10.6092/issn.1973-9494/1401
Sedimentary rocks are natural porous materials with a great percent of microscopic interconnected
pores: they contain fluids, permitting their movement on macroscopic scale. Generally, these rocks
present porosity higher then metamorphic rocks. Under certain points of view, this feature represents
an advantage; on the other hand, this can constitute an obstacle for cultural heritage applications,
because the porosity grade can lead to a deterioration of the lapideous monument for water
capillary absorption.
In this paper, CT (Computerized Tomography) image techniques are applied to capillary absorption
kinetics in sedimentary rocks utilized for the Greek temples as well as baroc monuments, respectively
located in western and southeastern Sicily. Rocks were sampled near the archaeological
areas of Agrigento, Segesta, Selinunte and Val di Noto. CT images were acquired at different times,
before and after the water contact, using image elaboration techniques during the acquisition as well
as the post-processing phases. Water distribution into porous spaces has been evaluated on the
basis of the Hounsfield number, estimated for the 3-D voxel structure of samples. For most of the
considered samples, assumptions based on Handy model permit to correlate the average height of
the wetting front to the square root of time. Stochastic equations were introduced in order to
describe the percolative water behavior in heterogeneous samples, as the Agrigento one.
Before the CT acquisition, an estimate of the capillary absorption kinetics has been carried out by
the gravimetric method. A petrographical characterization of samples has been performed by stereomicroscope
observations, while porosity and morphology of porous have been surveyed by SEM
(Scanning Electron Microscope) images. Furthermore, the proposed methods have also permitted
to define penetration depth as well as distribution uniformity of materials used for restoration and
conservation of historical monuments.
application/pdf
1973-9494
1401
en
Fortunato Sorrentino
Conservation Science in Cultural Heritage
Study of capillary absorption kinetics by X-ray CT imaging techniques: a survey on sedimentary rocks of Sicily
Text.Serial.Journal
https://conservation-science.unibo.it/
8
Articles
2009-04-17
2008-04-17
2015-11-02
91-110
CSCH
Fortunato Sorrentino
2008
10.6092/issn.1973-9494/1401
91
1973-9494
en
110
Study of capillary absorption kinetics by X-ray CT imaging techniques: a survey on sedimentary rocks of Sicily
https://conservation-science.unibo.it/article/download/1401/770
8
S
    TUDY OF CAPILLARY ABSORPTION KINETICS BY X-RAY CT
    IMAGING TECHNIQUES: A SURVEY ON SEDIMENTARY ROCKS
    OF SICILY·

Tiziano Schillaci *, Maria Brai, Antonio Cimino
Dipartimento di Fisica e Tecnologie Relative
Università degli Studi di Palermo, Italy
Antonio Lo Casto, Fortunato Sorrentino
Dipartimento di Biotecnologie Mediche e Medicina Legale
Università degli Studi di Palermo, Italy




1. Introduction

    The knowledge of capillary absorption kinetics in porous materials represents a fun-
damental aspect in recovery and conservation of Cultural Heritage. Capillary absorption
in sedimentary rocks is the consequence of different attraction forces between pore wall
and fluid, with a resultant upwards tracking force. Rates of the advance front inside the
pores can be described by both diffusive and frontal advance equations, depending on
validity of the reliable assumptions. In the first case, the diffusion coefficient is propor-
tional to the partial derivative of capillary pressure as regards water saturation; further-
more, calculated displacements are essentially of diffusive kind (percolative behavior).




                                                                                                     Conservation Science in Cultural Heritage, 8/2008
    The second case considers the wetting front rate to be proportional to capillary pres-
sure gradients as the distance, taking into account flat advance fronts (piston like dis-
placement). This phenomenon mainly depends on rock permeability, porosity, wetting
tendency and interface tension between intrinsic phase (air/water steam biphasic blend)
inside the pores and imbibition phase (advancing water).
    Basic assumptions are that the capillary forces overcome the floating and viscous
ones and that the movements take vertically place upwards. Water volume variations in
sedimentary rock pores, due to different temperature conditions (daily as well as sea-
sonal), in addition to chemical reactions with pollutants transported by fluids (air and
water) inside the porous space of sedimentary rocks, lead with the time to the deteriora-


· BCNanoLAb – APQ, POR Sicilia.
  Project leader: Prof. P. Livreri.
* Author for correspondence (tschillaci@difter.unipa.it).


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T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                     Figure 1. Geographic location of the most known Greek temples in the Western
                                                                                                     sector of Sicily. Baroc Val di Noto area is placed in the South-Eastern corner of
                                                                                                     the Island.

