Ionic aqueous diffusion through unsaturated cementitious materials – A comparative study

Construction and Building Materials 51 (2014) 1–8

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Construction and Building Materials

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Ionic aqueous diffusion through unsaturated cementitiousmaterials – A comparative study

0950-0618/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.conbuildmat.2013.10.026

⇑ Corresponding author. Tel.: +33 5 61 55 99 14; fax: +33 5 61 55 99 00.E-mail address: [email protected] (S. Lorente).

Hugo Mercado-Mendoza a, Sylvie Lorente a,⇑, Xavier Bourbon b

a Université de Toulouse, UPS, INSA, LMDC (Laboratoire Matériaux et Durabilité des Constructions), 135 Avenue de Rangueil, F-31077 Toulouse Cedex 04, Franceb ANDRA, 1/7 Rue Jean Monnet, Parc de la Croix Blanche, 92298 Chatenay-Malabry, France

h i g h l i g h t s

� The chloride diffusion coefficient is measured as a function of the saturation level by impedance spectroscopy.� 4 Types of materials made of Portland cement and blended cement are tested in a saturation level ranging from 0.2–1.� The evolution of the diffusion coefficient with the saturation level is closely related to the pore size distribution.

a r t i c l e i n f o

Article history:Received 21 July 2013Received in revised form 2 October 2013Accepted 15 October 2013Available online 8 November 2013

Keywords:Cement-based materialsSaturation levelDiffusion coefficientImpedance spectroscopy

a b s t r a c t

The diffusion coefficient is a highly important parameter either as a durability indicator in the field ofcivil engineering or as an assessment criterion in the domain of nuclear waste disposal. In this paperwe address the fundamental issue of the diffusion coefficient evolution with the water saturation levelof cement-based materials. The study is comparing concretes and cement pastes cast with either blendedcement or Portland cement. The analysis emphasizes the impact of the pore size distribution on the dif-fusivity as a function of the saturation degree.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The mechanism of diffusion through porous media is the abilityof a species, ionic or molecular, to move across the porous materialwhen a concentration difference is applied as driving force. Thisability can be quantified by a diffusion coefficient, which is aparameter of great importance in several scientific domains. Itmay allow for instance to assess the suitability of a determinedstorage solution for nuclear waste disposal. It can also be used toevaluate the durability of a concrete structure vis-à-vis either thecorrosion of its reinforcement bars by chloride ion penetrationthrough the concrete cover, or the expansive products generatedby sulphate ions entering the material.

The diffusion coefficient is a macroscopic parameter that de-pends on the characteristics of both the diffusing species and theporous material involved in the diffusion process [1–3]. Thus, thematerial microstructure, which characteristics ensue both fromthe properties of the material itself as well as from its history

and environmental conditions, plays a main part when dealingwith the diffusion coefficient.

In a recent paper [4], we documented the lack of research workson molecular transport through unsaturated systems (cf.references ibid.) and the lack of data establishing a relationship be-tween the diffusion coefficient and the saturation level of porousmaterials. Moreover, the techniques widely used in civil engineer-ing to measure diffusivity through cementitious materials are sui-ted for fully saturated conditions. These techniques cannot be usedwhen it comes to partially saturated materials for the very reasonthat they request to place the samples of material between com-partments containing solutions at various concentrations. Thewater content gradients thus created prevent from maintainingthe initial saturation level inside the material.

Climent et al. [5], followed by De Vera et al. [6], published amethod for measuring the diffusion coefficient of chloride ionsthrough partially saturated concrete, from a natural diffusion testand by means of Fick’s second law of diffusion. Guimarães et al.[7] presented another experimental set-up for the natural diffusiontest allowing also to calculate the chloride diffusion coefficientthrough unsaturated concrete using Fick’s second law. Ben Frajet al. [8] proposed a new experimental set-up aiming at character-

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0

0.05

0.1

0.15

0.2

0.25

0.0010.010.1110100

Pore access diameter D [µm]

dV [

mL

/g]

/ dlo

gD

Portland cement paste

Blended cement paste

Fig. 1. Pore size distribution of the cement pastes.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.0010.010.1110100

Pore access diamater D [µm]

dV [

mL

/g]

/ dlo

gD

Portland-cement concreteBlended-cement concrete

Fig. 2. Pore size distribution of the concretes.

