Concrete gas permeability from different methods: Correlation analysis

Accepted Manuscript Concrete gas permeability from different methods: Correlation analysis Dongdong Zhang, Kefei Li PII:

S0958-9465(19)30441-X

DOI:

https://doi.org/10.1016/j.cemconcomp.2019.103379

Article Number: 103379 Reference:

CECO 103379

To appear in:

Cement and Concrete Composites

Received Date: 6 April 2019 Revised Date:

18 July 2019

Accepted Date: 23 July 2019

Please cite this article as: D. Zhang, K. Li, Concrete gas permeability from different methods: Correlation analysis, Cement and Concrete Composites (2019), doi: https://doi.org/10.1016/ j.cemconcomp.2019.103379. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Concrete Gas Permeability from Different Methods: Correlation Analysis

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

1 Introduction

Dongdong Zhang, Kefei Li1 Key Laboratory of Safety and Durability of Civil Engineering of China Education Ministry,

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Civil Engineering Department, Tsinghua University, Beijing 100084, China Abstract: The paper explores the relation of gas permeability from different methods through both theoretical and experimental investigations. The theoretical basis of different methods is reviewed and the analysis error is derived with respect to their present interpretation methods. The theoretical relations among these methods are further explored. Concrete specimens of 12 mixtures were then prepared and subject to gas

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permeability measurements, validating the established relation. Further use of gas permeability as durability indicator is elaborated finally. The study shows that (1) theoretical relations exit among the different methods and the key parameter of conversion is the

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Klinkenberg factor; (2) the gas permeability depends strongly on the binder type, w/b ratio and pore saturation, and the relation between the intrinsic permeability (CemBureau) and Torrent permeability is confirmed; (3) there is urgent need to benchmark the moisture pre-conditioning to make better use of gas permeability as quality indicator.

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Keywords: Gas permeability, Durability, Correlation, Steady flow, Klinkenberg factor

Gas permeability is one of the fundamental properties for structural concretes, and this

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property is also one of the central parameters for concrete durability [1]. Concrete durability is closely related to the mass transfer between the internal pores and external environments, involving the transport of gas, liquid and ions species [2]. The gas permeability describes the

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transport rate of gas phase under pressure gradient, relevant to the gas molecules movement in pores [3,4]. Accordingly, the gas permeability is regarded pertinent to gas transport processes, such as the diffusion of CO2 and O2 in concrete [5]. Since gas can penetrate easily into tiny pores, gas permeability was also used to detect the characteristics of fine pore structures [6]. Besides its fundamental nature, the gas permeability has been also used as an efficient parameter to characterize the compactness of structural concretes [7-10]. Different experimental methods have been developed so far to measure the gas permeability in-situ or in laboratory. The laboratory methods usually follow a specific

1

Corresponding author, E-mail: [email protected]; ORCID:0000-0003-1635-6362

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procedure to pre-condition the moisture state of concrete specimens, conduct the gas permeation tests following steady flow or transient flow schemes, and interpret the gas permeability from the results. The most used methods include the CemBureau method (steady flow) [11], OPI method (transient flow) [5,12], low pressure method (transient flow) [13,14], and other transient flow methods [15,16,17]. The infiltrating gas includes oxygen (O2), nitrogen (N2) and dry air. The gas permeability is interpreted either from the steady gas flow rate or from the pressure change. The in-situ methods normally cannot pre-determine

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the temperature and moisture conditions of the concrete. A group of borehole (drilled-hole) methods are available [18] and the most typical one is the Figg’s method [19,20] which creates a negative pressure in a borehole and uses the pressure rise during given time to deduce the gas (air) permeability. The Torrent method [21] and AutoClam method [22] create the gas flow directly on concrete surface and deduce the gas permeability (coefficient)

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from steady flow (Torrent) or transient pressure change (AutoClam). Some laboratory methods apply also to in-situ measurements, e.g. Schönlin and Hilsdorf device [16], and Paulini device [17]. Because the in-situ methods cannot control the concrete temperature or

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moisture during the measurement, the inherent dispersion is usually larger than the laboratory methods [23]. However, the in-situ methods have unique virtue: they measure actually the achieved compactness of hardened concrete, which is more relevant to the on-site concrete quality.

So far, the data of gas permeability accumulate through laboratory and in-situ measurements but the gas permeability measured from different methods cannot be

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compared directly due to the different test principles and interpretation methods. Such a benchmarking is necessary to establish global database for gas permeability towards international standards for concrete quality control. Aiming at this lack, this paper retains several typical laboratory and in-situ test methods, reviews the experimental principles and

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the corresponding interpretation methods, and identifies the relations among these different permeability values. Further, this study performs gas permeability experiments to validate the identified relations. This study expects to provide theoretical basis for the benchmarking of gas permeability results. To this purpose, this paper is organized as follows:

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Section 2 is dedicated to experimental principles, result interpretation and relations among different values; Section 3 presents the materials and experiments; using gas permeability as durability indicator is elaborated in Section 4; the concluding remarks are given in Section 5.