                                                                                                 tions of materials. Studies exposed in the present paper deal with sedimentary rocks
                                                                                                 used for building the Greek temples in the archaeological sites of Agrigento, Segesta,
                                                                                                 Selinunte as well as for the Baroc buildings in the Sicilian Val di Noto area [1].
                                                                                                    Fig. 1 shows the geographic location of the considered archaeological areas.
                                                                                                    CT (Computerized Tomography) scanning results [2], referred to samples relevant to
                                                                                                 the above situated archaeological quarries, allow us to state the rule of average height
                                                                                                 variations of wetting front in Val di Noto porous rocks. This behavior can be illustrated by
                                                                                                 a flat pattern based on the Handy model [3]. The same assumptions are valid for the
                                                                                                 samples coming from the archaeological areas of Selinunte and Segesta. In fact, these
                                                                                                 specimens are homogeneous enough, at least at the resolution scale of CT scanning (a
                                                                                                 tenth of millimeter). On the contrary, sedimentary rock, pertaining to the quarries of the
                                                                                                 archaeological area of Agrigento, presents a relatively great heterogeneity as regards the
                                                                                                 other samples. This is the reason for which the wetting front variation can be schema-
                                                                                                 tized by a stochastic law as the Langevin one [4]. In this model a stochastic term, denom-
                                                                                                 inated “quenched disorder”, describes the heterogeneity of the material [5].

                                                                     92
   In order to protect cultural heritage against the adsorbed capillary water into the lapi-
deous materials, hydrorepellent and consolidating materials are used to permit a possi-
ble restoration of the damaged structures. Imaging techniques, by CT scanning, permit
to evaluate the performances of protecting test products.

2. Principles of capillary absorption

   The capillary absorption is a typical phenomenon of porous media, strongly connected
with the interfacial wettability regarding two surfaces and governed by the Washburn law.
The capillary absorption in a porous material occurs only in case of wettability and, of course,
when the structure is not entirely immersed in the water (porous could be full). Capillary
absorption can be minimized or reduced by means of a hydrophobic substance. In the next
paragraphs, the most important parameters linked to capillary absorption phenomenon as
well as related noticeable models and approaches will summarily be described.

2.1. Imbibition

   The imbibition is expressed as the movement of a fluid from a porous medium for the
action of another fluid, as a consequence of the sole capillary forces.
   In the past, various differential equations have been proposed for describing the air
displacement due to the water imbibition process, but these equations are not analytical-
ly resolvable [6]. Nevertheless, approximate solutions for water-air imbibition have been
found, leading towards the derivate of an equation describing the piston advance of the
wetting front, based on the assumptions of the Handy model.

2.2. Handy model

   The Darcy law states the efflux velocity of a fluid with µ viscosity through a porous            Conservation Science in Cultural Heritage
media v(z) (or the discharge Q(Z) = v(z) ⋅ A). In detail, the Darcy law is defined by this
well-known relation:



where

        = hydraulic gradient

   φ = z + ψ = total piezometric head
   z = gravitational head
   ψ = suction head.

                                                                                                   93
                                                                                                     The proportionality constant K is called hydraulic conductivity: it can be considered as
                                                                                                 a measure of movement capability of water into a porous space. This coefficient depends
                                                                                                 on the fluid parameters (that is viscosity, density) as well as on the pore parameters of
                                                                                                 the medium (that is dimension, shape, tortuosity, specific surface, porosity, saturation
                                                                                                 grade). In particular, if the saturation S increases, also K augments; if S → 1 ⇒ K → Ks,
                                                                                                 where Ks expresses the hydraulic conductivity in saturation state.
                                                                                                     In a number of cases, the imbibition rate is analogous to the capillary rise in a porous
                                                                                                 medium. From this analogy, fundamental assumptions are:
                                                                                                 •   water penetrates by a piston advance;
                                                                                                 •   pressure gradient of the gaseous phase, above the wetting front, can be neglected.
                                                                                                     In the vertically upwards imbibition, the efflux velocity depends on water permeability
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 and viscosity, gravity acceleration, water/air density difference and wetting front position,
                                                                                                 the capillary pressure being considered constant.
                                                                                                     In the kinetics of a capillary tube, sorptivity acquires a notable importance. It is defined
                                                                                                 as the tendency of a porous medium to absorb or desorb a liquid by capillarity, and it is
                                                                                                 mathematically illustrated as the cumulative infiltration at time t. In general, this parame-
                                                                                                 ter roughly expresses the described phenomena when saturation gradients occur.
                                                                                                 Nevertheless, the here considered data, pertinent to the rock samples of Val di Noto area,
                                                                                                 satisfy the assumption to retain the gravitational forces lower than the capillarity ones. On
                                                                                                 the other hand, data relevant to Agrigento area exhibit a different behavior, due to the
                                                                                                 greater heterogeneity of the material (assigned as “quenched noise”), as it will be high-
                                                                                                 lighted in the successive paragraphs.

