art%3a10.1023%2fb%3aints.0000042339.92990.4c
TRANSCRIPT
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
1/11
INTERFACE SCIENCE 12, 411421, 2004
c 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
The Interfacial Transition Zone (ITZ) Between Cement Paste and Aggregate
in Concrete
KAREN L. SCRIVENER
Ecole Polytechnique Federale de Lausanne, Switzerland
ALISON K. CRUMBIELyon, France
PETER LAUGESEN
Dansk Beton Technik, Denmark
Abstract. This paper describes the so called interfacial transition zoneITZin concrete. This is the region of
the cement paste around the aggregate particles, which is perturbed by the presence of the aggregate. Its origin lies
in the packing of the cement grains against the much larger aggregate, which leads to a local increase in porosity
and predominance of smaller cement particles in this region. The ITZ is region of gradual transition and is highly
heterogeneous, nevertheless the average microstructural features may be measured by analysis of a large numbers
of backscattered electron images of polished concrete samples. Such measurements show that the higher porositypresent initially is significantly diminished by the migration of ions during hydration.
Keywords: cement, concrete, image analysis, scanning electron microscopy, porosity
Introduction, Importance of the ITZ
The interfacial transition zone (ITZ) between cement
paste and aggregate is the most important interface
in concrete. Concrete is often considered to be a two
phase composite materialcement paste plus aggre-
gates. However even in the most basic phenomena the
critical role of the ITZ is clear. This is graphically illus-
trated by comparison of the stress strain curves for ce-
mentpaste, aggregatesand concrete under compression
loading (Fig. 1). Individually cement paste and aggre-
gates both show brittle elastic behaviour, that is to say,
linear, reversible deformation up to a limit, followed by
sudden failure. In contrast, concretethe composite
materialshows significant quasi-ductile behaviour.
The load bearing capacity continues to increase be-
yond the linear elastic limit and there is a progressive
To whom all correspondence should be addressed.
decrease in load bearing capacity after the peak load.
Such behaviour, which has important practical conse-
quences, is due to the development of multiple micro-
cracking predominantly in the ITZ. This well known
behaviour leads to the common view of the ITZ as the
weak link in concrete.
TheoriginoftheITZliesinthesocalledwalleffectof packing of cement grains against the relatively flat
aggregate surface (Fig. 2). This is directly responsible
for the features of the ITZ, particularly its higher poros-
ity. Due to the way it is formed the ITZ is not a definite
zone, but a region oftransition. It effective thickness
varies with the microstructural feature being studied
and during the course of hydration. As cement is a
particulate material, the details of this transition zone
are different around each aggregate particle. The effect
of the ITZ on mechanical properties has already been
alluded to. The impact on transport properties is less
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
2/11
412 Scrivener, Crumbie and Laugesen
Figure 1. Comparative stress strain curves for aggregate, paste and
concrete, the quasi-brittle behaviour of concrete illustrates the im-
portance of the ITZ on the macroscopic properties of concrete.
straightforward, but nevertheless significant. Methods
of modifying the ITZ are critical in the development
of high performance concrete. The ITZ is also critical
in determining the effective water to cement ratio of
mortars and concretes.
The aim of this article is to present the features that
give rise to the formation of the ITZ and to discuss how
Figure 2. Illustration of the wall effect. A flat solid object placed at random in an assembly of cement grains would cut through grains. As
this is impossible the packing of grains is disrupted to give a zone of higher porosity and smaller grains in the zone close to the aggregate.
this affects the properties of concrete. The Interfacial
Transition Zone has already been the subject of threetechnical committees of RILEM, whichhave published
state of the art reports [1, 2].
The Origin of the ITZPacking of Cement Grains
Against Aggregate
Cement grains range in size from less than a micron to
up to 100 microns. Aggregate particles are several or-
ders of magnitude larger. This difference in size means
that each aggregate particle is a mini wall which dis-
rupts the packing of the cement grains, resulting in the
wall effect as illustrated in Fig. 2. If a large objectwere placed in a random assembly of grains, it would
cut through many grains. As this is physically impos-
sible in the case of aggregate particles in cement paste,
the normal packing of the grains is disrupted. The re-
sult is that a zone closest to the aggregate contains pre-
dominately small grains and has a significantly higher
porosity, while larger grains are found further out.