2 Gas permeability of measurement: principle and methods 2.1 Constant Flow Method – CemBureau method The most widely used constant flow setup is CemBureau method [11]. The schematic illustration of the permeation cell is given in Figure 1: P1, P2 are respectively the inlet pressure and outlet pressure (Pa), kept constant during the measurement. The gas permeability is deduced from steady gas flow (oxygen, nitrogen or dry air) through the

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permeation cell. Normally, the outlet of permeation cell is connected to the atmosphere.

87

q=−

100

k A dP µ dx

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(1)

where kA is the apparent permeability (m2) , μ is the viscosity of infiltrating gas, taking 1.75 10-5Pa·s for nitrogen under 25oC [24]. Applying (1) to the CemBureau setup and considering

k A = 2µ L

P12

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the gas compressibility give, P2 Q − P22 A

gas flow does not strictly observe viscous flow at the pore wall and boundary slipping occurs [25], the intrinsic permeability, k0, is deduced through a Klinkenberg factor b (Pa) from the apparent permeability kA,  b  P1 + P2 k A = k0 1 +  with Pm = P 2 m  

(3)

Actually, the Klinkenberg factor b scales to what extent the collisions between gas molecules and the pore wall contribute to the global gas flow [26]. In CemBureau measurements, the apparent permeability is measured under a series of inlet pressures P1, and the parameters, k0 and b, are regressed through (3).

Gas flowmeter

Lateral pressure

P2 (Patm)

Outgoing gas (O2/N2)

Infiltrating gas (O2/N2)

107 108

(2)

where A is the cross-sectional area of specimen (m2) and L the specimen thickness (m). Since

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(m3/m2/s), and the pressure gradient, dP, observe the Darcy's law,

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7bar is usually needed to avoid the gas leaking around the specimen. The steady gas flow, q

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materials, the inlet pressure ranges from 1bar to 5bar and the lateral pressure as high as

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Thus P2 can take the atmospheric pressure Patm, i.e. 1.01×105Pa (1.0 bar). For concrete

P1 (> Patm)

Figure 1: CemBureau setup for gas permeability measurement of concrete.

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given pressure (gradient) is imposed at the beginning of measurement, across the specimen thickness or measured zone, and the transition change of imposed pressure during the gas flow is recorded to interpret the gas permeability. Several experimental setups are reviewed

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in the following. (1) Torrent method

Torrent method measures the air permeability of concrete surface (covercrete) following a non-destructive approach. The device creates a unidimensional air flow with the help of the double chambers of which the inner chamber is the functional one, cf. Figure 2(a). Under the

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high vacuum maintained in the inner chamber, the air is assumed to follow a steady flow within a depth of L, and the air permeability is interpreted through the (small) variation of gas pressure Pi in the inner chamber. While detailed equations are derived in the reference

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[27] some key relations are recalled here.

The air volume under consideration is in the zone of a cylinder with the section area A and length of Y, subject to a pressure gradient Pi (y=0) and Patm (y=Y). The quantity of air, ng (mol), is noted as,

ng RT = PmVg with Pm =

Pi + Patm , Vg = φg AY 2

(4)

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Instead of steady gas flow, the variable pressure methods record the change of pressure: a

with φg for the gas-occupied porosity, R for the ideal gas constant (J/mol/K) and T for the absolute temperature (K). Under this pressure gradient, the gas entering into the inner chamber can be expressed, similar to (2), as

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2.2 Variable Pressure Methods

2 − Pi2 RT dng kT A Patm = = Pi dt Pi dt 2 µgY

dVg

(5)

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where μg is the air viscosity. Putting (4) into (5) and regarding Pm as constant give the solution of the time-dependent depth of the flowing air,

  t  Y =  2kT Patm   µ φ     g g  

1 2

(6)

Note that in deriving (6) we assume Pi<
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VC

2 = ( Patm − Pi 2 )

kT A dt 2µgVCY ( t )

with VC for the volume of inner chamber. Integrating (7) between two states, the initial state of stabilized inner chamber (t0, Pi0) and the final test state (tf, Pif), gives the explicit solution of gas permeability kT, 2 µg   VC  kT =     A  2φg Patm 

(

tf − t0

)

−1

Note two important assumptions used in deriving the permeability in (8): first both Pif and Pi0 should be negligible compared to Patm, otherwise neither (6) nor (8) holds; second the depth of flowing air Y during the test should be less than the thickness of specimen (element), i.e.,

  t  2 L > Y ( tf ) = 2kT Patm  f   µ φ   g g   

159 Pump

Outer chamber

Working flow

P0

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Steady flow

(9)

Patm

Outer chamber

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P0

Pi

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Inner chamber

160 161 162 163 164 165 166 167 168 169 170 171

2

 P + ∆Pi   f 0 ln  atm   with ∆Pi = Pi − Pi = Patm (8)  Patm − ∆Pi  

1

158

(7)

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152

dVg

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147 148 149 150 151

dPi = Pi

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t

t+dt

Pi

Pi

Transient flow

PH (>Patm)

Y

Pressure vessel (Oxygen)

dY

Patm Patm

Gas inlet

Pressure transducer

(a)

(b)

Figure 2: Two variable pressure methods for gas permeability measurement: (a) Torrent method for surface concrete and, (b) OPI method for concrete specimens.

