-
VIII International Conference on Fracture Mechanics of Concrete
and Concrete StructuresFraMCoS-8
J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang
(Eds)
STUDY OF CONCRETE CRACKING DURING ACCELERATEDCORROSION TESTS IN
REINFORCED CONCRETE
B. SANZ1∗, J. PLANAS1 AND J.M. SANCHO2
1Universidad Politécnica de MadridE.T.S. de Ingenieros de
Caminos, Canales y Puertos
C/ Profesor Aranguren s/n,28040 Madrid, Spain
e-mail: [email protected]
2Universidad Politécnica de MadridE.T.S. de Arquitectura
Avda. Juan de Herrera 4,28040 Madrid, Spain
Key words: Cohesive Crack, Accelerated Corrosion Tests, Finite
Element Simulations
Abstract. Cracking of reinforced concrete can occur in certain
environments due to rebar corrosion.The oxide layer growing around
the bars introduces a pressure which may be enough to lead to
thefracture of concrete. To study such an effect, the results of
accelerated corrosion tests and finite ele-ment simulations are
combined in this work. In previous works, a numerical model for the
expansivelayer, called expansive joint element, was programmed by
the authors to reproduce the effect of theoxide over the concrete.
In that model, the expansion of the oxide layer in stress free
conditions issimulated as an uniform expansion perpendicular to the
steel surface. The cracking of concrete issimulated by means of
finite elements with an embedded adaptable cohesive crack that
follow thestandard cohesive model. In the present work, further
accelerated tests with imposed constant cur-rent have been carried
out on the same type of specimens tested in previous works (with an
embeddedsteel tube), while measuring, among other things, the
main-crack mouth opening. Then, the tests havebeen numerically
simulated using the expansive joint element and the tube as the
corroding electrode(rather than a bar). As a result of the
comparison of numerical and experimental results, both forthe crack
mouth opening and the crack pattern, new insight is gained into the
behavior of the oxidelayer. In particular, quantitative assessment
of the oxide expansion relation is deduced from the ex-periments,
and a narrower interval for the shear stiffness of the oxide layer
is obtained, which couldnot be achieved using bars as the corroding
element, because in that case the numerical results wereinsensitive
to the shear stiffness of the oxide layer within many orders of
magnitude.
1 INTRODUCTION
Cracking of reinforced concrete structurescan occur in certain
environments as a conse-quence of the corrosion of the rebars. The
ox-ide layer growing around the bar exerts a pres-sure on the
surrounding concrete which may beenough to crack the concrete cover
[1].
In the present work, the cracking of concreteproduced by rebar
corrosion is studied combin-ing the results of accelerated
corrosion tests andfinite element simulations.
To reproduce the mechanical action of theoxide on the concrete,
a numerical so-calledexpansive joint element was developed by
the
1
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B. Sanz, J. Planas and J.M. Sancho
authors in which the formation of the oxide issimulated as an
uniform expansion proportionalto the corrosion depth which is
assumed to begiven at any specified time [2].
For the cracking of concrete, finite elementsare used with an
embedded adaptable cohesivecrack as described in [3]. The embedded
crackfollows a simple 3D extension of the standardcohesive model
introduced by Hillerborg [4] .
The parameters that characterize the crack-ing of concrete are
experimentally determinedin three point bending tests and brazilian
tests,following the method described in [5].
In previous works, the model was appliedto a simple specimen,
consisting in a concreteprism cast around a smooth steel bar.
Para-metric simulations allowed to find bounds forthe parameters of
the expansive joint element,which are not directly accessible to
experiment[2, 6].
In parallel, accelerated corrosion tests werecarried out under
current intensity control us-ing concrete prisms of the same
dimensions asthose used in the simulations, but with a cast-in
steel tube instead of a steel bar. The exper-imental crack pattern
was revealed under ultra-violet light of cross-sectional slices of
the cor-roded specimens impregnated with resin con-taining
fluorescein. The experimental crack pat-tern was found to agree
well with the numericalpredictions [7].
For the present work, further acceleratedtests with imposed
constant current have beencarried out on the same type of specimens
testedin previous work (with an embedded steel tube),while
measuring, among other things, the main-crack mouth opening. Then,
the tests have beennumerically simulated using the expansive
jointelement and the tube as the corroding electrode(rather than a
bar). As a result of the compari-son of numerical and experimental
results, bothfor the crack mouth opening and the crack pat-tern,
new insight is gained into the behavior ofthe oxide layer.
The paper briefly describes the numericalmodel and its
underlying parameters and out-lines the experimental procedure.
Then the re-
sults are summarized and the implications of thecomparative
parametric analysis are discussed.
2 OUTLINE OF THE NUMERICAL ANDEXPERIMENTAL PROCEDURES
As already pointed out, the cracking of theconcrete surrounding
a corroding rebar is stud-ied in this work combining the results of
accel-erated corrosion tests and finite element simula-tions. In
this section, we give a short account ofthe essential features of
both numerical simula-tions and tests.
The finite element simulations rest on twobasic models: the
cracking model, which is as-sumed to follow a cohesive crack
behavior, andthe oxide layer model, which is implementedas a layer
of interface elements with zero initialthickness which expand as
the corrosion depthincreases.
2.1 About concrete crackingThe cracking behavior of concrete can
be
characterized in independent tests in which itsfracture
properties are determined by well es-tablished procedures [5, 8].
Likewise, a rela-tively large experience exists about the
numeri-cal modeling of concrete cracking. The authorsuse a
relatively simple implementation consist-ing of constant strain
elements with an embed-ded cohesive crack with limited adaptability
[3].