In concrete this means that the sizeof the ITZ is com-
parable with the size of the cement grains. As packing
is a random process, each individual region of ITZ will
be differentthe ITZ is heterogeneous on the same
scale as the cement grains, therefore the average ef-fects may not be immediately apparent in images of
concrete microstructure, as for example Fig. 3. Most
diagrams of the ITZ found in the literature do not give
a correct idea of scale. As will be discussed there is no
discrete boundary between the ITZ and the bulk paste.
The changes are progressive and are most significant
in the first 1520 m closest to the aggregate (white
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
3/11
Interfacial Transition Zone (ITZ) in Concrete 413
Figure 3. Backscattered electron(BSE)image of concrete,aggregateon left. Thewhite linesindicates distancesof 20and 50m frominterface.
lines marked on Fig. 3 are at approximately 20 and
50m from the interface). Therefore in good quality
concretes the ITZ is NOT apparent as distinct band of
higher porosity in, for example, thin sections impreg-
nated with florescent resin, by light microscopy.
However, even in good quality concretes, it is quite
usual to observe heterogeneities in the microstructure
on a scale of several hundred microns. Figure 4, illus-
trates sucha casewhere severalaggregatesare clustered
together. In the oval labelled 1 the microstructure hasa significantly higher porosity. In the oval labelled 2
there is a concentration of calcium hydroxide along the
lower edgeof the aggregate, butsuchconcentrationsare
not observed around all aggregates.
The challengein characterising theITZ is to measure
the average microstructure in real concretes. This can
be done by backscattered electron (BSE) image analy-
sis of polished sections of concrete [36]. Results ob-
tained from this technique (mainly from the PhD thesis
of Crumbie [6]) form the bulk of this paper. The ma-
jor advantage of this technique is that the ITZ can be
studied in context in normally prepared concretes. The
disadvantages of the technique are that it is very time
consuming and that observations are made on a two-
dimensional sections through a three dimensional mi-
crostructure. The sectioning effect means that the dis-
tance measured on 2D sections are on average greater
than the perpendicular distances in the 3D microstruc-
ture, it hasbeen estimatedthat the average lengthening
factor is around 1.2 [6]. The distances quoted here are
the uncorrected distances measured on 2D sections.In the development of the BSE/image analysis tech-
niques considerable work was done to establish the
number of fields which needed to be measured to ob-
tain representative results from a concrete. With im-
age analysis, the compromise must always be made,
between having the best resolution (highest magnifica-
tion) to observe thefeaturesof interest,whilst analysing
a large enough area to be statistically significant. Dif-
ferentmagnifications, bandwidths and number of fields
were studied in the PhD thesis of Crumbie [6]. As a re-
sult of these investigations the fractions of anhydrous
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
4/11
414 Scrivener, Crumbie and Laugesen
Figure 4. BSE image of concrete illustrating typical inhomogeneities. Several aggregate grains are clustered together resulting in the formationof a porous zone (1). Along the bottom of one aggregate there is a high concentration of calcium hydroxide (2).
cement, calcium hydroxide, other hydration products
and porosity were evaluated in 30 bands of about 3 m
in width around aggregate in 100 randomly chosen im-
ages for each concrete. Taking into account the spec-
imen preparation, image acquisition and image analy-
sis, several days were needed to analyse each concrete.
Therefore, this is not a technique to be applied rou-
tinely to concretes. However, the detailed study made
by Crumbie allows the way in which the ITZ forms to
be understood.
The measured distribution of unhydrated cement in
a standard concrete at a w/c = 0.4 at different ages are
shown in Fig. 5. The earliest age at which it is practical
to prepare a polished section is 1 day; by which time,
considerable reaction of the cement has already taken
place. However the original distribution can be back-
calculated from the amount of unhydrated cement at
one day and the amount of hydration products. This
curve indicates that a deficit in anhydrous grains is only
significant in a region of about 15 m adjacent to the
aggregatesimilar to the size of the average cement
grain.
As hydration continues, the more detailed effects of
the disrupted packing on the grading of the cement
particles becomes apparent. The small grains quickly
hydrate completely, while the larger grains have a core
of unhydrated cement. At any given time the thickness
of each grain that has reacted will be the roughly the
same, so the unhydrated fraction will be greater for
larger grains. This explains the observation that, the
width of the zone with a reduced amount of anhydrous
material increases with age up to one year. At 1 year a
reduction in the amount of anhydrous cement is appar-
ent over a zone of more than 40 m.
