On the time dependency of the chloride migration coef?cient in concrete
K.Audenaert a,*,Q.Yuan a,b ,G.De Schutter a
a Magnel Laboratory for Concrete Research,Department of Structural Engineering,Technologiepark-Zwijnaarde 904,B-9052,Ghent (Zwijnaarde),Ghent University,Belgium b
School of Civil Engineering and Architecture,Central South University,Hunan,China
a r t i c l e i n f o Article history:
Received 25September 2008
Received in revised form 22June 2009Accepted 26July 2009
Available online 30October 2009Keywords:Chloride Diffusion
Time dependency
Self-compacting concrete
a b s t r a c t
From studies of the chloride penetration behaviour in laboratory tests and real structures,a clear time dependency of the chloride diffusion coef?cient is observed.In order to get insight in this complicated problem,laboratory tests were performed with the non-steady state migration test,described in NT BUILD 492,up to 5years concrete age.The in?uence of the type and amount of cement and ?ller and the amount of water on the migration coef?cient and the so-called age factor of 16self-compacting con-crete mixes (SCC)and four traditional vibrated concrete mixes (TC)were investigated.
The capillary porosity was introduced as parameter to describe the in?uence of the concrete composi-tion.An increasing capillary porosity leads to an increased non-steady state migration coef?cient and a decreasing age factor.
ó2009Published by Elsevier Ltd.
1.Introduction
In a marine environment,chloride penetration into concrete is the determining factor for the service life of concrete structures.This implies that a good insight in the chloride penetrating process is of utmost importance.Unfortunately,chloride ion transport is a rather complicated process,which involves diffusion,capillary suc-tion,migration in an electrical ?eld,a pressure induced ?ow and wick action when water absorption and water vapour diffusion are combined.
In saturated conditions,diffusion is the primary penetration process of chlorides into concrete.In this process,the chloride ions diffuse in presence of a chloride concentration gradient,which is created when at least one face is continuously exposed to water and salt.This process is described by Fick’s second law,which is written as follows for one dimensional problems:
@C ?@D @C e1T
where C is the total chloride content,t time and D the diffusion coef?cient.If the following boundary conditions are considered: a single spatial dimension x ,ranging from 0to 1for the semi –in?nite case,
C =C 0at x =0and t >0(boundary condition), C =0at x >0and t =0(initial condition).
and under the assumptions of:(1)homogenous concrete,(2)con-stant chloride concentration at the exposure surface (3)constant diffusion coef?cient (4)linear chloride binding (the line has to pass through the origin)and (5)constant effect of co-existing ions,the analytical solution of the Eq.(1)has the form:
C ?C 01àerf x
2??????
Dt
p
e2T
in which C 0is the surface concentration,and erf (á)represents the er-ror function.From Eq.(2)follows that the diffusion process of chlo-ride depends on two factors:(1)The intrinsic permeability of the concrete,which is changing during the process of cement hydration with time and (2)the surface chloride concentration,in?uencing the chloride concentration level in the pore solution,which is also changing due to the continuous chemical reaction of chlorides with the cement hydration products.On the other hand,the variation of the pore structure depends on the W /C ratio,degree of hydration,cement type,etc.and is also changing with time at various loca-tions.As a result,both the chloride ion concentration and diffusivity are time and space variables.
This paper deals with one of these dependencies,more speci?-cally the time dependency of the diffusion coef?cient created by the ongoing hydration of the concrete.It will discuss the mathe-matical questions (how to adjust Eq.(2))and the experimental determination of an age factor.
For the experimental determination of this time dependency,non-steady state migration tests,following NT BUILD 492[1]were carried out on 16self-compacting concrete compositions and four traditional vibrated concrete compositions.Due to the short duration of these tests,approximately 24h,they determine the
0950-0618/$-see front matter ó2009Published by Elsevier Ltd.doi:10.1016/j.conbuildmat.2009.07.003
*Corresponding author.Tel.:+3292645532;fax:+3292645845.E-mail address:Katrien.Audenaert@UGent.be (K.Audenaert).Construction and Building Materials 24(2010)
396–402
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journal homepage:www.e l s e v i e r.c o m /l o ca t e /c o n b u i l d m a
t
instantaneous migration coef?cient.The tested concrete ages vary between28days and5years.
