Advances in Materials Science and Engineering

Volume 2016 (2016), Article ID 7853156, 10 pages

http://dx.doi.org/10.1155/2016/7853156

## Pore Size Distribution Influence on Suction Properties of Calcareous Stones in Cultural Heritage: Experimental Data and Model Predictions

Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Università degli Studi di Cagliari, Piazza d’Armi, 09123 Cagliari, Italy

Received 3 January 2016; Accepted 23 March 2016

Academic Editor: Michael Aizenshtein

Copyright © 2016 Giorgio Pia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Water sorptivity symbolises an important property associated with the preservation of porous construction materials. The water movement into the microstructure is responsible for deterioration of different types of materials and consequently for the indoor comfort worsening. In this context, experimental sorptivity tests are incompatible, because they require large quantities of materials in order to statistically validate the results. Owing to these reasons, the development of analytical procedure for indirect sorptivity valuation from MIP data would be highly beneficial. In this work, an Intermingled Fractal Units’ model has been proposed to evaluate sorptivity coefficient of calcareous stones, mostly used in historical buildings of Cagliari, Sardinia. The results are compared with experimental data as well as with other two models found in the literature. IFU model better fits experimental data than the other two models, and it represents an important tool for estimating service life of porous building materials.

#### 1. Introduction

Cultural heritage preservation is an important issue in Material Science field. The main damage causes of historical bricks, earth masonry, and stones are related to the circulation of water in their microstructures [1–3]. The water presence may be owing to several origins:* infiltrations from different parts of buildings* such as walls, roof, water, and sanitary systems;* atmospheric conditions* and* environmental events* such as high air relative humidity, rain, snow, flooding, hygroscopic salts, and capillary rise. Certainly, the latter represents the most common phenomenon, by which the water is conveyed within the microstructure of porous building materials [4, 5].

Indeed, capillary rise is involved in several damage processes, such as salt-crystallisation cycles [6], freezing-thawing cycles [7], dissolution of soluble fractions [8], biological decay [1], chemical attack in polluted environment [1], swelling of clays [9], and reduction of mechanical properties [10]. Consequent on these deteriorations of microstructures, the open porosity and the resulting capability of absorbing water are increased and material’s durability is further compromised.

The presence of damp walls as well as reduced durability of materials gives rises to uncomfortable indoor thermal-hygrometric conditions owing to the high values of air relative humidity and the lower thermal insulation performance [1].

In order to diminish the movement of water into the material’s microstructure, several surface treatments for consolidation and protection are usually applied. The results consist of the reduction of sorption properties by partly occluding pores or by altering material’s hydrophilic behaviour [11, 12].

Although consolidating and/or protective treatments reduce the kinematic of weathering, they should not arrest completely liquid water and water vapour flux between the material and the internal or external environment [13]. In fact, the possible presence of water or water vapours trapped behind a treated surface could represent a material damage cause (capillary overpressure, salt-crystallisation cycles, freezing-thawing cycles, etc.) [1, 14].

In this context, water sorptivity (), defined as water volume absorbed per unit surface area per square root time, results in a key parameter to evaluate the service life of porous building materials as well as of the entire building [1]. Water sorptivity test on stone is performed on regular samples (prisms or cylinders) in accordance with the Italian Guideline NORMAL 20/85 [15]. This test is very simple to perform in the laboratory, but it requires large quantities of materials in order to statistically validate the results. This fact is incompatible when the sorptivity is measured on materials from cultural heritage, which are subjected to specific and strict regulations for their safety. In these cases, only small and irregular samples may be withdrawn from historical buildings, but they do not have suitable dimensions to measure sorptivity coefficient. However, these small samples can be used to perform Mercury Intrusion Porosimetry (MIP) tests. The possibility to develop analytical procedure for indirect sorptivity valuation from MIP data would be highly beneficial. In this regard, in order to correlate sorptivity with properties of both liquid (density, surface tension, contact angle with material, and viscosity) and material (open porosity, average pore radius, and tortuosity), diverse models have been proposed [12, 16]. However, these modelling procedures are validated only for specific category of materials. Several applications have led to values generally different from the experimental data even by an order of magnitude [16].

Such difficulties in reproducing experimental data are probably owing to the extreme simplicity, with which the microstructure is described. These formulas take into account total open porosity, average pore size, and tortuosity by ignoring entire pore size range and pore size distribution, which generally have been studied much less [16, 17]. These characteristics influence the sorption phenomenon; for example, thinner pores absorb water slower than larger pores, but height of water rise is higher [12]. In this way, considering the only average pore size results in significant computational errors in sorptivity predictions, and it can only provide a rough description of complex systems such as real natural stones, which can have pores with different and varying size.

In order to elaborate a model procedure capable of predicting sorptivity values, the description of microstructure features must be taken into account. For this reason, fractal geometry results are of great interest. It has been formalised and developed during 1970s by Mandelbrot [18] that fractals are characterised by noninteger dimension (), intricate and fine structure, geometric construction based on iteration procedure, and self-similarity, which consists of structure configurations that are repeated at different scales [19].

Fractal characteristics have been recognised in a large number of forms in organic as well as inorganic systems of nature and even, more importantly, in several aspects of the microstructure of the materials [18, 19].