The secondary minimum at around 35 m, was
found to occur in all the concretes measured. From
this it is deduced that as smaller grains pack close
to the interface, the region further out is depleted of
small grains, so for the large grains remaining there
is less reaction of anhydrous materials between 1 and
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
5/11
Interfacial Transition Zone (ITZ) in Concrete 415
Figures 5 and 6. Distribution of unhydrated cement in concrete (w/c = 0.4) at various ages. From the way in which this changes during
hydration, the effect of the aggregate on the grading of the cement grains in the ITZ can be deduced (Fig. 5). Schematic representation of grading
of cement grains in ITZ (Fig. 6).
28 days. These effects are shown schematically in
Fig. 6.
Given the relatively large zone in which the packingof the cement grains is disrupted by the aggregate par-
ticles, it is debatable if the term bulk paste really has
any meaning in concretefrom the surface area of the
aggregate and the volume of paste it can be calculated
that the average thickness of paste around aggregate
particles is only of the order of 50 m and the typical
maximum distance between aggregatesseen in sections
of concrete is only a few hundred microns. However, as
already indicated, and as will be discussed further, the
most significant differences occur in a much narrower
zone.
Effective Water to Cement Ratio of Concrete
The measurements discussed above, show that thewall effect produced by the aggregate leads to a zone
of the order of 15 m in width around each aggregate
particle, in which there are less cement grains in the
fresh state. This is equivalent to a zone of higher water
to cement ratio. In a typical concrete some 2030% of
the cement paste lies within 15 m of the aggregate.
Therefore, a higher water to cement ratio in this zone,
means that the water to cement ratio of the bulki.e.
paste more than 15 m from the aggregate must be re-
duced. For a concrete with an overall w/cratio of 0.4,
the w/cratio of this bulk paste is only around 0.35.
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
6/11
416 Scrivener, Crumbie and Laugesen
Figure 7. Fluorescent light micrographs of thin sections of mortars with the same water to cement ratio but different sand contents. At lower
sand contents the lighter appearance of the paste indicates a higher water to cement ratio. The apparent water to cement ratio decreases with
increasing sand content.
The impact of aggregate content on theeffectivew/c
ratio, can be seen more dramatically in Fig. 7, from
work by Laugesen [7]. This shows a series of mortars
all with the same w/c (0.45), but with different sand
contents. The mortars are impregnated with fluorescent
resin and thin sections prepared. The individual pores
are not resolved, but the average luminosity of the hy-
drated areas is proportional to the amount of resin they
contain and so to their porosity.
It can be seen that as the sand content increase, the
paste areas become darker, indicating a lower porosity
due to a lower effective w/c ratio in the bulk of these
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
7/11
Interfacial Transition Zone (ITZ) in Concrete 417
paste areas. It is estimated that for a standard mortar
the overall w/c of 0.45 gives an effective w/c in thebulk paste of 0.38.
Distribution of Hydration Products in the ITZ
The packing of the anhydrous cement grains is the
origin of the ITZ, but its eventual structure is also
determined by the way in which the hydration prod-
ucts are deposited in this region. During hydration,
the microstructural development of Portland cement is
dominated by the formation of the two major hydrate
phasescalcium silicate hydrate, C-S-H1 and calcium
hydroxide, Ca(OH)2, CH1. After the first few seconds,
the concentration of silicate in solution remains very
low and consequently the C-S-H phase is mostly de-
posited directly around the cement grains. In contrast
the concentration of calcium in solution is much higher
and calcium hydroxide is mainly deposited in the open
pores. Furthermore, it has been suggested that silica
inhibits the nucleation of calcium hydroxide, which
favours the precipitation of this phase as far from the
cement grains as possible. The resulting microstructure
is shown schematically in Fig. 8.
As explained above, the packing of cement grains
leaves an initially more porous zone around the ag-gregate. This favours the deposition of more calcium
Figure 8. Schematic representation of the microstructure of
Portland cement pasteC-S-H product deposits around the ce-
ment grains, while calcium hydroxide precipitates in the pore
spaces.
