De Pauw, Peter

Franchois, Ann

Taerwe, Luc

Van Damme, Stephan

English

Ghent University Academic Bibliography

Comparison of Two Coaxial Probes for Measuringthe Steel Fiber Content in Fiber ReinforcedConcrete SlabsS. Van Damme∗ A. Franchois∗ P. De Pauw† L. Taerwe†Abstract — Recently, a non-destructive measuringtechnique to measure the steel fiber content in steelfiber reinforced concrete was proposed by the au-thors. The technique is based on permittivity mea-surements using an open-ended coaxial probe. Inprevious work, a moderate sized probe was used.From the results using this probe, the need for alarger probe was clear. In this paper, measure-ments using an in-house designed large probe arecompared with the measurements from the moder-ate sized probe.1 INTRODUCTIONIn steel fiber reinforced concrete (SFRC), steelfibers are randomly added to the concrete, yieldinga better tensile strength. This type of reinforce-ment is used more and more in applications suchas slabs on grade and pavements. An importantquality aspect is the uniform spatial distributionof the fibers throughout the concrete. Locationswith lower fiber contents have a lower strength.The fibers also should have a random orientation towithstand tensile forces in different directions. To-day, the fiber content in SFRC slabs is checked in adestructive manner by drilling out a core, crushingit and counting the number of fibers [1]. This tech-nique has a lot of drawbacks. Recently, we devel-oped a non-destructive technique based on the useof microwaves [2]. It combines an accurate open-ended coaxial probe reflectometry method, in or-der to measure the effective permittivity of the re-inforced concrete, with a classical mixing formula,which establishes the relationship between the ef-fective permittivity and the fiber content. Measure-ments performed with a moderate sized probe onSFRC slabs showed important local spatial fluctu-ations in the permittivity. This was probably due tothe limited size of the probe aperture with respectto the dimensions of the fibers. Therefore, a spa-tial averaging of the measurements was introduced∗Dept. of Information Technology (INTEC-IMEC),Ghent University, St. Pietersnieuwstraat 41, 9000 Gent,Belgium, e-mail: stephan.van.damme@intec.ugent.be, tel.:+32 (0)9 2649995, fax: +32 (0)9 2649969; e-mail:ann.franchois@intec.ugent.be†Dept. of Structural Engineering, Ghent University,Technologiepark Zwijnaarde 904, 9052 Gent, Belgium, e-mail: Peter.DePauw@ugent.be, tel.: +32 (0)9 2645530, fax:+32 (0)9 2645845; e-mail: Luc.Taerwe@ugent.beto improve the homogenization. In this paper wehave built a larger probe. It is shown that with thisprobe spatially stable results can be obtained.In Section 2 a Maxwell-Garnet mixing rule isgiven for SFRC. In section 3, the open-ended coax-ial probe method is described. Results obtainedwith the moderate sized probe are shortly discussedin section 4 and in section 5 measurements with thelarge probe are reported. In section 6 the resultsfrom both probes are compared.2 MIXING RULE FOR STEEL FIBERREINFORCED CONCRETEConcrete is made by mixing cement, water, fine andcoarse aggregates. After the mixing, the concretehardens as a result of a chemical reaction betweenwater and cement. Steel fibers can be added tothe fresh concrete as reinforcement. The amountof steel fibers depends on the type of fiber and onthe required strength and is typically in the range of20 kg/m3 to 80 kg/m3, which corresponds to sparsemixtures with volume fractions between 0.002 and0.01. The length l and diameter d of the fiber are inthe ranges 10 mm < l < 80 mm and 0.1 mm < d <1 mm.Concrete and SFRC are heterogeneous materi-als, but for wavelengths that are large comparedto the dimensions of the composing particles, theycan be considered as homogeneous. In this case,homogenization theories can be applied. In thispaper SFRC is considered as a homogeneous con-crete backgound material with