## 3 Conflicting OPS Limestone Hygric Property Characterisation  
Figure 1 presents the moisture retention curve (left) and liquid and vapour permeability curves (right) for the OPS limestone based on the parameter values stated above. This vapour permeability is not \(\delta_{\text{p}}\), related to gradients in vapour pressure, but its translated version, linking it to gradients in capillary pressure. For this aim, the Kelvin equation was applied:  
\[\text{G}_{\text{v}}=-\delta_{\text{p}}\
abla\text{P}_{\text{v}}=-\delta_{ \text{p}}\frac{\text{d}\text{P}_{\text{v}}}{\text{d}\text{P}_{\text{c}}} \
abla\text{P}_{\text{c}}=-\delta_{\text{p}}\frac{\text{P}_{\text{v}}}{\text {R}_{\text{v}}\text{T}\text{P}_{\text{w}}}\
abla\text{P}_{\text{c}}=-\text{k }_{\text{v}}\
abla\text{P}_{\text{c}} \tag{5}\]  
where R\({}_{\text{v}}\) (J/kgK) is water vapour gas constant and T (K) is temperature. The last terms define k\({}_{\text{v}}\) (kg/msPa), the vapour permeability for capillary pressure gradients, which is depicted in Figure 1 (right). This transformation was done to allow for a direct comparison of liquid and vapour permeabilities. These moisture retention and permeability curves expose a number of abnormalities concerning the hygric characterisation of the OPS limestone. Firstly, the inversely characterized moisture retention deviates strongly from the moisture retention curve determined from mercury intrusion porosimetry. The latter has been determined with the Young-Laplace equation from the porosimetry results included in [1]'s supplementary material. This is a well-established technique [9], and its accuracy has recently been reiterated [8]. Whereas the mercury-intrusion-based curve presents a (very) steep slope, in agreement with this limestone's narrow 1-20 \(\upmu\)m range of pore radii, the inversely characterized curve is far smoother, which does not concur with that narrow pore radii range. Secondly, the liquid and vapour permeability curves show that the liquid permeability always exceeded the vapour permeability, even at the very low capillary pressures and hence very low  
Figure 1: (**left**) Moisture retention curve for the OPS limestone, as inversely characterized or based on mercury intrusion; (**right**) liquid and vapour permeability (both related to gradients in capillary pressure) curves for the OPS limestone. moisture contents. In the capillary pressure range from \(-10^{8}\) to \(-10^{9}\) Pa, representing relative humidity values between 0.1 and 50% and moisture contents of about 1 to 2 kg/m\({}^{3}\) only, the liquid permeability is on average five times higher than the vapour permeability. This is unheard of, as it is widely accepted that vapour diffusion is the exclusive and dominant moisture flow mechanism at such low humidity [10]. When using these permeability curves for a simulation of a dry cup vapour diffusion test, the discusser acquires a moisture flow that translates to a vapour permeability \(\delta_{\mathrm{p}}\) of roughly 3 \(\times\) 10\({}^{-10}\) kg/msPa, 50% above the vapour permeability of air and about 40 times higher than typical limestone vapour permeabilities presented in the literature [11]. For that simulation, a 5 cm thick sample was placed in between environments at 54 and 12% RH, and the resulting steady-state moisture flow was translated to the reported vapour permeability. The employed parameter values were obtained by fitting FLoW1D simulation results to the measured moisture mass evolution during a capillary absorption test. The resulting agreement of the simulated and measured moisture absorption is depicted in Figure 2 (left), and the resulting moisture content profiles as calculated with FLoW1D are shown in Figure 2 (right). Though the fit in Figure 2 (left) is acceptable, the moisture content profiles in Figure 2 (right) deviate from the sharp infiltration moisture fronts that are generally observed when building materials (certainly when having a narrow pore size distribution like the OPS limestone analysed here) undergo capillary absorption [12].