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10th International Conference on Fracture Mechanics of Concrete and Concrete StructuresFraMCoS-X
G. Pijaudier-Cabot, P. Grassl and C. La Borderie (Eds)
FIBRE REINFORCED CONCRETE:FROM FLEXURAL TESTS TO SOLID SLABS
MARCO DI PRISCO∗, ALI POURZARABI† AND MATTEO COLOMBO‡
∗Politecnico di MilanoMilan, Italy
e-mail: [email protected]
†Politecnico di MilanoMilano, Italy
e-mail: [email protected]
‡Politecnico di MilanoMilan, Italy
e-mail: [email protected]
Key words: Fibre Reinforced concrete, Slab, Reliability, Design approach
Abstract. Tensile behavior of fibre reinforced concrete is assessed based on flexural tests wherespecifically the post cracking strength values are of interest. However, the residual tensile strengthvalues obtained based on such characterization test exhibit a very high scatter which is mainly dueto the variation of number and orientation of fibres at the fracture plane. This rather unrepeatablebehavior may cast doubt on the overall performance of a structure reinforced only with fibres and mayquestion the validity of estimated tensile strength parameters that are used in the design of such fromone specimen to another structures. While there is evidence that fibre reinforced concrete structuresshow a behavior that can be predicted by the average material properties, no strong proof is yetavailable. If so, then the low characteristic value of residual strength values may be a very conservativestarting point for design of such structures To validate the reliability of design approach proposed forfibre reinforced concrete structures, twelve nominally identical fibre reinforced concrete slabs sized2000×2000×150 mm, and twelve notched specimens sized 150×150×600 mm are tested, and theresults are compared. Further, a yield line method is employed to predict the ultimate load bearingcapacity of the slabs based on the tensile parameters obtained from the characterization tests. Theresults show that the average material properties can satisfactorily predict the bearing capacity of theslabs. FraMCoS X Conference.
1 INTRODUCTION
Fibre reinforced concrete (FRC) has very at-tractive features both in terms of mechanicaland durability properties [1, 2]. Considerablepost-cracking residual strength in a FRC ma-terial can significantly increase the load bear-ing capacity of structural elements and limit theopening of cracks. Complete or partial exclu-
sion of conventional rebars can remarkably re-duce the labor cost and allow for more archi-tecturally pleasant forms to be cast. Althoughhas a higher cost of production, FRC can yetbring savings in the total costs by reducing thevolume of material and by cutting constructioncosts [3]. To better place this material in a cost-driven market, it is of paramount importance to
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
exploit its capacity to its full extent.The tensile behavior of a FRC material is
commonly characterized through a flexural teston standard beam specimens with or without anotch. In either case, the results obtained forresidual tensile strength parameters from suchtesting methods exhibit a high scatter. Propaga-tion of a single crack at the position of the notchin a three point bending test, or at very few loca-tions, if ever, in a four-point bending test, makesthe response of these testing methods very de-pendent on the number and orientation of fibresat a single cross section along the beam spec-imen, which can considerably vary from onespecimen to the other depending on the cast-ing method. This is unlike the behavior of FRCstructural elements that show a highly repeat-able structural response. Consequently, a lowcharacteristic value for material tensile proper-ties sets a starting point for design of a FRCstructure, which leads to overly safe structures.Filling the unnecessarily large gap between thecomputed design resistance of a structural ele-ment with what may be obtained in a real-lifecase is a reservoir of strength that if left unno-ticed, may undermine the sustainability of FRCas a structural material.
In this work, to examine the extent to which aSteel Fibre Reinforced Concrete (SFRC) struc-ture outperforms the predictions coming froma design perspective, we have tested twelvenotched prismatic beams following the EN14651 [4] methodology in a three-point bend-ing setup, and twelve nominally identical slabsthat were reinforced only with steel fibres whilebeing supported on four corners and loaded inthe center.
2 EXPERIMENTAL PROGRAM2.1 Materials and specimens
A self-consolidating SFRC material is usedto cast all the specimens whose mix designis given in Table1. The mix design contains35 kg/m3 of double hooked steel fibres with alength of 60 mm and a diameter of 0.9 mm. Thefibres have a tensile strength of 1500 MPa anda Young’s modulus of 210 GPa.
