Forecasting Damage and Consolidation: Mathematical Models of Reacting Flows in Porous Media

In this paper we present a survey about a series of works developed in the last 20 years, with our group, on chemical aggression of stone artifacts. Here we describe the modelling of different phenomena responsible for exterior and internal degradation of porous materials, such as the evolution of gypsum crust in marble stones, the sodium sulphate crystallization inside porous stone (masonry brick), or the effect of injection of consolidants in stones. For sulfation and other surface reactions we adapted our previous models to take into account more possible features, as for instance rugosity of stones and the possible interaction between chemical and mechanical damage, to evaluate the propagation of cracks in stones under stress. For the problem of salt crystallization, a new mathematical model describing the effect of protective products on sodium sulphate crystallization inside bricks has been proposed and tested against experiments. Finally, a mathematical model for evaluating the penetration and the ultimate depth of filtration of a consolidant product (ethyl silicate) on tuff was proposed and calibrated using experimental data. The proposed models were calibrated by tuning model parameters with numerical fitting procedures based on the comparison between simulation results and available experimental data. Since the obtained results were in qualitative and quantitative accordance with data, this confirmed the soundness of implemented procedures and the effectiveness of the proposed methods.