Otherwise some corrections should be made for the gas permeability expression, cf. Appendix A. The Torrent devices [27] set the initial and final working pressures in the inner chamber as 40mbar and 60mbar (Pi0,f=0.04-0.06Patm), so the first condition is assumed to be satisfied while the second condition (9) should be checked at measurement. The last point comes to the porosity φg: this value refers, conceptually, to the air-occupied space in concretes pores. However, as the pores contain liquid moisture (water) to a high level, the gas permeation path will be blocked and this threshold of liquid saturation is found to be

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measurement [7]. (2) OPI method The OPI (Oxygen Permeability Index) method measures the gas (oxygen) pressure change in a closed chamber, and deduces the gas (oxygen) permeability of the specimen from the

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pressure change [1,5,12]. The permeation cell setup is illustrated in Figure 2 (right): the specimen is placed between the closed oxygen cell (pressure vessel) with an imposed pressure PH, and the external atmospheric condition with Patm (< PH). As the experiment starts the oxygen gas penetrates through the thickness of specimen and the pressure in the chamber decreases accordingly, e.g. to PH’ at time t. The oxygen permeability is deduced

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from these values. The underlying principle is briefly described as follows.

Actually, if relating the outgoing oxygen gas and the pressure change (decrease) in the

dP k A = O dt 2 ( P − P ) 2µgVC L 2 atm

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closed chamber, one can apply (7) with constant penetration depth of specimen thickness L,

(10)

Integrating this equation between two states, the initial state of the chamber (t0, PH) and the end of test (t1, PH’), provides the explicit evaluation of oxygen permeability,

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under high liquid saturation, which demands relatively dry condition of concrete surface for

( Patm + P 'H )( PH − Patm ) with P ' < P V  µ L 1 kO =  C  O ln H H  A  2 Patm t1 − t0 ( Patm + PH )( P 'H − Patm )

(11)

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around 0.85 for gas permeation [28]. Accordingly, Torrent devices cannot work properly

If, further, the pressure decrease in the closed chamber is relatively small, i.e. PH-PH’<
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∆PH V  µ L 1 kO =  C  O ln  A  2 Patm ∆t ∆P 'H

(12)

with ∆t=t1-t0, ∆PH=PH-Patm, ∆P’H=P’H-Patm. It is from this equation that OPI method interprets the oxygen permeability. Note that the important assumption is the pressure decease should sufficiently small to ensure the linearity of between the logarithm term and the test time in (12). Obviously, kO calculated by Eq. (11) is smaller than that calculated by Eq. (12). In other terms, as the pressure change is not negligible compared to Patm, (11) should be used instead of (12) and forcing (12) to this case will introduce an error ξo,

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( Patm + P 'H ) kO(11) − kO(12) = ln (11) kO ( Patm + PH )

ln

(P (P

atm

+ P 'H ) ∆PH

(13)

atm + PH ) ∆P 'H

Figure 3(a) illustrates the magnitude of this error in terms of the initial chamber pressure PH and the pressure drop PH-PH’. The error is calculated for the pressure and time values from literature [5, Fig.7]. It can be seen that lower initial pressure PH and smaller pressure drop help to decrease the approximation error.

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ξO =

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208

215

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Hamami et al. [15] also developed a permeation cell similar to OPI method: the cell is composed of an upper chamber, with high air pressure PH maintained to (>100 kPa), and a low chamber, with the air pressure PL vacuumed to around 8.5 kPa at the beginning of test. Then, driven by pressure gradient a gas flow occurs through the specimen placed between

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the two chambers. The pressure change in low chamber over time is recorded until PL rises to around 35kPa, and an apparent permeability kH (m2) can be deduced from the pressure change versus time. The same interpretation principle and limit apply as in (11) and (12).

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(a) (b) Figure 3: Interpretation error analysis: (1) OPI method in terms of the chamber pressures, (b) Low pressure method with the change of water head.

(3) Low pressure method Another variable pressure setup is due to Yssorche et al. [13] and used by Caré and Derkx [14], cf. Figure 4. This setup exposes one surface of specimen to the atmosphere pressure Patm, and the other surface to a vacuumed pressure, measured by the water height in an outlet tube. The experiment begins with the vacuum treatment of the outlet tube, the vacuum pressure, about 0.1bar (vacuum degree of 0.9), acts on the outlet of specimen surface and the air flows through the specimen thickness. Accordingly the vacuum degree in the outlet tube is decreased and the water head drops with time. The movement of water head in the outlet tube is recorded with time and the air permeability is deduced accordingly.

