Estimating crack widths in steel fibre-reinforced concrete - Bekaert-Maccaferri · 2019-02-11 · Estimating crack widths in steel fibre-reinforced concrete &1 Eyre Hover MEng, PhD

Estimating crack widths in steelfibre-reinforced concrete&1 Eyre Hover MEng, PhD

Tunnel Design Engineer, UNPS Limited, Rugby, UK

&2 Sotiris Psomas Dipl-Ing, MSc, CEng, MICESenior Engineering Manager, UNPS Limited, Rugby, UK

&3 Colin Eddie BSc, FREng, CEng, FICEManaging Director, UNPS Limited, Rugby, UK

1 2 3

The use of steel fibres as reinforcement for sprayed concrete tunnel linings offers significant potential savings in time

and cost. These provide a degree of crack control and an increase in ductility to the otherwise brittle material, and

while the properties of steel fibre-reinforced concrete (SFRC) are well understood, its ability to control cracks is not

quantifiable or justifiable in the design of concrete sections. This paper describes the novel application of particle

image velocimetry (PIV) to the study of cracking in plain concrete and SFRC four-point flexural beam tests. Strain

hardening under bending was observed, as was the propagation of multiple cracks (multicracking) in SFRC beams, in

contrast to the brittle failure of the plain concrete specimen. The stress–strain behaviour of the material was

quantified by means of digital photographs of the test, and Young’s modulus of the SFRC was found to be similar to

that of plain concrete. Cracks on the side of the beam as small as 0·05mm and up to 4mm were measured with an

error <0·02mm, making PIV a viable option for crack width analysis for the basis of SFRC design assisted by testing,

supported by BS EN 1990.

Notationb breadth of the beamE Young’s modulus of the materialEi initial elastic modulusEs secant elastic modulusfct tensile strength of the concretefctd design tensile strength of the concretefct,fl flexural strength of the concretefctk characteristic tensile strength of the concretefctm mean tensile strength of the concretefctm,fl mean flexural strength of the concreteh height of the beam or thickness of the concrete liningkn characteristic fractile factorL length of the test beamlg length of the fibre optic Bragg grating optical

fibresM bending momentSn particle image velocimetry (PIV) measured spacing

between interrogation areas at the nth depthincrement

Sna,c1 PIV measured spacing between interrogation areason the neutral axis at first crack

Sna,i PIV measured spacing between interrogation areason the neutral axis at the ith load stage

So original PIV measured spacing between interrogationareas

t timeVX coefficient of variation of Xw crack width on the surface of the beamwn crack width at depth n into the beamX measurement dataαct,pl coefficient taking into account the long-term effects

of tensile strengthγc safety factor for concreteΔxn x distance between a pair of IAs at depth nΔyn y distance between a pair of IAs at depth nδxi,n x displacement of the ith interrogation area (IA) at

depth nδyi,n y displacement of the ith IA at depth nεg gauge strain

1

Construction Materials

Estimating crack widths in steelfibre-reinforced concreteHover, Psomas and Eddie

Proceedings of the Institution of Civil Engineers

http://dx.doi.org/10.1680/coma.15.00019Paper 1500019Received 09/03/2015 Accepted 04/06/2015Keywords: concrete structures/strength and testing of materials/tunnels & tunnelling

ICE Publishing: All rights reserved

Downloaded by [] on [15/02/17]. Copyright © ICE Publishing, all rights reserved.

εy longitudinal strainεy,c1 longitudinal strain at first crackεy,el longitudinal elastic strainεy,i,n longitudinal strain at the ith load stage, at depth n

1. IntroductionSprayed concrete linings have been used since the 1960s tostabilise tunnels in rock and self-supporting soils such as theLondon Clay. Traditionally built using shotcrete reinforcedwith steel rebar or mesh, more recent tunnels have incorpor-ated the use of steel fibres distributed homogeneously in theconcrete mix. Steel fibres are more durable than steel rebar insevere exposure environments and are generally more cost andtime efficient than traditional methods of reinforcement inlinings.

