A mathematical approach to model diffusion properties of sedimentary rocks relevant to Sicily cultural heritage

Cultural heritage vestiges represent complex physical systems, able to interact with the environment through continuous exchanges of heat and fluids (water, air). In this wide context, particular relevance is assumed by transport phenomena and diffusion of pollutant, vehiculated inside the considered structure by water itself. Interaction mechanisms can be considered at various observation scales, depending on the material provenance and on its geometry and location. Involved materials are commonly constituted by porous rocks - more or less altered - belonging to geological sedimentary formations, as limestone, calcarenite and travertine. Their appreciable porosity affects significantly liquid movements; on the other hand, relevant vacuole size and geometry are likely influenced by the interactions themselves. As a matter of fact, interconnected pores increase the proper vulnerability of the materials, causing a progressive deterioration of the cultural heritage due to the close liquid-rock relations through capillarity absorption as well as gravity movements. This contributes to enlarge the whole cultural heritage risk, imposing quick and skill interventions in order to mitigate the endangerment for progressive intrusions of water-pollutant complexes. In fact, the principal aim is the protection of vestiges by means of protective products, the efficiency of which can be tested by the integration of innovative techniques and methods. In the described circumstances, analyses of transport and diffusion seem to be fundamental for understanding the mechanism of deterioration processes and the remedial actions to prevent the decay of the cultural heritage. In this paper Authors summarize integrated experiences already performed on samples, building materials and archaeological sites of Sicily, pointing the attention to temples, tombs and other ancient remains belonging to Sicilian Aeneolithic, Greek and Baroc periods. In detail, the integrated physical techniques were X-Ray Diffractometry (XRD), X-Ray Fluorescence (XRF), Hg Porosimetry, SEM analyses, Magnetic Resonance Relaxometry (MRR), Magnetic Resonance Imaging (MRI) and X-Ray CT imaging. Applied in situ equipments were portable geophysical instruments for non-destructive prospecting. Absorption kinetics studies and internal micro-porosity surveys on samples, both through MRI and X-ray CT, were performed too, leading to preliminary interpretations of porosity and diffusion features. The entirety of measures have given a first picture of the liquid intrusion in porous rocks, well depicted by imaging elaboration procedures and sets of diagrams illustrating the physical phenomena. A notable improvement toward the proper rock knowledge could be represented by considering the pollution source features as well as the different physical-chemical interactions of liquids/contaminants with the mean. Indeed, the phenomena are relatively complex, especially in quantifying the effects of diffusion processes. Moreover, a strong consequential inaccuracy must be considered due to insufficient geometrical considerations on the single components of the system (i.e., geological layers and/or granulometric anisotropy). Therefore, a reliable step has to be represented by analytic solutions of these mechanisms, taking into account non-stationary phenomena too, occurring in fractured rocks. Furthermore, the intrinsic properties of the considered system (sample, archaeological site, quarry) can lead to a more complicated representation of the processes, worsening the correct modeling of the liquid/pollutant flow. Thus, adopted solutions should be essentially of numerical kind, they being conditioned by the model calibration by statistical analysis between calculated and measured values. Discretization and modeling in meshes of pixels and voxels, referred to easily workable matricial numerical values, concur to the elaboration of thematic and summarized representations, with the aid of dedicated software’s, also performing a likely depiction of the cultural heritage.