The cohesive crack is the simplest 3D ex-tension of the standard
cohesive crack proposedby Hillerborg and co-workers in 1976 [4]. It
isfully characterized by a single scalar softeningfunction, the one
for pure Mode I crack growth,and the extension consists in assuming
that theforces are central, i.e., that the cohesive tractionvector
on one crack face is proportional to therelative displacement
vector of the two crackfaces.
A generic softening function is displayed inFigure 1, in which
the initial linear approxima-tion is also shown. The initial linear
approxi-mation of the softening curve and a bilinear fitto the full
curve can be obtained in closed formfrom a combination of diagonal
splitting testsand stable bending tests on notched beams sub-
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B. Sanz, J. Planas and J.M. Sancho
jected to three-point bending [5].The limited adaptability of
the crack is actu-
ally a numerical expedient to avoid crack lock-ing while keeping
the formulation strictly lo-cal. It consists in allowing the crack
to rotateto adapt itself to the local stress fields while thecrack
opening is smaller than a certain thresholdwth, which, by default,
is taken to be 0.2GF1/ft,in which GF1 and ft are defined in Figure
1.
GF1
σ
ww1
σ
w
GF
ft
GF1 ≈ 0.5GF
softening curve
linear approximationft
Figure 1: Softening curve of concrete and linear approxi-mation.
The area under the linear curve GF1 is, approxi-mately, half of the
the fracture energy GF , the area underthe full softening
curve.
2.2 The expansive joint modelContrary to cracking behavior, the
mechani-
cal behavior of the oxide layer cannot be inde-pendently
measured, and its basic mechanicalproperties have to be inferred
from the resultsof the accelerated corrosion tests. To reproducethe
effect of the expansion of the oxide at thesurface of corroding
steel, a so-called expansivejoint element was devised that
simulates the me-chanical action of the oxide layer on its
neigh-borhood. It is a four-node element with zeroinitial thickness
that reproduces the growth ofthe oxide as a normal expansion.
During the corrosion process, there is a partof steel that is
transformed into oxide, the cor-rosion depth x (Fig. 2), but there
is also a volu-metric expansion, due to the specific volume ofthe
oxide being greater than the specific volume
of the steel. However, in order to simplify thecalculations, the
expansive joint element onlyincludes the volumetric expansion βx of
the ox-ide and the steel section remains constant, asshown in Fig.
2, and the composite behavior isfound by a series-coupling
model.
Initialsteel
section
x: corrosion depth
ßx: volumetric expansionexpansivejoint elem.oxide
Figure 2: Expansive joint element to reproduce the vol-umetric
expansion of the oxide in finite element simula-tions [2].
The free volumetric expansion is assumed todepend linearly on
the corrosion depth and onan expansion factor β, which is defined
by theratio of the specific volumes of the oxide voxand the steel
vst as
β =voxvst− 1 (1)
For a free expansion of the oxide, withoutany other mechanical
actions, the traction vec-tor t of the element is assumed to be
zero. How-ever, when there is a mechanical displacementw apart from
the free expansion, the tractionvector is calculated as
t = kn(w · n− βx)n + kt[w− (w · n)n] (2)where n is the normal
direction to the elementand kn and kt are, respectively, the normal
andshear stiffnesses of the expansive joint element.
The composite stiffnesses kn and kt are cal-culated to maintain
mechanical equivalence ofthe real and the simulated systems, based
on theproperties of the steel, the real oxide and the ex-pansion
factor β using a series coupling model.
From a simple analysis, it turns out thatthe stiffnesses are
inversely proportional to thethickness of the oxide layer and,
thus, also tothe corrosion depth, i.e.,
kn ∝ 1x
, kt ∝ 1x
(3)
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B. Sanz, J. Planas and J.M. Sancho
which means that, as one might expect, the stiff-ness of the
corrosion layer is infinite when itsthickness is zero.
To avoid numerical instabilities during thecalculations for very
small values of corrosiondepth, a cut-off is stablished for a
certain corro-sion depth x0, assuming that the stiffnesses
areconstant for corrosion depths smaller than x0,as shown in Fig.
3.
k0n
kn
x0 x
analytical curvenumerical curve
Figure 3: Analytical and numerical curves of the normalstiffness
of the expansive joint element. A cut-off of thestiffness is set to
avoid numerical instabilities during thecomputations.
Thus, the numerical law for the normal stiff-ness is written
as
kn =
{k0n if x ≤ x0k0nx0x
if x > x0(4)
and likewise for the shear stiffness.The model incorporates a
debonding ability
to allow easy relative movement of the steeland the concrete in
shear and tension, whichis necessary to achieve proper localization
ofthe cracks. This is accomplished by taking ashear stiffness
substantially less than the normalstress (kt � kn) and by strong
directionality ofthe normal stiffness, implemented through a
di-rectionality factor η, which is equal to one forcompression and
much less than one for ten-sion, i.e.,
η =
{1 if w · n− βx ≤ 0ηt � 1 if w · n− βx > 0 (5)
with the joint equation (2) replaced by
t = ηkn(w · n− βx)n + kt[w− (w · n)n] (6)
2.3 Experimental proceduresAccelerated corrosion tests have been
car-
ried out on concrete prisms cast around a steeltube which is
corroded at constant current in-tensity. The samples in this study
are concreteprisms with a cross-sectional section of 100 mmwidth
and 90 mm height, with a steel tube in-side simulating a rebar of
20 mm diameter anda cover equal to the diameter of the rebar.
Thethickness of the tube is 1 mm. A sketch of thegeometry of the
samples is shown in Fig. 4.
a b
1/2 b
D
a
D
Figure 4: Geometry of the samples, with a = 90 mm, b =100 mm, D
= 20 mm
During the tests, the samples are submergedin water to provide
electrical contact betweenthe working- and the
counter-electrodes.
In the experiments, a constant density cur-rent of 400 µA/cm2 is
applied to the rebar for3 days. A corrosion depth of 35 microns
hasbeen estimated according to the Faraday´s lawas described in
[9].