Table 1: Mix design of the SFRC material
Cement (Cem IV 42.5) [kg/m3] 380Sand 0/4 [kg/m3] 425Sand 0/8 [kg/m3] 850Gravel [kg/m3] 425
Carbonate filler [kg/m3] 100w/b 0.36
Fibre [kg/m3] 35Superplasticizer (% of cement weight) 1.2
Twelve 150×150×600 mm prismatic beamsand twelve 2000×2000×150 mm slabs werecast in a job-site from the same concrete batchthat was delivered by a truck mixer. The slabswere cast from the center of the molds and theflowability of the concrete obviated any needfor vibration. After casting, all the specimenswere covered with a moist burlap for a coupleof days, and afterwards they were transferred tothe laboratory where they were kept in atmo-spheric condition until the age of testing. Ateach testing age we tested one notched beamand a companion slab. Further, six cubes with a150 mm side were cast together with the slabsand prismatic beams for the assessment of thecompressive strength. Three of the cubes weretested on the first testing age at 59 days, andthree of the cubes were tested on the last dayof testing, at 134 days. The average compres-sive strength obtained was respectively 47.4 and59.8 MPa with a coefficient of variation of 3%for both testing ages.
2.2 Three-point bending testThe prismatic beams were notched in the
mid-length to a depth of 25 mm and were testedin a three-point bending scheme according toEN 14651 with a span of 500 mm. During thetest the Crack Mouth Opening Displacement(CMOD) was measured with a clip gauge at thenotch. The results of the test are representedin terms of nominal stress-CMOD. Specifically,according to the EN 14651 and the fib ModelCode 2010 [5], the values of nominal residualstress at a CMOD of 0.5, 1.5, 2.5, and 3.5 mmare reported as fR1, fR2, fR3 and fR4.
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
2.3 Slab testThe twelve slabs were tested under a cen-
tral concentrated load and they were supportedat the four corners on square steel plates of200×200×25 mm welded on top of a steel col-umn made of two UNP200 profiles. An electro-mechanical jack with a capacity of 1000 kNwas used and a constant displacement rate of20 µm/sec was imposed to the loading head.A piece of neoprene sheet was placed betweenthe slab and supports and beneath the loadingpoint to prevent erratic local effects. The slabswere connected to the supports by means of ananchorage device to create a bilateral restraint.However, measurements on the rotation of theslab corners showed that for the most part ofthe test, the anchorage device is not in tension,and in fact the slabs are allowed to rotate at thesupports. The details on the support dimensionsand placement can be found in [6]. A schematicrepresentation of the slab setup is shown in Fig-ure 1.
Figure 1: Schematic representation of the dimensions ofthe slab.
For each slab, the deflection is measuredfrom the bottom of the slab at the center. Fur-thermore, ten measurements are carried out todetect the propagation of cracks on the slabsby means of LVDTs (Linear Variable Differen-tial Transducer). The position, gauge length,and the label of these instruments are shown inFigure 2. Four instruments are positioned onthe top surface of the slabs at the location of
the supports to capture possible negative cracks,which are shown by CODt and two letters show-ing its position in the plane of the slab. Six in-struments record the propagation of cracks atthe bottom of the specimens. The four instru-ments in the center of the slab are designatedby CODb and the two longer instruments aremarked with CODLb. These are accompaniedby one letter showing the direction of the in-struments.
Figure 2: Position, label, and gauge length of instrumentson (top) top face; and (bottom) bottom face of slabs.
3 Results and discussion
3.1 Notched beams
Figure 3 shows the results of the tests car-ried out on the notched beams in terms of nom-inal stress-CMOD. On the figure, the gray areashows the scatter of the results, the black solidline is the average of the curves, and the solidgrey line is the characteristic curve correspond-ing to a 5% percentile considering a lognormaldistribution for the residual strength values.
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
Figure 3: Stress-CMOD result of twelve tested notchedbeam specimens.
The stress-CMOD results show that aftercracking, the SFRC material exhibits a harden-ing behavior up to a CMOD of approximately1.5 mm, and then comes the softening phase.The residual strength values with statistical pa-rameters obtained for these values are reportedin Table 2. According to the classificationmethodology suggested in the MC 2010 theSFRC material is categorized as a ”5c”. In viewof the focus of the present work, the dispersionof these results is of specific interest where acoefficients of variation in the range of 15% to19% is obtained.
Table 2: Results obtained from the notched beam testswith statistical parameters
Average 5% percentileV∗[%]
[MPa] [MPa]fct,fl 5.7 4.9 7fR1 7.6 5.6 15fR2 9.3 6.7 17fR3 7.7 5.4 16fR4 5.8 4.0 19
∗coefficient of variation
3.2 SFRC slab behaviourFigure 4 shows the load-deflection result of
each of the twelve tested slabs. The tests werestopped, and the specimens were unloaded,upon demonstration of a softening behavior.Other than two of the slabs that show an er-
ratic different initial stiffness, the other ele-ments show an almost equal initial slope in theload-deflection response. After this initial lin-ear phase, the slabs display a hardening behav-ior before going through a softening response.The average of the maximum load sustained bythe slabs is 132.2 kN with a coefficient of vari-ation of 5.2%. The characteristic value of themaximum load considering a lognormal distri-bution is 122.9 kN. The dispersion of the struc-tural maximum load is considerably differentfrom that of the residual tensile strength valuesthat were obtained in case of the notched beamtests. This stark difference highlights the in-born distinction between the structural test, anda characterization test carried out on the sameSFRC material.
Figure 4: Load-deflection response of the twelve slabs.
As compared to the maximum load, the de-formation capacity of the slabs shows a highervariation. The deflection corresponding to themaximum load has an average of 16.2 mmwith a coefficient of variation of 13%. Over-all, slabs reinforced only with fibres may showlimited ductility as opposed to R/C slabs, whichneeds attention when dealing with slabs with-out conventional reinforcement and where ulti-mate limit state is of concern. This was shownearlier in [6] where the behavior of SFRC slabsand R/C ones where compared. The results pre-sented here show that for SFRC slabs, determi-nation of the maximum deflection may also besubjected to a rather high uncertainty.
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
In Figure 5 the crack pattern at the bottomof one of the SFRC slabs is presented as an ex-ample. In all slabs two perpendicular bands ofcracks are formed stretching from the middleof one side to the opposite side. In the middleof the slabs and beneath the loading point thecracks show a more irregular pattern, however,away from this zone cracks show a parallel con-figuration. The average spacing of the cracks atthe edge of the slabs varies from around 60%of the slab depth to 150 mm which is the slabdepth. No cracks appeared on the top faceof the slabs and therefore the results recordedby CODt instruments are not discussed and re-ported here. It is also pointed out that the de-tection of the cracks has been done visually andcracks has been marked at different loading lev-els.
Figure 5: The bottom-crack pattern of one of the slabs.
The measurements carried out on the propa-gation of cracks at the bottom of the slabs withthe CODb and CODLb instruments are shownin Figure 6. Taking into account the record-ings made by each single instrument, it is notedthat at a certain load level in each slab, the de-formation is concentrated in those instrumentsthat capture the localized cracks, while the othermeasurements show constant or slightly de-creasing values. In Figure 6, only the measure-ments that capture the localized crack are re-ported and they are averaged for each specimenfor the instruments of the same group. In Figure6(bottom) ten curves are presented as the resultsmeasured for two of the slabs were lost due to
technical problems.In general, the curves obtained for the crack
opening measurements in the slabs are similarto those of the deflection response. Table 3reports the average load and the coefficient ofvariation of load level at crack openings of 0.5,1.5 and 2.5 mm measured by CODb and CODLb
instruments. The values of coefficient of varia-tion fall below 5% which indicates that not onlythe SFRC slabs show a very repeatable struc-tural response in terms of load-deflection, butalso the cracking behavior of these elements isvery similar. While not a sound comparison, thedistinction between the behavior of the notchedbeams and the slabs may also be underlined bylooking at the coefficient of variation at corre-sponding crack openings, where in the slabs,these values are less than three times of those ofthe notched beams for the same value of crackopening.
Figure 6: Crack opening measurement on the slabs with(top) CODb instruments in the center; and (bottom) twoCODLb instruments. The results are averaged for thoserecordings that capture the localized crack.
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
Table 3: Average load and coefficient of variation of loadfor the slabs at a CODb and CODLb of 0.5, 1.5, and 2.5mm
COD (mm) Loadave (kN) VLoad (%)
CODb
0.5 98.9 4.11.5 121.7 4.82.5 131.4 4.7
CODLb
0.5 96.2 3.81.5 118.8 4.52.5 129.4 5
4 ULTIMATE LOAD PREDICTIONA yield line approach is adopted to compare
the experimental average and characteristic re-sistant load of the slabs with those that would beobtained following a limit state analysis startingfrom average and characteristic values of ma-terial properties that were determined from thecharacterization tests. Further, the design resis-tant load that would be obtained from such anapproach is also compared with the experimen-tal values. To do so, the yield line pattern shownin Figure 7 is considered which also coincideswith the experimental failure mechanism.
Figure 7: The yield line pattern considered for predictionof the resistant load.
For the tensile behavior of the SFRC mate-rial the provisions of MC 2010 is followed. Aplane section approach is assumed for the com-putation of the positive and negative resistingbending moments and the chosen characteris-tic length equals the depth of the slab, 150 mm.
Figure 8 shows the tensile constitutive behav-ior of the SFRC for the mean, characteristic anddesign value of material properties. The designvalue of material properties is obtained by in-troducing a partial safety factor of 1.5.
Figure 8: The tensile constitutive law of the SFRC mate-rial based on average, characteristic, and design value ofstrength values.
The development of the formulations to de-rive the ultimate resistant load according to theselected yield line pattern results in an almost70% contribution from the positive bending mo-ment and 30% from the negative bending mo-ment (Pu = 5m+ + 2m− ). However, experimen-tal evidence shows that no negative cracks ap-peared during the tests on the SFRC slabs whichowes mainly to the specific support conditionadopted in the study which allows the rotationof the slab corner. The ductility of the slabscould not accommodate the formation of thenegative cracks at the support position beforethe unfolding of the softening phase. Hence,introduction of the m− in the formulation mayunrealistically overestimate the load bearing ca-pacity of the slabs. Therefore, the ultimate loadof the slabs is computed once with the assump-tion of the presence of the negative cracks andonce without their contribution. The compu-tation is carried out with the mean, 5% per-centile, and design tensile constitutive relationswhich are shown in Figure 9 with horizontallines marked with m, k, and d letters. Further-more, Figure 9 shows the envelope of the ex-
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
perimental results with the mean and character-istic value of the experimental load-deflectionresults.
According to Figure 9, it is clearly ob-served that adoption of a failure mechanism thatcomprises the negative cracks which does notmatch the experimental crack pattern, will sub-stantially overestimate the resistant load of theslabs. On the contrary, excluding the nega-tive cracks from the computations and imple-menting the mean tensile constitutive relation,gives a very close prediction for the averageresistant load. The predicted ultimate load is128 kN as opposed to the 132.2 kN obtainedexperimentally. This evidence draws attentionto the importance of adopting a proper failuremechanism when performing a yield line ap-proach. Measures should be taken to assure suf-ficient structural ductility so that the predictedfailure mechanism, conforms with the real-lifecrack patterns [6]. Nevertheless, in a monolithicstructure the support rigidity may suffice to trig-ger the creation of negative cracks.
In case of the yield line pattern that cor-responds with experimental evidence, it is re-markable to notice the difference between theexperimental characteristic maximum load (themaximum on the solid grey line in Figure 9),and the one obtained from the yield line methodby means of the characteristic tensile proper-ties. Although the average material propertiesnicely catches the average structural response ofthe slabs, the high scatter of the residual tensilestrength parameters leads to a very conservativeprediction for the characteristic maximum load,and since a structural design procedure is basedon characteristic properties of material param-eters, the excessive safety margin compromisesthe efficiency of structural applications of FRCmaterials. In an economical structural design,the design value of resistance equals the de-sign value of load effects, although in practicethe design value of resistance is larger whichprovides additional safety margin [7]. There-fore, ideally, we aim to predict the character-istic behavior of the structure with the charac-teristic material properties. Here, the predicted
characteristic resistant load is 91 kN versus the122.9 kN of the experimental results, whichgives a ratio of Pu-Exp/Pu-Predicted=1.35. Hence,the computed design resistant load can be in-creased with a factor of 1.35 without penaliz-ing the required reliability level. This is in ac-cordance with the idea of the redistribution fac-tor, κRd, introduced in the MC 2010, which al-lows the magnification of the computed designresistant load computed by using characteristicstrengths for FRC structures that are capable ofredistributing stresses. This topic has also beendiscussed elsewhere [8].
