Predicting capillary absorption of porous stones by a procedure based on an intermingled fractal units model Giorgio Pia a,⇑ , Enrico Sassoni b , Elisa Franzoni b , Ulrico Sanna a a Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Università degli Studi di Cagliari, Piazza d’Armi, Cagliari 09123, Italy b Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Università degli Studi di Bologna, Via Terracini 28, 40131 Bologna, Italy article info Article history: Received 9 April 2014 Accepted 31 May 2014 Available online 3 July 2014 Keywords: Capillary absorption Fractal model Porosity Pore size distribution Sorptivity abstract This study presents an intermingled fractal model capable of simulating the porous micro- structure of natural stones used in historical buildings. The developed model is aimed at predicting, by an analytical approach, the sorptivity of these materials. To verify the actual ability of the proposed method to predict stone sorptivity, in this study the intermingled fractal units model was applied to eight types of natural stones. The results are in very good agreement with sorptivity values obtained by experimental tests on the investigated stones. Compared to other analytical formulas proposed in the literature for predicting the sorptivity of porous materials, the newly proposed method better matches with the experimental results, and this can be attributed to that fact it takes into consideration the whole pore size distribution of the analyzed material, rather than the average pore radius only. Thanks to the proposed method, the sorptivity of natural stones used in histor- ical buildings can be calculated from their pore size distribution determined by MIP, which, contrary to standard tests for sorptivity determination, only requires small and irregular samples. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction In porous building materials, such as concrete, brick, mortar and stone, water sorptivity (i.e., water capillary absorption rate) is a key parameter, which describes the amount of water that penetrates into the material per unit surface area per square root of time. Since water is responsible for many weathering processes that affect porous building materials, such as salt-crystallization cycles (Scherer, 2004), freezing-thawing cycles (Martínez-Martínez, Benavente, Gomez-Heras, Marco-Castaño, & García-del-Cura, 2013), dissolution of soluble fractions (Franzoni & Sassoni, 2011), swelling of clays (Wangler & Scherer, 2008), reduction of mechanical properties (Gentilini, Franzoni, Bandini, & Nobile, 2012), the important role of sorptivity in evaluating materials durability is evident. Moreover, as a consequence of microstructural modifications induced by the above mentioned weathering processes, water absorption and sorptivity progressively increase with increas- ing weathering level (Franzoni, Sassoni, Scherer, & Naidu, 2013; Tug ˇrul, 2004), so that materials durability is progressively further threatened by high sorptivity, which becomes a consequence of degradation, in addition to being its cause. In the field of cultural heritage conservation, surface treatments for consolidation and protection are usually applied to improve materials durability (Amoroso & Fassina, 1983). These treatments have the effect of either partly occluding pores or altering http://dx.doi.org/10.1016/j.ijengsci.2014.05.013 0020-7225/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +39 0706755051; fax: +39 0706755067. E-mail address: giorgio.pia@dimcm.unica.it (G. Pia). International Journal of Engineering Science 82 (2014) 196–204 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci