## 7 Conclusions  
In this study, the seismic bearing capacity of a strip footing placed over an unsupported void has been assessed. Dimensionless factors describing the horizontal seismic acceleration, the soil strength and heterogeneity, the internal friction angle of the soil, the shape, size, depth, and eccentricity of the void have been accounted for.  
Three ML techniques have been exploited to estimate the aforementioned bearing capacity: MLP; GMDH; and ANFIS-PSO. All the hyperparameters affecting the performance of the ML models have been investigated, to ensure the attainment of optimal solutions in all the cases. The results obtained by training the ML models have shown a good fitting of the seismic bearing capacity provided by numerical FELA simulations, here handled as the ground-truth data. More specifically, MLP, and ANFIS-PSO have performed better than GMDH. Overall, almost independently of the adopted statistical performance index used to assess the goodness of the fit of the models, MLP has been shown to be superior to the other models. This outcome has also been testified by means of concrete results regarding a case study.  
A major concern regarding the use of a data-driven ML approach to foresee the information related to limit states of a structural system, typically highly sensitive to some parameters unknown or difficult to assess, is related to the quality of the dataset. In future activities, the proposed approach will be fed also with experimental data, to assess the credibility of the ML models. To this purpose, collecting empirical data of the seismic  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Estimate \(q_{\mathrm{m}}\)[kPa]** & **Error** \\ \hline MLP & 3184.23 & 1.96\% \\ GMDH & 3325.11 & 2.38\% \\ ANFIS-PSO & 3091.24 & 4.82\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Case study: seismic bearing capacity of the strip footing estimated by the investigated ML tools, and error with respect to the ground-truth to the value given by the Optum G2 software.  
bearing capacity of the strip footing above voids would be worthwhile, to finally establish an effective tool to design strip footing, especially in urban areas.  
In this study, only rectangular voids have been considered. Having established the reliability of the offered methodology, additional datasets will be considered in the future to allow for voids with a different geometry, aiming to increase the awareness of strip footing behavior over voids.  
Conceptualization, M.S.E.-h. and M.A.; methodology, M.S.E.-h. and M.A.; software, M.S.E.-h.; validation, M.S.E.-h. and M.A.; formal analysis, M.S.E.-h.; investigation, M.S.E.-h.; resources, M.S.E.-h.; data curation, M.S.E.-h.; writing--original draft preparation, M.S.E.-h.; writing--review and editing, S.M., M.S.E.-h. and M.A. and H.A.; visualization, M.S.E.-h.; supervision, H.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: Data, models, and codes that support the findings of this study are available from the corresponding author upon request.  
**Conflicts of Interest**: The authors declare no conflict of interest.