## 4 Conclusions  
In this study, P-wave velocities under natural, dry, and saturated conditions, as well as the UCS, PLI\({}^{\text{A}}\) and PLI\({}^{\text{D}}\), the ITS, and the SHV, were measured for 190 limestone core samples with various sample dimensions. The P-wave velocities and the mechanical properties of limestone samples with various diameters were correlated by means of linear regression analyses, and the equation of the best-fit line and the correlation coefficient, R, were determined and interpreted. Furthermore, we investigated the effect of the sample diameter on the P-wave velocities and mechanical features of limestone. Based on the test results, the following conclusions were attained:  
1. In general, a notable increasing trend of R-values for the UCS and P-wave velocities of limestone was observed with increasing sample diameter, with the exception of a correlation coefficient value of 0.04 for V\({}^{\text{d}}\)\({}_{\text{P}}\) and the 63.2-mm sample diameter. This result indicates that the UCS and P-wave velocities are affected by the sample diameter. Moreover, the variations in R-values with different P-wave velocities were negligible for a given sample diameter excluding 63.2-mm.
2. The R-values for the PLI\({}^{\text{D}}\) and P-wave velocities of limestone showed fluctuations for various sample diameters. Nevertheless, an effect of sample diameter on the P-wave velocity and PLI\({}^{\text{D}}\) was still visible. Furthermore, the variations in R-values for different P-wave velocities at a constant diameter were limited, except for the NX sample diameter.
3. Due to data fluctuations, there was no specific trend in R-value for the PLI\({}^{\text{A}}\) and P-wave velocities of limestone for different sample diameters. Thus, it was difficult to interpret the direct influence of specimen diameter on the P-wave velocity and PLI\({}^{\text{A}}\). Moreover, variations in R-values for different P-wave velocities at a given diameter were observed, particularly for a sample diameter of 47.7 mm.
4. There was a notable trend in correlation coefficient values, R, for the ITS and P-wave velocities of limestone for various sample diameters, except for the 24.9-mm sample diameter. Thus, an influence of specimen diameter on the P-wave velocity and ITS was observed. In addition, variations in R-values for different P-wave velocities at a constant diameter were observed, but were generally insignificant.
5. An increasing trend of P-values for the SHV and P-wave velocities of limestone for different sample diameters was observed. Accordingly, the SHV and P-wave velocity were visibly affected by the sample diameter. Furthermore, variations in R-values for different P-wave velocities at a constant diameter were observed, except for the 47.7-mm-diameter samples.  
Conceptualization, methodology, investigation, data acquisition, validation, supervision, writing--original draft, writing--review and editing, H.A. and investigation, data acquisition, validation, S.P. Both authors have read and agreed to the published version of the manuscript. This study was financially supported in part by the United Arab Eminates University, Research Affairs under a SURE 2016 grant. The laboratory work was conducted at the Environmental and Engineering Laboratory at the Department of Geosciences, the United Arab Eminates University. The authors would like to thank the United Arab Eminates University, Research Affairs, for their generous support and encouragement.