During the tests, the relative displacement w′
between the two faces parallel to the main crackis measured with
a longitudinal extensometer,as indicated in Fig. 5, at the middle
section ofthe sample.
After corrosion, the samples are cut intoslices and impregnated
under vacuum with resincontaining fluorescein to study the
crackingalong the bar. Previous to the impregnation,the surface of
the slices is grounded, then theslices are dried in an oven until
constant weight,next they are kept in vacuum atmosphere for 24hours
to empty the pores of concrete and finallythey are impregnated with
the resin. That pro-cedure is described in detail in [7].
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B. Sanz, J. Planas and J.M. Sancho
ww’
A B
Figure 5: Relative displacementw′ between the two facesparallel
to the main crack, which is measured with anextensometer at points
A and B during the tests andrecorded in the simulations and which
slightly differsfrom the opening width of the main crack w.
Complementary tests consisting on threepoint bending tests and
diagonal splitting(Brazilian) tests have been carried out
follow-ing the method described in [5] to determine thefracture
parameters of concrete.
2.4 Numerical simulationsIn the simulations, the geometry with
the
tube is reproduced, but also simulations with abar are carried
out to compare with the resultsobtained in previous studies, and a
total radialexpansion of 10 microns is applied in 100 steps,to
focus only on the earliest state of cracking.
The concrete is modeled with elements withembedded adaptable
crack, the oxide with ex-pansive joint elements and the steel with
en-hanced strain quadrilateral elements.
A minimum number of 3 elements in thethickness of the tube and
16 elements per quar-ter of circumference was found to be
adequateto capture the bending of the tube wall. Themesh is
automatically generated using Gmshprogram [10].
The properties of the materials in the simu-lations have been
chosen similar to those in theexperiments and they are shown in
Table 1.
Standard values have been assumed for thesteel, but, in the case
of the concrete, a lin-ear curve fitted to the initial part of
softening,
as shown in Fig. 1, has been used to speed-upthe calculations.
That curve has a fracture en-ergy GF1 that is approximately half of
the ac-tual fracture energy GF of the softening curveof concrete,
but it properly reproduces the frac-ture of concrete at early
stages of cracking.
Table 1: Mechanical properties of steel and concrete,where E is
the elasticity modulus, ν is the Poisson co-efficient, α′ is the
adaption factor of the crack, ft is thetensile strength and GF1 is
the fracture energy in the lin-ear softening curve.
Steel ConcreteE (GPa) 200 30
ν 0.3 0.2α′ – 0.2
ft (MPa) – 3.0GF1 (N/mm) – 0.05
For the oxide layer, the parameters were ini-tially assumed
based on the literature, with abulk stiffness similar to that of
water [11], andthe cut off selected to keep the computationsstable
[6]; they are shown in Table 2. The para-metric study for a
corroding steel bar showedthat a wide range of values for the
tangent stiff-ness produced nearly indistinguishable valuesof the
crack pattern and maximum crack width.However, the results of the
present tests indi-cate that the shear stiffness of the oxide
layerkt need to be reconsidered when the corrodingelectrode is
thin-walled tube. Also, the effec-tive expansion factor β turned
out to be largerthan previously considered as shown in the
nextsection.
Table 2: Reference values for this study, where k0n is
thecut-off normal stiffness in compression, k0t is the cut-offshear
stiffness, ηt is the directionality factor to reduce thenormal
stiffness in tension and β is the expansion factor.
oxidek0n (MPa/mm) 7.0 · 106k0t (MPa/mm) 7.0 · 10−14x0 (mm) 1.0 ·
10−3ηt 1.0 · 10−11β 1.0
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B. Sanz, J. Planas and J.M. Sancho
3 RESULTS AND DISCUSSION3.1 Experimental crack pattern
After corrosion, all the samples are cut intoslices and
impregnated under vacuum with resincontaining fluorescein as
described in section2.3. The experimental pattern of a slice of
asample corroded with a density current of 400µa/cm2 for 3 days is
shown in Fig. 6.
The crack pattern is analyzed combining twoviews of the same
sample: In the first view, inwhich the slice is illuminated with
natural light(top part of the figure), the main crack and theroot
of some secondary cracks are detected. Inthe second view, in which
the slice is illumi-nated with UV ligth (bottom part of the
fig-ure), the thinner cracks are observable, whilethe main crack
seems to be full of black ironoxide and not to have taken so much
resin in-side.
3.2 Main crack opening: β fittingThe relative displacement w′
between the
faces parallel to the main crack is measured inthe experiments
as indicated in Fig. 5 at themiddle section of the sample and it is
also cal-culated in simulations with a bar and a tube asrebars,
using the parameters indicated in Tables1 and 2. The results are
shown in Fig. 7. Thecurves of the simulations with a tube
reproducethe shape of the experimental curve better thanthe
simulations with a bar, as expected. How-ever, in both cases, the
results are lower than theexperimental ones, although the model
properlyreproduced the crack pattern of samples with abar with
those parameters [2, 6].
Thus, new simulations have been computedonly for the case of a
tube, varying the expan-sion factor β to scale the curves, as seen
inFig. 8, finding out that the curve for β = 2 isthe one that
better fits the experimental results.
3.3 Crack pattern: kt fittingThe simulations of the samples with
a bar
and with a tube have been computed again us-ing the value of β
determined in section 3.2 butmaintaining the values of stiffness
shown in Ta-ble 2.
Figure 6: Experimental crack pattern in a sample with
anestimated corrosion depth of 35 microns, observed undernatural
light (top) and under UV light (bottom).
Figure 7: Relative displacement w′ in the tests and in
thesimulations with a bar and a tube as rebars for β=1.