Table 2Artificial solutions composition.

Solution Na+ K+ OH�

(mol m�3)

N� 1 (Portland-cement concrete) 31.5 122.8 154.3n� 2 (blended-cement concrete) 70.7 173.9 244.6

2 H. Mercado-Mendoza et al. / Construction and Building Materials 51 (2014) 1–8

ising chloride ingress in non-saturated concrete. Chloride profilesmeasured when concrete is partially saturated can also be foundin [9].

Our group proposed recently an approach to determine the dif-fusion coefficient of any ionic species through a partially saturatedporous medium [4]. This approach was proven effective in the caseof a Portland-cement concrete. We could determine experimen-tally the diffusion coefficient for different saturation levels of thematerial. This allowed to show the correlation between the diffu-sion coefficient and both the porous network characteristics(porosity, porosimetry) and the hydric state of the material.

On that basis, the approach is extended in this paper to differenttypes of cementitious materials: a blended-cement (with mineraladditions) concrete and the two corresponding cement pastes(Portland and blended). Once the diffusion coefficient in non-satu-rated conditions is measured, a comparative analysis allows toidentify the leading paths for diffusion through the different kindsof material. Besides, a brief review is first made on the validation ofthe present method, carried out on saturated materials and de-tailed elsewhere [10], by means of an electrokinetic technique. Thisreview permits to verify the coherence with respect to thenon-saturated sample results presented here, and to make somescale effect considerations.

2. Materials, characterisation and sampling

Two different kinds of cementitious materials were tested, namely cementpaste and concrete. Each of them was prepared using two different varieties of ce-ment: a common Portland one and a blended one (containing mineral additions:flying ashes and blast furnace slag). The composition of both types of concretewas presented before [10]. A water-to-cement ratio of 0.43 and 0.41 was used,respectively. The same ratio was adopted to prepare the two corresponding typesof cement pastes. At the end of a curing period of 6 months under controlled con-ditions (humid chamber, 20 �C), the apparent density and the water porosity ofthe four types of materials were measured (Table 1).

Mercury intrusion porosimetry tests completed the characterisation of thematerials. The pore size distribution of the cement pastes is presented in Fig. 1and in Fig. 2 for the concretes.

In addition, pore solution extractions were performed on the two types of con-crete, and the ionic compositions of these solutions determined. That led to the def-inition of representative artificial solutions having identical sodium and potassiumconcentrations and which are in practice equivalent to the pore solutions extracted,especially from an electrochemical point of view. In fact, the presence of calciumand sulphate ions was found to be negligible vis-à-vis the ionic strength due to theirvery low concentrations. The ionic compositions of the two artificial solutions areshown in Table 2.

The samples used for this study were disks with a diameter of 28 mm and athickness of 20 mm. These dimensions were chosen as a compromise betweenthe time needed to reach hydric equilibrium and the largest size of aggregates inconcrete. Three samples (coming from three different specimens) of each materialwere placed inside hermetic containers at 20 �C where supersaturated saline solu-tions were previously put. Seven relative humidity were tested, i.e. 94%, 84%, 75%,66%, 55%, 44% and 33%. These values are actually reference ones because the hydricstate of the material was characterised by its saturation level. The samples werekept inside the container until hydric equilibrium was reached, before proceedingto impedance measurements. The saturation level of a sample was measured asthe ratio between the water volume in its pores and the total volume of its pores,following the AFPC-AFREM protocol [11].

