## 3 Results
### Correlations between Parameters  
Correlations have been proposed in this work to predict the variation in the drillability with temperature from variations in the physical and mechanical propertiesfor both air and water-cooled samples. Properties correlated in this study are obtained from different fragments within the same samples, which prevents providing pairs of values for the same fragments. This is because drillability tests performed here are destructive, and therefore it is not possible to make other tests such UCS on the same rock specimens. In other words, since DRI and UCS tests are destructive, for each temperature they are performed using different fragments (whose values are averaged and then correlated). Thus, regression curves are calculated using the mean values of each property determined at each temperature in line with other authors [10; 27; 50] since the pairs of correlated values of each sample that define the scatter cannot be considered for adjusting such functions. Different correlation functions exist between SJ, S\({}_{20}\), and other physicochemical parameters of the intact rock, but they do not refer to thermally treated samples. This research novelty explores the variation in SJ and S\({}_{20}\) with temperature, and their correlation with other physicochemical features in a thermally treated rock. To provide the most accurate  
Figure 9: Variation with temperature of Siever’s J miniature drillability SJ (**a**), brittleness S\({}_{20}\) (**b**), and drilling rate index (**c**) for air- and water-cooled samples. Categories have been represented for SJ and S\({}_{20}\) according to [PERSON] et al. [49], and for DRI according to [PERSON] [41]. predictions of drillability parameters for making preliminary decisions about the drilling process (e.g., drilling rig type and excavation process), we propose correlations to explore the best fitting functions based on coefficients of determination (Table 3), and we evaluate their suitability based on residuals and absolute relative errors (Table 4). We also discuss if correlations can provide reference values for the drillability features of thermally treated rocks, and so we consider valid those correlations providing coefficients of determination greater than 0.80 and relative errors smaller than 10%. In general, the best fitting functions for SJ were logarithmic, while linear functions showed best results for \(\mathbb{S}_{20}\) correlations for most parameters and cooling methods (Table 3). Coefficients of determination were higher in the case of \(\mathbb{S}_{20}\) predictions for almost all regression functions and parameters. The best correlation functions derived from Table 3 have been plotted to discuss trends. Thus, predictions from mechanical variables (UCS, elastic modulus, and Poisson's ratio) are represented for SJ in Figure 10 and for \(\mathbb{S}_{20}\) in Figure 11. Predictions from physical variables (P- and S-wave velocities) are depicted in Figure 12 for SJ and in Figure 13 for \(\mathbb{S}_{20}\). Residuals have been also plotted as the differences between values measured in laboratory tests and predicted from regression functions. To evaluate the quality of predictions, absolute residuals and absolute relative errors have been represented for the average temperatures where DRI exhibited greatest variation (400, 500, and 600 \({}^{\circ}\)C) (Table 4).