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Air flow

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h0 h1

Vacuum Pump

251 252 253 254 255 256 257 258 259 260 261 262 263 264 265

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kg =

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The apparent air permeability, kg (m2), is evaluated as follows [14],

µg SL 1 h  ln  0  ρw gA t1 − t0  h1 

(14)

where t0,1 stand for beginning time and ending time of experiment, h0,1 represent the initial and final water head in the outlet tube, A, S are respectively the cross sections of the specimen and the outlet tube (m2), µg is the air viscosity (Pa·s), and ρw the liquid water density (kg/m3). Nevertheless, air compressibility is not considered in deriving (14). The air

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Figure 4: Low pressure device from Yssorche et al. [13] and Caré and Derkx [14].

permeability considering the air compressibility writes,

µg SL 1  2 Patm h0 − ρ w gh02  kg = ln   ρw gA t1 − t0  2 Patm h1 − ρw gh12 

(15)

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Water

The mathematical details are given in Appendix B. By considering the air compressibility, the obtained air permeability is systematically smaller, i.e. the kg value in (15) is always smaller

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than the value from (14). The relative error ξC= (kg(15)-kg(14))/kg(15) is illustrated in Figure 3(b). The interpretation error is evaluated for an initial water head corresponding to 50-90% vacuum degree. Both the lower initial water head h0 and the drop of water head h1 help to narrow the interpretation error. For a same initial water head (vacuum degree), the estimation through (14) using dropped water head h1 in later stage gives more reliable interpretation. 2.3 Comparison among different methods The air permeability measured by CemBureau method is used as reference to investigate the possible relations (correlations) with the air permeability from other methods. This comparison bears significant engineering senses: first the database for air permeability will

ACCEPTED MANUSCRIPT largely increase if quantitative relations exist among permeability values from different methods; second, the inter-laboratory durability tests on same concretes (robin-round tests) would be possible for laboratories with different facilities. (1) Torrent permeability vs. CemBureau permeability We derive the relation between the two quantities under the premise that all the conditions are met for Torrent device measurement such as humidity and temperature conditions. The

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kT value from (8) is derived from a laminar gas flow under a pressure gradient between Patm in concrete pores and vacuum pressure in the inner chamber Pi. Taking the Klinkenberg factor b in (3) as a material property intrinsic to the concrete pore structure, one can expect the following relation, −1

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In other terms, there exists such a relation for Torrent permeability kT and CemBureau intrinsic permeability k0, on condition that the factor b is known. This relation is to be verified in the later experimental part.

(2) OPI permeability vs. CemBureau permeability

First issue concerning OPI permeability is that in the literature [5] the air permeability, kSA, is defined through the mass flow,

qgm = −

kSA grad ( P ) g

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(16)

(17)

in which kSA bears the unit (m/s) and the mass flow qgm has the unit (kg/m2/s). To relate this

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kT,0

quantity to the conventional air permeability defined on the basis of volumetric flow, one can writes,

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 Patm + Pi 0,f b  = kT  1 + , P = B 0.5 Patm  m Pm  2 

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qgm = ρ g qgv = − ρ g

kO

µg

grad ( P ) and kSA =

ρg g k µg O

(18)

Note that the relation between the two quantities depends on the pressure since the gas density ρg is pressure-dependent. Suppose we can use the pressure in the closed chamber, PH or PH’, to determine the gas density in (18). Actually the same principle applies for the relation between OPI permeability kO and CemBureau permeability k0. Then, one needs to know the corresponding pressures and the factor b to obtain the intrinsic permeability. For OPI measurement, the pressure in closed chamber undergoes a change, not in the negligible range in [5]. Thus, it is rational to use the pressures, PH and PH’, to determine the estimation

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−1

(19)

For the low pressure setup in Figure 4, the same principle in (19) can apply if the correct expression is used for the air permeability calculation. Table 1 summarizes the experimental procedures and the relation with CemBureau permeability. Table 1:

Summary of different gas permeation methods Infiltrating

Pressure

Method

gas

Inlet

Outlet

CemBureau [11]

0.1-0.5 MPa

Patm

Torrent [21]

Patm (pores)

20-60mbar

Air

OPI [5,12]

200-150 kPa

Patm

Hamami et al. [15] Low pressure

150-250 kPa

N2 /O2

8kPa to 35kPa

from 10 kPa

Patm

Measurement

Relation

principle

with k0

Steady flow

/

Transient pressure

(16)

O2

Transient pressure

(19)

Air

Transient pressure

(3)

Air

Transient flow

(19)

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[13,14]

3 Materials and experiments

This part is dedicated to the experimental investigation of gas permeability of structural

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concretes with different binders, using CemBureau method and Torrent device. Because the moisture content of concrete is always a major issue in gas permeability measurement, the air permeability is measured at different levels of pore saturation. Then, the correlation between the values from CemBureau and Torrent methods, identified in the theoretical part,

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−1

'  Patm + PH( ) b  (') P < k0 < 1 + , =   m 2 ρg ( P 'H ) g  P 'm 

kSA µg

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kSA µg  b  1 +  ρ g ( PH ) g  Pm 

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range for the intrinsic permeability k0,

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is validated for same saturation levels. 3.1 Materials and specimens A total of twelve concretes were prepared and Table 2 gives the detailed proportioning and basic properties. Three binders were used: ordinary Portland cement (OPC), OPC incorporating 30% fly ash, OPC incorporating 50% slag, and the corresponding concretes are denoted as CO, CF and CS. For each binder, four w/b ratios, 0.3, 0.4, 0.5 and 0.6, were adopted to prepare the concrete materials. To study purpose, the same volumetric ratio between cement paste and aggregates, 0.35:0.65, is used for all concretes.