3. Experiments – electrochemical impedance spectroscopy (EIS)

The approach used involves the determination of the electricalohmic resistance of a given porous medium by means of its imped-

Table 1Material characteristics.

Cement Apparent density (kg m�3) Water porosity

Cement paste Portland 1580 0.39Blended 1594 0.37

Concrete Portland 2330 0.13Blended 2285 0.14

ance (AC) response. The technique is based on the formation factorFf concept [12,13], i.e. the ratio between the electrical conductivityof the pore solution ro (S/m) contained in a porous material at a gi-ven state, and the conductivity of the material itself rmat (S/m) atthat state. The results obtained in this way needed to be corrobo-rated by means of a well-known test method. On that purpose,an electrokinetic test, based on chloride ions migration under anelectrical field, was used. More details on this test can be foundelsewhere [10]. This is why the approach described hereafter isused to calculate the diffusion coefficient of chloride ions De,Cl�through a given porous material. Nevertheless, by using the appro-priate value of Do,i in Eq. (4), it may possible to assess any ionic spe-cies diffusion coefficient.

The formation factor writes:

Ff ¼ro

rmatð1Þ

Terminals(electrodes inside)

Sample

Clamps

H. Mercado-Mendoza et al. / Construction and Building Materials 51 (2014) 1–8 3

The Nernst–Einstein relationship specifies the linear correlationbetween ionic diffusivity and ionic electrochemical mobility[12,13]:

l ¼ zFDo

RT; ð2Þ

where lu is the electrochemical mobility of the ionic species(m2 s�1 V�1), z is the charge number, F is the Faraday constant(96 480 C mol�1), Do is the diffusion coefficient in an infinitedilution (m2 s�1), R is the ideal gas constant (8.314 J K�1 mol�1),and T is the absolute temperature (K).

The ionic electrochemical mobility is linearly correlated to theelectrical conductivity following [14]:

l ¼ Fzr ð3Þ
Fig. 3. EIS test cell and terminals.
Q E

R E

Q mat

R mat

R CP Q DP

Fig. 4. EIS test cell electrical model.

Combining Eqs. (1)–(3) together, we obtain:

Ff ¼Do;i

De;i¼ ro

rmatð4Þ

where Do,i is the diffusion coefficient (m2 s�1) of a given ionic spe-cies in an infinite dilution obtained from related literature (e.g.[14]), and De,i is the diffusion coefficient (m2 s�1) of the same spe-cies through the material.

Because the main target here is to evaluate De,i, in order to applyEq. (4) from a practical point of view, one can readily notice theimportance of determining the electrical conductivity rmat as per-tinently and accurately as possible. ro can be measured in a ratherdirect way or calculated following existing models such as the oneproposed by Snyder et al. [15] (provided that it is possible to haveaccess to the pore solution and to its ionic composition [10]).

An Electrochemical Impedance Spectroscopy (EIS) test was pro-posed in order to calculate rmat [4,10]. Therein, the main featuresof this test as well as some electrochemical criteria regarding itsmetrology were presented. One can highlight the fact that AC resis-tivity measurements allow to avoid some disadvantages that maypertain to the DC techniques, especially associated to ionic dis-placement, electrode reactivity and dissociation of ohmic dropsources throughout the test cell.

For the sake of clarity we give here some information regardingthe EIS test: A commercial Impedance Analyser was used (Agilent4294A). The amplitude of the AC potential difference signal appliedto the sample was 200 mV and the frequency of this signal ranfrom 40 Hz to 110 MHz. Beyond all connection and wiring features,each of our own-designed terminals includes an electrode made ofcopper and a stainless steel mattress, the whole protected by a PVCshell. Fig. 3 shows a view of the EIS test cell used for this work, to-gether with the terminals that allow the connection to the Imped-ance Analyser.

