Semi-empirical models to describe the absorption of liquid water in natural stones employed in built heritage before and after the application of water repellent treatments

This study aims at validating an easily implementable and effective methodology to simulate the capillary imbibition rate of porous building materials, with special attention to stones employed in historical architecture. Two models selected from the literature are discussed from both a theoretical and practical viewpoint and their effectiveness in describing the imbibition process is evaluated on a large set of water absorption data of four different natural stones. It is shown that these models can be used in a predictive way to calculate the sorptivity of stones with fairly good approximation. Furthermore, they may represent a useful tool for the study of porous materials of built heritage, since, contrary to standard tests for sorptivity determination, they only require small samples to determine the pore size distribution and the maximum water saturation of the investigated materials. Finally, it is shown that the same models can also be used to simulate the reduction in water absorption after the application of water-repellent products, affording some insight into the protection mechanism and the criteria that determine the performance of protective treatments.