ACCEPTED MANUSCRIPT Table 2: Proportioning and basic properties of concretes (FA for “fine aggregates”, CA for “coarse aggregates”) Concrete

Cement

(-)

(kg/m )

3

Fly ash

(kg/m )

3

(kg/m )

(kg/m )

(kg/m )

(kg/m )

3

Slag

FA

Compressive

Water

3

CA 3

3

strength 90d/180d (MPa)

0.3

563

169

/

/

689

1033

86.5

CO4

0.4

485

194

/

/

689

1033

74.5

CO5

0.5

426

213

/

/

689

1033

66.8

CO6

0.6

380

228

/

/

689

1033

55.3

CF3

0.3

394

169

169

/

689

1033

96.7

CF4

0.4

340

194

146

/

689

1033

79.8

CF5

0.5

298

213

128

/

689

1033

60.9

CF6

0.6

266

228

114

/

689

1033

49.2

CS3

0.3

282

169

/

282

689

1033

98.5

CS4

0.4

243

194

/

243

689

1033

75.4

CS5

0.5

213

213

/

213

689

1033

65.6

CS6

0.6

190

228

/

190

689

1033

57.7

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CO3

The raw materials were mixed and poured into cylinder molds with diameter of 150 mm and height of 200 mm and demoulded at the end of 72h, and then cured in water with ambient temperature controlled to 20±2oC. The specimens of CO series were taken out of water at the age of 90d while CF and CS at the age of 180d. In parallel, cube specimens of 100mm were prepared following the same curing procedure and the compressive strength was

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tested at these ages, cf. Table 2. Such curing ages were used to ensure the properties of specimens to be stabilized. From each cylinder were cut out three disc specimens of thickness 50mm, labeled as “1”, “2”, “3” for upper, middle and down positions respectively. These concrete discs were subject to water-vacuum treatment during 24h to achieve total

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saturation. Afterwards, these saturated specimens were coated laterally with epoxy-resin for gas permeability tests.

The specimens were 600C-oven drying to four pore saturations: 70%, 50%, 30% and 0%, and

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w/b

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the gas permeability tests were performed at these levels. To make this saturation pretreatment, the slice specimens of 5mm thickness were sawed out from the cubes and the porosity is evaluated through gravimetry method under 600C-oven-drying. The detailed description can be found in [28]. Using this pre-measured porosity, the specimens were first oven-dried to the expected mass at 70% saturation. Then the moisture state of specimens were homogenized during 14d following the RILEM procedure [8], followed by a room cooling to 200C. Afterwards, the specimens were subject to CemBureau measurement and Torrent device measurement. To facilitate the comparison, the CemBureau and Torrent measurements ensure the gas flow across the specimens in the same direction. This procedure is repeated for pore saturation of 50%, 30% and 0% (constant weight under 600C-oven drying). At the end of the measurement, the pore saturations were recalibrated

ACCEPTED MANUSCRIPT using the mass of specimens at constant weight. Due to intrinsic dispersion of porosity and the possible moisture loss during measurements, the real saturation, calibrated by constant weight at 0%, is deviated more or less from the expected values with a dispersion of +/-4% (brute values can be found in the attached dataset). 3.2 Gas permeability measurement

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(1) CemBureau method

The infiltrating gas is nitrogen. The literal pressure is set to 7bars to ensure the gas tightness and the inlet pressure P1 is set from 1.5bar to 5bar. The steady state gas flow is recorded and apparent permeability kA is evaluated using (2). From the apparent permeability values of all inlet pressures, the intrinsic permeability k0 and Klinkenberg factor b are regressed by (3).

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The regression is illustrated in Figure 5(a) for CO4 and CO5 specimens under different saturations, and the obtained intrinsic permeability values are given in Figure 5 (b)-(d) for CO/CF/CS specimens. The k0 values are clearly related to both w/b ratios and pore

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saturations. Among different binders, the CS specimens have the highest intrinsic permeability, due to the high connectivity of its pore structure [28]. The CF specimens achieve the lowest gas permeability.

(a)

(b)

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(c) (d) Figure 5: Intrinsic gas permeability from CemBureau method: (a) regression for CO4/CO5 specimens, (b) CO specimens, (c) CF specimens, (d) CS specimens.

ACCEPTED MANUSCRIPT (2) Torrent method Following the principle in Section 2.2, the value kT was read directly from the device, and the linear relation between the pressure change term and the time terms in (8) is illustrated for CO specimens at all saturations in Figure 6(a). From the results, the assumed linearity is well observed between the pressure change term and the time term. The kT values are presented in Figure 6(b)-(d) for all specimens. Similarly, the Torrent permeability is also influenced notably by both w/b ratio and pore saturation. Again, the CS specimens show the highest gas

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permeability and the CF specimens have the lowest values. In terms of the dispersion of measurement, the dispersion of Torrent measurement is at the same order of CemBureau measurements. In other terms, the two methods have comparable measurement dispersion for given moisture states of specimens under same laboratory conditions.

