## 3 Modeling of a Dynamic Rocking Foundation Test
The values assumed for the degradation parameters \(\xi_{95}\) and \(\delta_{rem}\) are the medium values based on the ranges of relevant values assumed for those parameters by [43]. The acceleration time history measured at the bottom of the container in the experiment (converted to prototype scale and filtered to remove the noise) is applied to the bottom boundary of the soil. The soil nodes at the model side-wall boundaries and the symmetry plane are restricted against displacements perpendicular to the boundaries and rotations around the two other directions. The soil boundaries on the frontward and backward sides in the direction of shaking are set to move together with the container walls while being free to settle down under the gravity loads. Two different types of contact conditions are tried for the interaction between the footings and the soil. One is a hard contact that allows for separation after contact, with a friction coefficient of 0.27, which is based on measurements for similar materials by [52]. This type of separable contact with friction does not allow any tension to develop between the surfaces; it was used in an earlier study for rocking foundations on dry sand [3]. The other type of contact is termed \"cohesive contact\" in ABAQUS terminology, which allows for more control over the behavior of the contact interaction in tension. In the case of a foundation on saturated undrained clay, a limited tensile traction can develop between the soil and foundation due to suction before they separate. Cohesive contact was used for modeling the suction and uplift capacity of mat foundations on a marine clay seabed by [53; 54] and for modeling pile-raft foundations in undrained clay by [55]. In this paper, the maximum tension in the cohesive contact is assumed to be 10 kPa, which is a typical value of triaxial tensile strength in low confining pressures, according to [56]. Figures 2 and 3 compare the moment-rotation and settlement rotation curves, respectively, of the experiment, with the curves obtained from the FE analysis considering the two different contact models. It is obvious that using the cohesive contact between the foundation and soil, which allows for limited tension in the separation of the surfaces (due to suction), improves the overall agreement between the FE and experimental results. As \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(K\) & 2.787 GPa \\ \(G\) & 5000 kPa \\ \(\sigma_{y0}\) & 20 kPa \\ \(H_{\text{iso}}\) & 0.01 kPa \\ \(H_{\text{kin}}\) & 50,000 kPa \\ \(H_{\text{nl}}\) & 0.3 kPa \\ \(S_{\text{i}0}\) & 100 kPa \\ \(\xi_{95}\) & 30 \\ \(\delta_{rem}\) & 0.25 \\ Mass Density & 1440 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties for undrained stiff clay (San Francisco Bay mud). seen in Figure 3b, with the right choice of contact method, the material model is capable of correctly simulating the ranges of settlement and rotation that the foundation experiences. Although the model with cohesive contact (Figure 2b) slightly overestimates the ranges of moment in some of the cycles, it increases the width of the hysteresis loops compared to the model with hard contact (Figure 2a), thus providing a better fit to the experimental curves. The settlement-rotation plot of the model with cohesive contact (Figure 3b) offers a better estimation of the final settlement of the foundation compared to the model with hard contact (Figure 3a) and shows a better fit to the gradually increasing ranges of rotation in the experiment. A sufficient agreement of the ranges of settlement, rotation and moment is observed between the results of the model with cohesive contact and the experimental data. Figure 2: Comparison of moment–rotation curves of the experiment with FE analysis; (**a**) with hard contact, (**b**) cohesive contact.