Structural concrete is generally a material of low hydraulic con-ductivity; however, tunnel concrete linings commonly sufferfrom the ingress of groundwater. This is due to the presence ofcracks which increases the mass permeability of the lining andreduces both its performance and its exposure protection,making crack control a significant issue in tunnelling. Steelfibres eliminate spalling damage, assist in controlling shrinkage-induced cracking and ensure corrosion protection – as long ascrack widths are limited (to <0·3mm) to allow autogenoushealing of the concrete to take place. The tensile properties ofsteel fibre-reinforced concrete (SFRC) are similar to those ofplain concrete up to first crack for low-fibre dosages, while thecompressive properties are essentially unaffected (Bentur andMindess, 2007). After the first crack (formation), an increase inductility can be observed both in tension and compression.

While the performance of SFRC linings under loading is wellunderstood, the cracking behaviour cannot be predicted and itcannot easily be determined whether a design will ensure a suf-ficient control of crack widths, for low dosages of steel fibresused in practice (up to 1·0% per volume).

For tunnel linings, crack widths at a given strain level cannotbe determined through finite-element analyses (FEAs) alone,and therefore they need to be supplemented by representativestructural testing. An alternative approach is the determinationof stress–crack width relationship by adopting non-linear frac-ture mechanics principles (Vandewalle and RILEM TC162-TDF, 2002).

However, a combination of structural testing and calibratedFEA is more compatible with current structural codes (such asBS EN 1990:2002 (BSI, 2002) and fib model code 2010) andcan be used to form the basis of a tunnel lining design pro-vided that ductility and multi-cracking is ensured. Designassisted by testing is an approach covered by BS EN

1990:2002 (BSI, 2002), and supports the use of experimentaldata to justify the use of novel techniques in construction. Thispaper presents part of a testing procedure using particle imagevelocimetry (PIV) and four-point flexural tests on concrete andSFRC beams.

These tests supported part of the design for the lining ofLondon’s Lee Tunnel (7·2 m internal diameter, 300 mm thicksecondary tunnel lining), for which a 0·15 mm crack widthlimit was specified for durability by the designer. The details ofthis design are expected to be published in due course, andwere discussed at the British Tunnelling Society Conferenceand Exhibition 2014. The aim of this test series was to predictcrack widths in full-depth specimens (300 mm) based on theaverage and worst-case strains that are expected to occur alongthe tunnel.

2. PIVPIV is an image processing technique that uses software totrack displacements on or inside a moving body (Adrian andWesterweel, 2011; Take, 2015). Originally developed tomeasure displacements and calculate flow velocities in the fieldof fluid mechanics, it has since been adapted for studying awide range of geotechnical engineering applications, includingdisplacements around piles (Ni et al., 2010) and helical screwpiles (Stanier et al., 2013), tube sampling disturbance (Hoveret al., 2013), tunnelling-induced ground movements (Ahmedand Iskander, 2011), soil deformation (White et al., 2003) andtensile cracking in clay (Thusyanthan et al., 2007). In recentyears, PIV has also been applied to strain measurement(Dutton et al., 2013; Hoult et al., 2013).

PIV works by analysing photographs taken during a test andderiving displacements or velocities by recognising the move-ment of small patches of texture.

In a traditional PIV set-up, particles are added to the transpar-ent fluid or material (Iskander, 2010) to produce a scattering oflight, as a single plane within the fluid is illuminated by meansof laser and photographed using a digital camera. White lightsources can also be used to study displacements on the surfaceof a non-transparent body (White et al., 2003) or on a singleplane within a transparent solid material (Hover et al., 2013).

Digital photographs are captured at a frame rate adapted tothe rate of displacement observed in the test, from <1 to thou-sands of frames per second, depending on the application.

The initial photograph is divided into a grid of interrogationareas (IAs)/subsets. The changing locations of these smallsquares of texture over the series of images taken during thetest are tracked to sub-pixel accuracy by the PIV software, to

2

Construction Materials Estimating crack widths in steelfibre-reinforced concreteHover, Psomas and Eddie


produce displacement vectors that can be used to derive crackwidths and strains.