(a)

(b)

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(c) (d) Figure 6: Gas permeability from Torrent method: Inner pressure change with time (CO) (a), and kT values for OPC specimens (b), CF specimens (c) and CS specimens (d). 3.3 Correlation analysis between CemBureau/Torrent methods (1) Correlation between k0 and kT The kT and k0 values of all the specimens are shown in Figure 7(a)-(d) for all saturation levels. Generally the kT values are one order of magnitude larger than k0 values for same specimens, and an overall correlation exists between the two quantities. The underlying reason can be

ACCEPTED MANUSCRIPT explained through (16): kT values refer to gas permeability under a specific pressure gradient (Pi and Patm). The distance of kT values from the equality line in Figure 7 scales actually the magnitude of Klinkenberg factor b in (16). From this reasoning, the CS specimens are expected to have lower b values while CF specimens will have higher b values, especially for high pore saturation level (70%). The discussion is to be deepened in next section, together with the regression of b values.

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(b)

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(a)

(c) (d) Figure 7: Correlation between k0 and kT measured for CO/CF/CS specimens at different saturation levels: (a) 0%, (b) 30%, (c) 50%, (d) 70%. Each subfigure consists of 36 data points (3 binders, 4 w/b ratios and 3 specimens).

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(2) Klinkenberg factor b

As aforementioned, the Klinkenberg factor b is a crucial parameter for converting the apparent permeability from different methods to intrinsic permeability. From the CemBureau measurements, the factor b is regressed for all specimens and given in Figure 8. Theoretically, this factor scales to what extent the collision between gas molecules and pore wall contribute to the gas transport in pores [29]. Thus, this value is closely related to the concrete pore structure and pore saturation [30]. From Figure 8, the impact of the pore structure patterns is highlighted: CS specimens, as expected, have lowest b values while CF specimens have rather high b values, which is in line with the connectivity characteristics, high for CS and low for CF, deduced from other properties [31]. Conceptually, for a same

ACCEPTED MANUSCRIPT specimen the increase in pore saturation will also increase the chance of gas-pore wall collision thus the b factor since the pore liquid narrows the gas transport path. However, this reasoning is not confirmed by the results in Figure 8, which is possibly related to the non-elastic collision between the gas molecules and liquid (film) in pores [32].

(a)

(b)

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(c) (d) Figure 8: Klinkenberg factor b for different concretes at different saturations: (a) 0%, (b) 30%, (c) 50%, and (d) 70%. (3) Intrinsic permeability converted from kT values Using the regressed Klinkenberg factor b in Figure 8, the Torrent permeability kT can be

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converted to the intrinsic permeability using (16) and Pm=0.5Patm. This converted intrinsic permeability is noted as kT,0. The correlation between the intrinsic permeability k0 from CemBureau measurements, in Figure 5, and the obtained kT,0 values is given in Figure 9. To illustrate the conversion, the correlation kT-k0, before conversion, is also put side by side in Figure 9. Rather good correlation is observed for the two quantities, confirming the sound basis of the relation (16). This observation bears important information for engineering use: through the Klinkenberg factor b, the durability requirements, specified in terms of CemBureau permeability, can be converted to requirements for in-situ measurement, making possible the durability quality control though non-destructive methods. Nevertheless, the kT,0 and k0 values are not strictly equal one to the other, with

ACCEPTED MANUSCRIPT kT,0/k0=0.84-1.70. Another analysis consists of deducing the average gas pressure from (16) using k0 as kT,0: the obtained average pressure Pm is given in Figure 10. The average pressure Pm> 0.5Patm or Pm < 0.5Patm means the gas pressure in pores is higher or lower than Patm. Normally the local evaporation in pores will increase the local gas pressure while the vacuum action can decrease the gas pressure in the pores where the liquid phase blocks locally the gas transport path. These two factors interplay in different specimens, under different saturations, which could be the underlying reasons for the deviation of estimated

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average pressure from 0.5Patm.

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(a) (b) Figure 9: Correlation between permeability values from CemBureau and Torrent measurements: (a) before conversion, (b) after conversion. The figure consists of 144 data points (3 binders, 4 w/b ratios, 4 saturation levels and 3 specimens)

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Figure 10: Deduced average pressures for Torrent measurement at different levels.

ACCEPTED MANUSCRIPT 4 Durability indicators Multiple efforts have been dedicated to the application of these permeability parameters, in laboratory or in-situ, to the quality control of structural concrete [1,18,33]. From the return of experiences, the compactness of structural concrete has been classified through the gas permeability values from different methods: values below 10-17m2 (Torrent), 10-18m2 (CemBureau) or 10-9.5m/s (OPI) correspond to high compactness while values above 10-16m2

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(Torrent), 10-15m2 (CemBureau) or 10-9m/s (OPI) indicate low quality [1]. Note that moisture pre-conditioning is different in these methods. Some limit values of gas permeability are presented in Table 3 from technical guides and standards [1,7,33] and real project application [9,10,33]. In the table the pre-conditioning of concrete specimens is also provided, and the environmental classifications (carbonation exposure) follow European

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standards EN-206-1 [34]. It can be seen that for moderate environmental actions (XC1, XC2) and shorter service lives (<100 years) the specification of gas permeability is not necessary; for severe exposure (XC3, XC4) with long service lives (≥100 years), the requirements on gas

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permeability become explicit: usually k0 value (CemBureau) of 10-17m2 or kSA value (OPI) of 10-9m/s is required. The bridge projects in Table 3 are exposed to marine environments and subject to chlorides actions, adopting CemBureau k0 value requirement of 10-17m2 or achieving Torrent kT value on the order of 10-18m2. These values provide quantitative ranges for concrete quality control via gas permeability.

