A non-linear model of sulphation of porous stones: Numerical simulations and preliminary laboratory assessments

Sandstones, limestones, and marble stones with different porosity were used as building materials for thousands of years. In the last century these materials have become vulnerable to atmospheric pollutants; the reaction of sulphur dioxide with calcareous (and decorated) surfaces is well known to form gypsum and black crusts. More recently, some mathematical models used for civil works have been applied to study the evolution of degradation phenomena; however, they did not fit sufficiently for artistic and historical hand-works, since they only give an averaged description of the damage. Between these mathematical models the Lipfert formula is the more diffuse, based on statistical models of atmospheric corrosion. In this paper a differential model was approached, which gives a quantitative description of the diffusion and the chemical action of sulphur dioxide on the porosity of calcium carbonate stones starting from the hypothesis that the interaction between stone surface and polluted air is due to its diffusion in the porosity of the material. The model has been validated by numerical simulations and a number of experimental tests in the laboratory. This approach gives a quantitative law for the penetration of the sulphation front inside of the stone, in accordance with the experimental data. Moreover, it is important to assess and prevent damage on the surfaces of historical monuments, considering also the local geometry, the nature of the polluted air, and the type of exposures.