                                                                                                 2.3. Percolation

                                                                                                     The capillary water adsorption in a porous medium can be described by the percola-
                                                                                                 tion theory, for which the dynamic process of imbibition simulates the movement of a fluid
                                                                                                 caused by another one. When the water comes in contact with a porous medium, the
                                                                                                 capillary forces overcome the viscous forces: so, the process dynamics are determined
                                                                                                 by the local radium r of the pore. The capillary forces are greater in narrowest porous
                                                                                                 necks. This fact is consistent with experimental observations in order to depict displace-
                                                                                                 ments as a series of discreet time jumps, where water expels the air from the smallest
                                                                                                 available porous.

                                                                                                 2.4. Stochastic approach to the efflux in a porous medium
                                                                                                     The fluid efflux in porous medium is a classic experimental result of the non-equilibri-

                                                                94
um motion of an interface in a disordered environment. In a typical case, a d-dimension-
al self-affine interface characterized by h(x, t) height, moves in a disordered (d + 1) dimen-
sional medium. In literature, two main classes of disorder have been discussed. The for-
mer, called thermal or “annealed”, depends only on time. The latter, assigned as
“quenched”, is connected with the medium. The presence of the “quenched” disorder per-
mits an analogy with the critical phenomena, describing two classes of universality [7].
   The continuous interface motion needs the application of a push force F. A critical
value Fc takes place so that – for F < Fc – the interface will be blocked by the disorder
after a certain time t. For F > Fc , interface moves indefinitely with a constant v velocity.
This means that the push motion of a corrugated interface in a disordered medium can
be considered as a transition phase, called “depinning transiton” [8, 9, 10].
   A universality class is described by a Langevin type non linear equation, given by
Kardar-Parisi-Zhang equation [11], in which various characterizing parameters are
involved. In particular, a “quenched noise” term depicts the corrugation effect of the surface.
   A second universality class is described by a more simple Langevin-type equation,
given by the Edward-Wilkinson equation [12], For a number of different models [8, 9]
belonging to the second universality class – referred as isotropic growth – the “depinning
transition” coefficient of the Kardar-Parisi-Zhang equation can be λ = 0 or λ → 0.
   For a better understanding of the above illustrated phenomenon, a square network is
considered with L side and periodical contour conditions along the L direction, as shown
at the left in fig. 2, instead the right part of the same figure reports the corrugation of the
wetting front as a consequence of the “quenched noise”, in the Agrigento” sample.



                                                                                                   Conservation Science in Cultural Heritage




Figure 2. Left image shows the formation of the corrugated wetting interface. White, dark
and gray squares refer respectively to non-blocked dry cells, to blocked dry cells and to
wet cells. Right image exhibits the corrugated wetting profile as a consequence of the
“quenched noise” in the Agrigento sample.

                                                                                                  95
                                                                                                    To every I cell of the side, a uncorrelated random number is assigned, that is the ηi
                                                                                                 disorder, with uniformly distributed amplitude in the [0,1] range. The role of ηi is to model
                                                                                                 the “random pinning” forces generated by the disorder. Now, the “pinning” forces are com-
                                                                                                 pared with the F push force, where 0    ≤ F ≤ 1. If the “pinning” forces in a definite cell is
                                                                                                 greater than the push force, then the cell is well recognized as “blocked”, otherwise it is
                                                                                                 identified as “non-blocked”.
                                                                                                    Considering that this model has been developed for imbibition studies, the “invading”
                                                                                                 region is considered as “wet”, instead the “invaded” region as “dry”.
                                                                                                    At t = 0 time, all the cells of the first row below in the network are wetted. Then, a col-
                                                                                                 umn was randomly selected and all the “unblocked” cells, pertaining to the column near-
                                                                                                 est to the wet cell, are wetted. Besides, a rule is imposed that all the dry “blocked” cells
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 under a wet cell become wetted, calling it “rule of overlying erosion”.
                                                                                                    A “pinning cluster” is defined as any group of blocked cells connected with the near
                                                                                                 or quite near groups delimiting blocked cells. Any “pinning cluster”, the linear dimension
                                                                                                 of which is lower than the system size, can not prevent from the interface advance.
                                                                                                    Indeed, every “pinning cluster” – that does not expand the system – will eventually be
                                                                                                 circumscribed by the invading fluid, because the invading front can move only around
                                                                                                 finite “obstacles” and the overlying erosion rule states that – after encircled – the “pinning
                                                                                                 clusters” become wet. Lastly, when the “pinning” forces overcome the push forces – or
                                                                                                 when the “pinning clusters” have expanded the whole sample length – the wetting front
                                                                                                 is stopped with the front corrugation effect.

                                                                                                 3. Experimental section
                                                                                                 3.1. Materials and methods
                                                                                                    Surveys have been carried out on samples coming from quarries of the archaeologi-
                                                                                                 cal areas of Agrigento, Segesta, Selinunte and Val di Noto area, in Sicily. Samples were
                                                                                                 cut in cubic shape, with 50 mm side. After a warming at 65 °C for a week in a “muffle”
                                                                                                 oven, samples were subjected to a successive cooling, up to environmental temperature,
                                                                                                 for three hours in a drier, with the aim to remove any humidity trace.
                                                                                                    An appropriate plexiglas container was designed to hold in continuous contact the
                                                                                                 sample bottom with water. This container is illustrated in fig. 3. Continuous supply of
                                                                                                 water, with the aim to maintain fixed its level, is guaranteed by a small pump and a tube
                                                                                                 system for the exceeding inlet-outlet water. Various samples have been arranged for
                                                                                                 every origin site. CT images, constituted by 60 different slices 0.625 thick, have been per-
                                                                                                 formed over every sample.