Though some specifications in Table 3 relate the gas permeability requirements to the

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service lives and the concrete cover thickness, these specifications are of empirical nature. There is not yet a rigorous proof for the relation between the specified gas permeability and the expected durability performance for given service lives and environmental actions. In other terms, the gas permeability is only a quality control parameter, providing the

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minimum requirement for the compactness. To turn the gas permeability into a performance indicator related to service lives, one has to accomplish two crucial steps: (1) benchmarking of gas permeability from available different methods, and (2) establishing rigorous relation between gas permeability and mechanism-based durability properties such

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as the CO2 diffusivity for carbonation and the chloride diffusivity for chloride ingress. This study contributes to the first step while benchmarking the moisture pre-conditioning of specimens remains unsolved. For the second step, some experimental studies have been engaged to investigate the correlation between gas permeability and other durability properties [31,35,36].

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classification/Case

Preconditioning

XC1

kT (10-16m2)

/

Preconditioning

k0 (10 m2)

k0 (10-16m2)

k0 (10-16m2)

(>120 a)

(100-120a)

(50-100a)

0.1(30mm)

1(30mm)

/

/

1(30mm)

/

0.1(30mm)

0.1(30mm)

1(30mm)

0.1(30mm)

0.1(30mm)

/

/

0.1(28d)

/

<0.1-1

/

80 C

/

oven-drying

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Wet, rarely dry

28d,

XC3

/

Moderate humidity

<1 (40mm)

Vasco da Gamma Bridge (1995-1998) Monaco floating dike (1999-2002)

Temperature

2.0

o

>10 C; moisture content

7d,

/

Cooled to room

<5.5% or

Temperature

/

during 24h

kΩcm

(2002-2004)

/

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Resistivity <10-20

Millau bridge Miami Tunnel

0.057 (28d)

(2010-2014)

0.027 (84d)

Zhuhai

Macau sea link project

<1 (40mm)

50 C oven-drying

o

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Cyclic wet and dry

0

105 C to constant weight

Concrete surface

XC4

(2010-2018)

kSA (10-9m/s)

CemBureau -16

0

XC2

HongKong

Pre-conditioning

/

Dry, or permanently wet

517 518

OPI

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Torrent

Environmental

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Table 3: Specifications of gas permeability values for durability and service lives [1, 7, 9,10,33](n.a. for not available)

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0.069 (56d)

/

n.a. 0

/

80 C oven-drying 28d

/

n.a.

/

<0.1 (90d)

/

/

/

/

/

/

/

/

/

/

/

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5 Conclusions

554

Acknowledgement

555

The research is supported by National Key R&D Program of China No. 2017YFB0309904, and

556 557 558

NSFC project No. 51778332.

This paper explores the relations among the gas permeability measurements from different methods via both theoretical analysis and experimental investigations. The following conclusions can be reached from the study. (1) The CemBureau and Torrent methods measure the steady gas flow, and Torrent

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permeability kT can be converted to intrinsic permeability once the Klinkenberg factor is known. The OPI method measures the pressure change in transient flow process and the present interpretation tends to overestimate the true permeability value and this error can be reduced by limiting the pressure change in the closed chamber. Also, the OPI permeability can provide estimate range for intrinsic permeability using the Klinkenberg factor and average pressures in the test. The low pressure method, using the present

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interpretation, presents larger error for gas permeability, but low initial vacuum degrees, interpreted with later water head readings, help to narrow the error.

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(2) Experimental results show that gas permeability, measured by CemBureau or Torrent methods, is sensitive to the pore saturation, binder type and water to binder ratio. A good overall correlation exits between the intrinsic permeability (CemBureau) and the Torrent permeability. The Klinkenberg factor is regressed from the CemBureau measurement, and the values are used to convert the Torrent permeability to the corresponding intrinsic permeability. The converted intrinsic permeability agrees well with the CemBureau values, confirming the proposed theoretical relation between the two quantities. This conversion permeability values.

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makes possible the specification of quality control of structural concretes using different gas

(3) The review of the gas permeability values used in the durability specifications shows that

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gas permeability is more taken as a quality indicator. The return of experiences proposes to limit CemBureau intrinsic permeability below 10-17m2 for long service lives (>100 years) or exposure to severe environmental actions. The corresponding requirements on OPI values

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and Torrent values are respectively below 10-9m/s and 2×10-16m2. Recent engineering projects give much lower values from in-situ Torrent measurements, on the order of 10-18m2. To make full use of the gas permeability data from different methods, we definitely need to benchmark the moisture preconditioning for different experimental methods, in addition to the theoretical identification of their relations.