The accuracy of PIV depends on the set-up and on the experi-ence of the user. The software itself can be a source of errorsand the analysis parameters must be carefully chosen to ensurethat the results reflect the observed displacements. The factorsinfluencing the choice of these parameters are discussed inWhite and Take (2002). Other critical factors in this set-upinclude

& camera resolution& size of area under consideration& lighting& orthogonality between the camera and the beam.

The first two elements control the detail recorded in the photo-graph; a combination of high resolution and small area sizeis beneficial to high accuracy. Poor lighting and non-orthogonality reduce accuracy by increasing the amount ofnoise or by producing optical distortions.

3. MethodologyOne unreinforced concrete and three SFRC 960�300�5400 mm3 (b�h�L) beams were manufactured for thepurpose of four-point flexural beam testing. The beams weremade of a C40/50 concrete mix with 380 kg/m3 of cement and40 kg/m3 of fibres (Bekaert 5D-65/60BG – used for the firsttime in tunnel linings) added for the SFRC specimens. The

effectiveness of the fibres in providing crack bridging can resultin different failure modes and therefore different types weretested. The fibre type (aspect ratio 65, yield strength 2300MPa) and content were chosen through previous three-pointflexural notched beam tests (to EN 14651 (CEN, 2005)), todetermine the SFRC mix that exhibited the best deflection-hardening behaviour.

These were tested at 28 d by applying four hydraulic jacksarranged in pairs under the beam, spaced at 1645 mm centres.The top of the beam was restrained at 200mm from eitherend; however, this condition was only effective once a certainamount of load was applied and the beam was held in placebetween the jacks and the supports. Six linear variable differ-ential transformers (LVDTs) were installed under the beam,and ten fibre optic Bragg grating (FBG) strain gauges werefixed to its tensile surface, as illustrated in Figure 1. Under thisloading arrangement, the portion of the beam between thehydraulic jacks experiences a near-uniform bending moment.

A remotely controlled 20MP resolution camera (Canon EOS6D) was positioned orthogonally to the beam at a distance of2500mm, so that the portion of the beam between the appliedloads occupied the entire field of view.

To ensure that the camera’s axis was orthogonal to the beam,a check was carried out using a perspex cylinder placedagainst the side of the beam at the centre of the desired field ofview. The position and angle of the camera were adjusted until

Camera

FBG array

Restraint frame

LVDTHydraulic ram

Hydraulic power pack

Time and load display

PIV target array

PIV camera

Figure 1. Full-scale performance-based test arrangement

3



the two crosses in the centre of the discs at either end of thecylinder were aligned. The cylinder was thereafter removed.

A ruler was placed against the surface of the beam and photo-graphed prior to the test to allow a conversion between thepixel and millimetre size at a later stage.

A second remotely controlled camera (Pentax K-r, 12·2MP)was fixed above the set-up to record the crack development onthe top surface of the beam, but was not intended to be usedfor the PIV analysis. Clocks were placed so as to be visibleduring the test by both cameras.

Some 1400 photographs were taken during each beam test.The frame rate was increased partway through the test, from 1frame per second (until 80% of the ultimate load observed inthe concrete beam test) to 3 thereafter.

The beams were prepared prior to testing to facilitate the analy-sis procedure. During PIV analysis, the side surface of thebeam would be divided into a grid of IAs by the software, eachof which would be tracked over the series of photographs todetermine its location. For this to be performed accurately, thetexture in each IA needed to be unique, have high contrast andbe easily recognisable by the software – therefore plain concretewould not be effective. An irregular pattern was created on theside of the beam by adding circular and triangular ink marksspaced at 10 mm centres. To increase the accuracy, additionaltexture was added by dotting the surface using marker pens sothat at least four spots appeared between each set of four orig-inal markings. This increased the variation in pattern over thelength of the beam so that no two IAs were identical.

Figure 2 shows the beam with the two types of IA grids usedfor the analysis, overlain on the photograph for illustrative pur-poses only: the left-hand side shows two columns of IAs sur-rounding an individual crack, while the size and location ofhalf of the IAs used for overall strain calculations are shownon the right-hand side of the beam.