                                                                 96
            Figure 3. Picture of the plexiglas container with the positioned
            sample. In this case, prospected rock comes from Agrigento area.
            Inlet and outlet tubes of water are also shown. A small thickness,
            carved by the cutter in the sample, guarantees the contact
            between a constant water level and the bottom of the sample.


   CT images have been acquired by means a computerized tomography instrument
multislice Philips Brilliance 40 (Philips Medical Systems, Eindhoven, The Netherlands). In
fig. 4, the CT tomography is shown together with the experimental apparatus used for the
imaging acquisition.


                                                                                              Conservation Science in Cultural Heritage




         Figure 4. A schematic picture of the CT computerized multislice tomog-
         raphy with the experimental apparatus used for the sample imbibition.

                                                                                             97
                                                                                                    The voltage of the electronic tube was fixed to 120 kV value and the current to 600
                                                                                                 mA, with the aim to guarantee the maximum penetration of X-rays and a good imaging
                                                                                                 quality. During imaging acquisition and post-processing, a bone filter was used. Besides
                                                                                                 the contact with water, the time-recorded images, before and after the treatment with pro-
                                                                                                 tective materials, have been utilized for the evaluation of water distribution within the
                                                                                                 porous spaces.
                                                                                                    Hounsfield unit is used in CT radiology applications [13]; this is defined by the follow-
                                                                                                 ing equation:
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 where µvoxel, µair e µwater are the absorption linear coefficients of X-rays for – respective-
                                                                                                 ly – the generic considered voxel, the air and the water. In this way, it is possible to set-
                                                                                                 tle the scale of Hounsfield values. According to this representation, if the voxel is filled of
                                                                                                 water, the Hounsfield value is –1000 and assumes zero for water. In this scale, the corti-
                                                                                                 cal bone, for example, assumes the value of about +1000.
                                                                                                    A schematic illustration of the Hounsfield scale is showed in fig. 5.
                                                                                                    Due to the essentially carbonate origin of the sampled rocks, the average value of the
                                                                                                 Hounsfield number results occurs – in the considered region of interest (ROI) – in the 900
                                                                                                 ÷ 1400 range, depending on density and heterogeneity presented by samples. The aim
                                                                                                 is to calculate the different values of the Hounsfield number for every voxel relevant to all
                                                                                                 the slices, in both dry and wet conditions and at different contact times with water.
                                                                                                    In the imbibition process, water expels the air from the porous spaces, with a conse-
                                                                                                 quent increase of X-rays absorption as well as of the Hounsfield number. Being the
                                                                                                 dimension of any image of 512 × 512 pixels, size of any voxel results 0.35 mm × 0.35
                                                                                                 mm, with a 0.625 mm thickness.
                                                                                                    By recording the Hounsfield values for every voxel, a matrix of scalar values A(Hi,j tk)
                                                                                                 is obtained for every slice, in such a way permitting a 3-D representation of the dynamic
                                                                                                 evolution of the wetting front within the porous spaces of the sedimentary rock. Measures
                                                                                                 have been repeated, in the same conditions, after a treatment with hydrophobic products.




                                                                                                         Figure 5. Scale of Hounsfield values.

                                                                98
An estimation of the time acquisition for CT imaging has been executed by means of the
gravimetric method, carried out according to UNI 10859 standard (determination of water
absorption by capillarity). As a result of the carried out measurements, the sample com-
ing from the archaeological area of Selinunte showed very speed kinetics of capillary
absorption. An opposite behavior was exhibited by the sample relevant to the Alcamo
site. Samples of Agrigento and Val di Noto showed intermediate temporal kinetics: in
detail, the Agrigento sample displayed a greater velocity of absorption. In order to opti-
mize the CT acquisition measurements, because the used apparatus were located in a
hospital unit, measures were executed only on the Agrigento and Val di Noto samples. A
further study on morphology of pores has been carried out by a stereomicroscope and by
a scanning electronic microscope (SEM).

3.2. Results

   The petrography features of sedimentary rock samples, considered in this paper, are
reported in tab. 1.
   Fig. 6 illustrates pictures of sample fragments and images given by SEM microscope,
executed at two different observation scales.
   The SEM images of Agrigento and Selinunte are shown, respectively at center and at
right – at 100 µm and 30 µm observation scales. Instead, SEM images of Val di Noto and
Segesta are related to 30 µm e 3 µm respectively. In particular, the SEM image of the
Agrigento sample exhibits a small shell with 2 µm size. These images confirm the notable
heterogeneity of the Agrigento rock as regards the other more homogeneous samples,
when observed at the observation scale of the CT resolution (a tenth of millimeters).
Furthermore, the same Agrigento sample offers also the presence of shells of consider-
able size as well as of pebbles of the same magnitude order. These examinations will             Conservation Science in Cultural Heritage
reveal, as it will be detailed below, a different behavior of the wetting front motion in the


Table 1. Petrography features of rock samples.