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B. Sanz, J. Planas and J.M. Sancho
Figure 8: Relative displacement w′ in the tests and in
thesimulations with a tube varying the expansion factor β.
The crack width in millimeters and the pos-itive maximum
principal stresses in MPa areshown in Fig. 9 for the bar (top) and
the tube(bottom).
It is found out that although the model prop-erly reproduces the
crack pattern in the case ofa bar (Fig. 9-top) and the relative
displacementw′ in both cases, the pattern in the sample with atube
(bottom of the same figure) differs from theexperimental pattern
(Fig. 6): only a main crackat the cover and an opposite secondary
crackpredominate, while all other relevant secondarycracks are
closed as these two cracks grow dur-ing the calculations, whereas
in the simulationswith the bar several relevant secondary
cracksdistributed around the bar appear. This effectseems to be due
to the stiffness of the tube be-ing much less than that of the bar.
As a conse-quence, while for the stiffer bar the crack pat-tern
results were insensitive to the shear stiff-ness kt of the oxide
layer over many orders ofmagnitude, it appears that kt has a much
greatereffect on the cracking in the case of the tube.
Then, new simulations have been computedin order to delimit the
values of kt which repro-duce the real cracking observed in the
experi-ments, covering a range from 7·10−14 MPa/mm(virtual zero) to
7·106 MPa/mm (equal to kn).
0 3
body: t = 100
0 0.098
crack: t = 100
0 0.0987
crack: t = 100
0 3
body: t = 100
Figure 9: Simulated crack pattern for a corrosion depthof 10
microns, an expansion factor β = 2 and the stiffnessparameters
shown in Table 2 in a concrete sample with abar (top) and with a
tube (bottom) as rebars.
For values of kt lower than 700 MPa/mm,only the main crack and
an opposite crack ap-pear, obtaining a crack pattern very similar
tothe pattern shown in Fig. 9-bottom. Thereis a range of values
between 1000 and 2000MPa/mm for which the crack pattern
resemblesthose found in the experiments. But for val-ues higher
than 7000 MPa/mm, although thenumber of secondary cracks increase,
they are
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B. Sanz, J. Planas and J.M. Sancho
clamped at the root and there are points of stresslock-in, as it
was disclosed in [2] revealing thenecessity of reducing the shear
stiffness.
In Fig. 10, the crack patterns for kt 1000,2000 and 7000 MPa/mm
are shown. For a shearstiffness equal to 1000 MPa/mm (top), there
is asecondary crack that predominates, apart fromthe main crack,
but there are two more sec-ondary cracks still remaining. For a
shear stiff-ness of 2000 MPa/mm (middle), the crack op-posite to
the main crack has a smaller length andthere are other six
secondary cracks around thetube, all of them with similar length,
resemblingthe experimental pattern observed in Fig. 6.
The pattern obtained for 7000 MPa/mm ap-parently is very similar
to that obtained for 2000MPa/mm, except for a greater number of
sec-ondary cracks. However, if only the crackswith a width greater
than 0.005 mm are plot-ted, more differences are observed. In Fig.
11,a detail of the cracking around the rebar isshown. In all the
cases there are only three orfour cracks wider than 0.005mm, so the
cracksthat do not appear are microcracks with open-ing width near
to zero. But only in the case of7000 MPa/mm (right) there is a jump
betweenthe tube and some of the cracks, what meansthat those cracks
are clamped at the root due toan excessive shear stiffness kt of
the expansivejoint element.
It must be pointed out that the corrosiondepth in the
simulations is lower than the cor-rosion depth estimated in the
experiments, whatmight explain a difference in the length of
thecracks. However, a greater corrosion depthis not simulated
because, at this stage of thestudy, a linear softening curve is
being used forthe cracking of concrete, which properly repro-duces
the fracture of concrete for early stages ofcracking only.
Finally, in Fig. 12 the relative displacementw′ is represented
versus the corrosion depth forall the values of shear stiffness of
this study,showing that the curves of relative displacementobtained
in the simulations using the new valuesof kt are in agreement with
the experimental re-sults.
0 0.0916
crack: t = 100
0 3
body: t = 100
0 0.0875
crack: t = 100
0 3
body: t = 100
0 0.0861
crack: t = 100
0 3
body: t = 100
Figure 10: Crack pattern in a concrete prism with a steeltube,
for a corrosion depth of 10 microns and kt 1000(top), 2000 (middle)
and 7000 (bottom) MPa/mm.
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B. Sanz, J. Planas and J.M. Sancho
0body: t = 100
0.005 0.0916crack: t = 100
00.005 0.0875crack: t = 100
0 0body: t = 100
0 0body: t = 100
0.005 0.0861crack: t = 100
1000 MPa/mm 2000 MPa/mm 7000 MPa/mm
0body: t = 100
0.005 0.0916crack: t = 100
00.005 0.0875crack: t = 100
0 0body: t = 100
0 0body: t = 100
0.005 0.0861crack: t = 100
Figure 11: Detail of the cracking around the rebar in aconcrete
sample with a steel tube and a corrosion depth of10 microns for a
shear stiffness of 1000 (left), 2000 (mid-dle) and 7000 (right)
MPa/mm. Only the cracks widerthan 0.005 mm are shown.
Figure 12: Maximum crack width versus the corrosiondepth in
concrete prisms with a steel tube depending onthe shear stiffness
kt of the expansive joint element.
4 CONCLUSIONSAccelerated corrosion tests have been car-
ried out on concrete prisms with a steel tubeinside as a rebar
to study the cracking of con-crete due to rebar corrosion. During
the tests,the main crack mouth opening is measured, and,after
corrosion, the samples are cut into slicesand impregnated under
vacuum with resin con-taining fluorescein to improve the detection
ofcracks.