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Appendix A: Complementary solution of gas permeability for Y(tf) > L

564

tL =

which can be calculated by (6),

L2 µ gφg

(A1)

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2k T Patm

The flow process is thus divided into two stages: (1) t0 < t ≤ tL during which the influence length Y gradually increases from 0 to L, and (2) tL < t ≤ tf during which the air flows across the specimen thickness (Y = L). The pressure increase, ∆Pi, can be expressed similar to (7),

570

dPi kT A k A = dt + T dt 2 P − Pi 2µgVCY ( t ) 2µgVC L

571 572 573

Integrating (A2) from t0 to tf gives,

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Patm + Pi f )( Patm − Pi 0 ) kTφg ( VC = ln 2 APatm ( Patm − Pi f )( Patm + Pi 0 ) 2µg L

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2 atm

(

)

tL − t0 +

kT

2 µg L

(A3)

Substituting (A1) into (A3) provides a quadratic equation in terms of kT, from which the kT value can be solved.

Appendix B: Air permeability from low pressure method

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Q2 = − A

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The air flow rate at the outlet, similar to (5), can be written following Darcy's law as, kg  Patm + P2  ( Patm − P2 ) with Patm − P2 = ρ w gh   µg  2 P2  L

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( tf − tL )

(A2)

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Assume that the vacuum front reaches the thickness L of the specimen (element) at time tL

(B1)

where h is the height of water head in the tube (m), Q2 is the volumetric air flow across the specimen (m3/s), kg is the air permeability (m2), µg is the air viscosity (Pa s). The air volume change in the tube, induced by the air inflow, can be also expressed as the water head change,

dV = Sdh

(B2)

with S standing for the cross section of the outlet tube. The equality between the inflow air volume and the air volume change in tube gives,

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Q2dt = dV :

2 ( Patm − ρ w gh ) dh 2 Patm − ρ w gh h

=−

kg A S µg L

ρ w gdt

(B3)

Integrating (B3) between two states, the beginning of test (t0, h0) and the end of test (t1, h1), gives the explicit solution for air permeability,

kg =

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µg SL 1  2 P h − ρ w gh02  ln  atm 0  ρ w gA t1 − t0  2 Patm h1 − ρ w gh12 

(B4)

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34(1986)8179-8181.

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to air of the concrete cover on site, Mater. Struct. 25(1992)358-365. [22] K. Yang, P.A.M. Basheer, Y. Bai, B.J. Magee, A.E. Long, Development of a new in situ test method to measure the air permeability of high performance concretes, NDT & E Int. 64(2014)30-40.

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[23] M. Romer, Effect of moisture and concrete composition on the Torrent permeability measurement, Mater. Struct. 38(2005)541–547. [24] D.R. Lide, H.P.R. Frederikse, CRC Handbook of Chemistry and Physics, 84th ed., CRC Press LLC, New York, 2003.

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[25] D.S. Scott, F.A.L. Dullien, The flow of rarefied gases, AIChE J. 8(1962)293-297. [26] L.J. Klinkenberg. The permeability of porous media to liquids and gases, Drilling and Production Practice, New York, 1941:200–213.

[27] http://m-a-s.com.ar/eng/product.php (April 6, 2019) [28] Q. Gui, M.F. Qin, K.F. Li, Gas permeability and electrical conductivity of structural concretes: Impact of pore structure and pore saturation, Cem. Concr. Res. 89(2016)109-119. [29] D.S. Scott, F.A.L. Dullien, Diffusion of ideal gases in capillaries and porous solids, AIChE J. 8(1962)113-117. [30] F. Civan F. Effective correlation of apparent gas permeability in tight porous media, Trans. Por. Med. 2010;82:375-384.

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regard to reinforcement corrosion and alkali–silica reaction, Association Française de [34] CEN, Concrete - Part 1: Specification, performance, production and conformity (EN 206: 1-2000), European Standard, Brussels, 2000.

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[36] H. Beushausen, M.G. Alexander, The South African durability index tests in an international comparison, J. S. Afr. Inst. Civ. Eng. 50(2008)25-31.

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Figure 1: CemBureau setup for gas permeability measurement of concrete. Figure 2: Two variable pressure methods for gas permeability measurement: (a) Torrent

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method for surface concrete and, (b) OPI method for concrete specimens. Figure 3: Interpretation error analysis: (1) OPI method in terms of the chamber pressures, (b) Low pressure method with the change of water head.

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Figure 4: Low pressure device from Yssorche et al. [13] and Caré and Derkx [14].

Figure 5: Intrinsic gas permeability from CemBureau method: (a) regression for CO4/CO5

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specimens, (b) CO specimens, (c) CF specimens, (d) CS specimens.

Figure 6: Gas permeability from Torrent method: Inner pressure change with time (CO) (a), and kT values for OPC specimens (b), CF specimens (c) and CS specimens (d). Figure 7: Correlation between k0 and kT measured for CO/CF/CS specimens at different saturation levels: (a) 0%, (b) 30%, (c) 50%, (d) 70%. Each subfigure consists of 36 data points

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(3 binders, 4 w/b ratios and 3 specimens).

Figure 8: Klinkenberg factor b for different concretes at different saturations: (a) 0%, (b) 30%, (c) 50%, and (d) 70%.

Figure 9: Correlation between permeability values from CemBureau and Torrent measurements: (a) before conversion, (b) after conversion. The figure consists of 144 data

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Figure Captions

points (3 binders, 4 w/b ratios, 4 saturation levels and 3 specimens) Figure 10: Deduced average pressures for Torrent measurement at different levels.

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