## 4 Conclusions  
After having carried out the tests of uniaxial compressive strength for 31-mm specimens, and point load with irregular samples of saturated limestone and dry traverting, the corresponding values of \(I_{s}\) and \(I_{s(50)}\) were obtained to generate the scale effect models and correlate these parameters with \(\sigma_{c(31)}\) and \(\sigma_{c(50)}\), respectively. For the correlations between \(\sigma_{c(31)}\) and \(I_{s}\), factors (\(\beta_{1}\)) of 17 and 21 were obtained for limestone and traverting, respectively, close to the 19 proposed by [PERSON] [13] for 30 mm (Table 3). The associated errors for both rocks are less than 3 MPa (3.5%) on average, which makes it reliable to estimate the \(\sigma_{c(31)}\). In the case of limestone, the scale effect turned out to have an ascending model (greater resistance at a larger diameter); however, due to the range of the diameter (33.5-66.9 mm), it was not possible to determine whether around 67 mm the model could change to a descending model. This uncertainty is based on the \(\sigma_{c}\) results obtained by [PERSON] [44] for limestone (ascending-and-descending model), and on the scale effect graph plotted from the estimated values of bibliographic \(\sigma_{c}\) (Figure 6), which may change the trend to a descending model over 54 mm of diameter. Noting the dispersion of the results of \(I_{s}\) (\(R^{2}=0.046\)), it was decided to consider only the ascending model, obtaining coefficients \(k_{1}\) and \(k_{2}\) of \(-0.2545\) and \(-0.3126\), respectively. The difference between both coefficients (0.06) generated a margin of error of 19% with respect to \(k_{2}\), the only experimental value used as a reference. Regarding traverting, the experimental results of \(I_{s}\) determined a descending model for the scale effect, with a much lower dispersion than in the case of limestone (\(R^{2}=0.6198\)) at a range of 46.7-84.8 mm for the diameter. On the other hand, the trend of the curve of the scale effect from the bibliographic estimates of \(\sigma_{c}\) (Figure 9) was clearly upward. This reason was attributed to the fact that the bibliographic correlations were directly related to limestone and not to traverting, since, despite being practically 100% CaCO\({}_{3}\), the crystalline structure was not the same (calcite versus calcite and aragonite), nor was the distribution of internal pores. Likewise, the test with the Schmidt hammer was carried out to estimate more values of \(\sigma_{c}\) and help with the downward trend, with Equations (20) and (24)--proposed by [PERSON] and [PERSON] [10] and [PERSON] and [PERSON] [25], respectively--that were close to the values published by [PERSON] et al. [60] and [PERSON] et al. [61] for 54 mm, around 40 MPa. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(\mathbf{N}\) & **Mean** & **Standard Deviation** & **Maximum** & **Minimum** \\ \hline \(\beta_{1}\) & 200 & 13.445 & 0.85 & 16.18 & 10.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Results of the normal distribution of the linear fit for the \(\sigma_{c}\) and \(I_{s}\) pairs of the traverting. Figure 14: Histogram (**a**) and normal distribution graph (**b**) of the slope \(\beta_{1}\) of the linear fit by ordinary least squares of 10 data pairs, of \(\sigma_{c(50)}\) and \(I_{s(50)}\) of the traverting, randomly selected from 200 random samples. Although a descending model was considered in its entirety, it could not be ruled out that, for values of diameters lower than 31 mm (the experimental reference value in Figure 9: \(\sigma_{c(31)}\)), the model was descending, having a mixed (ascending-and-descending) model with a \(d_{i}\) around 31 mm. For the descending model, which included the estimates of \(\sigma_{c}\) (from \(I_{s}\), \(I_{s(50)}\), and \(R_{N}\)) that favored this trend, coefficients \(k_{1}\) and \(k_{2}\) of +0.858 and +1.160, respectively, were obtained whose difference of 0.30 generates an error of 25.9% with respect to \(k_{2}\), the only experimental value.