## 4 Conclusions and Future Works  
The combined effect of \(v_{p}\), \(\rho_{dry}\) and \(n\) in UCS for traverting-saturated cylindrical specimens was studied. It is evident that \(v_{p}\) and \(n\) have a synergistic effect in UCS (both individually and combined), while \(\rho_{dry}\) does not have a statistically significant influence (linear, exponential, potential, and quadratic) on the dependent variable. This is explained by the fact that, for the same rock type, the density remains relatively constant, since the measured porosity only affects the external pores of the test specimen, which do not necessarily have to be interconnected with the internal ones. Therefore, \(v_{p}\) may vary, but density does not, and, therefore, there is no correlation between them. The experimental results were analyzed through simple regression analysis (or in its absence, after log transformation) to develop the analytical models that best adapt to UCS depending on \(v_{p}\) (as developed by most authors). Subsequently, multiple regression analysis and an artificial neural network model (ANN) were performed, to obtain a predictive model of UCS from \(v_{p}\), \(n\) and \(\rho_{dry}\). Simple regression analyses (using only \(v_{p}\) or \(n\) as independent variable) showed a better R\({}^{2}\) value of 0.7573 for the univariate model, dependent only on porosity, while the univariate model dependent on \(v_{p}\) turned out to be the quadratic adjustment, with an R\({}^{2}\) of 0.6804. On the other hand, a multiple regression analysis, considering interactions between factors and quadratic terms resulted in a better R\({}^{2}\) value (0.8447), which indicates a better adjustment when additional explanatory variables are considered. Multiple regression analyses were also able to identify \(\rho_{dry}\) as a statistically non-significant independent variable for predicting UCS from ultrasonic pulse transmission tests. Finally, the ANN-based model presented a competitive fit with the single and multiple linear regression \begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **Equation/Architecture** & **R\({}^{2}\)** \\ \hline Linear \(\left[\sigma_{c}\big{(}v_{p}\big{)}\right]\) & (14) & 0.6028 \\ Linear \(\left[\sigma_{c}\big{(}n\big{)}\right]\) & (15) & 0.6788 \\ Exponential \(\left[\sigma_{c}\big{(}v_{p}\big{)}\right]\) & (16) & 0.6324 \\ Exponential \(\left[\sigma_{c}\big{(}n\big{)}\right]\) & (17) & 0.7114 \\ Potential \(\left[\sigma_{c}\big{(}v_{p}\big{)}\right]\) & (18) & 0.6167 \\ Potential \(\left[\sigma_{c}\big{(}n\big{)}\right]\) & (19) & 0.7223 \\ Quadratic \(\left[\sigma_{c}\big{(}v_{p}\big{)}\right]\) & (10) & 0.6804 \\ Quadratic \(\left[\sigma_{c}\big{(}n\big{)}\right]\) & (21) & 0.7573 \\ Multiple simple \(\left[\sigma_{c}\big{(}v_{p}\cdot\rho_{dry},n\big{)}\right]\) & (22) & 0.6788 \\ Multiple quadratic \(\left[\sigma_{c}\big{(}v_{p}\cdot\rho_{dry},n\big{)}\right]\) & (23) & 0.8447 \\ ANN \(\left[\sigma_{c}\big{(}v_{p}\cdot\rho_{dry},n\big{)}\right]\) & (1 layer, 2 neurons) & 0.6975 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Coefficients of determination of the generated models. models in predicting UCS (R\({}^{2}\) = 0.6975), showing that UCS is directly dependent on the independent variables \(v_{p}\), \(\rho_{dry}\) and \(n\). To continue this research line with travertine, the incorporation of a greater number of independent variables in the analysis and a larger number of samples is planned. This research aims to identify the variables that explain the experimental variability of UCS under sampling conditions, and to model the dynamics of the system using machine learning algorithms, such as neural networks or Bayesian networks [46]. The possible variables to be considered are the corrected point load index (I\({}_{8(50)}\)), and the number of [PERSON]'s hammer rebounds (R\({}_{\text{N}}\)). Further tests will be carried out to try to improve the analytical models.