This fact has been found relevant to describe and predict different aspects of their macroscopic behaviour. For example, in cement and concrete materials, fractal geometry has been used to estimate the pore surface complexity as a function of the kneading water. The results have indicated that kneading water does not change the pore surface, but it is only responsible for the swelling of the structure [20]. It has also been demonstrated that hydrated cement pastes have highly irregular surfaces with fractal characteristics, which are responsible for the anomalies observed in vapour sorption experiments to determine surface area [21].

Moreover, a general model developed from fractal modelling of a porous medium was used in order to match experimental capillary pressure for the geyser rock [22]. It has been demonstrated that the heterogeneity of this rock-type can be evaluated quantitatively using the calculated fractal dimension [22]. An important application of fractal geometry to describe physical phenomena of porous materials has been conducted by Cai and his work group [23–25]. They described spontaneous imbibition of wetting liquid into porous media with an analytical fractal model, which take into account tortuosity effect [26, 27], finding a good agreement with experimental data. Recently, an Intermingled Fractal Units (IFU) model has been proposed to correlate structure and properties (thermal performance, mechanical behaviour, and water circulation into the microstructure) of several categories of materials: cement and concrete [28], ceramics [29, 30], earth based materials [31, 32], and stones [33, 34].

IFU model is characterised by a close correlation with porous microstructure, and it is also capable of reproducing nonfractal pore size distributions. This represents an important aspect as all microstructures cannot be considered being fractals. After microstructure reproduction, being fractals geometries analytically known, the model can lead back to mathematical expressions for calculating the physical properties.

In this paper, an IFU model has been proposed in order to predict sorptivity coefficient of porous materials used in cultural heritage. This approach facilitates evaluating water absorption without the necessity to have large quantities of materials. The experimental tests are carried out on calcareous stone, from quarries, commonly used in historical building of Cagliari (Sardinian). IFU calculated sorptivity coefficient has been compared with experimental data as well as with the results obtained by two other models. IFU model predictions are better in agreement with experimental data than the other models’ calculations reported in Scherer and Wheeler [12] and Raimondo et al. [16].

#### 2. Materials and Methods

The experimental investigation was carried out on a limestone from the quarries of Cagliari, popularly named Cantone stone. This stone, owing to easy availability and workability, has been widely used in this city for most of the popular and noble historical buildings. However, it is predominantly susceptible to atmospheric agents as well as to the effects of degradation caused by water.

For this study, three blocks of limestone (, , and ) of size were investigated. They have been withdrawn from different parts of the quarry for the evaluation of the heterogeneity of this stone.

Therefore, the tests were conducted on samples visibly free from damage and macroscopic fossils’ remains. Subsequently, the blocks were cut into cubes of 5 cm using a rotating diamond blade saw. Each block has been divided into ten samples (A1–A10, B1–B10, and C1–C10).

The porosity, cumulative pore volume curves, and relative pore size distribution are evaluated with the help of Mercury Intrusion Porosimetry Technique. The porosimeter is the Micrometrics AutoPore IV, which automatically records pressure, pore radius, intrusion volume, pore surface area, and bulk density.

The capillary absorption test was performed in accordance with UNI EN 15801 [35]. Before the test, the samples were dried in the ventilated oven at a temperature of 60°C for 24 hours until constant weight. Subsequently, the samples were exposed to the distilled water on one face by placing them on a pan over the sheets of filter paper, which is kept constantly wet. The samples, at regular time intervals, have been extracted from the pan, towel-dried, and weighed using a balance, and then the amount of water absorbed was calculated with respect to the cross section area of the specimens. The amount of water absorbed per unit area (mg/cm^{2}) at time (s) is calculated using , where (mg) is the mass of the specimen at time , (mg) is the mass of the dry specimen, and (cm^{2}) is the area of the sample in contact with the water.

The sorptivity () is the slope of the linear section of the curve obtained by plotting the mass change per area () versus the square root of time () and was determined by linear regression using at least 5 successive aligned points.

#### 3. Intermingled Fractal Units Model

The Intermingled Fractal Units model consists of different base units and filled surface, which represent the porous and the nonporous parts of the model, respectively. Obviously, base units are fractal geometric figures based on Sierpinski carpet outline. The most popular design of Sierpinski carpet is achieved by commencing from a square with sides, which are divided according to a factor () of 3, resulting in a figure consisting of 9 subsquares, out of which one is removed. The remaining 8 subsquares () are involved in a new iteration process, which replicates the same configuration. In this way, the sides of the 8 subsquares are divided by the same length scale factor () of 3, generating a further 9 subsquares, from which 1 is again removed. The number of iterations () may continue* ad infinitum*, but reproducing an experimental pore size distribution depends on the pore size range.

The analytical expression to calculate fractal dimension () of this Sierpinski carpet isThe number of subsquares removed as well as the number of iterating and noniterating (*solid forever*) subsquares generates new type of Sierpinski carpet with different and consequently with diverse pore volume fraction (), pore size distribution, pore surface, and so forth. Figure 1(a) shows a Sierpinski carpet with a single pore at first iteration and the repetition of this configuration at every successive iteration. Figure 1(b) exhibits Sierpinski carpet with a single pore at first iteration but, from the second iteration onwards, the subsquares present 5 iterating squares as well as 3* solid forever* squares.