                                                                                                99
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 Figure 6. The left column shows – up to down – images of sedimentary rock samples
                                                                                                 coming from the archaeological areas of Agrigento, Selinunte, Val di Noto and Segesta.
                                                                                                 The successive right columns represent images obtained by the SEM microscope at two
                                                                                                 different observation scales.

                                                                                                 various samples, being possible to propose the piston motion, based on the Handy
                                                                                                 hypotheses, for the Selinunte, Segesta and Val di Noto samples. The Agrigento sample,
                                                                                                 in consideration of its considerable heterogeneity, does not present a piston motion
                                                                                                 behavior, but it suggests a stochastic approach based upon the percolation theory.
                                                                                                    A first evaluation of the capillary absorption kinetics for any kind of sedimentary rock
                                                                                                 has been proposed by means of the gravimetric method executed according to the UNI
                                                                                                 10859 normative. Fig. 7 shows the water quantity Qi adsorbed, for surface unit
                                                                                                 (expressed in milligrams to square centimeters), by the test specimen at ti time and in
                                                                                                 function of the square root of time.

                                 100
Figure 7. Capillarity index Qi for samples coming from Val di Noto (at left) and Agrigento
(at right).

   Four samples have been prepared for every kind of rock; they have been weighed in
dry as well as in wetting conditions at different contact times with water, up to saturation.
   The time sequence of the X-Ray CT image acquisitions is reported in tab. 2.
   After the CT image acquisition, matrices of scalar values A(Hi,j tk), obtained for every
slice, have been elaborated by MATLAB software. Fig. 8 shows the false color images in
Hounsfield units: they exhibit the variations of Hounsfield number with the capillary water
invasion into porous spaces. In particular, images shown in the same figure are related
to the middle slice of the Val di Noto sample.
   Fig. 9 shows a comparison among the images of the last column of fig. 8 and the rel-           Conservation Science in Cultural Heritage
evant CT images at 256 grey-scale.


Table 2. Time sequence of the X-Ray CT image acqusitions (seconds) relevant to the
Agrigento and Val di Noto samples.




                                                                                                101
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 Figure 8. The water imbibition in the sedimentary rock (Noto sample) is shown through
                                                                                                 the variations of the Hounsfield number in the CT images. The first upper image (at left)
                                                                                                 is related to dry conditions, the other ones are related to images acquired at different con-
                                                                                                 tact times with water and with a temporal sequence equal to 120, 240, 360, 900, 1320,
                                                                                                 2100, 3300 and 5100 seconds.


                                                                                                    The lower part of samples reveals a greater absorption of X-rays as regards the
                                                                                                 medium part, due to the greater upwards absorption of capillarity water. The best fitting
                                                                                                 of the obtained data confirms the good agreement with the Handy model (see above
                                                                                                 equation), as reported in fig. 10.
                                                                                                    Fig. 11 presents the false color images in Hounsfield units for the central slide of the
                                                                                                 Agrigento sample.
                                                                                                    In fig. 12, the comparison among the images of the last column of fig. 11 relevant
                                                                                                 to the time sequences 90, 600, 1470 seconds and the corresponding CT images at
                                                                                                 256 grey-scale shows that – in this case – it is not possible to correlate the wetting
                                                                                                 front advance with a law describing a piston type displacement. Indeed, the hetero-

                                        102
Figure 9. A comparison is illustrated among the false color images obtained by MATLAB
procedure and the corresponding CT images at 256 grey-scale.




                                                                                              Conservation Science in Cultural Heritage


Figure 10. Best fitting of
data with the Handy
model.


geneity of the material causes an excessive corrugation of the wetting front. This per-
mits to conclude that, for this typology of materials, the imbibition process can be
described by the percolation theory. The Kardar-Parisi-Zhang equation well agrees
with the description of dynamic evolution of the wetting front for this typology of mate-
rial.

                                                                                            103
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 Figure 11. The water imbibition in the sedimentary Agrigento rock sample is shown
                                                                                                 through the Hounsfield number variations in CT images. The first upper image (at left) is
                                                                                                 referred to dry condition, the other ones are related to the images acquired at different
                                                                                                 contact times with water, and with a temporal sequence equal to 30, 90, 180, 300, 600,
                                                                                                 780, 1200 and 1470 seconds.