Table 4 reports the predicted values for bothyield line patterns and for the three state of ma-terial properties and the ratios with respect tothe experimental values. Assuming that the de-sign resistance could be increased by a factorof 1.35, the final design resistant load would be59×1.35= 79.6 kN, which leads to a safety fac-tor of γs=127.9/79.6=1.6.
Figure 9: Ultimate load prediction of the SFRC slabs bymeans of a yield line approach with mean, characteristicand design value of tensile constitutive relations for thecases with and without the negative cracks.
5 CONCLUSIONSWe have discussed and compared the differ-
ence in the scatter of results of twelve notchedbeams tested in a three-point bending test andthe structural response of twelve slabs made of aSFRC material and have highlighted the conse-quences of such distinction. The deflection re-
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M. DI PRISCO, A. POURZARABI, and M. COLOMBO
Table 4: Experimental mean and characteristic values of resistant load and the predicted values following a yield lineapproach
Material Experimental With m− Without m−
properties load PuExp (kN) PuExp/PuPredicted PuExp (kN) PuExp/PuPredicted
Mean 132.2 179 0.74 127.9 1.035% perc 122.9 127.5 0.96 91 1.35Design - 83 - 59 -
sponse and the cracking behavior of the twelveSFRC slabs were closely repeated with a coef-ficient of variation lower than 5%. This was de-spite of the fact that the same SFRC materialshowed a coefficient of variation between 15%to 19% in the post-peak tensile strength in thecharacterization tests. Unlike the load carryingbehavior, the ductility of the SFRC slabs wassubjected to more variation with a coefficient ofvariation of 13% for the deflection correspond-ing to the maximum load with the minimum andmaximum values being 13.9 mm and 20.1 mm.
We then predicted the design resistant loadof the SFRC slabs with the mean, 5% per-centile, and the design value of material proper-ties through a yield line approach. We observedthat adoption of a yield line pattern that doesnot correspond with the experimental crack,can lead to unsafe prediction of the maximumload. Further, we showed that the mean materialproperties can well predict the maximum loadsustained by the slabs, while the very conser-vative values of characteristic tensile strengthparameters, greatly underestimates the 5% per-centile of the maximum load in the slabs witha ratio of 1.35. Finally, the design resistantload obtained from the yield line procedure wasmagnified by the 1.35 coefficient which led to areasonable safety factor of 1.6 for the slab.
References[1] di Prisco, M., Felicetti, R., and Plizzari,
G.A. PRO 39: 6th International RILEMSymposium on Fibre-Reinforced Concretes(FRC) - BEFIB 2004 (Volume 1). RILEM,2004.
[2] Berrocal, C.G., Lofgren, I., and Lundgren,
K. The effect of fibres on steel bar corro-sion and flexural behaviour of corroded rcbeams. Engineering Structures, 163:409–425, 2018.
[3] Blanco, A., de la Fuente, A., and AguadoA. Sustainability analysis of steel fibre re-inforced concrete flat slabs. In II Interna-tional conference on concrete sustainabilityICCS16, 2016.
[4] EN 14651: Test method for metallicfibered concrete-Measuring the flexuraltensile strength (limit of proportionality(LOP), residual). Brussels: European Com-mittee for Standardization, 2005.
[5] Federation internationale du beton. Modelcode 2010: final draft. International Fed-eration for Structural Concrete (fib), Lau-sanne,Switzerland, 2013.
[6] di Prisco, M., Colombo, M., and PourzarabiA. Biaxial bending of sfrc slabs: Is conven-tional reinforcement necessary? Materialsand Structures, 52(1):1, 2019.
[7] Gulvanessian, H. and Holicky M. Eu-rocodes: using reliability analysis to com-bine action effects. Proceedings of the In-stitution of Civil Engineers-Structures andBuildings, 158(4):243–252, 2005.
[8] di Prisco, M., Martinelli, P., and Parmen-tier P. On the reliability of the design ap-proach for frc structures according to fibmodel code 2010: the case of elevatedslabs. Structural Concrete, 17(4):588–602,2016.
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