4. Analysis

4.1 Accuracy of PIVThe accuracy of the PIV in this set-up was quantified bymeans of a simple test. The initial photograph taken for eachtest series was copied, and the first 36 pixels on the left of thephotograph were cropped, making it appear that all elementsin the image had been shifted 36 pixels to the left. A PIVanalysis was run between the original and modified images,and the difference between the calculated and ‘real’ displace-ments were compared for 1000 IAs. The average absolute errorfor each IA size is given in Figure 3. It can be seen that asthe IA size increases, errors reduce. An IA size of 96 pixels –

corresponding to a physical size of 30 mm – was adopted as acompromise between accuracy and vector density. An averageerror of ±0·6 μm (0·002 pixels) could be expected for purelytranslational displacements, for the PIV parameters usedduring the analysis.

During tests, small apparent movements (0–2 pixels) can becaused by camera shake, a phenomenon caused by the shuttermechanism of the camera. Where displacements are beingmeasured, a correction must be applied using image regis-tration (described in Ni et al., 2010). For derived quantities,such as crack widths and strains, this is not necessary providedthat no rotation of the camera has occurred.

4.2 Longitudinal strainBoth the crack width and the overall strains were derived fromthe displacement data generated using the PIV software,GeoPIV (White and Take, 2002). The longitudinal strain wascalculated for elements at varying vertical offsets from thebeam’s top surface between 15 and 252mm, using a 9�54 IAmesh (Figure 2) and Equation 1a.

Four loading stages were analysed pre-crack, as were the fivefirst cracks for the SFRC beams. Small but non-negligibledecreases in dimensions were observed between photographs ofthe test in the elastic range, in the order of 0·8 pixels/0·2 mm.

Figure 2. Examples of IAs used for PIV analysis

4



These resulted from out-of-plane movements caused by thebeam moving away from the camera, due to insufficientrestraint, up until 75–100 kN loading.

To account for these movements prior to the first crack,the length of the neutral axis was calculated from PIV data atits known location at half the height of the section. This wasdone at each load stage, and the strain was calculated inrelation to this value. After the first crack, the position andlength of the neutral axis are unknown, but the apparent lengthof the neutral axis immediately after the first crack wasassumed to remain constant until the end of testing due to thehigher amount of restraint (i.e. no further movement of thebeam away from the fixed camera due to the beam being tightagainst the restraints). Equation 1a can be modified toEquation 1b to calculate the average strain at each depth afterthe first crack

1a: εy;i;nð%Þ ¼ 100�PSn �PSna;i

PSna;i

1b: εy;i;nð%Þ ¼ 100�PSn �PSna;c1

PSna;c1

where εy,i,n is the longitudinal strain at the ith load stage, atdepth n; Sn is the PIV measured spacing between IAs at the

nth depth increment; Sna,c1 is the spacing between twoelements on the neutral axis at first crack; and Sna,i is thespacing between two elements on the neutral axis at currentload stage.

4.3 Crack widthThe locations of the cracks were identified by visualinspection of the photographs in both the plan and sideviews, and a mesh comprising two columns of IAs wascreated to surround each individual crack. The spacingbetween the columns was tailored so as to enclose the crackover its entire depth (Figure 4), since it rarely propagated per-fectly vertical. The PIV analysis for measuring crack widthsincorporated some 250 photographs per run. The crack width(wn) at any depth n was calculated using Equation 2 so as toexclude the elastic strain at first crack from the spacingmeasurement

2:wn ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΔxn

2 þ Δyn2

q� Soð1þ εyÞ

wn ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΔxn

2 þ Δyn2

q� Soð1þ εy;c1Þ

9=;

Before first crackAfter first crack

with

Δxn ¼ So þ δx2;n � δx1;n

0·0

0·5

1·0

1·5

2·0

2·5

20 40 60 80 100 120 140Ave

rage

abs

olut

e er

ror:

µm

IA size: pixels

Figure 3. Average absolute error measured for varying IA size

IA 1 IA 2

Initial position

Position at t = n

Original IA spacing, So

δx1,nδy1,n

δy2,nδx2,n

Crack

Figure 4. Using IAs to measure crack widths

5



Δyn ¼ δy2;n � δy1;n

where So is the original PIV measured spacing between IAs; εyis the longitudinal strain at the ith load stage, at depth n; andεy,c1 is the longitudinal strain at first crack.