Then, two views of every slice are combinedto study the
experimental crack pattern: undernatural light, a main crack is
observed at the
concrete cover, but also some secondary cracksand microcracks
are detected when illuminatingthe slice under UV light.
A model called expansive joint element pro-grammed by the
authors to simulate the ef-fect of the volumetric expansion of the
oxide,combined with finite elements with embeddedadaptable cohesive
crack has been proved toreproduce the cracking of real samples
bothfor the crack pattern and the quantitative crackopening.
The combination of the tests and the numeri-cal simulation leads
to a quantitative assessmentof the oxide expansion relation —factor
β inFig. 2 and Eq. (2.2).
The simulations show that the crack patternfor a corroding tube
is much more sensitiveto the parameters of the expansive joint
modelthan for a bar, presumably because of the re-duced stiffness
of the tube with respect to thebar.
In particular, the order of magnitude of theshear stiffness kt
of the oxide layer can be es-timated from the tests with a
corroding tube,while the results for a bar were insensitive tokt
over various orders of magnitude.
ACKNOWLEDGEMENTSThe authors gratefully acknowledge the Sec-
retarı́a de Estado de Investigación, Desar-rollo e Innovación
of the Spanish Ministeriode Economı́a y Competitividad for
providingfinancial support for this work under
grantBIA2010-18864.
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FRAMCOS-8Plenary LecturesFailure Mode Scaling Transitions in RC
Beams in Flexure: Tensile, Shearing, CrushingProbabilistic
Treatment of Rebar Depassivation and Its Influence in the
Calculation of Structural LiApplication of Fracture Mechanics to
Investigate Durability of Concrete under LoadOn the Use of 3D
Images and 3D Displacement Measurements for the Analysis of Damage
Mechanisms in CoHigh Performance Fibre Reinforced Concrete:
Fundamental Behaviour and ModellingApplications of the Cohesive
Crack Models to Concrete, Ceramics and PolymersMultiscale
Interaction Potentials: A Convenient Way for Addressing Size
Effects and Boundary Conditi
Keynote LecturesModeling of THCM Behavior of Concrete: from
Multiphasic Hydration of Composed Binders to Early Age MEngineering
Damage Indicators Based on Advanced Finite Element ModellingBond
Characteristics and Transfer Length of Prestressing Strand in
Pretensioned Concrete StructuresInterfacial Bond Characteristics of
Fiber Reinforced Cementitious Matrix for External Strengthening
Failure due to Delamination in Concrete Elements Strengthened with
Cementitious CompositesNumerical Analysis of Screw Anchor for
ConcreteStrengthening of Shear Deficient RC Beam-Column Joints in
MRFs under Seismic LoadingWeibull-strength Size Effect and Common
Problems with Size Effect ModelsA New Model to Forecast the
Response of Concrete Structures under Severe Loadings: the μ Damage
ModeExperimental Studies of Brick and Mortar Composites Using
Digital Image AnalysisA Probabilistic Fatigue Model Based on the
Initial Distribution to Consider Frequency Effect in PlaiDynamic
Tensile Resistance of Concrete - Split Hopkinson Bar TestFracture
Behaviour of Concrete at High Strain RateFiber Orientation in Ultra
High Performance Fiber Reinforced Concrete and Its
VisualizationCharacterisation of 3D Fracture Evolution in Concrete
Using In-situ X-Ray Computed Tomography TestinConstitutive Model
for Steel Fibre Reinforced Concrete in TensionEffects of
Temperature and Strain Rate on the Behavior of Strain-Hardening
Cement-based Composites (Generalized Mathematical Homogenization of
the Lattice Discrete Particle ModelComputational Simulation of
Reinforced Concrete Using the Micropolar State-Based Peridynamic
LatticeBending Tests on Reinforced Concrete Beams: Numerical
Modelling using a Second Gradient TheoryExperimental Tests and
Numerical Modeling to Identify the Asymptotic Shear-Compression
Mode IIa of CFracture Analysis of Cement Treated Demolition Waste
Using a Lattice ModelCombined Acoustic Emission and Simulation
Approach to Study Fracture Behavior of Concrete under
FireMicrostructure-Property Relationships and the NDE of Concrete
Damage and FractureFracture Mechanics to Illustrate Cracking of
Alkali-sensitive GrainsStress Corrosion Cracking and Fracture
Toughness of High Strength SteelsModeling Damage of Concrete Caused
by Corrosion of Steel ReinforcementA Fracture Testing Based
Approach to Assess the Self Healing Capacity of Cementitious
CompositesNumerical Modeling of Crystallization-induced Damage
Regular ContributionsControl of Cracking in RC Structures:
Coupling Phenomena and Crack IndicatorsCracking Analysis of
Reinforced Concrete Beams Using a Finite - Discrete Element Methods
ApproachSimulation of Crack Propagation in RC Shear Wall Using a 3D
Rigid-Body-Spring Model with Random GeomNumerical Simulation of
Shear Wall in CONCRACK BenchmarkNumerical Prediction of the
Response of a Squat Shear Wall Subjected to Monotonic Loading
through PAControl of Cracking in R.C. Structures: Numerical
Simulation of a Squat Shear WallAnalytical Formulation of the
Fracture Path and Shear Resistance for RC Beams Interface Analysis
between Steel Bars and Recycled Steel Fiber Reinforced
ConcreteModeling of Crack Development in Young ConcreteMonitoring
of the Creep and the Relaxation at Very Early Age: Complementary
Results on the CEOS ConcA Hygro Thermo Mechanical Model For
