## 3 Results and Discussion  
Open porosity predominantly increases with temperature across all lithologies (Figure 2). This trend clearly reflects thermally induced microcracking and structural degradation [56,57]. Limestones display variable sensitivity, with some (e.g., MC, BG) showing marked open increases, while others (e.g., EN, LZ) exhibit only minor porosity, indicating greater structural resilience to thermal stress. Marbles exhibit limited open porosity change up to 300 \({}^{\circ}\)C, with an average increase of around 367%, which becomes significantly aggravated at 600 \({}^{\circ}\)C, reaching a mean rise of approximately 1300%. Travertine and breccia show the highest open porosity gains, particularly travertine, indicating their high susceptibility, mostly due to irregular and porous internal structures. These results underline that thermal exposure significantly alters open porosity--especially in stones with pre-existing heterogeneity like breccia--and/or weakens grain contacts, as observed in marbles. Open porosity increase promoted by thermal fissuration processes is known to impact the capillary coefficient, as such microstructural discontinuities promote faster water ingress in natural stones [58]. This connection is reinforced by previous studies emphasizing the influence of micro-fissures and elongated pores in enhancing preferential water pathways [59,60]. Given that capillary action is governed by surface tension forces and the interaction between water and pore surfaces, structural anisotropy can impose a directional dependence in moisture uptake [61,62,63]. The correlation between Leeb hardness (HL) and capillary coefficients varies significantly across the studied lithologies (Figure 3). Among the limestones (Yellow Group on Figure 3), the predictive performance of HL varied widely. Some lithologies, such as  
Figure 2: Bar plots with porosity values (%) for the thirteen carbonate stones at reference conditions, 300 \({}^{\circ}\)C, and 600 \({}^{\circ}\)C. Lithologies are grouped by lithology: limestones, marbles, breccia, and travertine. Error bars represent standard deviation. BM (R\({}^{2}\) = 0.87), BML (R\({}^{2}\) = 0.79), HB (R\({}^{2}\) = 0.75), and AV (R\({}^{2}\) = 0.72), demonstrated strong exponential fits, while others, like EN (R\({}^{2}\) = 0.29) or MC (R\({}^{2}\) = 0.49), revealed weaker or more scattered responses. These differences can be attributed to the presence of variable structures such as stylolites and grain alignments (Figure 4a,b), which can influence the cracking pattern and are not fully captured by a surface technique like Leeb hardness. Marbles (Pink Group on Figure 3) showed notably higher consistency. Both MR and RV reached R\({}^{2}\) values of 0.91, while MB displayed the highest fit at R\({}^{2}\) = 0.94. This can be explained by the generally lower porosity and higher textural homogeneity of marbles, which enhances HL sensitivity to microstructural change and reduces data dispersion (Figure 4c,d). In contrast, HL showed poor predictive capacity for the breccia (Blue Group on Figure 3, B: R\({}^{2}\) = 0.13) and the travetrine (Green Group on Figure 3, TV: R\({}^{2}\) = 0.13). These lithologies are highly heterogeneous in terms of pore geometry and distribution, with irregular textures that weaken the mechanical response consistency. As such, HL measurements on these stones were less representative of internal damage affecting capillarity. These results aligned with previous bibliography that states that marbles, by having low porosity, high crystallinity, and granoblastic texture, lead to more predictable energy dissipation and uniform damage propagation under thermal stress [20]. This reflects a practical limitation of HL in porous or heterogeneous stones, where rebound energy loss at the surface reduces its consistency as an indicator of internal structural changes, particularly those affecting capillarity.