                                                                                                    3-D representation methods, as surface contour lines, allow us to evaluate penetra-
                                                                                                 tion and distribution uniformity of hydrophobic products used like hydrorepellent, consol-
                                                                                                 idant materials in the restoration and conservation of historical lapideous monuments. In
                                                                                                 particular, fig. 13 exhibits a couple of 3-D surface contour lines related to the Agrigento
                                                                                                 sample.
                                                                                                    The left part of this figure shows the 3-D surface contour line relevant to the Agrigento
                                                                                                 non treated sample. The right part is referred to the same sample treated with an ethyl
                                                                                                 silicate (Rodhorsil RC 90). Images have been elaborated by MIRATM software, using a
                                                                                                 threshold Hounsfield value of +900.


                                   104
Figure 12. A comparison is shown among the false color images obtained by MATLAB
elaboration and the corresponding ones at 256 grey-scale.




                                                                                               Conservation Science in Cultural Heritage




Figure 13. The left part of this figure shows the 3-D surface contour line relevant to the
Agrigento non treated sample. The righ part is referred to the same sample treated with
an ethyl silicate (Rodhorsil RC 90).


                                                                                             105
                                                                                                 4. Conclusions

                                                                                                    The outcomes of this paper confirm the validity of CT imaging techniques for detailed
                                                                                                 studies of capillary kinetics of water absorption in sedimentary rocks. The motion of the
                                                                                                 wetting front in a porous medium is described by stochastic equations of Langevin-type.
                                                                                                 Furthermore, under certain assumptions (Handy model), it is possible to correlate the
                                                                                                 average height of the wetting front by a relatively simple law exhibiting a dependence by
                                                                                                 the square root of time. Evaluations of the Hounsfield number in a voxel matrix and MAT-
                                                                                                 LAB processing permit to define the kinetic evolution of the wetting front into the porous
                                                                                                 medium.
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                    3-D images show the dynamic evolution of the wetting front as well as the distribution
                                                                                                 into porous spaces of hydrophobic, consolidant products used for the protection and con-
                                                                                                 servation of lapideous historical works. The use of diagnostic medical techniques in cul-
                                                                                                 tural heritage studies, supported by specific data processing, appears to be promising for
                                                                                                 characterizing and analyzing the protective effects on the involved materials.
                                                                                                 Furthermore, the obtained experimental results permit to validate the solving of complex
                                                                                                 differential equations as the Kardar-Parisi-Zhang stochastic equation: this describes the
                                                                                                 percolative behavior of water in heterogeneous media as the sample coming from the
                                                                                                 archaeological area of Agrigento.

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Summary
Sedimentary rocks are natural porous materials with a great percent of microscopic interconnected
pores: they contain fluids, permitting their movement on macroscopic scale. Generally, these rocks
present porosity higher then metamorphic rocks. Under certain points of view, this feature repre-
sents an advantage; on the other hand, this can constitute an obstacle for cultural heritage applica-
tions, because the porosity grade can lead to a deterioration of the lapideous monument for water
capillary absorption.
In this paper, CT (Computerized Tomography) image techniques are applied to capillary absorption
kinetics in sedimentary rocks utilized for the Greek temples as well as baroc monuments, respec-
tively located in western and southeastern Sicily. Rocks were sampled near the archaeological
areas of Agrigento, Segesta, Selinunte and Val di Noto. CT images were acquired at different times,       Conservation Science in Cultural Heritage
before and after the water contact, using image elaboration techniques during the acquisition as well
as the post-processing phases. Water distribution into porous spaces has been evaluated on the
basis of the Hounsfield number, estimated for the 3-D voxel structure of samples. For most of the
considered samples, assumptions based on Handy model permit to correlate the average height of
the wetting front to the square root of time. Stochastic equations were introduced in order to
describe the percolative water behavior in heterogeneous samples, as the Agrigento one.
Before the CT acquisition, an estimate of the capillary absorption kinetics has been carried out by
the gravimetric method. A petrographical characterization of samples has been performed by stere-
omicroscope observations, while porosity and morphology of porous have been surveyed by SEM
(Scanning Electron Microscope) images. Furthermore, the proposed methods have also permitted
to define penetration depth as well as distribution uniformity of materials used for restoration and
conservation of historical monuments.


Riassunto
Le rocce sedimentarie naturali sono materiali porosi con una grande frazione di pori microscopici e

