## 1 Introduction  
The ultrasonic pulse velocity (UPV) test is a convenient, rapid, and low-cost method for evaluating rock samples under different environmental conditions, both in the laboratory and in situ using portable equipment. Due to its nondestructive nature, simplicity, and reliability, the UPV test has been broadly accepted and used in several disciplines, such as civil engineering, mining, and geo-engineering. Several researchers have utilized this test to investigate a variety of phenomena and parameters, including microstructural material properties, grouting assessment, the efficiency of different applications, deformation, stress, weathering degrees in rock mass, detection of rock material variations, characterization of rock and rock mass, fracture zone extensions around underground openings, and the thermal conductivity of rocks [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. Furthermore, ultrasonic propagation in fractured rock, geotechnical characterization of monument and building stones, and the relationships between the UPV and rock properties have been intensively studied and reported by various researchers [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. These studies have established correlations between the UPV and rock properties for various types of rocks. Rock seismic properties are greatly influenced by shape and grain size, rock type, porosity, density, pore water, anisotropy, temperature, clay content, confining pressure, weathering and alteration zones, bedding planes, joint properties (e.g., roughness), water, filling material, and strike and dip directions and angles [26; 27; 37]. The mechanical properties of rock must be defined under various environmental conditions for the planning and design of any civil, mining, or geotechnical application. Such works require great attention in sample preparation and testing, and test results must be reported within an acceptable accuracy level. The UPV test, which is a reliable and convenient technique, can be applied under various environmental conditions to predict the mechanical features of rock based on correlations. In addition, the expected effects of sample diameter on the ultrasonic P-wave velocity (V\({}_{\text{p}}\)) and mechanical features of limestone can be investigated by using various sample diameters. In the literature, few studies have directly correlated natural (V\({}^{\text{n}}\)p), dry (V\({}^{\text{d}}\)p), and saturated (V\({}^{\text{s}}\)p) ultrasonic P-wave velocities with the mechanical properties of rocks with various sample diameters. [PERSON] [37] investigated the predictability of wet-rock V\({}_{\text{p}}\) based on the dry-rock V\({}_{\text{p}}\) on 41 various rock types. He reported that the wet-rock V\({}_{\text{p}}\) can be assessed from the dry-rock V\({}_{\text{p}}\) using derived equations. [PERSON] et al. [38] evaluated the possible influence of sample length on P-wave velocities for 200 dry and saturated core specimens of volcanic rocks and limestones. The authors found that the sample length strongly affected the P-wave velocities; moreover, they developed a method to determine the threshold specimen length of the studied rocks as 109 mm for limestones. [PERSON] et al. [39] examined the effect of core size on the dry and saturated UPV of limestone samples. They reported that the reduction in V\({}_{\text{p}}\) and uniaxial compressive strength (UCS) might depend on the weakening of solid/solid interfaces between grains and variations in the chemical and mineralogical composition of limestone. A core length of 75 mm was found to be ideal for dry and saturated UPV tests. [PERSON] [40] conducted a correlative study on pulse wave velocities and quartz-mica schist properties. She noted that the physicochemical properties of rocks may be associated with ultrasonic P- and S-wave velocities and suggested that proposed empirical equations be validated for a rock type from a project site before being used in designing and planning goals. [PERSON] et al.