Figure 9. Average distribution of calcium hydroxide in the ITZ.
hydroxide in this region as can be seen from the experi-
mental results shown in Fig. 9. As the quantity of anhy-
drous material in this region is low, most of this calcium
hydroxide must form from calcium ions coming from
the reaction of anhydrouscement outside theinterfacial
region. From the calculated initial distribution of the
anhydrous cement grains and the amount remaining at
a given time the amount of calcium hydroxide, coming
from the cement grains in each band can be calculated.
By comparison with the actual amounts, the amount
of excess or deficit, relative to the case of local depo-
sition can be calculated. These calculated amounts are
shownin Fig.10.From Figs. 9 and 10it can beseen that
the zone of increased calcium hydroxide corresponds
very closely to the zone which is deficit in anhydrous
material on mixingi.e. has excess porosity. Most of
the excess calcium hydroxide is precipitated in the first
Figure 10. Redistribution of calcium hydroxide in the ITZthe
area of excess is the % area above that which would have been
formed from the local reaction of anhydrous material. This indicates
that there hasbeen a netdiffusion of calcium andhydroxide ions into
the 10 m closest to the aggregate.
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
8/11
418 Scrivener, Crumbie and Laugesen
day, with a slight increase to 28 days, but negligible
further increase to one year.Although it has been shown that the ITZ contains
excess calcium hydroxide compared to the bulk, this
amount in the ITZ is by no means a continuous layer
around all aggregates, as Fig. 3 illustrates. Even in the
3 m band closest to the aggregate the amount of cal-
cium hydroxide is only on average around 13%i.e.
about one eighth of the total volume. Higher excesses
of calcium hydroxide may be seen locally as in Fig. 4.
These heterogeneities are a normal feature of well for-
mulated concrete. In poorly formulated concrete mi-
crobleeding may occur and lead to the formation of
lenses of water beneath aggregate particles which be-
come filledwith calcium hydroxide.Such features werenot included in any of the measurements shown in this
paper.
With the BSE imaging technique it is not possible to
measure the orientation of the calcium hydroxide. Ear-
lier work from the group at Toulouse University using
X-ray diffraction and progressive polishing on model
specimens, with cement paste cast against a single mas-
sive aggregate indicated that there is a preferential ori-
entation of Calcium hydroxide with thec-axis parallel
to the aggregate surface [8].
The distribution of C-S-H and its redistribution com-
pared to formation solely from anhydrous material inthe immediate area is shown in Figs. 11 and 12. Despite
the lower mobility of silica, there is still significant re-
distribution of this product between the interfacial zone
and the bulk during the first day. However, it is appar-
ent that redistribution occurs at a more local scale
material deposited in the first 5 m is compensated by
a deficit in the next 10 (515) m. After the first day,
there is little further change over 1 year. These obser-
Figure 11. Average distribution of other hydration products, pre-
dominantly C-S-H.
Figure 12. Redistribution of C-S-H in ITZ (excess of C-S-H over
that which would be formed by the local reaction of anhydrous ma-
terial).
vation confirm the lower mobility of silica (needed to
form C-S-H) compared to calcium.
The other hydrate whose distribution in the ITZ has
been studied is ettringite. Monteiro and Mehta [9] mea-
sured an increase in ettringite in theITZ (usingin model
specimens by the Toulouse XRD technique). The small
crystals of ettringite cannot be easily resolved in BSE
images, so it has not been possible to confirm this mea-
surement in real concretes. The ions forming ettringite
are highly mobile in cement pastes, as witnessed by
the recrystallisation of ettringite into pores and voids
in mature concretes. Therefore an increased concen-
tration of this phase in the more porous ITZ would be
expected.
Porosity in the ITZ
Porosity is the volume not filled by cement grains or
hydration products and therefore is the result of all the
effects described above. The variation in distributions
with age is shown in Fig. 13. The importance of hy-
drate redistribution in modifying the excess porosity
in the ITZ are clear. On mixing the porosity adjacentto the interface is some 40% higher than that in the
bulk. After the first day this difference is reduced to
only 1020 % and the gradient is less steep. At greater
ages the porosity in the ITZ reduces by about the same
amount as it is reduced in the bulk. As there is much
less anhydrous material remaining in the ITZ, this re-
duction must be attributed to the deposition of hydrates
from the migration of ions from the reaction of cement
further from the interface.