2.Theoretical background
In literature,different aspects of the time dependency of the dif-fusion coef?cient are discussed.Roughly,they could be divided in three topics:?rstly,the mathematical expressions that describe the time dependency,secondly,the experimental determination of the age factor m based on laboratory testing and in situ experi-ments,lastly,empirical relationships for an age factor,based on different test procedures and environments.
2.1.Mathematical expressions
As concrete matures,additional hydration occurs which serves to reduce the diffusion coef?cient.The time dependency of diffu-sion through concrete has been observed to be an exponential function[2–4]:
DetT?D ref
t ref
t
m
e3T
where D(t)is the diffusion coef?cient at time t,D ref the diffusion coef?cient at some reference time t ref and m a constant,normally referred to as the age factor which is depending on the concrete composition.Some other relations are also given in the literature [5–7],but will not be considered in this paper.
However,this equation could not be inserted in Eq.(2)because that one is derived based on the assumption of a constant diffusion coef?cient.However,in many researches this method is applied, leading to large errors as discussed in[8].In[8,9],the mathematics of these equations are investigated and the correct solution of Eq.
(1)with a time dependent diffusion coef?cient is obtained by substituting D in Eq.(2)by the apparent diffusion coef?cient D a [8,9]:
D a?
D0
1àm
1t
t ex
D t
1àm
à
t ex
D t
1àm
"#
t0
t
m
e4T
with D0and t0a pair of known diffusion coef?cient and age of the concrete,t ex the age of the concrete at the start of exposure to chlo-rides,D t the exposure duration and m the age factor.
2.2.Experimental determination
As stated in[10],values for m for different concretes have yet to be well established,although some values have been published [2,9,11–14].In the Model Code for Service Life Design[4],a table is given with age factors depending on the cement type used in the concrete.The problem with the experimentally determined age factors is that several data which are obtained in very different ways on different concrete compositions are compared with each other. Some data are obtained from chloride pro?les in real structures, including a large in?uence of the environment,which is often accounted for by an environmental factor.Other data are deter-mined based on diffusion tests,wherein it is not clear how the age factor is mathematically derived.Some are using a non-steady state migration test,determining an instantaneous migration coef?cient. By performing migration tests on different concrete ages,the age factor could be determined.This experimental method will be followed in this paper.Unfortunately,by following this method, two new problems are created and will be discussed:?rstly,the rela-tionship between the non-steady state migration coef?cient and the diffusion coef?cient should be established.Secondly,the time (in)dependency of this relation is unclear.
Relationships are established to calculate the diffusion coef?-cient D from the non-steady state migration coef?cient D nssm deter-mined with NT BUILD492[15]and veri?ed for self-compacting concrete[13]:
D?D nssm1tK b
W gel
/cap
!
e5T
In this formula,K b is a binding parameter in m3/kg gel.For a10%NaCl solution,as used in NT BUILD492,this parameter is0.28?10à3m3/ kg gel for100%Portland cement concrete.W gel is the amount of gel in
the concrete in kg
gel
=m3
concrete
and is calculated as:
W gel?1:25a Ce6T
with a the degree of hydration and C the amount of cement.In Eq.
(5),u cap is the capillary porosity of the concrete.These relationships are not explicitly function of time,but are function of the degree of hydration and the porosity and thus implicitly function of time.In this way,a supplementary time dependent factor should be imple-mented in Eq.(3),if this equation is written for non-steady state migration coef?cients instead of diffusion coef?cients:
D nssm1?D nssm2
1tK b W gel2
cap2
1tK b W gel1
cap1
t2
t1
m
?D nssm2B
t2
t1
m
e7T
In order to get an idea of the value of B,the following calculation was made:for concrete with350kg/m3of ordinary Portland ce-ment,165kg/m3water and1865kg/m3of sand and coarse aggre-gates the value for B is estimated at two different time intervals t1–t2:28days–56days and28days–5years.At28days,a degree of hydration of0.7is supposed,from this a capillary porosity of7.4% is derived with Eq.(8),which is based on the theory of Powers [13,16,17]:
/
cap
?
