# Hypoplastic Modeling of Soil-Structure Contact Surface Considering Initial Anisotropy and Roughness
## 4 Finite Element Implementation of the Interface Constitutive Model
### Numerical Model  
Figure 11 illustrates the geometric configuration and boundary conditions of the direct shear test model. The upper soil specimen utilizes sand from the river sand of the Karmaphuli River tunnel project in Chittagong, Bangladesh, with dimensions of 25 \(\times\) 25 \(\times\) 5 cm. The structural component consists of C30 concrete with dimensions of 35 \(\times\) 25 \(\times\) 5 cm, modeled as a linear elastic material with a Young's modulus of 1 \(\times\) 10\({}^{6}\) kPa and a Poisson's ratio of 0.25. Both the soil and structural elements are discretized using eight-node linear elements (C3D8). The soil-structure interface is modeled using a surface-to-surface contact, with the master surface being the concrete surface and the slave surface being the soil surface. The interface behavior is described using both the Mohr-Coulomb model and the proposed constitutive model for comparative analysis. The model parameters and boundary conditions are detailed in Tables 6 and 7, respectively.  
Note that, in Table 6, the critical friction angle \(\varphi_{c}\) was estimated from the angle of repose of the sandy soils in the site; the particle hardness \(h_{s}\) and index \(n\) are obtained from the material compression curve; the value of \(e_{d0}\) can be computed by Equation (49):  
\[e_{d0}=e_{d}\exp\biggl{[}\biggl{(}\frac{\sigma_{n}+2\sigma_{p}}{h_{s}}\biggr{)} ^{n}\biggr{]} \tag{49}\]  
where the value of \(e_{d}\) can be obtained by the relationship of \(e_{d}-C_{u}\), according to the experimental results in Youd [41].  
Figure 11: Schematic diagram of the geometric structure and boundary conditions of the finite element model for direct shear test: (**a**) front view and (**b**) side view.  
The model boundary conditions are depicted in Figure 11, with the corresponding finite element mesh shown in Figure 12. As illustrated in Figure 11, the model configurations include the following boundary conditions: during the shear, the horizontal displacement of the soil is fixed, and the vertical displacement at the bottom of the structure is also constrained. In the front view (in Figure 11a), the bottom of the structure is assigned a free boundary in the horizontal direction. During the calculation, a continuous horizontal displacement is applied to the structure to perform a soil-structure interface shear test. In contrast, in the side view (in Figure 11b), the horizontal displacement of the structure is fixed. These configurations ensure that the test accurately simulates the interaction between the soil and structure under shear loading conditions. The testing procedure follows these steps:  
1. Application of gravity loading;
2. Application of normal stress, specified as 100 kPa;
3. Progressive application of shear displacement up to a maximum of 5 cm.  
This study conducts a comprehensive analysis of the response characteristics under varying normal stresses, shearing velocities, and material properties of both the soil mass and the interface, utilizing direct shear testing.