These results of image analysis show how the over-
all amount of porosity changes in the ITZ. This overall
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
9/11
Interfacial Transition Zone (ITZ) in Concrete 419
Figure 13. Average porosity in ITZ at various ages.
amount will be the major factor determining the me-
chanical properties of this region. However, the trans-
port properties will depend more on the connectivity
of the porosity. It is not possible to obtain information
about connectivity from a two-dimensional polished
section of a three-dimensional structure. Nevertheless,some other work [10] gives some indication that the
connectivity of the ITZ is increased. In this study, con-
crete specimens were subject to mechanical testing.
At various load levels the samples were intruded with
Woods metal while under load and subsequently sec-
tioned and polished. In the polished sections it was
observed that the penetration of the Woods metal oc-
curred preferentially around the aggregate particles,
which suggests a higher connectivity of the porosity
in the ITZ (Fig. 14). It must be borne in mind that the
samples treated with Woods metal were dried prior
to the experiment and heated to 80C to allow the in-
trusion of the Woods metal. Although this treatmentcould have led to microcracking, linking pores which
were not connected in the original state, such cracks
were not seen.
What Happens Right at the Interface
We have seen that the ITZ arises from the packing of
the anhydrous cement grains, which produces a region
of high porosity in the first 1520 mm. However, the
other feature of the ITZ is what happens right at the in-
Figure 14. Concrete impregnated with Woods metal, which has
penetrated better through the ITZ.
terface. Early work on model systems [11] found that
a film of calcium hydroxide frequently precipitated in
this region. However, observations in real concretes
and mortars indicate that there is more often the pre-
cipitation of a thin layer of C-S-H directly at the in-
terface [12]. As discussed above during the very early
stages of hydration both calcium hydroxide and C-S-H
form through solution, so the aggregate surface may
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
10/11
420 Scrivener, Crumbie and Laugesen
act as a heterogeneous nucleation site for both phases.
Siliceous rock types are essentially inert (leaving asidethe possibilities of alkali silica reaction on much longer
time scales) and there is no chemical bonding at the in-
terface. Calcareous aggregates may react very slightly
leading to the formation of calcium alumino monocar-
bonate in the ITZ.
Modification of the ITZ
Quantitative image analysis clearly shows that the ITZ
is caused by the disruption of packing the anhydrous
cement grains in this region. Thus the ITZ may be mod-
ified by changing the particle size distribution of thecementitious materials. This is now done routinely by
adding around 510% of silica fume, which consists
of particles of amorphous silica ranging in size down
to about 100 nm (0.1 m). This technology is used
widely in the production of high strength concretes.
Early work with the backscattered electron image anal-
ysis techniqueby theauthor andBentur [4]showed how
additions of silica fume densified the packing in the in-
terfacial transition zone (Fig. 15). Even at 1 day the
porosity in this region is much reduced.
Consequences of the ITZ
Despite theclear difference of theITZ from a bulk paste
it is still very difficult to precisely quantify its effect.
This is first because it is not a discrete zone but a re-
Figure 15. Distribution of Porosity in the ITZ of concretes with
and without silica fume. Adapted from [4].
gion of gradually changing microstructure. Secondly,
the preparation of model specimens in which the prop-erties of the ITZ can be measured separately tend to
produce different ITZs from those in real concrete.
As described in the introduction the impact of the
ITZ on mechanical properties is not in doubt. Never-
theless, evaluation of the mechanical properties of the
ITZ from those of the overall concrete is an inverse
problem. Monteiro has reviewed the possibilities for
mechanical modelling [13] and recently published an
analysis with Hashin [14] based on the generalised self
consistent scheme in which the elastic modulus of the
ITZ was estimated to be about 50% lower then the
bulk paste.
Theimpact of theITZ on Transport properties, whichdetermine durability, is more complex and has been
well reviewed by Marchand and Delagrave [15]. Al-
thoughthe higherporosity andprobablehigher connec-
tivity of this porosity suggest that transport of species
should be faster in the ITZ, this effect is counteracted
by several other effects:
The overall volume of the cement paste (the perme-
able component of concrete) is reduced.
The presence of aggregates increases the tortuousity
of the path for transport.