W
q w
à0:362a C q
w
C
q
c
tW q
w
tA q
G
e8T
For q c and q G values of respectively3115kg/m3and2625kg/m3 are supposed.W gel equals315kg/m3.At56days the following val-ues are used:a=0.72;u cap=7.1%and W gel=324kg/m3.For a con-crete age of5years:a=0.725;u cap=7.1%and W gel=327kg/m3. With these values,B equals for the time period28days–56days 1.036and for28days–5years1.045.Also for other concrete com-positions and realistic values for the degree of hydration,the value of B is never larger than1.05.If the method of[4]is followed,this factor could be set equal to1.Consequently,Eq.(3)could be writ-ten with diffusion coef?cients or non-steady state migration coef-?cients,keeping in mind that a small error is introduced.
2.3.Empirical relations for predicting m
In literature,some empirical relationships are described for the age factor m.Mostly they are depending on the W/C ratio[2,18,19], undoubtedly a very important parameter.Surprisingly,the in?u-ence of the W/C ratio is different:in the relationships of[2,19]an increasing W/C ratio leads to a higher age factor.In[18],a higher W/C ratio leads to a lower m.This is illustrated in Fig.1.
3.Experimental programme
During5years,chloride migration tests were carried out at dif-ferent ages on concrete specimens of16self-compacting concrete mixes and4traditional concrete mixes.With a chloride migration test(NT BUILD492),an instantaneous value for the chloride migra-tion coef?cient is obtained.With the migration coef?cients on dif-ferent concrete ages,a value of the age factor for each concrete mix
K.Audenaert et al./Construction and Building Materials24(2010)396–402397
was determined.In the next section,the dependency of the age fac-tor on different in?uencing parameters,such as W/C ratio, (i)
studied.
3.1.Concrete mix design
At the Magnel Laboratory for Concrete Research,16self-com-pacting concrete mixes(SCC)and four traditional concrete mixes (TC)were investigated.In the?rst nine mixtures a constant amount of powder materials(cement and?ller)is considered:600kg/m3,as well as a constant amount of water,sand and gravel,respectively 165k/m3,853kg/m3and698kg/m3.Four types of cement are used (Portland cement CEM I42.5R,CEM I52.5,CEM I52.5HSR and blast furnace slag cement CEM III A42.5LA),three types of?ller(?y ash and two types of limestone?ller BETOCARB P2and Super?ne S,the last one having a?ner grading).In the next three mixes,the amount of powder is varied(500kg/m3,700kg/m3and800kg/m3).In the following three mixes,the amount of water is varied(144kg/m3, 198kg/m3and216kg/m3).In SCC16crushed limestone gravel was used instead of river gravel.The chemical composition as well as the physical and mechanical properties of the four cements used are given in Table2.The grading curves of the cements,?llers and aggregates are given in respectively Figs.2–4.The grading curves of the cements and?llers were determined by laser diffraction with a He–Ne laser.
In the traditional concrete mixes,three types of cement are used and the amount of cement is varied.The four traditional mixes are corresponding with respectively the self-compacting mixes1,3,6and4.
The amount of superplasticizer was determined in order to ob-tain a suitable?owability without segregation.Also the?owing time in the V-funnel was measured(values between5s and 10s),air content(values between1%and3%)and the U-box requiring self levelling.In Table1the mix composition is given to-gether with the compressive strength at28days measured on con-crete cubes with side150mm.
From the mixes described above,cubes150?150?150mm3 were made and were stored in a climate room at20°C±2°C and more than90%R.H.At an age of21days,three cores with a diam-eter of100mm and a height of50mm were drilled from each cube.
3.2.Test method
As described in section‘concrete mix design’,cores with a diam-eter of100mm and a height of50mm were drilled from each cube. Afterwards the concrete cores were placed back in the fog room until the testing date.On these cores a non-steady state migration test was performed following the method of Tang and Nilsson[20] as described in NT BUILD492and shown in Fig.5.The correspon-dence of this method with the natural ingress of chlorides by diffu-sion was validated in previous research carried out at the Magnel Laboratory for Concrete Research,Ghent University[13,21,22].
Firstly the specimens are vacuum saturated with a saturated Ca(OH)2solution.Afterwards,an external electrical potential(for the tests described in this paper between25V and40V)that forces the chloride ions from the10%NaCl solution(catholyte)to migrate into the specimens,is applied across the specimen for a limited duration.The test duration was24h,as prescribed by NT BUILD 492.Three specimens were tested simultaneously.After the test, the specimens are axially split.On the freshly split sections,a 0.1M AgNO3solution is sprayed and the chloride penetration depth is measured on each part at7points from the visible white silver chloride precipitation.This colorimetric method is
described Fig.1.Age factor in function of W/C ratio.
