## 3 Parametric Study
### Void Parameters  
Results are depicted in Figure 5 showing the variation of the bearing capacity induced by varying the void parameters related to its shape and location. At constant seismic action measured through \(k_{h}\), the capacity \(Q=q_{u}/\gamma B\) is shown to increase with the void depth \(D\) until a saturation value that depends on its own \(k_{h}\). Similar conclusions can be drawn considering the effect of the horizontal distance \(S\) from the footing central line. It has also been reported that the bearing capacity decreases as the ratio \(\alpha\) related to the void width increases, with instability triggered for a value approaching \(\alpha=3\). For a void located below the centerline of the footing (namely \(S=0\)), the effect of the ratio \(\beta\) related to the void height is to first marginally reduce the bearing capacity, and then attain a constant value.  
Figure 4: Parametric analysis: effects on the bearing capacity \(Q=q_{u}/\gamma B\) under different values of the seismic acceleration coefficient \(k_{h}\), of: (**a**) the dimensionless soil parameters \(c_{0}/\gamma B\) (blue plots) and \(kB/c_{0}\) (yellow plots); (**b**) internal friction angle \(\varphi\).  
As the data have to be handled through ML approaches, the quality of the dataset is one of the dominant aspects to assure the accuracy of the predictions. To assess the bearing capacity of the strip footing above a void, the adopted dataset has been made of 38,000 models, each one featuring its own values of the parameters describing the soil properties and the void geometry. According to the parametric study presented above, the values of the parameters have been selected within their domains to cover all the effective situations related to the interaction between the strip and the void. The aforementioned effective values of the parameters are collected in Table 4.  
As already remarked, for each analysis, only the average value between the upper and lower bounds on the strip footing bearing capacity has been considered as an entry of the dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Shape of Void**} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{5}{c}{**Effective Parameters**} & \multirow{3}{*}{\(\boldsymbol{\varphi}\)} & \multirow{3}{*}{\(\boldsymbol{k_{h}}\)} & \multirow{3}{*}{\(\boldsymbol{\text{Total Number}}\)} \\ \cline{3-3} \cline{5-10}  & & & & & & & \(\boldsymbol{\alpha}\) & & \(\boldsymbol{\beta}\) \\ \hline \multirow{4}{*}{**Rectangular**} & Selected & 2, 4, & & 0.75, & & 1 & 3 & & \\  & Values & 6, 8 & 0, 0.5, 1 & 1.5, 3, & 0, 1, 2, & 1 & 2 & 0, 10, 20, & 0, 0.1, \\  & & & 4.5, 6 & & 3.5, 5 & 1 & 30, 40 & 0.2, 0.3 & \\ \cline{2-10}  & Number of & & & & & 3 & 1 & & \\ \cline{2-10}  & scenarios & 4 & 3 & 5 & 5 & 5 & 5 & 4 & 30,000 \\ \hline \multirow{4}{*}{**Square**} & Selected & 2, 4, & & 0.75, & & 0.5 & 0.5 & & & \\  & Values & 6, 8 & 0 & 1.5, 3, & 0, 1, 2, & 1.5 & 1.5 & 0, 10, 20, & 0, 0.1, & \\ \cline{1-1}  & Values & 6, 8 & & 4.5, 6 & 3.5, 5 & 2.0 & 2.0 & 30, 40 & 0.2, 0.3 & \\ \cline{1-1}  & Number of & & & & 2.5 & 2.5 & & & \\ \cline{1-1}  & scenarios & 4 & 1 & 5 & 5 & 4 & 5 & 4 & 8000 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Effective parameters and selected values for each model.  
Figure 5: Parametric analysis: effects on the bearing capacity \(Q=q_{u}/\gamma B\) under different values of the seismic acceleration coefficient \(k_{h}\), of the dimensionless void parameters \(\alpha\) (red plots), \(\beta\) (blue plots), \(5\) (green plots), and \(D\) (black plots).