## 4 Discussion
### Link between Mechanical Properties and Surface Properties
#### 4.3.1 Weakening Mechanism Linked to Surface Energy Reduction  
The surface energy decrease as a possible mechanism for water weakening is in agreement with the observations made by [PERSON] et al. (2018) on a set of sandstones: based on a model for the prediction of the critical pressure P* from Hertzian contact theory ([PERSON] et al., 2018), these authors claim that the wet-to-dry ratio WDR(P*) should scale as \(\lambda^{3/2}\) where \(\lambda~{}=~{}\gamma^{(sat)}/\gamma^{(dry)}\) is the wet-to-dry ratio of the surface energy (Table 8). In accordance with this model, the surface energy values to be used are the ones derived from the KIC analysis; indeed, the underlying assumption in the model is that crack propagation is favored when the surface energy is lowered, leading to the weakening of the rock. Taking \(\lambda\) = 0.79 for the Obourg Chalk and \(\lambda\) = 0.83 for the Ciply Chalk (Table 8), the predicted wet-to-dry ratios are 0.70 and 0.76, compared to the measured values 0.50 and 0.37 for Obourg Chalk and Ciply Chalk, respectively (Table 7). To account for the lower ratios measured in our experiments, additional weakening mechanisms most likely exist in these chalks. This will be discussed in the next section.  
Note that the \"fracture\" surface energy values (i.e., derived from fracture toughness) in Table 8 are comparable to data found in the literature. Indeed, [PERSON] et al. (2018) derived a surface energy of 0.32 and 0.15 J/m\({}^{2}\) for dry and fully water saturated conditions, respectively, through double torsion experiments on calcite. [PERSON] (2018) and [PERSON] and [PERSON] (2018) derived through fracturing experiments a surface energy of 0.23 and 0.347 J/m\({}^{2}\), respectively, which are much closer to our mechanical-derived values. Nonetheless, the contact angle and AFM methods provided a surface energy approximatively one order of magnitude lower than the fracture surface energy. Similar differences between the surface energy estimated through mechanical tests and through surface characterization can be found in the literature. [PERSON] et al. (2018) obtained a value of 0.046 J/m\({}^{2}\) in their study of calcite precipitation with a method that does not involve fracturing processes, a value similar to our estimation through contact angle and AFM. The main reason for this discrepancy may be found in the experimental procedure. Both for the Semi-Circular-Bending and double torsion ([PERSON] et al., 2018) tests, part of the energy may have been dissipated to produce some ductile deformation, which is reasonable on calcite even at ambient temperature and pressure, or to produce microcracking other than the macroscopic fracture at the peak load. In this way, the surface energy can be overestimated. In addition, the length scale for the mechanical tests (in the centimeter range) is very different to that of the contact angle measurement (the radius of the droplet is in the millimeter range) and even more for the AFM measurements (in the sub-micrometer range). Another major difference is the fact that the surface energy derived from the contact angle, and the AFM studies are based on thermodynamics principles, with no actual surface creation such as in cracking processes.  
Another parameter that might be important is the surface roughness. For example, a higher surface energy was obtained on calcite crystals (0.098 J/m\({}^{2}\)) with the Owens-Wendt method, compared to both chalks. Normally, the surface energy of a material does not depend on its roughness, but an increase in roughness would increase the actual surface area in contact with the liquid droplet causing a stronger interaction and a lower contact angle, which finally would result in a higher estimation of the surface energy. Indeed, we have shown in Table 6 that a higher surface roughness was obtained for the calcite crystals.