In order to examine the resulting data, the impedance measure-ments were represented under a Nyquist plot form (see next sec-tion). An electrical model (equivalent circuit) of the test cell wasproposed to analyse the obtained impedance spectra, and in partic-ular to determine Rmat (X), which is the ohmic resistance of thesample under test. This physics-based model, composed of conven-tional electrical elements (i.e. resistors R and constant phase ele-ments Q) related to the different conductive paths within the testcell, is presented in Fig. 4. The material is modelled by a combina-tion of continuous conductive paths representing the fraction ofopened and connected pores which electrical resistance is Rmat, anon-ideal capacitor representing the solid matrix Qmat (F), togetherwith discontinuous pore paths (pore paths separated by solid lay-ers). The association in series of a resistance RCP and a constantphase element QDP represents this path, where CP means continu-ous portion and DP discontinuous point. The microstructure model

is then associated in series with the block representing the contri-bution of the electrodes and interfaces.

As proposed by Orazem and Tribollet [16], a reasoning in termsof the total current flowing through the test cell was used to definethe type of assembly between the different elements of the equiv-alent circuit. All the current arriving through one electrode istransferred to the material, via their interface, and from the mate-rial, via the opposite interface, to the other electrode. One can seethen that the same current will flow through the material (leftblock in the model of Fig. 4) and the interfaces (right block in themodel of Fig. 4), i.e. no current addition will occur between theseblocks. These two blocks are then assembled in series. Followingthe same logic, when flowing through each of the two blocks ofthe model, the total current will be the addition of the amount ofcurrent transferred through the different paths in each block.A parallel assembly between these paths is then adopted. Fromthe well known circuit theory, the corresponding impedancefunction can be found, which gives [4]:

Zx;me ¼1

Rmatþ 1

RCP þ 1QDPði xÞaDP

þ Q matði xÞamat

!�1

þ 1REþ Q Eði xÞaE

� �ð5Þ

Accordingly, a data treatment procedure – based on the Simplexalgorithm following the Nelder–Mead method [17,18] – wasimplemented under the Matlab environment. This procedure al-lowed to quantify accurately Rmat from the measured impedance

x 104

Z the (b) 40 Hz

110 MHz

27 KHz1,1 MHz

Blended-cement concreteSl = 0.90

0 2000 4000 6000 8000 10000 12000 14000 160000

1000

2000

3000

4000

5000

6000

7000

-ImZ

[ Ω]

Z theZ exp

40 Hz

110 MHz

(a)

34 KHz

3,9 MHz

(c) Portland-cement concreteSl = 0.89

x 104

Z the (b) 40 Hz

110 MHz

27 KHz1,1 MHz

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

0

0.5

1

1.5

2

x 104

-ImZ

[Ω]

Z theZ exp (b) 40 Hz

110 MHz

27 KHz1,1 MHz

(d)

Portland-cement concreteSl = 0.76

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 105

0

5

10

15

x 104

-ImZ

[Ω]

Z theZ exp (c)

54 Hz

62 Hz

62 KHz

110 MHz

(b)


40 Hz


0 1 2 3 4 5 6x 104

0

0.5

1

1.5

2 x 104

ReZ [Ω]

ReZ [Ω] ReZ [Ω]

ReZ [Ω]

-ImZ

[Ω]

Z theZ exp (a)

110 MHz 1,8 KHz

40 Hz


Fig. 5. Experimental (Z exp) and modelled (Z the) impedance spectra. Blended-cement concrete samples with a saturation level Sl of: (a) 0.90 and (b) 0.74. Portland-cementconcrete samples with a saturation level Sl of: (c) 0.89 and (d) 0.76.

x 105

Z the

97 Hz46 KHz110 MHz

(d)(a)


(b)Blended-cement concreteSl = 0.55

x 104

Z the

888 KHz

(c) 40 Hz

5,7 KHz

110 MHz


0

x 105

Z the

110 MHz292 KHz

(d)78 Hz


Z the

97 Hz46 KHz110 MHz

(d)(a)


0 2 4 6 8 10 12 14 16x 105

0

1

2

3

4

5

ReZ [Ω] ReZ [Ω]

