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: bsanz@mater.upm.es

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

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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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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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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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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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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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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.

REFERENCES[1] Andrade, C., Alonso, M.C. and Molina,

F.J., 1993. Cover cracking as a function ofbar corrosion: Part i - experimental tests.Materials and Structures, 26:453–464.

[2] Sanz, B., Planas, J., Fathy, A.M. andSancho, J.M., 2008. Modelización conelementos finitos de la fisuración en elhormigón causada por la corrosión de lasarmaduras. Anales de la Mecánica de la

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Fractura, 25: 623–628, publication inSpanish.

[3] Sancho, J.M., Planas, J., Cendon, D.A.,Reyes, E. and Galvez, J.C., 2007. An em-bedded cohesive crack model for finite el-ement analysis of concrete fracture. Engi-neering Fracture Mechanics, 74, 75–86.

[4] Hillerborg, A., Modéer, M. and Petersson,P.E., 1976. Analysis of crack formationand crack growth in concrete by means offracture mechanics and fracture elements.Cement and Concrete Research, 6:773–782.

[5] Planas, J., Guinea, G.V., Galvez, J.C.,Sanz, B. and Fathy, A.M., 2007. Exper-imental determination of the stress-crackopening curve for concrete in tension, re-por 39, chap. 3. Technical report, RILEMTC 187-SOC Final Report.

[6] Sanz, B., Planas, J. and Sancho, J.M,2011. Parametric study of the expansivejoint model for cracking of concrete dueto rebar corrosion. Anales de la Mecánicade la Fractura, 28: 475–480.

[7] Sanz, B., Planas, J. and Sancho, J.M.,2010. Comparison of the crack patternin accelerated corrosion tests and in fi-nite elements simulations. Anales de laMecánica de la Fractura, 27: 265–270.

[8] Guinea, G.V., Planas, J. and Elices, M.,1994. A general bilinear fitting for thesoftening curve of concrete. Materials andStructures, 27:99–105.

[9] RILEM TC 154-EMC. Test method foron-site corrosion rate measurement ofsteel reinforcement in concrete by meansof polarization resistance method. Materi-als and Structures 37:623–643.

[10] Geuzaine, C. and Remacle, J.F., 2009.Gmsh: a three-dimensional finite elementmesh generator with built-in pre- and post-processing facilities. International Jour-nal for Numerical Methods in Engineer-ing, 79:1309–1331.

[11] Molina, F.J., Alonso, M.C. and Andrade,C., 1993. Cover cracking as a function ofbar corrosin: Part ii - numerical model.Materials and Structures, 26:532–548.

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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