                                                                                                        107
                                                                                                 fra loro interconessi, che contengono fluidi e permettono il loro trasporto su dimensioni macrosco-
                                                                                                 piche. In generale esse si presentano maggiormente tenere rispetto alle rocce metamorfiche. Sotto
                                                                                                 certi punti di vista questa caratteristica costituisce un vantaggio; d’altra parte, questo può essere un
                                                                                                 inconveniente per applicazioni nei beni culturali, poiché il grado di porosità può condurre al dete-
                                                                                                 rioramento del monumento lapideo per assorbimento capillare di acqua.
                                                                                                 In questo lavoro, sono presentate tecniche di immagine TC applicate allo studio delle cinetiche di
                                                                                                 assorbimento capillare in rocce sedimentarie siciliane utilizzate nella costruzione dei templi Greci
                                                                                                 della Sicilia occidentale e dei monumenti storici del periodo barocco della Sicilia sud-orientale. Le
                                                                                                 rocce sono state campionate in cave nelle prossimità delle aree archeologiche di Agrigento,
                                                                                                 Segesta, Selinunte e della Val di Noto. Sono state acquisite immagini TC a tempi differenti, prima e
                                                                                                 dopo il contatto con acqua, usando tecniche di elaborazione delle immagini, sia in fase di acquisi-
                                                                                                 zione che di post-processing. La distribuzione dell’acqua all’interno degli spazi porosi è stata valu-
                                                                                                 tata sulla base del numero di Hounsfield stimato sulla struttura 3-D a voxel dei campioni. Per la
                                                                                                 maggior parte dei campioni considerati, assunzioni basate sul modello di Handy permettono di cor-
                                                                                                 relare l’altezza media del fronte di bagnamento alla radice quadrata del tempo. Equazioni di tipo
                                                                                                 stocastico sono state introdotte per descrivere il comportamento percolativo dell’acqua in campioni
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




                                                                                                 eterogenei, quale è quello di Agrigento. Prima delle acquisizioni TC, una valutazione delle cinetiche
                                                                                                 di assorbimento capillare è stata eseguita mediante il metodo gravimetrico. Una caratterizzazione
                                                                                                 petrografia dei campioni è stata effettuata mediante osservazioni allo stereomicroscopio e conside-
                                                                                                 razioni sulla porosità e morfologia dei pori sono state eseguite mediante l’esecuzione di immagini
                                                                                                 al microscopio SEM. Il metodo proposto permette inoltre la determinazione della profondità di pene-
                                                                                                 trazione e della uniformità di distribuzione dei materiali usati per il restauro e la conservazione di
                                                                                                 monumenti storici.


                                                                                                 Résumé
                                                                                                 Les roches sédimentaires naturelles sont des matériaux poreux avec une grande fraction de pores
                                                                                                 microscopiques et interconnectés entre elles, qui contiennent des fluides et permettent leur
                                                                                                 transport sur des dimensions macroscopiques. En général, elles se présentent plus tendres par rap-
                                                                                                 port aux roches métamorphiques. Sous certains points de vue, cette caractéristique constitue un
                                                                                                 avantage; d’autre part, ceci peut être un inconvénient pour des applications dans les biens cultu-
                                                                                                 rels, puisque le grade de porosité peut conduire à la détérioration du monument pierreux par
                                                                                                 absorption capillaire d’eau.
                                                                                                 Dans cet ouvrage, sont présentées des techniques d’image TC appliquées à l’étude des cinétiques
                                                                                                 d’absorption capillaire en roches sédimentaires siciliennes utilisées dans la construction des tem-
                                                                                                 ples Grecs de la Sicile occidentale et des monuments historiques de la période baroque de la Sicile
                                                                                                 sud-orientale. Les roches ont été échantillonnées dans des gorges dans les environs des zones
                                                                                                 archéologiques d’Agrigente, Ségeste, Sélinonte et de Val di Noto. Des images TC à temps diffé-
                                                                                                 rents, avant et après le contact avec l’eau, ont été acquises, en utilisant des techniques d’élabora-
                                                                                                 tion des images, tant en phase d’acquisition que de post-processing. La distribution de l’eau à l’in-
                                                                                                 térieur des espaces poreux a été évaluée sur la base du nombre de Hounsfield estimé sur la struc-
                                                                                                 ture 3-D à voxel des échantillons. Pour la majeure partie des échantillons considérés, des suppo-
                                                                                                 sitions basées sur le modèle de Handy permettent de corréler la hauteur moyenne du front de
                                                                                                 mouillement à la racine carrée du temps. Des équations de type stochastique ont été introduites
                                                                                                 pour décrire le comportement percolatif de l’eau dans des échantillons hétérogènes, tel celui
                                                                                                 d’Agrigente. Avant les acquisitions TC, une évaluation des cinétiques d’absorption capillaire a été
                                                                                                 effectuée moyennant la méthode gravimétrique. Une caractérisation pétrographique des échan-
                                                                                                 tillons a été effectuée moyennant des observations au stéréomicroscope et des considérations sur
                                                                                                 la porosité et la morphologie des pores ont été effectuées moyennant la réalisation d’images au
                                                                                                 microscope SEM. La méthode proposée permet, en outre, la détermination de la profondeur de
                                                                                                 pénétration et de l’uniformité de distribution des matériaux employés pour la restauration et la
                                                                                                 conservation de monuments historiques.


