## 3 Results and Discussion
The R-values exhibited weak to strong correlations, ranging from 0.34 to 0.71 (Table 1). The maximum and minimum correlation values (R) were obtained for V\({}^{\mathrm{n}}\)\({}_{\mathrm{p}}\) and V\({}^{\mathrm{d}}\)\({}_{\mathrm{p}}\) at sample diameters of 63.2 and 47.7 mm, respectively. The previous researchers commonly focused on correlations between the UPV and rock properties, mechanical and physical, for various types of rocks [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. Only few researchers investigated the predictability of wet-rock V\({}_{\mathrm{p}}\) based on the dry-rock V\({}_{\mathrm{p}}\), correlated the physicochemical properties of rocks with ultrasonic P- and S-wave velocities, assessed some geotechnical parameters under various environmental conditions using ultrasonic S- and P-wave measurements, and suggested a multi-exponent model to predict the UCS for various rock types [37; 40; 41; 42]. Moreover, limited researchers studied the effects of sample length on P-wave velocities of dry and saturated core samples. They reported that the sample length strongly affected the P-wave velocities and suggested 75 or 109 mm as the ideal or the threshold specimen length of core specimen for limestones. The variation in the suggested sample length and the threshold could be due to sample origin, chemical characterization, texture, etc., since samples were collected from different locations [38; 39]. Figure 1: Variation in uniaxial compressive strength (UCS) values. UCS plotted as a function of (**a**) \(\rm V^{n}{{}_{p}}\), (**b**) \(\rm V^{d}{{}_{p}}\), and (**c**) \(\rm V^{s}{{}_{p}}\) for different sample diameters. Figure 2: Variation in \(\mathrm{PLI}^{\mathrm{D}}\) values. \(\mathrm{PLI}^{\mathrm{D}}\) plotted as a function of (**a**) \(\mathrm{V}^{\mathrm{n}}_{\mathrm{p}}\), (**b**) \(\mathrm{V}^{\mathrm{d}}_{\mathrm{p}}\), and (**c**) \(\mathrm{V}^{\mathrm{s}}_{\mathrm{p}}\) for different sample diameters. Figure 3: Variation in PLI\({}^{\rm A}\) values. PLI\({}^{\rm A}\) plotted as a function of (**a**) \(\rm V^{n}_{p}\), (**b**) \(\rm V^{d}_{p}\), and (**c**) \(\rm V^{s}_{p}\) for different sample diameters. Figure 4: Variation in indirect tensile strength (ITS) values. ITS plotted as a function of (**a**) \(V^{\mathrm{n}}{}_{\mathrm{p}}\), (**b**) \(V^{\mathrm{d}}{}_{\mathrm{p}}\), and (**c**) \(V^{\mathrm{s}}{}_{\mathrm{p}}\) for different sample diameters. Figure 5: Variation in Schmidt hammer value (SHV). SHV plotted as a function (**a**) \(\mathrm{V^{n}}_{\mathrm{P}}\), (**b**) \(\mathrm{V^{d}}_{\mathrm{P}}\), and (**c**) \(\mathrm{V^{s}}_{\mathrm{P}}\) for different sample diameters. In the present study, beside the correlation of the natural, dry, and saturated P-wave velocities with the mechanical properties of limestone, the effects of sample diameter on the ultrasonic P-wave velocities and mechanical properties of limestone, which were not addressed before in literature, were studied in detail. There are no similarities in terms of the main concept of this study with the previous investigations. As it was used in some previous studies, limestone was selected as a rock material for the UPV tests under various environmental conditions and mechanical tests due to availability and accessibility in the study area. Nevertheless, the study provides a new perspective especially on how the ultrasonic P-wave velocities and mechanical properties of limestone are affected by the core sample diameter.