5. Results

5.1 Longitudinal strainsThe load on the beams was steadily increased at an approxi-mate rate of 0·40 kN/s, and the tests lasted for about 10 min.The unreinforced concrete beam (C-1) failed suddenly ataround 100 kN with a single crack developing near instan-taneously midway between the hydraulic jacks. The three fibre-reinforced beam tests (from SFRC-1 to SFRC-3) showed con-sistent results: the load at first crack was increased from100 kN to an average of 123·6 kN, which was reached after~5min, and a progressive failure developed thereafter(Figure 5, with cracks highlighted for clarity and numbered inthe order they were analysed using PIV, not in the order theyinitiated).

Multiple cracks developed in all SFRC beams, and are evidentfrom the successive sudden drops in load shown in Figure 6,where deflection hardening behaviour can also be observed.

Six cracks developed in SFRC-1, while nine and ten cracksdeveloped in SFRC-2 and SFRC-3, respectively. No discernible

pattern of cracking was observed, most probably due to thesensitivity of the test to factors such as loading rates andloading geometry.

The strain was calculated for each test at nine depths, usingEquations 1a and 1b. A linear trendline for each load stageallowed the data to be extrapolated to the surface of the beam.The migration of the neutral axis and the correspondingincrease in the area of the tensile zone are visible in Figure 7.The corresponding values for all tests are presented in Table 1.

The stress–strain behaviours of the four tests are plotted inFigure 8, where it can be observed that the addition of steelfibres had no discernible effect on Young’s modulus of the con-crete, while strain hardening is seen to occur after first crack.

5.2 Flexural and direct tensile strengthsThe flexural strength of the concrete at first crack ( fct,fl) was cal-culated using Equation 3, based on the bending moment (M)calculated for the beam under self-weight at the average firstcrack load. The average surface flexural tensile strain values foreach test, determined by PIV analysis, are given in Table 2

3: fct;fl ¼ 6� Mbh2

The elastic moduli of the materials were calculated usingEquation 4. The initial elastic modulus (Ei) was determinedfrom test C-1 and the mean secant elastic modulus (Es) was

1 6 5 4 3 2 1

10

9 8 71234567

8 6 5 4 3 2 1

Figure 5. End of test cracks in the section of the beam underuniform bending (plan view)

6



Surface strain: μεLoad stage

Test 25 kN 50 kN 75 kN 100 kN First crack Second crack Third crack Fourth crack Fifth crack

C-1 36 78 97 116 — — — — —

SFRC-1 33 62 84 125 173 330 626 1030 1438SFRC-2 37 58 68 100 199 237 354 578 815SFRC-3 27 25 42 73 149 178 365 599 997

Table 1. PIV strains for all beam tests

0·0

50·0

100·0

150·0

200·0

250·0

–0·04 –0·02 0 0·02 0·04 0·06 0·08 0·1 0·12 0·14 0·16

Dep

th: m

m

Strain: %

25·25 kN

50·08 kN

73·76 kN

100·08 kN

First crack

Second crack

Third crack

Fourth crack

Fifth crack

Figure 7. Development of strains in test SFRC-1 (PIV analysis)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

Load

: kN

Deflection: mm

C-1

SFRC-1

SFRC-2

SFRC-3

Figure 6. Development of load in concrete and SFRC beams(LVDT data)

7



derived from the average values of the SFRC tests

4: E ¼ fct;flεy

The flexural strength is linked to the direct tensile strength ( fct)through Equation 5 (Fib, 2013). For a specified minimumlining thickness of 300mm, this ratio is 0·76. The procedurefor obtaining the characteristic and design values from meantest results is outlined in BS EN 1990:2002, Annex D (BSI,2002). The characteristic and design values are derived usingEquations 6 and 7