ConcreteNumerical Modelling of Large Reinforced Concrete Specimens
Based on Experimental Tests from Benchmar
Bond Cracking, Modeling, Design Provisions of
Reinforcing/prestressing Steels, Anchors, Fibers and FEvaluation of
Diagonal-Tension Failure Load in Reinforced Concrete Beams without
Stirrups. Critical Shear Strength of Dry Keyed Joints and
Comparison with Different FormulationsStrength and Modes of Failure
of Adhesive Anchors in Confined Concrete under Direct Tensile
LoadingModel to Simulate the Behavior of RC Beams Shear
Strengthened with ETS BarsEffect of Rib Geometry on Bond Behavior
and Failure ModesAnchorage Strengths of Lap Splices Anchored by
High-Strength Headed BarsShear Reinforcement of RC Members Using
Post-reinforcing BarsShear Reinforcement of RC Members with
Continuous Fiber RopeMulti-layer Shear Lag Model for Post-installed
Anchor used in Retrofit of Concrete Structures
Application of Fracture Mechanics to Debonding Problems of
Composite Materials from Concrete and MasCharacterization of the
Bond Behaviour between Glass and GFRPPeel Strength Testing of FRP
Applied to Clay BricksA Coupled Interface-Body Nonlocal Damage
Model for the Analysis of FRP Strengthening DetachmentFinite
Element Simulation of Sandwich Panels of Plasterboard and Rock Wool
under Mixed Mode FractureEdge Debonding in FRP-strengthened
Concrete Beams: an Analytical Approach Based on the Cohesive
CracCompetition and Interplay between Different Failure Mechanisms
in Concrete Beams strengthened by FRPImpact of Surface Roughness on
the Debonding Mechanism in Concrete Repairs
Fracture, Fatigue and Time-dependent Effects in Concrete and
Concrete StructuresMechanical Model of Adhesive Post-Installed
Anchor Subjected to Cyclic Shear ForceSeismic Behaviors of
ECC/Concrete Composite Beam-Column Joints under Reversed Cyclic
LoadingExperimental and Numerical Investigations of Size Effects in
Reinforced Concrete Beams with Steel orExperimental Study on the
Fracture of Lightly Reinforced Concrete elements Subjected to
Eccentric CoPrediction of Mechanical Consequences of Drying: from
Laboratory to Concrete StructuresMechanical Behaviour of Reinforced
Stone Beams in Bending: Experimental and Numerical ResultsEffects
of Drying Shrinkage on Shear Tension Strength of Reinforced
Concrete BeamsFlexural Behavior of Concrete under the Uniaxial and
Biaxial Stress StatesA Discussion on Mechanical Properties of
Interface in Repaired Concrete Based on Analyses with New
2Construction and Structural Analysis of the Dome of the Cathedral
of ValenciaFracture Energy of Concrete and Shear Strength of RC
Beams Internally Cured Using Porous Ceramic-RooFracture and
Microstructural Studies on Normal and High Strength Concretes with
Different Types of AComplexity of Structures: A Possible Measure
and the Role for RobustnessEffect of Restraints on the Response of
RC Columns in a Parametric FireA Simple Two-stage Model for
Simulating Drying Shrinkage vs. Mass-loss Evolution of
ConcreteFracture Energy of Concrete at Very Early Ages by Inverse
AnalysisDigital Quantification of Effects of Admixtures on Early
Shrinkage CrackingThe Effect of Circular Openings on the
Brittle-ductile Fracture of Ferrous Flat BarsTime-Dependent
Behavior of Cracked Concrete Beams under Sustained LoadingConcrete
Behavior under Triaxial Load: Experimentation and Improvement of a
Damage and Plasticity CoElastoplastic Constitutive Law for Concrete
Exposed to High Temperature: Chemoplastic ModelingInfluence of
Measurement Uncertainties on Results of Creep Prediction of
Concrete under Cyclic LoadiFrequency Effect on the Compressive
Fatigue Behaviour of Plain and Fiber-reinforced ConcretesModelling
of Fatigue Crack Propagation in Concrete Using Dissipation
PotentialA Study on Fatigue Crack Growth in Concrete in the
pre-Paris RegionInfluence of Mineral Admixtures on Fatigue
Behaviour of Self Compacting Concrete - Scanning ElectronFinite
Element Analysis on the Fatigue Damage under Compression of a
Concrete Slab TrackStatistical Evaluation of Fatigue Tests of Plain
C30/37 and C45/55 Class Concrete Specimens Simulation of Cracking
in Masonry Arch BridgesRenovation Design of Aging RC Sewers as
Semi-Composite Structures Based on Non-linear Response
AnalyNumerical Modelling of Textile Reinforced ConcreteAssessment
of Materials Nonlinearity in Framed Structures of Reinforced
Concrete and CompositesNew Double-K Criterion for Crack Propagation
in Quasi-Brittle Fracture under Moderate Dynamic Loadin
Dynamic Response of Concrete in Tension-experimental Evidence
and ModelingA Rate-dependent Multi-scale Crack Model for
ConcreteFracture of Concrete Structural Members Subjected to BlastA
Mesoscale Modelling Perspective of Cracking Process and Fracture
Energy under High Strain Rate TenEffect of Loading Rate on
High-strength Concrete: Numerical SimulationsA Viscoelastic
Retarded Damage Material Law for Concrete Structures Exposed to
Impact and ExplosionsDrop Weight Impact Strengths of Porous
Concretes Investigated with a Measurement Technique Using
LasProperties of Ultra High Performance Concrete (UHPC) in Tension
at High Strain RatesModelling of Preloaded Reinforced-concrete
Structures at Different Loading Rates
Testing Methods for Characterisation of Fracture Behaviour of
Fibre-reinforced Cement-based CompositUpgrading the Push-Off Test
