## 4 Discussion
The category of brittleness, or the ability to be crushed by repeated impacts (measured by S\({}_{20}\)), varied with temperature from medium to high, and rock surface hardness or resistance to indentation (represented by SJ) varied from medium to low (both in the scale of [PERSON] et al.). We attribute this effect to the increase of porosity and the propagation and coalescence of micro fissures due to thermal treatment. That is noticeable in the case of S\({}_{20}\), where the trend is consistent with microstructural changes due to thermal treatment (2019). Incipient transgranular fissures and porosity developed when heated to 400 \({}^{\circ}\)C match a gentle increase in S\({}_{20}\). At 500 \({}^{\circ}\)C the pore-sizes increase and fissures were larger and more connected, in agreement with a marked increase in crushability by repeated impacts represented by S\({}_{20}\). It is noteworthy that at 600 \({}^{\circ}\)C, SJ values were smaller for water-cooled samples, and S\({}_{20}\) values were equal for both cooling methods. These results contradict the general observed trend of greater decay in mechanical and physical parameters when cooling with water for the studied range of temperatures. Finally, the variation on DRI with temperature almost copied that for S\({}_{20}\), and so variation with temperature of DRI is more influenced by S\({}_{20}\) than by SJ. We have explored different correlations to predict the variation in the drillability with temperature from variations in the physical and mechanical properties. In this study, those correlations providing coefficients of determination greater than 0.80 and relative errors smaller than 10% have been considered. Logarithmic functions were predominant for SJ predictions, and the best correlations at high temperatures were found from UCS and Poisson's ratio for all cooling methods, and from P- and S-wave velocities for water-cooled samples. SJ predictions from UCS showed good values of relative error for the highest temperatures, but a low coefficient of determination was measured for water-cooled samples, although it strongly improved when skipping UCS value at 200 \({}^{\circ}\)C (R\({}^{2}\) = 0.99). This good correlation with UCS can be explained as vertical pressure on the bit and bit rotational speed (represented by SJ value), which have proven to be the most significant parameters in the penetration rate for rotary drilling [7]. In addition, SJ represents surface hardness [49], and therefore good correlations with UCS and other tests measuring surface hardness in the intact rock, such as Schmidt hardness test [6; 53], have been observed. [PERSON] et al. [13] stated that elastic or plastic deformations affect rotary drilling, and this explains correlations with deformational parameters obtained in our research. Correlation with elastic modulus was weaker than with UCS, which is consistent with conclusions from other researchers [11; 13]. Finally, good correlations with P- and S-wave velocities were previously reported in existing research [12] being higher for water-cooled samples in this case study. Coefficients of determination and residuals were remarkably better for S\({}_{20}\) predictions and linear functions were predominant, providing good predictions for all variables and cooling methods. Correlations with UCS were the weakest when compared with the other parameters. It should be pointed out here that [PERSON] et al. [49] explained this result by the fact that S\({}_{20}\) and UCS are two very different test methods for determining the strength properties of rock, since S\({}_{20}\) is determined by applying repeated impacts on the sample material, causing crushing of the sample material, while UCS is performed by applying load on the sample, at a relatively slow constant rate, until failure occurs. The correlations between SJ and S\({}_{20}\) with physical and mechanical parameters in thermally treated rocks derived from this work showed greater coefficients of determination than those reported for intact rocks by most authors [11; 12; 13].