5:fctfct;fl

¼ 0 � 06� h0�7

1þ 0 � 06� h0�7

6: fctk ¼ fctm � ð1� kn � VX Þ

7: fctd ¼ αct;pl � fctkγc

where fctk is the characteristic tensile strength; fctm is the meantensile strength; fctd is the design tensile strength; kn is thecharacteristic fractile factor, specified in Table D1 of BS EN1990:2002 (BSI, 2002); VX is the coefficient of variation ofdata set X; αct,pl is the coefficient taking into account the long-term effects of the tensile strength for plain or lightlyreinforced concrete (BS EN 1992-1-1:2004, 12.3.1(2) (BSI,2004a, 2004b), recommended value in UK National Annex);and γc is the safety factor for concrete (to BS EN 1990:2002(BSI, 2002)).

0

20

40

60

80

100

120

140

160

0·00

Forc

e: k

N

Strain: %

C-1

SFRC-1

SFRC-2

SFRC-3

0·05 0·10 0·15

Figure 8. Force–strain behaviour from beam test results (PIVanalysis)

TestNumber of

cracksLoad at firstcrack: kN

Bending momentat loading points atfirst crack, M: kNm

Max flexural strengthat first crack,fct,fl: MPa

Flexural tensilestrain at surface,

εy,c1: %

Elasticmodulus,E: GPa

C-1 1 99·5 61·98 4·30 0·0116 37 (Ei)SFRC-1 6 122·8 82·37 5·72 0·0173 33 (Es)SFRC-2 9 123·7 82·29 5·71 0·0198 29 (Es)SFRC-3 10 124·3 82·79 5·75 0·0149 39 (Es)Average (SFRC) 8 123·6 82·48 5·73 0·0173 33 (Es)

Table 2. Stress and strain results at first crack

8



For an unknown coefficient of variability, Eurocode 0 statesthat it is often preferable to assume a conservative upperestimate of VX (but no <10%) and to use the ‘VX known’parameters for kn. Using this approach, the calculateddesign tensile strengths are summarised in Table 3. A valueof 0·1 for VX is considered conservative from previousexperience.

5.3 Average strainsA number of FBG gauges measured the increase in elasticstrain along the uncracked sections of the beam. The strainincreased to a maximum, then fell at first crack. The averagepost-crack strain was comparable to that determined by PIVanalysis (Table 4).

5.4 Crack widthsThe PIV analysis measured the development of all singlecracks within the field of view over time (Figure 9). Where twocracks reached the edge of the beam within <50mm, or wherea single crack separated into two at the edge, it was not poss-ible to calculate the individual contribution of each. Tests

SFRC-2 and SFRC-3 showed similar cracking behaviours, butin test SFRC-1, crack 3 (midway between the hydraulic jacks)dominated the behaviour through a propagation of smallercracks (Figure 5), the individual contributions of which cannotbe derived. In this test, the difference in deflection between thesupports and the midbeam was lower than for the other testsuntil first crack, after which it reached double the differentialsettlement of the others, suggesting that the fibre content ordistribution in this beam was different from that in the twoothers.

The strain gauges installed on the tensile surface of thebeam in the SFRC tests captured the formation of approxi-mately half of the cracks at the centreline of the tensile face.Only two cracks per test were directly comparable to thosestudied using PIV due to issues such as failure of the FBGs athigh levels of strain, insufficient monitoring times of latercracks and cracks being missed by the sensors. The strainswere measured to a high degree of accuracy but the systemwas not able to isolate each crack’s individual contribution tothe strain, where the gauge was affected by two or morecracks.

The crack widths were calculated from the strain data usingEquation 8. This represents an upper bound estimation ofcrack widths: the elastic strain is taken as the maximummeasured by the gauges not overlying cracks, which is expectedto be lower than that in the vicinity of the crack. The develop-ment of cracks using both the FBG and PIV methods are pre-sented in Figure 10. It can be seen that both methods identifythe beginning of the crack development at the same time, butthe measured crack widths differ

8: w ¼ ðεg � εy;elÞ � lg

where w is the crack width on the surface of the beam; εg is thestrain measured by FBG; εy,el is the elastic strain measuredprior to crack; and lg is the length of fibre optics.

