# Hypoplastic Modeling of Soil-Structure Contact Surface Considering Initial Anisotropy and Roughness
## 3 Model Validation
### Experiment on Contact Surfaces of Toyoura Sand and Low Carbon Steel Plate  
We evaluated the effectiveness of the hypoplastic model in capturing the stress-deformation behavior of soil-structure contact surfaces with different roughness levels. The model was validated against direct shear test results of Toyoura sand interacting with structural surfaces of varying roughness, as reported by [PERSON] et al. [38], under constant  
Figure 5: Schematic diagram of strain–displacement relationship at the contact surface.  
normal stress conditions. The material of the structural surface used in the experiments is low-carbon steel, subjected to a normal stress of 78 kPa. The initial void ratio of the sand is 0.68, and the maximum roughness of the structural surfaces is defined as 46 \(\upmu\)m, 20.5 \(\upmu\)m, and 2.4 \(\upmu\)m, corresponding to friction parameters of 0.905, 0.66, and 0.21, respectively. Detailed model parameters are presented in Table 3.  
The experimental data and model prediction results for the contact surfaces between Toyoura sand and low-carbon steel plates of varying roughness are shown in Figure 6. The findings reveal a robust correlation between the model predictions and the experimental data, both in numerical values and trends, across all three roughness conditions. Moreover, the model adeptly captures the softening phenomenon observed under high roughness conditions, thereby validating its capacity to accurately depict the true shear behavior of the sand-structure contact surface across varying levels of roughness.  
Experiment on Contact Surfaces of Changing Composite Gravel/Uniform Gravel and Artificial Steel Plate  
To evaluate the effectiveness of the hypoplastic model in capturing the deformation behavior of sand-structure contact surfaces under varying normal stresses and roughness, monotonic shear tests were performed. These tests involved uniform gravel and composite gravel interacting with artificially roughened steel plates, as detailed by [PERSON] [41]. The experiments were conducted under controlled ideal contact surface boundary conditions, with normal stresses set at 200 kPa and 700 kPa. The composite gravel had a mean particle size of 10.0 mm, and the structural surfaces were artificially roughened steel plates with roughness values of 1 mm and 10 mm. The loading was displacement-controlled at a rate of 1 mm/min. Model parameter values are specified in Table 4, with an initial void ratio of the soil set at 0.75.  
Figure 6: Comparison of experimental results with simulation results for the contact surface between Toyoura sand and low-carbon steel plates.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameters** & \(\mathbf{\varphi}\)\(e^{\circ}\) & \(\mathbf{h_{s}}\)**/MPa** & \(n\) & \(e_{\mathbf{d0}}\) & \(e_{\mathbf{e0}}\) & \(e_{\mathbf{i0}}\) & \(\mathbf{\alpha}\) & \(\mathbf{\beta}\) & \(\mathbf{\lambda_{R}}\) \\ \hline Values & 30 & 2600 & 0.27 & 0.61 & 0.98 & 1.10 & 0.25 & 1.0 & 0.21/0.66/0.905 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model parameters for the experiment of Toyoura sand—low-carbon steel contact surface.  
Figures 7 and 8 show the shear stress-shear displacement relationship curves for the two roughness conditions of the artificial steel plates under different normal stresses. The curves predicted by the contact surface hypoplastic model closely match the experimental data points, both in terms of numerical values and overall trends. This alignment suggests that the model is adept at forecasting the mechanical behavior of contact surfaces under a range of normal stress conditions and roughness levels. Additionally, the figures demonstrate that there is no significant softening observed in the shear stress and shear displacement at the contact surface, a phenomenon that the model's predictions accurately capture.