The porosity of the bulk paste is reduced comparedto a pure paste with the same overall w/cratio.
Experimental studies (such as [16, 17]) in which the
aggregate content has been varied keeping the water
to cement ratio constant indicate that rates of trans-
port are decreased as aggregate content increases, de-
spite the increase in the amount of ITZ. This indicates
that the effects of decreasing paste volume and tortu-
ousity outweigh any effect of increased transport in the
ITZ.
Summary
The ITZ is a zone oftransitionnot radically differ-
ent to the rest of the cement paste and its effective
width depends on the microstructural feature be-
ing considered and the degree of reaction.
Quantitative characterisationof the interfacial transi-
tion zone (ITZ) between aggregate and cement paste
in concrete, confirms that it arises due to the packing
of cement grains against the larger aggregate par-
ticles. This initial packing leads to a more porous
zone some 15 to 20 m in width. The deposition of
-
7/23/2019 art%3A10.1023%2FB%3AINTS.0000042339.92990.4c
11/11
Interfacial Transition Zone (ITZ) in Concrete 421
hydration products, especially calcium hydroxide
tends to fill this zone, but even in mature pastes theITZ still has a significantly higher porosity.
Because of the packing effect extra water is incor-
porated in the ITZ and the effective water to cement
ratio of the bulk paste in reduced by around 0.05.
The most effective way to modify the ITZ is to add
a proportion of fine particles, such as silica fume,
which can pack closer to the aggregate surface.
The impact of the ITZ on mechanical properties is of
considerable significance, leading to increased duc-
tility amongst other effects.
Any impact of the ITZ on transport properties is
counteracted by other factors which generally lead
to a reduction of transport rates with increasing ag-gregate content if other variables are held constant.
Note
1. These abbreviations use cement chemist notation, C = CaO;
S = SiO2; A = Al2O3; F = Fe2O3; H = H2O; the nomencla-
ture C-S-H indicates the variable stoichiometry of this phase.
References
1. J.C. Maso(ed.), Interfacial Transition zonein Concrete, RILEM
report 11 (E&FN Spon, London, 1996).
2. M.G. Alexander, G. Arliguie, G. Ballivy, A. Bentur, and J.
Marchand, Engineering and Transport Properties of the Inter-
facial Transition Zone in Cementitious Composities, Report 20
(RILEM Publications S.A.R.L., 1999).
3. K.L. Scrivener and E.M. Gartner, in Bonding in Cementitious
Composites (Proc. Mat. Res. Soc. Symp., 114, 1988), p. 77.
4. K.L. Scrivener, A. Bentur, and P.L. Pratt, Adv. Cem. Res.1, 230
(1988).
5. K.L. Scrivener, A.K. Crumbie, and P.L. Pratt, in Bonding in Ce-
mentitious Composites(Proc. Mat. Res. Soc. Symp., 114, 1988),
p. 87.
6. A.K. Crumbie, PhD Thesis, University of London, 1994.
7. P. Laugesen, presentation 4th Euroseminar on Microscopy Ap-
plied to Building Materials, June 1993.
8. J. Grandet and J-P. Ollivier, inProceeding of 7th International
Congress of the Chemistry of Cement(Editions Septima, Paris,
1980), vol. III, pp. VII 6368 and 8589.
9. P.J.M. Monteiro and P.K. Mehta, Cement and Concrete Research
15, 378 (1985).
10. K.L. Scrivener and K.M. Nemati, Cement and Concrete Re-
search26, 35(1996).
11. B.D. Barnes,S. Diamond,and W.L. Dolch, Cement andConcrete
Research8, 233 (1978).
12. K.L Scrivener and P.L. Pratt, in Proc. 8th Int. Cong. on the
Chemistry of Cements, Rio de Janeiro (1986), vol. III, p. 466.
13. P.J.M. Montiero, in ref. 1, p. 64.
14. Z. Hashin and P.J.M. Montiero, Cement and Concrete Research
32, 1291 (2002).
15. J. Marchand and A. Delagrave, in ref. 2, p. 157.
16. A. Delagrave, J. Marchand, and M. Pigeon, Advanced Cement
Based Materials7, 60 (1998).
17. N.R. Buenfeld and E. Okundi, Magazine of Concrete Research
50, 339 (1998).