relative permittiv-ity εr,h containing a volume fraction fv of perfectlyelectrically conducting prolate spheroids. In [2], aMaxwell-Garnett mixing formula was derived, giv-ing the relationship between the real part of the rel-ative effective permittivity ε′r,eff of SFRC and thefiber volume fraction:ε′r,eff = ε′r,h[1 +fv3(1− fv)3∑i=11Ni], (1)where Ni, i = 1, 2, 3, are the depolarization factorsof an ellipsoid. From (1) it is clear that for smallvolume fractions, as used in this work, the relative                                                                                               																																																																																															                                                                                                                                                                                    PSfrag replacementsConnectorF2a 2bεr,cεrL2 L1Figure 1: Open-ended coaxial probe configuration.permittivity contrast (ε′r,eff−ε′r,h)/ε′r,h depends lin-early on the fiber volume fraction.3 OPEN-ENDED COAXIAL PROBEMETHODThe open-ended coaxial probe as a tool to measurethe relative complex permittivity εr = ε′r − jεr” atmicrowave frequencies has been studied intensivelyin the literature, e.g. [3]-[6]. The probe is schemat-ically presented in Fig. 1. The inner and outerconductors have radii a and b, respectively, and thespace between both conductors is filled with a ma-terial with relative permittivity εr,c. The lengthsof the straight and tapered sections are L1 and L2,respectively. A flange with dimension F , extendingthe outer conductor, allows to establish a stablecontact with the slab and it makes the electromag-netic modelling of the probe easier.The relative complex permittivity can be derivedfrom the TEM-mode reflection coefficient at theprobe aperture by using an appropriate model forthe aperture input admittance. In this paper twofull-wave models, that account in an exact way forthe evanescent higher order TM0n modes at theprobe aperture, are applied. Both models are basedon the assumption of a flange of infinite extent,which in practice is fulfilled if F > b. The firstmodel is the rational function approximation pro-posed by Stuchly et al. [4]. This model is valid forthe class of 50 Ω Teflon-filled probes applied againsta (possibly lossy) dielectric half-space and is com-putationally very efficient. The second model, pro-posed by De Langhe et al. [3], is computationallymore intensive, but it can be used in case of a one-dimensional layered medium, e.g. to account forthe finite thickness of a slab.4 MEASUREMENTS WITH A MODER-ATE SIZED PROBEThis is a 50 Ω Teflon-filled probe with the follow-ing parameters (Fig. 1): a = 5.9 mm, b = 20mm, F = 60 mm, L1 = 95 mm, L2 = 30 mm andεr,c = 2.1. It is shown in Fig. 2, together with restof the measurement setup (a flexible test-port cable,an Agilent 8714ET Vector Network Analyzer and aPC). This probe was used for the measurements re-ported in [2], that were performed on three differentconcrete slabs with dimensions 600 mm x 600 mmx 100 mm: slab S00 without fibers (fv = 0), slabS20 with 20 kg/m3 of fibers (fv = 0.0024) and slabS40 with 40 kg/m3 of fibers (fv = 0.0048).Before starting the measurements, a standardSOL (Short, Open, Load) calibration is carried out,establishing the reference plane at the end of theflexible cable. Then the probe is connected to itand the reflection coefficient is measured for threereference materials. With these measurements, cal-ibration factors are computed as with the SOL cal-ibration [6]. These calibration factors subsequentlycan be used to calibrate the measurements, yieldingthe true reflection coefficient at the aperture of theprobe. For the moderate sized probe, the inversionfor the relative complex permittivity can be donewith the model by Stuchly et al. [4].Figure 2: Moderate sized probe.S00 S20 S40ε’minr 4.963 5.705 5.784ε’maxr 6.192 13.702 