# Pore Structure and Water Transfer in _Pietra d'Aspra_ Limestone: A Neutronographic Study
## 3 Results and Discussion
### Neutron Radiography Analysis
In our case, however, the intrinsic heterogeneities, in terms of both natural constituents and pore size distribution, make the WC profiles not uniform; consequently, the evaluation of the IPs difficult to carry out. On the basis of these considerations, the IPs of the decreasing curves reported in Figure 7 and, hence, the position of the wetting front were approximated to the points corresponding to half of the maximum water content values, which are different in each investigated sample [58]. From a theoretical point of view, the behavior of \(h\) as a function of time can be predicted by using the analytical Lucas-Washburn (L-W) equation (Equation (6)) [59; 60]. \[h(t)=K\sqrt{t}, \tag{6}\]  
where \(K\) is a coefficient, known as sorptivity (m/s\({}^{0.5}\)), accounting for the tendency of a porous material to absorb/transmit liquid through natural imbibition. Generally, the L-W model assumes not only a complete saturation of the region behind the wetted front, but also a uniform pore size distribution of the material. Consequently, in materials characterized by a broad distribution of pores sizes, as in our case, deviation from the aforementioned model is often achieved. Nevertheless, by looking at the way in which the experimental values diverge from the expected ones, several considerations can still be made. In Figure 9, we report the \(h(t)\) vs. \(\sqrt{t}\) plot for all the investigated PA samples in the 0-13,310 s time range. The comparison of the \(h(t)\) vs. \(\sqrt{t}\) plots for the PA-TQ specimen with those calculated for the treated limestones not subjected to any artificial weathering test (PA3 and PA6) indicates that the impregnation of the stone surface with NS visibly modifies the water transfer properties of the limestone to a major extent compared to the treatment with NL, both at the early and, mostly, at the late stage of the absorption test. This was also qualitatively confirmed by the extremely slow water kinetics observed in PA1, PA2, and PA3 with respect to that observed in PA4, PA5, and PA6. The observed trends of \(h(t)\) vs. \(\sqrt{t}\) strongly deviate from the L-W model, especially for \(\sqrt{t}>\sim\)30 s\({}^{0.5}\), indicating a heterogeneity of the porous medium in which the capillary rise of water is due to the contribution of several pore families with different size distribution. Nevertheless, below \(\sqrt{t}\sim\)30 s\({}^{0.5}\), a diffusion-like behavior, as that predicted by the L-W model, can be reasonably hypothesized. This evidence can be justified thinking that, in the early stage of the test, the water motion is affected by the presence of a pore's distribution influenced by both the stone and the consolidating agents, limited to the penetrated thickness. Accordingly, the occlusion of pores having different dimensions (ranging from \(\sim\)0.01 to \(\sim\)100 \(\upmu\)m) leads the system from its natural widespread heterogeneity condition (see Figure 4) toward a more uniform one, with several pore families of different sizes partially or completely obstructed. Although the quantitative evaluation of the sorptivity \(K\) would not be reliable, since neither a full saturation of the region behind the water front (see Figure 6) nor a uniform pore network during all the imbibing process are satisfied, several considerations from Figure 9 can still be made. In the case of PA5 and PA6, an increased water absorption tendency can be detected with respect to PA-TQ, as reveled by the high rate of variation of \(h\) for \(\sqrt{\dot{t}}<\) -30 s\({}^{0.5}\). This means that during the initial stage of water imbibition, the presence of NL seems to enhance the water fluidity inside the porous network of the stone. This can be explained by considering that, close to the impregnated surface, the presence of NL does not occlude pores but rather reinforces them, resulting in a localized enhanced rate of capillary suction.