to Study the Mechanisms of Shear Transfer in FRC ElementsUniaxial
Fracture Energy of Waste Tyre Rubber ConcreteExperimental Study on
Mechanical Behaviors of Pseudo-Ductile Cementitious Composites and
Normal ConcDescription of Near-tip Fracture Processes in Strain
Hardening Cementitious Composites Using Image-bEvaluation of the
Tensile Strength of SFRC as Derived from Inverse Analysis of
Notched Bending TestsComparison of the Size-independent Fracture
Energy of Concrete Obtained by Two Test MethodsDevelopment of
Ductile Fiber Reinforced Geopolymer CompositesFlexural Tension Test
Methods for Determination of the Tensile Stress-strain Response of
Ultra-High Flexural Behavior of Cement Based Element Reinforced
with 3D FabricShear Database for Reinforced and Prestressed Beams
Made with Fiber Reinforced ConcreteUniaxial Tension Test Method
Using SHCC Prisms Molded into Dumbbell ShapeFlexural Toughness and
Ductility Characteristics of Polyvinyl-Alcohol Fibre Reinforced
Concrete (PVAEnergy Absorption and Flexural Toughness Evaluation of
Fibre Reinforced Polymer Modified ConcreteEffect of Fiber
Reinforcement on the Shear Behavior of Reinforced Concrete
BeamsExperimental Study on Flexural Behaviors of Engineered
Cementitious Composite Beams Reinforced With
Strength, Deformation and Failure Behaviour of Structures made
of, or Strengthened with, Fibre-reinfInfluence of Crumb Rubber on
the Mechanical Behavior of Engineered Cementitious
CompositesAnalytical Prediction of Crack Width of FRC/RC Beams
under Short and Long Term Bending ConditionExperimental Study on
the Behavior of SFRC Columns under Seismic LoadsA Unified View on
the Effect of Fibers and Loading on SFRC Creep through Linear
Projection to LatentPerformance of RC Beam-Column Joints with
Different Joint DetailingEvaluation of Time-Dependent Behaviour of
Composite Concrete Slabs with Steel Decking (An
ExperimentApplication of Tension Softening Curves to Investigate
the Shear carried by Fibers in Various Fiber Transverse
Reinforcement Effects on the Loading Behaviour of High Performances
Concrete BeamsThe Effect of Concrete Strength on Cracking of SFRC
MembersA Lattice-particle Approach for the Simulation of Fracture
Processes in Fiber-reinforced High-PerforAssessment Risk of
Fracture in Thin-Walled Fiber Reinforced and Regular High
Performance Concretes STailoring High-Strength SHCCModelling
Cracking and Bending Failure of SFRC Beams with Conventional
Reinforcement
Fracture Behaviour of Fibre-reinforced Cement-based Materials at
Sever Conditions - High or Low TempCyclic Response of Damaged
Members Repaired by Different Types SHCCsFailure Simulation of
Fiber Reinforced Concrete Beams Subjected to Dynamic
LoadingsInfluence of Loading Rate on the Fracture Behaviour of
Steel Fiber-reinforced ConcreteTensile Behavior of Ultra High
Performance Hybrid Fiber Reinforced Cement-Based Composites
Multi-scale Investigation of Concrete Fracture by Numerical and
Physical ExperimentationA Discrete Model for Alkali-silica-reaction
in ConcreteModeling Electrolyte Diffusion in Cracked Cementitious
Materials Using Cascade Continuum MicromechanMonitoring Acoustic
Emissions and Electrical Signals during Three-point Bending Tests
Performed on CStochastic Lattice Simulations of Flexural Failure in
Concrete BeamsA Multiscale Oriented Concept for the Analyses of
Steel Fiber Reinforced Concrete Materials and StruA Lattice Model
for Liquid Transport in Cracked Unsaturated Heterogeneous Porous
MaterialsA Two-Scale (FEM-DEM) Approach for ConcreteEvaluation of
Nonlocal Approaches for Modelling Fracture in Notched Concrete
SpecimensApplication of a Global/Local Analysis to Study Size
Effect in ConcreteA Multi-Scale Computational Scheme for
Anisotropic Hydro-Mechanical Couplings in Saturated HeterogenFrom
Tomographic Images to Mesoscopic Modelling of Triaxial Behaviour of
Concrete3D Measurements to Determine Micromechanical Energy
Dissipation in Steel Fiber Reinforced ConcreteMeso-scale Modeling
for Fiber Reinforced Concrete under Mixed Mode FractureMulti-Level
Investigations on Behaviour of Textile Reinforced Concrete with
Short Fibres under TensiCorrosion Induced Cracking of Reinforced
ConcreteA Novel Experimental Method to Characterize the Cyclic
Response of the Crack Tip Process Zone in a QMultiscale
Probabilistic Approaches and Strategies for the Modelling of
Concrete CrackingA New Interaction-based Non Local Model to Predict
Damage and Failure in Quasi-brittle MaterialsSmoothed Constitutive
Model for Concrete Based on Micromechanical SolutionsConsequences
of Internal Stresses generated by Hydration on the Concrete
Mechnical Behaviour
Nonlocal Computational Methods for Cementitious MaterialsCoupled
Elasto-plastic Model with Non-local Softening Enhanced by Viscosity
to Describe Dynamic ConcFracture Energy-based Thermodynamically
Consistent Gradient Model for Concrete under High
TemperaturModelling of Concrete Cracking for the Design of SHM
Systems: Comparison of Implicit Gradient DamageNumerical Analysis
of the Behaviour of Notched Specimens at Various Testing
Temperatures Using an El
Recent Advances in Numerical Modeling of Cohesive Fracture in
Concrete-like MaterialsLattice Modeling of Fracture Processes in
Numerical Concrete with Irregular Shape AggregatesNonlinear Finite
Element Analyses of Reinforced Concrete Slabs: Comparison of Safety
FormatsModelling Crack Initiation and Propagation in Masonry Using