Table1
Mix composition.
CEM I 42.5R (kg/m3)CEM I
52.5
(kg/m3)
CEM III/A
42.5LA
(kg/m3)
CEM I
52.5HSR
(kg/m3)
Limestone
?ller S
(kg/m3)
Limestone
?ller P2
(kg/m3)
Fly
ash
(kg/
m3)
Water
(kg/
m3)
Sand
0/5
(kg/
m3)
Gravel
4/14
(kg/m3)
Limestone
gravel2/14
(kg/m3)
W/C
(–)
C/P
(–)
Compressive
strength
(MPa)
SCC13602401658536980.460.6057.3 SCC23602401658536980.460.6068.0 SCC33602401658536980.460.6066.1 SCC43602401658536980.460.6070.1 SCC53003001658536980.550.5046.5 SCC64002001658536980.410.6764.2 SCC74501501658536980.370.7568.7 SCC83602401658536980.460.6056.9 SCC93602401658536980.460.6066.2 SCC103002001379237550.460.6060.1 SCC114003001927826400.480.5755.9 SCC124503502207125830.490.5650.9 SCC133602401448657070.400.6068.7 SCC143602401988356830.550.6046.6 SCC153602402168256750.600.6040.3 SCC163602401658167340.460.6074.7 TC136016564012250.46 1.0048.6 TC236016564012250.46 1.0049.7 TC340016562612000.41 1.0053.7 TC436016564012250.46 1.0050.2 398K.Audenaert et al./Construction and Building Materials24(2010)396–402
in[23].For each concrete core,two penetration pro?les are ob-
tained.In this way,6penetration pro?les are obtained for each composition and concrete age.From the mean penetration depth,the non-steady state chloride migration coef?cient D nssm can be calculated,as described in NT BUILD492,with:
Table2
Chemical composition,physical and mechanical properties of cement.
CEM I42.5R CEM I52.5CEM III/A42.5LA CEM I52.5HSR
SiO2(%)19.620.326.120.8 Al2O3(%) 5.0 4.57.8 3.6 Fe2O3(%) 3.0 2.3 2.0 3.9 CaO(total)(%)61.564.049.364.2 MgO(%)0.8 2.2 5.8 2.4 SO3(%) 3.3 3.3 3.0 2.7 Na2O(%)0.40.20.30.2 K2O(%)0.90.90.70.5 C3S(%)58.259.0–60.6 C2S(%)12.712.6–16.6 C3A(%)8.28.0– 2.7 C4AF(%)9.19.4–13.1 Speci?c surface Blaine(m2/kg)345465415405 Absolute density(kg/m3)3115312029653185
Compressive strength
2d(N/mm2)27.234.117.832.0 7d(N/mm2)43.552.637.650.2 28d(N/mm2)53.061.255.264.4
Tensile strength
2d(N/mm2) 5.3 6.1 4.0 6.0 7d(N/mm2)7.58.27.18.0 28d(N/mm2)8.58.89.38.6
Fig.5.Test method developed by Tang[15].
K.Audenaert et al./Construction and Building Materials24(2010)396–402399
D nssm
?RT x àa ???
x p e9T
with :E ?
U à2
L
and a ?2????????RT zFE r erf
à1
1à2C d C o
D nssm :non-steady state migration coef?cient,m 2/s.z :absolute value of ion valence,for chloride:z =1.F :Faraday constant,F =9.648?104J/(V mol).U :absolute value of the applied voltage,V.R :gas constant,R =8.314J/(K mol).
T :average value of the initial and ?nal temperatures in the ano-lyte solution,K.
L :thickness of the specimen,m.
x :average value of the penetration depths,m.t :test duration,s.
C d :chloride concentration at which the colour changes,C d =0.07N for Portland cement concrete.
C 0:chloride concentration in the catholyte solution,C 0=2N.3.3.Test results
For the self-compacting concrete mixes,tests were performed at the ages of 28,56,90days,1,2and 5years.For the traditional concrete mixes,no experiments at the age of 5year were per-formed.Based on these experimental results,age factors were de-rived with a regression analysis.In Fig.6,the experimental results of SCC 16are given.In Table 3the values for D 1(non-steady state migration coef?cient at 1year concrete age)and age factor m are given,together with the correlation coef?cient R 2for all concrete mixes.
