## 3 Numerical Modelling of the SSI System
The vertical load was applied directly on the foundation slab, while the horizontal load was applied at the top of the column. The recorded loading curve taken from the TRISEE experiment was imported to the numerical model as a Time history load. The comparison of experimental and numerical results (Figure 5) is presented through: (a) rocking angle-overturning moment curve; (b) time-rocking angle curve; (c) rocking angle-settlement curve; and (d) time-settlement curve. Observing Figure 5, it can be concluded that rocking of the foundation in the numerical model matches well with the experimental results, although the settlement of the foundation shows a difference in the numerical model (8.50 mm) and experiment (10.00 mm). Moreover, rocking of the foundation shows significant difference at the beginning until the plasticity of foundation soil is reached when the amplitude of rocking is matched well with the experiment. A preliminary parametric study showed that the numerical results are highly sensitive to both the shape of the force-displacement backbone curve and the hysteretic model selected to simulate the soil behavior. It is important to emphasize that the structural model of the experimental setup was not fully horizontally leveled when placed on the sand bed. It was assumed that tilting of the model resulted with plasticity of the sand on one end of the foundation. The model was tilted by around \(2^{\circ}\) in the loading direction which resulted in a horizontal shift of the top of the column by 3.33 mm. The implementation of an initial tilting in the numerical model would consider the adoption of additional assumptions, therefore tilting was not implemented into the numerical model. Furthermore, limitations of this numerical model have to be stressed out. The numerical model, specifically the model of the soil represent dry sand conditions in contrary to the experiment with saturated soil under the foundation. The saturation of the sand could be included into Equations (1)-(3) only by varying the Poisson's ratio which was determined not to have a large impact on the numerical results. Moreover, as it was mentioned earlier, imperfections of the model placement on the foundation soil were not included in the numerical model. With all this considered, more efficient numerical models might capture experimental results even more accurately. Figure 2:1 Scheme of the numerical model of the foundation slab. Figure 6 shows the comparison between the numerical and experimental horizontal displacement of the top of the column in the direction of the applied horizontal load. To exclude the tilting of the physical model, numerical results were shifted by 3.33 mm in the direction of the horizontal load. After the occurrence of pronounced plasticity under the action of the maximum horizontal force the numerical model describes the behavior of the experimentally tested model with a large degree of accuracy. In spite of all of the above, the hysteretic cycles in the moment-rocking angle, as well as rocking time-history and vertical settlement time history describe the behavior of the experimentally tested model with satisfactory accuracy, as shown in Figure 2:2  
Figure 2:3 Comparison of numerically and experimentally obtained data: (**a**) rocking angle-overturning moment; (**b**) time-rocking angle; (**c**) rocking angle-settlement; (**d**) time-settlement. Figure 2:4 Horizontal displacement time history of the top of the column.