It is worth noting that crack 3 in test SFRC-2 is in fact a com-bination of two cracks, 3 and 4, which begin opening at differ-ent times. Individual contributions to the overall width cannotbe ascertained.

Ratio γc αct VX kn fctm,fl: MPa fctm: MPa fctk: MPa fctd: MPa

Mean 0·76 — 1·00 — — 5·73 4·35 — —

Serviceability Limit State 0·76 1·00 0·80 0·1 1·89 5·73 4·35 3·53 2·8Ultimate Limit State 0·76 1·50 0·80 0·1 1·89 5·73 4·35 3·53 1·9

Table 3. Mean, characteristic and design concrete strengths

(�10−4)

Test

SFRC-1 SFRC-2 SFRC-3

εy, max εy, c1 εy, max εy, c1 εy, max εy, c1

Sensor 1 216 201 197 185 171 148Sensor 2 164 141 181 150 197 152Sensor 3 225 115 140 132 178 161Sensor 4 197 133 189 171 — —

Sensor 5 226 207 151 132 — —

Sensor 6 169 — — — — —

Average 200 159 171 154 182 154Averagemeasuredby PIV

173 198 145

Table 4. Maximum and post-crack elastic strains measured byFBGs

9



The PIV and FBG results show little correlation with respectto crack width and rate of crack width increase, for two mainreasons. First, the PIV analysis measures strains at the edge ofthe beam, while the gauges measure on the centreline. Viewingthe set-up from above, it becomes apparent that such differ-ences may occur since the crack typically propagates from thecentre of the beam to its side, generally not in a perfectlystraight line. A number of cracks have separated into two ormore, either at the edge, in the centre of the beam, or both.

Second, the PIV analysis measures strains at a depth of 15 mminto the beam, instead of on the tensile surface, due to the sizeof the IAs used. The behaviour at this depth is more represen-tative of the section’s behaviour since the concrete above this is

considered traction free due to the fully pulled out nature ofthe fibres. Below there exists a bridging zone, where stress istransferred by fibre pull-out and aggregate bridging, overlyingzones of microcracking and microcrack growth (Löfgren,2005).

Both methods, however, identify the cracks initiating at thesame time, and the relative magnitudes of the measurementsfrom both methods are within the expected range.

5.5 Strain at maximum crack widthThe average strain causing the limiting crack width is ofimportance, since it will determine the allowable strains in thestructure before the concrete can no longer be considered to be

–0·5

0

0·5

1

1·5

2

2·5

3

3·5

4

Cra

ck w

idth

: mm

Time


Figure 9. PIV measurements of crack development in SFRCbeams

–0·1

0

0·1

0·2

0·3

0·4

0·5

0·6

0·7

0·8

Cra

ck w

idth

: mm

SFRC-1, crack 2 (PIV)


SFRC-1, crack 2 (FBG)


SFRC-2, crack 3 and 4 (PIV)


SFRC-2, crack 3 and 4 (FBG)






Figure 10. Crack width results using FBG and PIV methods

10



self-healing. To identify these, the time corresponding to amaximum crack width of 0·15 mm – regardless of the numberof cracks developed at this point – was determined from thecrack development graphs. The strain at this time was foundfrom the corresponding average strain to time graph, derivedfrom the strain data at each load stage (Table 1). These resultsare included in Table 5. Tests SFRC-2 and SFRC-3 show asimilar behaviour, while SFRC-1 reaches the limiting crackwidth at a lower average strain level. This discrepancy is linkedto the lower amount of differential settlement (between therestraints and the midbeam) experienced during the test bySFRC-1 before first crack. The others experience higher andcomparable amounts of deflection, and therefore load, since theload–deflection response of all three SFRC beams are similar.

6. Study limitationsAs mentioned previously, the beam moved away from thecamera during testing, and the method used to correct forthis will not compensate for any additional movement after firstcrack. This, however, is expected to be negligible since a goodrestraint was provided when the load exceeded 75–100 kN.