3.4.Discussion of test results
3.4.1.Values of D and m
Regarding the experimental results of traditional concrete it is noted that the concrete composition with CEM III/A (TC2)has a migration coef?cient approximately half the value of the tradi-tional concrete mixes with the same amount of cement and W /C ratio (TC1and TC4).The age factor seems independent of the ce-ment type.For the traditional concrete with a higher amount of ce-ment and same amount of water,leading to a lower W /C ratio (TC3),the migration coef?cient is lower and the age factor is higher.
Comparing with the corresponding self-compacting concrete mixes (TC1versus SCC1,TC2vs.SCC3,TC3vs.SCC6and TC4vs.SCC4),the self-compacting concrete mixes have a lower migration
coef?cient.For the mixes with ordinary Portland cement,the migration coef?cient of SCC is around 90%of the migration coef?-cient of TC.
By studying the variation of the cement type of SCC,CEM III/A leads also to the lowest migration coef?cient,but in contrast with traditional concrete,the cement type has also a large in?uence on the age factor,which is more in correspondence with literature [4].By changing the amount of cement for a constant amount of water,the migration coef?cient is decreasing for an increasing amount of cement (SCC5–SCC1–SCC6–SCC7),which is explained by a decreasing porosity.However,for the age factor this relation-ship is not clear.
By changing the total amount of powder P (cement +?ller),keeping the W /C ratio and the C /P ratio constant (SCC10–SCC1–SCC11–SCC12),the migration coef?cient is increasing and the age factor decreasing with an increasing amount of powder,an increasing amount of cement and an increasing amount of water.But for a constant W /C ratio.This leads to the conclusion that for self-compacting concrete,the W /C ratio is certainly not the only parameter to describe the migration of chlorides.
By keeping the amount of cement constant,together with a con-stant amount of powder but with a changing amount of water (SCC13–SCC1–SCC14–SCC15),the migration coef?cient is increasing and the age factor is decreasing for an increasing amount of water and an increasing W /C ratio.From this conclusion –a decreasing m for an increasing W /C ratio –the same result is obtained as predicted by the relationship of Tang illustrated in Fig.1.However if the mixes SCC5–SCC1–SCC6–SCC7are stud-ied,this is not clear.This could be explained by the fact that an increasing amount of cement leads also to other changes in the concrete:more paste,other pore structure of the paste,etc.These two conclusions could be combined to one clear conclusion if the capillary porosity is used as parameter instead of the W /C ratio,as will be illustrated in the next section.
Three other aspects are also studied.Firstly,by changing the limestone ?ller by an other limestone ?ller with a ?ner grading curve (SCC8vs.SCC1),the migration coef?cient is decreasing and the age factor increasing.
Secondly,the use of ?y ash was studied in one mix (SCC 9).The migration coef?cient is very low and the age factor very high.This illustrates the very different behaviour of concrete with ?y ash.In SCC16,broken limestone aggregate was used instead of river gravel.The rest of the composition is identical as SCC1.This
leads
Fig.6.Non-steady state migration coef?cient in function of time (SCC16).
Table 3
Experimental D 1,m and R 2.
D 1(10à12m 2/s)
m (–)R 2(–)SCC1 5.550.280.89SCC2 3.310.350.97SCC3 1.660.430.93SCC4 6.590.170.75SCC58.390.220.94SCC6 5.380.190.95SCC7 3.090.340.93SCC8 4.950.370.95SCC90.15 1.380.97SCC10 5.090.380.90SCC11 6.110.300.94SCC127.420.220.98SCC13 3.650.400.90SCC149.160.220.94SCC1513.520.220.96SCC16 3.990.390.99TC1 6.320.230.83TC2 3.800.220.86TC3 4.840.300.89TC4
7.60
0.22
0.93
400K.Audenaert et al./Construction and Building Materials 24(2010)396–402
to a stronger contact between the gravel and the cement matrix, which leads to a lower migration coef?cient and a higher age factor.
3.4.2.In?uence of capillary porosity on migration coef?cient and age factor
In this paper the capillary porosity will be calculated based on the model of Powers[13,16,17]:
V cap?capillary porestfree water
?capillary porestwateràgel wateràbounded water
?0:185C a
q
c
t
W
q
w
à
0:28
0:72
C a
q
c
e1à0:185Tt
0:23C a
q
w
à
0:23C a
q
w
?à0:1319C a
q
c
t
1
q
w
eWà0:3194C aT?
