## 3 Results and Discussion
Similarly to the assessment of Leeb hardness, the correlation between ultrasonic pulse velocity (UPV) and capillary coefficients exhibited varying degrees of strength across the studied lithologies, although with generally stronger correlations overall (Figure 5). Figure 3: Scatter plots showing the relationship between Leeb hardness (HL) and capillary coefficient for the studied carbonate stones. Figure 4: Image documentation of selected stone features: (**a**) stylolites in EN limestone; (**b**) mineral alignments in MC limestone; (**c**) petrographic thin section of MB marble in crossed nicols; (**d**) petrographic thin section of RV marble in crossed nicols. Figure 5: Scatter plots showing the relationship between ultrasonic pulse velocity (UPV) and capillary coefficient for the studied carbonate stones. Among the limestones (Yellow Group on Figure 5), UPV achieved consistently strong correlations with water absorption by capillarity: BM (R\({}^{2}\) = 0.97), BG (R\({}^{2}\) = 0.96), and BML (R\({}^{2}\) = 0.90). Interestingly, in this assessment, EN presented a R\({}^{2}\) value of 0.93, unlike the previous one obtained for HL (R\({}^{2}\) = 0.29). These results confirm that UPV is highly sensitive to microstructural degradation, particularly that which influences water transport properties in the studied carbonate stones. MC limestone also experienced an R\({}^{2}\) increase from 0.49 to 0.72, highlighting a consistency of a stronger relationship between this technique and water transport behavior. Marbles (Pink Group on Figure 5) also experienced an increase in correlation values with this method, maintaining high predictive reliability already observed for Leeb hardness. MR and RV achieved R\({}^{2}\) = 0.97 and R\({}^{2}\) = 0.99, respectively, and MB closely followed with R\({}^{2}\) = 0.94. These results reinforce the suitability of UPV for detecting capillarity-relevant changes in compact and crystalline lithologies, where ultrasonic wave velocity is tightly linked to cohesion and density. Interestingly, the breccia (Blue Group on Figure 5) exhibited a surprisingly good fit (R\({}^{2}\) = 0.82), outperforming HL in the same lithology, with a previous R\({}^{2}\) = 0.13. This change can be linked to the bulk-scale heterogeneity of breccia, where UPV better integrates spatial variability than surface-based methods. Conversely, the traverting (Green Group on Figure 5, TV: R\({}^{2}\) = 0.09) once again showed negligible/nonexistent correlation. This suggests that the highly porous and heterogeneous structure of traverting interferes with the transmission of ultrasonic waves, making the results unreliable as indicators of capillary behavior. Compared to HL, UPV appeared to exhibit greater sensitivity and broader applicability across lithologies. The tighter clustering around fitted curves may suggest a more consistent relationship between UPV and capillarity-related deterioration under thermal stress. These results are in line with prior research, which highlights the strong sensitivity of UPV to internal degradation mechanisms such as microcracking, loss of cohesion, and increased pore connectivity [47; 64]. The strong inverse correlations found in limestones and marbles reflect the parallel evolution of structural weakening and water ingress capacity. Lithologies exhibiting lower porosity and higher textural homogeneity present optimal conditions for UPV-based detection of thermal degradation affecting capillary transport properties. This aligns with previous studies showing that UPV performs best in compact carbonate rocks, where ultrasonic wave scattering is minimally affected by large voids or fabric anisotropy [46; 64]. The significant UPV losses observed in thermally damaged marbles (up to 70% at 600 \({}^{\circ}\)C) are especially consistent with their increased capillary coefficients, reinforcing the reliability of this method in dense, crystalline matrices.