ReZ [Ω]ReZ [Ω]

-ImZ

[Ω]

-ImZ

[Ω]

-ImZ

[ Ω]

-ImZ

[ Ω]

Z theZ exp

97 Hz46 KHz110 MHz

(d)(a)


(b)Blended-cement concreteSl = 0.55

0 0.5 1 1.5 2 2.5x 106

0

2

4

6

8

x 105

Z theZ exp

141 Hz34 KHz

110 MHz

(e)(b)Blended-cement concreteSl = 0.55

Z the

888 KHz

(c) 40 Hz

5,7 KHz

110 MHz


0 2 4 6 8 10 12x 104

0

1

2

3

4

5Z theZ exp

888 KHz

(c) 40 Hz

5,7 KHz

110 MHz


Z the

110 MHz292 KHz

(d)78 Hz


0.5 1 1.5 2 2.5 3x 106

0

2

4

6

8

10Z theZ exp

110 MHz292 KHz

(d)78 Hz




spectra, via the electrical model and its corresponding theoreticalspectra through an optimisation procedure. Next, the electricalconductivity of the material was calculated with:

rmat ¼L

A � Rmatð6Þ

where L is the sample thickness (m) and A is the cross-sectional areaof the sample perpendicular to the electrical field lines (m2). Finally,

the diffusion coefficient of chloride ions De,Cl� was calculated ineach case using Eq. (4). It is worth mentioning that the electricalconductivity of the pore solution ro, in each case presented here,was directly measured after either preparation or extraction fromthe material, and using a commercial device, and checked by calcu-lation through an analytical model [15]. As mentioned before, thechoice of calculating De,Cl� was made in coherence with availabledata presented elsewhere [10], where the present approach was

Z theZ exp

90 Hz

(e)

71 KHz

110 MHz

(c)


Z theZ exp

67 Hz

4,3 KHz

110 MHz

(f)(a)


x 106

Z theZ exp (g)

113 Hz

110 MHz

2,0 KHz

(b)


x 106

Z theZ exp

255 Hz

3,4 KHz

110 MHz

(g)(d)


Z theZ exp

90 Hz

(e)

71 KHz

110 MHz

(c)


0 1 2 3 4 5x 106

0

0.5

1

1.5

2x 106

Z theZ exp

90 Hz

(e)

71 KHz

110 MHz

(c)


Z theZ exp

67 Hz

4,3 KHz

110 MHz

(f)(a)


0 1 2 3 4 5 6 7 8 9x 106

0

0.5

1

1.5

2

2.5

3

3.5x 106

ReZ [Ω]

ReZ [Ω]

ReZ [Ω]

ReZ [Ω]

Z theZ exp

67 Hz

4,3 KHz

110 MHz

(f)(a)


Z theZ exp (g)

113 Hz

110 MHz

2,0 KHz

(b)


0 0.5 1 1.5 2 2.5x 107

0

5

10

15Z theZ exp (g)

113 Hz

110 MHz

2,0 KHz

(b)


Z theZ exp

255 Hz

3,4 KHz

110 MHz

(g)(d)


0 5 10x 106

0

2

4

6

8

10

12

14 Z theZ exp

255 Hz

3,4 KHz

110 MHz

(g)(d)


-ImZ

[Ω]

-ImZ

[Ω]

-ImZ

[Ω]

-ImZ

[Ω]


10

10

10

10

10

10

0 10 20 30 40 50 60 70 80 90 100

Saturation level [%]

Dif

fusi

on c

oeff

icie

nt [

m2 /s

]

Blended-cement concrete ; Diam.=28mm

Blended-cement concrete ; Diam.=110mm

Blended-cement concrete ; Electrok. ; Diam.=110mm

Portland-cement concrete

-16

-15

-14

-13

-12

-11

Fig. 8. Chloride diffusion coefficient as a function of the water saturation level, Portland-cement and blended-cement concretes.


validated by comparison with a conventional migration test basedon chloride ions diffusion.

