\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Correlation** & \(R^{2}\) & **Rock Type** & **Phase** & **Reference** & **Equation** \\ \hline \(\rm UCS=9.95v_{\rm p}^{1.21}\) & 0.69 & \begin{tabular}{c} Diabase, dolomite, hematite, limestone, \\ marl, sandstone, and serpentine \\ \end{tabular} & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [21] & (1) \\ \hline \(\rm UCS=31.5v_{\rm p}-63.7\) & 0.80 & Dolomite, limestone, and marble & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [22] & (2) \\ \hline \(\rm UCS=2.304v_{\rm p}^{2.4315}\) & 0.94 & \begin{tabular}{c} Andesite, basalt, diorite, geniodierite, \\ limestone, marble, quartztite, sandstone, \\ traquite, travertite, and tuff \\ \end{tabular} & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [25] & (3) \\ \hline \(\rm UCS=0.26v_{\rm p}^{3.543}\) & 0.85 & Limestone, schist, and travertite & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [26] & (4) \\ \hline \(\rm UCS=12.75v_{\rm p}^{1.19}\) & 0.76 & \begin{tabular}{c} Clayey marl, claystone, dolomite, \\ limestone, marl, mudrock-shale, \\ sandstone, siltstone, slate, and travertite \\ \end{tabular} & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [34] & (5) \\ \hline \(\rm UCS=39v_{\rm p}-50.01\) & 0.93 & \begin{tabular}{c} Coal, dolomite, dolomite limestone, \\ limestone, gneiss, granite, massive basalt, \\ quartz-mica schist, quartztite, sandstone, \\ shale, tufaceous basalt, and weathered \\ basalt \\ \end{tabular} & \begin{tabular}{c} Cool, dolomite limestone, \\ gneiss, granite, massive basalt, \\ quartz-mica schist, quartztite, sandstone, \\ shale, tufaceous basalt, and weathered \\ \end{tabular} & \begin{tabular}{c} Dry \\ * \\ \end{tabular} & [35] & (6) \\ \hline \(\rm UCS=3.774v_{\rm p}^{1.706}\) & 0.72 & \
\begin{tabular}{c} Andesite, argillaceous limestone, \\ claystone, marl, ignimbrite, sandstone, \\ and tuff \\ \end{tabular} & Sat & [18] & (7) \\ \hline \(\rm UCS=131.77\ln v_{\rm p}-1048\) & 0.82 & Limestone &
\begin{tabular}{c} Dry \\ * \\ \end{tabular} & [28] & (8) \\ \hline \hline \end{tabular}  
* The authors do not explicitly indicate saturated or dry conditions, so it is assumed as dry (\(S_{\rm r}=0\)).  
\end{table} 
Table 2: Existing multiple correlations between UCS (MPa), \(v_{\rm p}\) (m\(\cdot\)s\({}^{-1}\)), n (\(\%\)), \(S_{\rm r}\), and ECC (\(\%\)) [18] for limestone. blocks of \(13\times 20\times 12\) cm\({}^{3}\), and seven of the rocks were limestone with a \(\mathrm{v_{p}}\) between 4.1 and 5.5 km-s\({}^{-1}\). The obtained Equation (1) is a potential equation with \(R^{2}=0.69\). [PERSON] and [PERSON] [22] studied the effect of \(\mathrm{v_{p}}\), \(\rho\), and \(\mathrm{E_{st}}\) on UCS but as simple regressions (one parameter at a time). They studied carbonate rocks from different places in Turkey. \(\mathrm{v_{p}}\) was measured in three cubes of unknown dimensions, and in five cylindrical specimens (42 mm in diameter and 105 mm in length). The results showed \(\mathrm{v_{p}}\) minimum and maximum values of 2.9 and 5.6 km-s\({}^{-1}\), respectively. The linear correlation (Equation (2)) obtained by the authors was based on average values of four different limestones, obtaining \(R^{2}=0.80\). [PERSON] and [PERSON] [25] collected 19 rock samples from Southern Anatolia (Turkey). Ten of them were igneous (seven were volcanic), two of them were metamorphic, and the remaining seven were sedimentary. Among the latter, there was a limestone. This limestone was studied by means of three cylindrical specimens (42 mm in diameter and 85 mm in length) and the mean resulting \(\mathrm{v_{p}}\) was 5.840 km-s\({}^{-1}\). The authors obtained Equation (3) with \(R^{2}=0.94\). [PERSON] [26] tested 10 specimens of nine different rocks (three of them were limestones) collected in Turkey. The author did not show the geometry of the specimens, but \(\mathrm{v_{p}}\) values were reported for each kind of rock. For the studied limestones, \(\mathrm{v_{p}}\) was between 3.8 and 5.0 km-s\({}^{-1}\). The author obtained a potential Equation (4) with \(R^{2}=0.85\).