Natural stones have been used as building material in architectural works and monuments since ancient ages. Originally, natural building stone was used for load-bearing masonry walls, but more recently it has been used as curtain walling for high rise buildings (Yates et al. 2012). Natural stones are widely used in flooring, stairs, cladding and decorative purposes due to their property of being a highly resistant building material and their color properties (Cetintas and Akboga 2020). The physical, chemical and mechanical properties of natural stones play an important role in determining the areas where they can be applied as building materials (Karaca 2010). Many different rocks such as granite, marble, limestone, sandstone, travertine, and andesite have been used as natural building material from past to present. Engineers are commonly using the uniaxial compressive strength (UCS) and tensile strength (TS) of rock for many engineering applications. The main problem in determining the strength of rocks is that this process is time consuming and expensive and requires sophisticated test machines and fixtures. For this reason, engineers often prefer to use indirect tests such as Brazilian tensile tests, bending tests, point load index, Schmidt rebound number, and ultrasonic tests to determine the strength of rocks. Sample preparation and application of these indirect tests are easier and cheaper compared to the UCS and TS tests (Kahraman et al. 2012; Raj and Pedram 2015).
TS is one of the primary characteristics of natural stones, which play a crucial role in the planning and project designing of many mining and civil engineering works. Several factors are effective on the TS of rock materials, e.g. discontinuities, lamination, foliation, mineral composition, and porosity. Rocks are less resistant to tension than to compression or shear (Tang et al. 2007; Liu et al. 2019).
Different testing methods have been proposed for the investigation of the tensile properties of rocks. Direct tensile testing of rock provides more exact and reliable results compared to indirect tensile testing. Due to the inherent nature of the tensile test, some undesirable results may occur during application such as bending, torsion, concentrated loads or stress concentration. These factors are usually caused by the alignment of the sample or unsuitable connections between the rock sample and the fixture caps. Therefore, the difficulties related to the direct tensile test application have led to the development of different indirect methods to determine the TS of materials. Brazilian test (ISRM 1978; ASTM D3967-08), 3 and 4-point bending tests (ASTM C880 2015; ASTM C99 2015; TS EN 12372 2007; TS EN 13161 2014), the confined tensile test (Hoek and Brown 1980) and the ring test (Hobbs 1965) have been used as indirect methods since they are easy-to-apply and low-cost methods for many years.
There are many different studies on determination of the tensile strength using direct and indirect testing methods. In some of these studies, it is stated that it is not appropriate to use indirect methods. The generally accepted view is that the most widely used method is the BTS test and it is more practical to use this test instead of the Uniaxial tensile strength (UTS) test. The BTS test is the most widely used indirect method for reasons such as ease of sample preparation, cheapness and simplicity. Many different researchers indicate that the values acquired from BTS test are higher than the UTS values. However, some researchers stated that the BTS test is not a suitable method for determining the TS because the test sample breaks under biaxial stress conditions (Fairhust 1964; Chen and Stimpson 1993; Erarslan and Williams 2012; Li and Wong 2013; Komurlu et al. 2017). In the study conducted by Fahimifar and Malekpour (2012), the suitable test conditions for the Brazilian test were proposed to obtain the closest results to the direct tensile test. Li and Wong (2013) stated that the stress occurring in the sample in the Brazilian test is not uniaxial. Therefore, they emphasized that tensile stress in rocks could be overestimated. Briševac et al. (2015) stated that numerous scientific studies have been carried out regarding the TS of materials and the BTS test, however, there have been still no practical approaches available. Researchers offered that a new approach or correction coefficients should be developed that would allow the accurate determination of the TS values of the rocks by using the Brazilian test. Perras and Diederichs (2014) suggested that the BTS should be corrected by multiplying a coefficient of 0.7–0.9 depending on the rock type. Because of the testing configuration and variability of test specimens, there is no general agreement about how to estimate the TS of rocks (Perras and Diederichs 2014). Some hybrid models have been proposed by Mahdiyar et al. (2019) to estimate the tensile strength of rocks using statistical methods. Moreover, some researchers proposed that the bending tests should be performed to determine the TS of material (Jaeger et al. 2007). Efe et al. (2019) studied the effect of sample dimension on 3- and 4-point bending tests of marble and its relationship with direct tensile strength test. In another study conducted by Efe et al. (2021), new correction coefficients were proposed to be able to estimate the direct tensile strength from BTS and bending strength tests. According to the results of that study, the coefficients were found to be 0.50 for BTS, 0.33 for the 3-point bending tests and 0.40 for the 4-point bending tests.
When the literature is examined, it is obvious that the results obtained from indirect methods do not always correctly predict the UTS value. In fact, the results obtained by indirect methods actually represent the TS value of the rock material that has been investigated for 70 years (Efe et al. 2021). In literature, it is seen that there is no general agreement on a test method which is suitable for rocks and rock-like materials (Efe et al. 2021). While determining the TS from indirect methods, the sample is not in a uniform state of stress as it is in the UTS. Therefore, when calculating the TS of rock materials using indirect tests, it may be useful to consider some rock properties such as P-wave velocity, density, porosity and unit volume weight. P-wave velocity has a crucial role in the determination of structural properties of the rock as it is related to the void and fracture-crack systems within the rocks. In addition, this method can be applied as a quick, simple, cheap, and non-destructive test in the laboratory and the field (Moradian and Behnia 2009). However, there are very few studies on the estimation of the mechanical properties of rocks using the ultrasonic test method. Rio et al. (2006) determined the characterization of granites using acoustic techniques on different samples obtained from many quarries. Yagız (2011) estimated the properties of rock such as the uniaxial compressive strength, modulus of elasticity, Schmidt hardness, slake durability index, water absorption and effective porosity, and saturated and dry density using the Vp. Uyanik et al. (2019) determined the physical and mechanical properties of rocks with the help of multi-parameter experimental relationships obtained by using a combination of P- and S-wave velocities. Garia et al. (2019) conducted a study based on laboratory measurements to find the interdependence between petrophysical properties and ultrasonic wave velocities. The propagation of seismic wave in the intact and jointed rocks subjected to triaxial loading condition was investigated by Liu et al. (2019) experimentally. Based on that field investigation, it was found that joint has a significant attenuation effect on seismic P-wave. In the light of the literature, it can be concluded that the research to estimate the TS value from ultrasonic methods is meager.
The main goal of this study is to investigate the predictability of the UTS of natural building stones using BTS, 3- and 4-point bending strength tests and physical-mechanical rock properties especially the P-wave velocity. To this aim, 9 different rock types (sedimentary, metamorphic and magmatic origin) used as natural building stone in the construction industry were tested. The test results were analyzed with statistical methods and the UTS values were correlated with the corresponding indirect tests and physical rock properties. As a result of the experimental studies, it was tried to reveal which indirect method would be more appropriate to use while determining the UTS value, as well as whether the physical properties of the rocks could be considered in combination with the indirect methods.