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Zusammenfassung
Die natürlichen Sedimentgesteine sind poröse Materialien mit einem großen Teil von mikroskopi-
schen und mit einander verbundenen Poren, die Flüssigkeiten enthalten und die solche
Flüssigkeiten auf makroskopischer Ebene transportieren. Normalerweise sind sie weicher als meta-
morphe Gesteine. Dieses Merkmal kann in gewisser Hinsicht Vorteile mit sich bringen aber kann
auch einen Nachteil für die Anwendungen in Kulturgütern darstellen, weil der Grad der Porosität
das Verderben des Monuments aus Stein wegen der kapillaren Wasserabsorption verursachen
kann.
In dieser Schrift werden TC Bilder- Techniken für die Studie zu den Kinetiken der kapillaren
Absorption in sizilianischen Sedimentgesteinen vorgestellt, die für den Bau von griechischen
Tempeln im westlichen Teil von Sizilien und für den Bau von historischen Monumenten der
Barockzeit im südöstlichen Teil von Sizilien verwendet wurden. Die Proben aus den Steinen wurden
in den Steinbrüchen in der Nähe der Ausgrabungsstätten von Agrigento, Segesta, Selinunte und
des Val di Noto genommen. Es wurden TC- Bilder zu verschiedenen Zeitpunkten aufgenommen,
bevor und nachdem die Steine mit Wasser in Kontakt gekommen waren, dabei wurden Techniken
für die Verarbeitung von Bildern angewendet, sowohl während der Aufnahme als auch in der Post-
Processing-Phase. Die Wasserverteilung in den porösen Räumen wurde durch die Hounsfieldzahl
bewertet, auf der Basis der 3-D Voxel-Struktur der Muster. Für die meisten bewerteten Muster
ermöglichen Aufnahmen auf der Basis des Modells “Handy”, die Mittelhöhe der
Durchfeuchtungsgrenze mit der Quadratwurzel der Zeit in Korrelation zu bringen.
Es wurden stochastische Gleichungen verwendet, um die Perkolation des Wassers in heterogenen
Mustern zu beschreiben, wie zum Beispiel im Muster von Agrigento. Vor den TC-Aufnahmen wur-
den die Kinetiken der kapillaren Absorption durch die gravimetrische Methode bewertet. Die petro-
graphische Charakterisierung der Muster erfolgte durch Beobachtungen durch ein Stereomikroskop
und die Porosität und die Morphologie der Poren wurden mithilfe von Bildern durch das SEM-
Mikroskop bewertet. Außerdem ermöglicht es die vorgeschlagene Methode, die Tiefe des
Eindringens und die Gleichmäßigkeit der Verteilung der Materialien festzustellen, die für die
Restaurierung und die Erhaltung von historischen Monumenten angewendet werden.


Resumen
Las rocas sedimentarias naturales son materiales porosos con una gran fracción de poros micros-
cópicos interconectados entre sí, que contienen fluidos y permiten su transporte en dimensiones
macroscópicas. En general se presentan más blandas que las rocas metamórficas. Bajo ciertos
puntos de vista, esta característica constituye una ventaja; por otra parte, eso puede ser un incon-
veniente para aplicaciones en los bienes culturales, ya que el grado de porosidad puede conducir         Conservation Science in Cultural Heritage
al deterioro del monumento lapídeo por absorción capilar de agua.
En este trabajo se presentan técnicas de imagen TC aplicadas al estudio de las cinéticas de absor-
ción capilar en rocas sedimentarias sicilianas utilizadas en la construcción de los templos Griegos
de Sicilia occidental y de los monumentos históricos del período barroco de la Sicilia sudoriental.
Las muestras de las rocas se han recogido en canteras en las inmediaciones de las áreas arqueo-
lógicas de Agrigento, Segesta, Selinunte y el Val di Noto. Se han tomado imágenes TC en momen-
tos distintos, antes y después del contacto con el agua, usando técnicas de elaboración de las imá-
genes, tanto durante la fase de adquisición como durante el post-procesado. La distribución del
agua dentro de los espacios porosos se ha evaluado a partir del número de Hounsfield estimado
en la estructura 3-D en voxel de las muestras. En la mayor parte de las muestras consideradas, las
estimaciones basadas en el modelo de Handy permiten correlacionar la altura media del frente de
humectación con la raíz cuadrada del tiempo. Se han introducido ecuaciones de tipo estocástico
para describir el comportamiento percolativo del agua en muestras heterogéneas, como en las de
Agrigento. Antes de las tomas TC, se ha efectuado una evaluación de las cinéticas de absorción
capilar mediante el método gravimétrico. Se ha efectuado una caracterización petrográfica de las


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                                                                                                 muestras mediante una observación con estereomicroscopio; también se han tomado imágenes
                                                                                                 con microscopio SEM para efectuar consideraciones sobre la porosidad y morfología de los poros.
                                                                                                 El método propuesto permite además determinar la profundidad de penetración y la uniformidad de
                                                                                                 distribución de los materiales usados para la restauración y conservación de monumentos históri-
                                                                                                 cos.
T. Schillaci et al. - Study of capillary absorption kinetics by X-ray CT Imaging techniques...




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