4. Results

The characteristic impedance spectra measured by EIS in thecase of Portland-cement concrete were presented in a previous pa-per [4]. In order to make a comparative analysis, regarding

specially the main features of these spectra and their evolutionwith the hydric state of the material, Figs. 5–7 show them togetherwith the different experimental Nyquist plots (Zexp) measured for anumber of saturation levels Sl of blended-cement concrete sam-ples. These saturation levels are considered to be stable along thetest duration (around 5 min).

When the saturation level of the concrete with mineral addi-tions Sl is equal to 0.90 (Fig. 5a), the impedance spectrum is very

R2 = 0,9979

10

10

10

10

10

10

10

Dif

fusi

on c

oeff

icie

nt [

m2 /s

]

Portland cement paste

Portland-cement concrete

-16

-15

-14

-13

-12

-11

-10

0 10 20 30 40 50 60 70 80 90 100


Fig. 9. Chloride diffusion coefficient as a function of the water saturation level, Portland cement paste.

10

10

10

10

10

10

10

Dif

fusi

on c

oeff

icie

nt [

m2 /s

]

Blended cement paste

Blended-cement concrete

-17

-16

-15

-14

-13

-12

-11

0 10 20 30 40 50 60 70 80 90 100


Fig. 10. Chloride diffusion coefficient as a function of the water saturation level, blended cement paste.


similar to that obtained for the fully saturated material. It is possi-ble to distinguish two different parts on the spectrum, following awidely spread way of reading this kind of plots (cf. for instance:[19,20]). First, an arc associated to the material response (left blockin the model shown in Fig. 4) exists on the left hand side of thespectrum, corresponding to high and very high frequencies. Sec-ond, the material-electrodes interface limb, at right (low frequen-cies) on the spectrum (right block on the model shown in Fig. 4)appears. Both concretes used in this study have very similar waterporosities (Table 1). However, the impedance values measured forthe blended-cement concrete are clearly higher than those forPortland-cement one (Fig. 5c). This reflects the impact of their dis-similarity in terms of pore network geometry (shape and size of thepores, Fig. 2).

It is only when Sl drops down to 0.74 (Fig. 5b) that two distinctarcs, merged until here, become visibly detached with an inflexionat around 62 kHz. These arcs result from the impedance character-istics of the ‘‘material block’’ (left block on the model shown inFig. 4) under specific hydric conditions. This very emergence of

two separated arcs was detected at an equivalent saturation level(0.76) in the case of the Portland-cement concrete (Fig. 5d).

A drastic change on the Nyquist plot for Portland-cement con-crete was found as the saturation level goes down to 0.52(Fig. 6d). It is characterised by: (i) a significant augmentation ofthe impedance values measured, and specially by: (ii) the remain-ing presence of the very-high-frequency arc (at the most left-handside on the spectrum), (iii) and a noticeable increase of the contig-uous material arc (high frequencies), which actually seems tomerge with the interface limb, making it disappear to form a solelarge partially visible second arc. When it comes to the blended-cement concrete, the equivalent behaviour appears as Sl falls downto 0.68 (Fig. 6a). Nevertheless, this change is somewhat milder.One can notice a very-high-frequency arc, and the disappearanceof a single interface limb forming the second arc, which size re-mains relatively close to that of the first arc, unlike the case ofthe Portland-cement concrete. The characteristics of the imped-ance spectrum remain quite similar down to a saturation level of0.42 (Fig. 7a).


The impedance spectrum shape found for the lowest saturationlevel tested for blended-cement concrete (Sl = 0.18, Fig. 7b), andthe one obtained for Portland-cement concrete at an almost equiv-alent hydric state (Sl = 0.16, Fig. 7d) are actually very alike. A singlecapacitive-shaped limb begins to arise from the two former arcs.However, this blended-cement concrete limb keeps a slightly high-er curvature than that of Portland-cement concrete one.

