted by the theoretical solution, with the overall discrepancy being quite minor. Notably, at higher void ratios, the theoretical and numerical results are almost indistinguishable, making the error effectively negligible. This close alignment between the two sets of results confirms the accuracy of the FRIC subroutine. Figure 14: Shear stress–displacement relationship curves for contact surfaces under different interface roughness conditions: (**a**) e = 0.65 and (**b**) e = 0.95. Figure 13: Comparison between the numerical results of the hypoplastic model for contact surfaces and the theoretical solution. Figure 15: Shear stress–displacement relationship curves for contact surfaces under different initial deposition angle conditions: (**a**) e = 0.65 and (**b**) e = 0.90. Figure 14 shows the shear stress-displacement relationship curves for dense sand (e = 0.65) and loose sand (e = 0.90) under different interface roughness conditions. It is noticeable that, with an increase in the roughness, \(R\), of the structural surface, the peak shear strengths for both loose and dense sands correspondingly increase. Moreover, the softening behavior in dense sand becomes more significant as roughness increases; when the structural surface is relatively smooth, dense sand exhibits minimal signs of softening. In contrast, the shear stress-strain relationship curve for loose sand remains largely unaffected by variations in roughness. Figure 15 shows the shear stress-displacement relationship curves for the aforementioned dense sand and loose sand under different initial deposition angle conditions. Notably, when the initial deposition angle of the sand approximately 30\({}^{\circ}\), the peak shear stress at the contact surface is minimized. Additionally, the deposition angle impacts only the peak stress and residual strength, leaving the shape and trend of the curves unaltered. The finding is consistent with the observations from Figure 3, which also demonstrate the influence of the deposition angle on the shear behavior of the contact surface.