W
q
w
à0:362
a C
q
w
e10T
with V cap the volume of capillary pores(m3),C the amount of ce-ment(kg),W the amount of water(kg),a the degree of hydration (–),q c and q w the mass density of respectively cement and water (kg/m3).
V concrete?V watertV cementtV coarse aggregatetV sandtV filler
?W
q
w
t
C
q
c
t
AtStF
q
agg
e11T
capillary porosity?/
cap ?
V cap
V concrete
e12T
with V concrete the volume(m3),A the amount of coarse aggregate (kg),S the amount of sand(kg),F the amount of?ller(kg)and q agg the mass density of aggregate(kg/m3).
The parameters W,C,A,S and F are known from the mix propor-tions.For the mass densities,a value of1000kg/m3is used for water,2625kg/m3for the aggregates,sand and?ller and 3115kg/m3for portland cement.In order to plot D1(non-steady state migration coef?cient at the age of1year)and the age factor m as a function of the capillary porosity,the ultimate degree of hydration is used to calculate u cap.This ultimate degree of hydra-tion is calculated by Mill’s formula(13)[24]:
h ultim?
1:031W=C
0:194tW=C
e13T
In Figs.7and8,respectively D1and m are plotted in function of the capillary porosity.The regression lines were calculated based on the results of the pure Portland cement concretes(thus excluding SCC3, SCC4,SCC9,TC2and TC4),but all mixes are given in the?gures. From these?gures,it is clear that the non-steady state migration coef?cient is increasing with an increasing capillary porosity.The age factor shows a decreasing tendency if the capillary porosity in-creases.Both conclusions are valid for self-compacting concrete and traditional vibrated concrete.However,the age factor is less in?u-enced by the concrete composition than the migration coef?cient it-self.For Fig.7,the equation of the regression line is given by:
D1?1:4502/capà5:1934e14Twith a correlation coef?cient of0.84.In Fig.8,the equation describ-ing the relation between the age factor m and the capillary porosity u cap has a correlation coef?cient of0.76and is written as:
m?à0:0318/capt0:5544e15TThe obtained results show that the capillary porosity seems to be an adequate parameter to describe the chloride transport in concrete. Nevertheless,it has to be added that,although the capillary porosity gives better results than W/C,further improvements still can be made.Introducing the connectivity of the pore system would en-able a further step forward in chloride transport modelling in cementitious materials.However,in order to do so,detailed3D hydration modelling combined with multi scale analysis would be needed,bringing the chloride transport analysis to a higher order of complexity.Without the multi scale analysis,the approach based on the capillary porosity seems to be defendable as a further improvement in chloride transport modelling,in comparison with models merely based on W/C.
4.Conclusions
By studying the time dependency of the chloride migration coef?cient of16self-compacting concrete mixes and four tradi-tional concrete mixes,the following conclusions are made:
–Eq.(3),generally used to describe the time dependency of the chloride diffusion coef?cient,can also be used to describe the time dependency of non-steady state migration coef?cients, determined with NT BUILD492.This introduces a small error of approximately5%,which is small in comparison with the var-iability of the diffusion and migration coef?cients itself.
–The migration coef?cient of the traditional concrete mixes is higher than the migration coef?cient of the self-compacting concrete mixes with the same cement type and W/C ratio.
–In literature,it is not clear whether the age factor is decreasing or increasing if the W/C ratio is increasing.In this research pro-ject,an increasing W/C ratio leads to a decreasing age factor.
Fig.8.Age factor(m)in function of capillary porosity(u cap).
K.Audenaert et al./Construction and Building Materials24(2010)396–402401
–With the experimental part of the paper,it is illustrated that the non-steady state migration coef?cient and the age factor are depending on many factors in the concrete composition such as the amount and type of cement,amount and type of?ller, amount of water.In this paper,these factors were combined in one parameter:the capillary porosity.This parameter seemed
a good tool to describe the migration coef?cient and the age fac-
tor.If the capillary porosity is increasing,the migration coef?-cient is increasing and the age factor decreasing. Acknowledgement
The?nancial support for the post-doctoral project of the FWO-Flanders is greatly acknowledged.
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