Regarding the two cement pastes used in this study, analogousimpedance spectra were measured (not shown in this paper). Infact, the same kind of observations on the main features that char-acterise the different regions of the spectrum, and their evolutionwith the hydric state of the material, can be made. As shown herein the case of two types of concrete, this evolution is defined byseveral saturation level values, according to each material and,very likely due to their porous network configuration.

Figs. 5–7 also include the theoretical impedance spectra (Zthe)calculated using the electrical model and the treatment proceduredescribed previously. For each spectrum the corresponding valueof the ohmic resistance of the sample under test Rmat was deter-mined (Eq. (5)). The formation factor of the material at a given sat-uration level can be then calculated from Eqs. (6) and (4). The verygood agreement between theoretical and experimental resultsshown in Figs. 5–7 allows to verify the suitability of the experi-mental protocol and the data processing approach.

5. Discussion

The diffusion coefficient of chloride ions was determined fromthe formation factor values calculated for each material at differentsaturation levels. The results are shown in Fig. 8 for Portland-ce-ment and blended-cement concretes and in Figs. 9 and 10 for Port-land and blended cement pastes, respectively.

The discrepancy range within measured values, as a result ofthe experimental characteristics, was assessed using the ratio be-tween the standard deviation of the formation factor obtainedthrough several measurements, performed on the same sample un-der the same conditions, as a percentage of the average formationfactor itself. This ratio was calculated for a given material vacuum-saturated with different pore solutions. The mean ratios found inthe case of Portland-cement and blended-cement concretes were6% [4] and 4%, respectively.

Regarding the Portland-cement concrete, it was mentioned ear-lier [4], that the formation factor may be seen as representative notonly of the geometry of the porous network (shaped by the solidphase), but also of the liquid phase content (the saturation levelof the material) and arrangement therein. As one can see throughFigs. 8–10, this remains valid for all the cementitious materialspresented here.

In other respects, we show also in Fig. 8 results obtained onfully saturated samples of a larger diameter (110 mm) than thatused for partially saturated samples. When it comes to the diffu-sion coefficient and from Fig. 8, one can observe two main aspectswith reference to fully saturated materials. Firstly, the fact that,after comparison between the results for two quite different sizesof samples (of blended-cement concrete in this case), a very littlescale effect is barely noticeable on the diffusion coefficients ob-tained by means of the EIS test. Then, one can see the very goodagreement between EIS-test-based results and those coming froman electrokinetic technique, especially when compared to the sat-uration level effect on the calculated diffusion coefficients. This hasactually permitted to confirm the validity of the EIS approach tocalculate the diffusion coefficient of an ionic species through a por-ous material.

The analysis of the evolution of the chloride diffusion coefficientthrough blended-cement concrete as a function of the saturation

level (Fig. 8) indicates a uniform decrease of the diffusion coeffi-cient immediately after losing complete saturation and down toa saturation level (Sl) of 0.74. This is quite a different behaviourthan that observed for Portland-cement concrete (Fig. 8), wherean initial plateau exists within a similar Sl range. Hence, theblended-cement concrete decrease could be ascribed to a progres-sive loss of continuity of the liquid phase contained in a pore mode(capillary porosity) centred between 0.1 and 0.01 lm (Fig. 2). As amatter of fact, the macroporosity situated beyond 0.07 lm doesnot seem to be a preferred path through which the electricalcharges, and so ionic species, will flow across the porous networkof the material. In that sense, the existence of the plateau corre-sponding to Portland-cement concrete was associated to a continu-ity of the liquid phase contained in the macroporosity of this kindof material, which indeed was found to be a preferred path for elec-trical charges passage [10,21].