Second, strains are calculated at times corresponding to eachcrack. This time was found by identifying the moments wherethe load on the beam dropped suddenly. It was observed onthe top surface that at this moment, cracks typically initiatedat the centre and propagated towards the side of the beam,meaning that any strains measured by PIV at these momentswould not include the newly formed crack, so the total strainat middle breadth would be slightly underestimated, whencompared with the FBG measurements.

Third, the PIV software itself was a source of minor errors,with a minimum average of 0·6 μm expected for the analysisparameters in this study. The combined error of the crack orstrain measurements would likely not exceed 20 μm.

One proposed recommendation for future tests is to installtarget markers strategically close to the concrete surface, bothabove and below the beam, in a manner that they wouldmeasure out-of-plane movements. An image registration pro-cedure using a transformation type such as ‘nonreflective simi-larity’ in MATLAB could be used to modify the testphotographs before analysis. Given sufficient targets, this

should be able to remove some of the small scaling errorscaused by the beam moving relative to the camera. Anotheroption would be to use multiple cameras (3D PIV), closerange photogrammetry calibration methods (White et al.,2003) or out-of-plane error reduction methods discussed inHoult et al. (2013).

To compare the FBG and PIV results, the same crack widthsshould be measured. In future tests, FBGs should also be fixedto the edge of the beam, on the surface.

7. ConclusionsOne unreinforced and three SFRC beam tests were carried outat the building research establishment (BRE) to assess theeffects of steel fibre reinforcement on the cracking behaviour ofbeams. The strains on the surface of the beams were measuredusing fibre-optic strain gauges, while PIV analyses were carriedout on the side of the beam, using digital photographs takenduring the tests.

The concrete beam failed suddenly at 100 kN, while the SFRCbeams failed by multiple cracking and an average first crackload of 123 kN, at a much higher strain providing evidence ofincreased ductility and stress redistribution.

Crack widths and strains were derived from the displacementdata generated by the PIV analysis. The strains on the tensilesurface of the SFRC beams were determined by PIV analysisto be, on average, 0·0173% at first crack. Strains at limitingcrack width were around 350 με, with one test reaching thelimiting width at a lower 214 με.

The relevance of the PIV method is that it provides a systemthat can measure small cracks and strains in concrete to areasonable degree of accuracy, and can be used in combinationwith other, more traditional methods of strain measurement.PIV is a non-intrusive method that can provide data across theentire side of the beam, where other systems can producemeasurements only at specific locations.

The results presented in this paper are intended to form thebasis of a study into the cracking behaviour of SFRC tunnellinings under loading. As in most concrete structures, theallowable crack width tolerances for durability are extremelytight, and this usually requires onerous traditional reinforce-ment designs. With the use of SFRC tunnel linings, the poten-tial cost and embodied energy savings are high, but the designsmust rely on a good understanding of the material’s behaviourunder load.

AcknowledgementsThe authors express their thanks to Mr Martin Rimes(Materials Engineer for UnPS) and his team for the beam


Strain: με 214 367 349Number of cracks <0·15mm 1 2 3

Table 5. Average strain at limiting crack width

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casting and the small-scale testing. Thanks are also due to MrDavid Brooke (Building Research Establishment StructuresLab Manager) for the work carried out in testing the concretebeams, Dr Vangelis Astreinidis (CEM) for the FBG measure-ments and analysis, Dr Qing Ni (Warwick University) for thePIV testing and to the Thames Water Project ManagementTeam and the MVB JV Management for supporting the casefor large-scale testing.

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http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0000538

http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0000538

http://dx.doi.org/10.1680/geng.13.00021



http://dx.doi.org/10.1139/cgj-2014-0080

http://dx.doi.org/10.1139/cgj-2014-0080

Estimating crack widths in steel fibre-reinforced concrete - Bekaert-Maccaferri · 2019-02-11 · Estimating crack widths in steel fibre-reinforced concrete &1 Eyre Hover MEng, PhD

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