Indirect test methods for the mechanical characterization of building stones

The main objective of this study is to evaluate the usefulness of indirect methods to estimate the uniaxial compressive strength (UCS) of building stones. For this purpose, the results of the UCS test on five types of stones from southern Italy, one igneous and four sedimentary stones are firstly correlated with the corresponding results from Schmidt hammer, point load and UCS direct tests. Then, derived correlations are compared with the equations obtained by different researchers in the mechanical stone characterization.


Introduction
The uniaxial compressive strength (UCS) is widely employed in civil engineering to define mechanical resistance of building materials. Current testing procedures especially refer to the most employed worldwide standards of the International Society for Rock Mechanics (ISRM) and the American Society for Testing and Materials (ASTM). The advantage of performing direct tests consists in obtaining results very close to the mechanical behaviour of the tested materials but, on the contrary, these methods suppose large costs to the sample preparation according to the above standards. Thus, indirect methods are always more frequently preferred thanks to their less cost and to their ease, especially for in situ tests.
The aim of this research consists in predicting UCS using indirect tests, in particular Schmidt hammer test and Point load test and to compare results with direct UCS in order to establish correlations.

Experimental procedure
The Schmidt hammer test (SHT) provides a quick and inexpensive measure of surface hardness and it is widely used for estimating the mechanical properties of stone materials in the field [5]. L-type SHT are conducted in situ directly in blocks or outcrops surfaces. All tests are carried out with the hammer held vertically downwards and at right angles to horizontal faces of large stone blocks. 60 readings are obtained for each analyzed block. Readings are rejected if any individual impact test results in cracking or any other visible damage. The average value is recorded as the SHT rebound value according to the ASTM standards [6]. Equations correlating the compressive strength to SHT number are given in Table  1.
The point load test (PLT) is often employed as an indirect test method in order to evaluate the compressive or tensile strength of rock [7]. Table 2 lists the equations correlating compressive strength to PLT employed in this study. According to the ISRM standards [8], the ratio between compressive strength and PLT varies between 20 and 25 [9]. 32 cubic specimens for each stone type of 100 ± 5 mm edge are tested through a portable PLT machine connected to a barometer to register the maximum pressure. Results are corrected to a specimen diameter of 50 mm and the average value is recorded as the PLT strength.  The direct uniaxial compressive strength (UCS) is evaluated through the Maschinen fabric Liezen system (MFL) testing machine at a constant speed rate of 1 mm/min with a maximum load capacity of 3000 kg. The test is repeated 10 times for each cubic stone specimen (50 ± 5 mm edge) and the average value is recorded as the UCS mean value.

Results and discussion
Test results are given in Table 3 and are analysed using the method of least squares regression. Indirect tests values are correlated with the corresponding direct UCS values. The equation of the best-fit line, and the correlation coefficient are determined for each regression. An exponential relation between SHT and UCS is found (Fig. 1) and the equation of the curve is: UCS = 20.08e 0.0316SHT r=0.95 (1)  Researchers used both linear and exponential equations to correlate SHT with UCS. Some researchers multiplied SHT by density to improve the correlation or by the porosity of the stone. In this study, exponential function gives the highest correlation coefficient. The relation found in this study is similar to the relations of As it is shown in the Fig. 1, the higher the stone strength the more scattered the data points are. The data points fall closer to the line at low strength values but become more scattered at higher strength values. This suggests that the ability to estimate the UCS of stones using SHT is better at low strength values, and is less reliable at higher strength values.  Although, ISRM [8] stated that the ratio between UCS and PLT varies between 20 and 25, many researchers found different ratios, lower and higher than the above interval [9]. While some equations conform to y=ax form, the others conform to y=ax+b form as well as derived in this study. The derived equation of PLT vs. UCS is compared with the equations conforming to y=ax+b form from literature. As shown in the Fig. 6, the obtained equation in this research shows a trend that is similar to some of the other equations. In particular it is similar to the equations of Deere and Miller (1966), Gunsallus and Kulhawy (1984) and Cargill and Shakoor (1990) [9] due to the proximity of the estimated values from this study to those obtained by the above researchers. Among them, the relationship of Cargill and Shakoor (1990)   Thanks to the Department of Civil Engineering of the University of Calabria (Italy) and to the IPG Laboratory of Castrolibero (Italy) where mechanical tests were performed. Thanks to the Universidad la Sabana (Colombia) for financing the research.

Conclusions
The uniaxial compression test, Schmidt hammer test and point load test are carried out on five Italian building stones (igneous and sedimentary) in order to develop predictive equations for uniaxial compressive strength. The usefulness of the indirect test methods is assured through test results. The obtained linear and exponential equations are compared to the relationships previously obtained by other researchers. It is found that there is no agreement between the equations suggested by different researchers. While some equations exhibit the same trend, the others differ. This is probably due to the differentiation of stone types and test conditions. Correlations show that the prediction of uniaxial compressive strength on the basis of different relationship gives in some cases inaccurate estimates and in others a good prediction. The most reliable results, especially in the case of the Schmidt hammer test, are obtained for stones with lower strength rather than for those that present higher uniaxial compressive strength. The most fitted relationship between other researches and this study is obtained by the equation of Fener et al. In the case of the point load test, the equation of Cargill and Shakoor shows the most similar trend to the estimated equation from this study. The application of the suggested equations must be practiced with care probably taking into account detailed stone features like the porosity or density.