## 1 Introduction  
Determining the compressive strength of a rock mass is one of the main objectives that geomechanical design projects address, because it depends not only on the rock material (intact rock), but also on the discontinuities that separate the intact rock blocks. The main parameter used to represent the strength of the intact rock is the uniaxial compressive strength (\(\sigma_{c}\)), and it is determined in the laboratory using cylindrical specimens according to the standards of American Society for Testing and Materials (ASTM) [1, 2] and International Society for Rock Mechanics and Rock Engineering (ISRM) [3].  
In the same way that it can be determined in the laboratory directly, indirect methods have also been developed to estimate \(\sigma_{c}\) for almost types of rock in general, and limestone and traverting in particular, because it can be correlated experimentally with its index properties. In this way, predictive models emerge that experimentally relate \(\sigma_{c}\) and porosity [4, 5, 6, 7, 8, 9], \(\sigma_{c}\) and density [7, 10, 11], and \(\sigma_{c}\) and the point load index [12, 13, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] or the number of rebounds of the Schmidt hammer [10, 18, 23, 24, 25], which will be seen throughout this work.  
This work emphasizes the effect of geometry of the specimens, due to its importance in the magnitude of the value of \(\sigma_{c}\), since both ASTM [1, 2] and ISRM [3] recommend cylindrical specimens with a diameter (\(d\)) between 50 and 54 mm--reference value according to the scale effect [26]--and a height/diameter ratio (\(H/d\)) of between 2 and 3 [27, 28, 29].  
Both \(d\) and \(H/d\) are very important in the experimental correlations because these are parameters directly related to the values used in the least squares adjustment and linear regression analysis, so the \(d\) of the specimen tested under uniaxial compressive stress will be the reference of the predictive model. Therefore, if the values of \(\sigma_{c}\) obtained from specimens of 48 mm diameter are correlated by means of a simple (or multiple) regression analysis with those corresponding to any index property, the predictive model will estimate a value of \(\sigma_{c}\) of 48 mm and not 50 mm. Between 48 and 50 mm there is almost no difference, but smaller diameters are also used in research, such as 21 mm [30], for example.  
For this reason, [PERSON] et al. [31] and [PERSON] et al. [32] used P wave velocity values (\(v_{p}\)), measured in cylindrical specimens of 31 mm diameter, in experimental correlations determined for other diameters, thus estimating an erroneous \(\sigma_{c}\) value. This led them to the generation of their own experimental predictive models.  
Finally, the objective of this research is to determine the experimental correlation between \(\sigma_{c}\) and \(I_{s}\) for limestone and traverine, for diameters of 31 mm and 50 mm, from the experimental \(I_{s(50)}\) and \(\sigma_{c(50)}\) estimated from the literature referring to the correlations between \(\sigma_{c}\) and \(I_{s}\). There was a special emphasis on the geometry of the specimen tested for each of the tests, which led to studying the scale effect for both rocks because (most of) the correlations referred to the 50 mm diameter.