A visible change of regime was detected for Portland-cementconcrete from a saturation level below 0.76, where the diffusioncoefficient diminishes with the saturation level in a more pro-nounced way than for saturation levels above 0.76 (Fig. 8). Thischange of regime, in a less drastic way due to the uniform decreaseabove Sl = 0.74, occurs in the case of the blended-cement concrete(Fig. 10), between Sl = 0.74 et Sl = 0.68, with a noticeable drop of thediffusion coefficient value. This change could be associated to a lostof continuity in the whole capillary porosity mentioned before.Next, below Sl = 0.68, the diffusion coefficient decreases again ina uniform way down to the lowest saturation level measured here,0.18.

The case of the Portland cement paste (Fig. 9) is clearly differentfrom those of all the other materials discussed here. Indeed, allover the range of tested saturation levels the diffusion coefficientdecreases in a very uniform way. As a matter of fact, an exponentialregression gives a determination factor almost equal to 1. The ini-tial plateau detected for Portland-cement concrete was not ob-served for Portland cement paste. This can be explained by thefact that cement pastes (Fig. 1) do not possess the macroporosity(largest pores) present in concretes. Moreover, the preferred pathsfor electrical conduction, and hence ionic diffusion, appear to bethose corresponding to a porosity mode centred around 0.03 lm(Fig. 1). Because no detectable regime change takes place for Port-land cement paste, unlike for the previously described materials,continuity may not be lost throughout the network of capillarypores, even for the lowest saturation level tested (0.18).

In the case of blended cement paste (Fig. 10) a strong similarityexists between this material behaviour and that of the concretemade from the same type of cement (Fig. 8). This points out that,in the case of the blended-cement concrete, the macroporosity(Fig. 2) does likely not represent the preferred paths described be-fore, because the corresponding cement paste does not comprisethis kind of pores (Fig. 1). The same kind of observations concern-ing the evolution curve of the diffusion coefficient throughblended-cement concrete apply here for blended cement paste.The first portion of uniform decrease of the diffusion coefficient(probably due to capillary pores drying) is distinguished here be-tween Sl = 1 and Sl = 0.76 (0.74 for blended-cement concrete). Theregime change slump (loss of continuity for the whole capillarypores) happens between Sl = 0.76 and Sl = 0.75. Next, anotherrather straight portion exists down to the lowest saturation leveltested (0.21). One should note that, as well as for all the othermaterials that are analysed in this paper, diffusion seems poten-tially still possible (an impedance spectrum giving an ohmic resis-tance of the material is measurable) even for such low saturationlevels as those measured here. Nevertheless, this probable diffu-sion shall most likely concern other and non negligible phenomena(related to solid phase-pore solution interface), in addition to thosethat govern diffusion in the core of the pore solution.


6. Conclusion

The main objective of this work was to report the comparativeanalysis of the diffusion coefficient of ionic species through fourdifferent non saturated cementitious materials (two cement pastesand two concretes). In order to measure the diffusion coefficient,an approach based on the formation factor concept and theNernst–Einstein relationship was used. The validity of the pertain-ing experimental protocol (impedance-spectroscopy-based) anddata processing (by means of a physics-based electrical model)was verified in all cases. A large saturation level range was tested(from around 20% up to fully saturated conditions).

The main results are:

– The impedance spectra of the concrete samples made ofblended cement exhibit a behaviour drastically differentthan the Portland cement concrete, for equivalent watersaturation levels.

– The diffusion coefficients for the blended cement concreteare one order of magnitude lower than the Portland cementconcrete diffusivity, whatever the water saturation level.

– The Portland cement paste diffusion coefficient decreasescontinuously with the water saturation level, unlike thecorresponding concrete which presents a plateau betweenSl = 0.8 and Sl = 1.

– In the case of blended cement, both cement paste and con-crete show a regular decrease of the diffusion coefficientwith the water saturation level, which indicates that thesame type of pores are solicited for the transport.

Acknowledgement

This work was supported by a contract from ANDRA (AgenceNationale pour la Gestion des Déchets Radioactifs).

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