the Partition of Unity MethodNumerical Simulation of Failure
Process on Concrete-Filled Steel Tube under Eccentric CompressionA
Finite Element Approach for Predicting the Ultimate Rotational
Capacity of RC BeamsSome Issues on Prediction of Massive Structures
Cracking at Early AgeXFEM using a Non Linear Fracture Mechanics
Approach for Concrete CrackGeneralisation of Non-Iterative
Numerical Methods for Damage-Plastic Behaviour ModelingAccuracy of
Approximation of Stress Field in Cracked Bodies for Failure Zone
Extent EstimationNumerical Dynamic Simulations for the Prediction
of Damage and Loss of Capacity of RC Column SubjectA Coupled
Continuous-discontinuous Approach to Concrete ElementsA Shear
Transfer Model for Rough Joints Based on Contact and Fracture
MechanicsA Testing Procedure for the Evaluation of Directional Mesh
BiasModelling the Postpeak Stress-Displacement Relationship of
Concrete in Uniaxial CompressionBranch-Switching to Bifurcation
Path for Diagonal Tension Failure of Reinforced Concrete Beam,
Based
NDT/AE Applications on Concrete and Concrete StructuresDamage
Evaluation of Cracked Concrete by DeCATMonitoring of Fatigue Crack
Growth in Concrete-Concrete Interfaces Using Acoustic
EmissionAcoustic Emission Monitoring and Quantitative Evaluation of
Damage in Concrete Beams under CreepLaboratory Investigations on
Concrete Fracture Using Acoustic Emission TechniqueMonitoring of
Crack Propagation in Reinforced Concrete Beams Using Embedded
Piezoelectric TransducerCrushing and Fracture Energies in Concrete
Specimens Monitored by Acoustic EmissionToward Hybrid-NDE for Rebar
Corrosion in Reinforced Concrete with Acoustic EmissionMonitoring
Elastic Properties of Concrete since Very Early Age by Means of
Cyclic Loadings, UltrasonPrediction Method of Rebar Corrosion
Degree in Reinforced Concrete by ThermographyAcoustic Emission
Wireless Transmission System for Structural and Infrastructural
NetworksDevelopment of Wireless Remote-Controlled Testing Machine
for Vertical Concrete WallStudy of Evolution of Fracture Process
Zone in Concrete by Simultaneous Application of Digital
ImageEvaluation of Crack Propagation in ASR Damaged Concrete Based
on Image AnalysisEstimation of Concrete Strength by Contrast X-rayA
6 DOF Testing Machine Controlled by Digital Image Correlation: an
Experimental Setup for New Nooru
Fracture Mechanics Prediction of Durability of ConcreteNumerical
Modelling of Non-uniform Steel Corrosion Development and Its
Mechanical Influences on ReinFreezing-Thawing Cycles Effect on the
Fracture Properties of Flowable ConcreteAn Appropriate Indicator
for Bond Strength Degradation due to Reinforcement
CorrosionDevelopments of Prediction Model for Crack Width due to
Rebar CorrosionCover Cracking of the Reinforced Concrete due to
Rebar Corrosion Induced by Chloride PenetrationSalt
Crystallization-Induced Damage of Cement Mortar Microstructure
Investigated by Multi-Cycle MercAnalytical Estimation for
Mechanical Characteristics of Concrete as a Permeable
MaterialReal-Time Evolution Water Permeability of a Localized Crack
in Concrete under LoadingEffect of Crack Width and Chloride Binding
on Chloride Diffusivity in Cracked RC BeamsCoupled Simulation of
Fracture Mechanics and Transport of Chlorid in Cracked Concrete
Submitted to PPermeability of Concrete at High Temperatures and
Modelling of Explosive SpallingNumerical Modelling of the Tensile
Splitting Test and Its Coupling with Gas
PermeabilityDual-lattice-based Simulations of Coupled Fracture-flow
in Reinforced ConcreteEffect of Microcraking on Gas Permeability
and Chloride Diffusion of ConcreteInvestigation on the Durability
of Fibre Reinforced Concrete (FRC) Exposed to Marine
EnvironmentLattice Based Simulation of Chloride Ingress in
Uncracked and Cracked Concrete: Model ValidationNumerical
Simulation of Chloride Diffusion in Reinforced Concrete Structures
with CracksShear Strength of ASR-Deteriorated RC Members and Shear
Reinforcing Effect of Repair by Adding RebarModeling of Chloride
Transport in Non-saturated Concrete. From Microscale to
Macroscale
Durability Characterization and Modeling of Multiple Cracked
Strain Hardening Cementitious CompositeInfluence of Hysteretic
Moisture Transfer on Concrete DurabilitySimulating Crack Width
Distributions in SHCC under Tensile LoadingThe Effect of
Self-Healing on the Durability Performance of Micro-Cracked ECCLoss
of Ductility and Strength of Reinforcing Steel due to Pitting
CorrosionStudy of Concrete Cracking during Accelerated Corrosion
Tests in Reinforced ConcreteStrain Hardening Cement Based Composite
(SHCC) with Fine and Coarse Sand under Tensile Load and
ChloEvaluation of Alkali Silica Reaction Effects on Mechanical
Behaviour of MortarCharacterization of the Interface between Strain
Hardening Cementitious Repair Layers and Concrete SOn the
Characterization of Strain Hardening Cement-based Materials by
Inverse Analysis of Bending TeMeasurement of the Relative Gas
Permeability of Ordinary Concrete: Influence of Saturation Degree
anHydrogen Embrittlement of High Strength Steels by Phase
TransitionsReview of Reinforced Concrete Biodeterioration
MechanismsModelling of Corrosion-induced Concrete
DamageSilica-additivated Cement Pastes Obtained from Different
Mixing Conditions: Influence on the HydratiLimit States of RC
structures: Reinforcement Corrosion, Reliability and Modelling
Index Authors