25.458ε”minr 0.066 0.124 0.042ε”maxr 0.418 0.805 2.929<ε’r> 5.45 7.77 9.54<ε”r> 0.16 0.27 0.39σε′r0.20 1.65 2.66σε′′r0.03 0.10 0.27Table 1: Results for the moderate sized probeThe optimum frequency range for this probe is be-tween 600 MHz and 1.3 GHz. We checked by meansof [5] that if the thickness of the SFRC slab is atleast twice the outer radius b, the slab can be con-sidered as a half-space. The measurements on theslabs S00, S20 and S40 were done on a grid of 23by 23 points, equally spaced 20 mm in both trans-verse directions. Table 1 shows for each slab theminimum and maximum complex permittivity val-ues over the grid εminr and εmaxr , the mean value<εr> and the standard deviation σεr , at 600 MHz.The spatial variations in the permittivity of S00are small. The mean value for S00, ε′r = 5.45, wastaken as the background permittivity εr,h for de-riving the fiber content of S20 and S40 with (1).The mean values for S20 and S40 are ε′r = 7.77and ε′r = 9.54, respectively, and the correspond-ing fiber volume fractions are 18.8 kg/m3 and 33.0kg/m3, respectively. The result for the smaller vol-ume fraction (20 kg/m3) thus is better than thatfor the higher volume fraction (40 kg/m3). Themeasurements on S20 and S40 show larger spatialfluctuations, i.e. this probe is quite sensitive to thelocal distribution of the fibers. Therefore the per-mittivities were averaged over subspaces of about20 by 20 cm of the grid, as explained in [2]. Toavoid this averaging procedure, a larger probe wasconstructed.5 MEASUREMENTS WITH A LARGEPROBEThis is a 50 Ω air-filled probe with the follow-ing parameters (Fig. 1): a = 43 mm, b = 100mm, F = 100 mm, L1 = 305 mm, L2 = 80 mmand εr,c = 1. Due to mechanical constraints theouter radius was limited to maximum b = 100mm. The choice for a Teflon filling was rejectedfor mechnical and cost reasons. The flange is nowmade in a square instead of a circular shape. Theprobe length was chosen to ensure that higher or-der modes are sufficiently attenuated at the probe -Figure 3: Large coaxial probe.cable discontinuity, e.g. the amplitude of the TE11mode (lowest higher order mode) is reduced to 1%over a distance of 330 mm. A picture of this probeis shown in Fig. 3. The inner conductor is sup-ported by two thin Teflon rings, one of which isvisible in the picture.The optimum frequency range for this probe isbetween 100 and 400 MHz. Measurements weredone on the same slabs as in the previous section.Now a grid of 4 by 4 points, equally spaced 65mm in both transversal directions is used. Dif-ferent calibrations of the probe were tested. Theone-standard calibration technique yielded betterresults than the three standard technique. The cal-ibrated reflection coefficient in this case is given byKcal = KmeasKstheorKsmeas, (2)where Ksmeas and Kmeas are the measured reflectioncoefficients of the known calibration material andthe unknown material respectively, and Kstheoristhe theoretical reflection coefficient of the calibra-tion standard. The calibration with a Teflon slabwas the best. Since the thickness of the slab is lessthan 2b, the inversion is done in an iterative waywith the model by De Langhe et al. [5].The results at a frequency of 100 MHz are shownin Table 2. The mean value for S00, ε′r = 5.24, istaken as the background permittivity εr,h for de-riving the fiber content of S20 and S40 with (1).The mean values for S20 and S40 are ε′r = 7.56and ε′r = 10.41, respectively, and the correspond-ing fiber volume fractions are 19.5 kg/m3 and 43.3kg/m3, respectively. These results now are closerto the expected fiber contents than the values ob-tained with the moderate sized probe.S00 S20 S40ε’minr 5.080 6.963 9.193ε’maxr 5.366 8.071 11.299ε”minr 0.149 0.179 0.276ε”maxr 0.157 0.208 0.339<ε’r> 5.24 7.56 10.41<ε”r> 0.15 0.20 0.31σε′r0.09 0.32 0.51σε′′r0.002 0.01 0.02Table 2: Results for the large sized probeRel. variances moderate sized probe (%)Variance S00 S20 S40σε′r3.65 21.23 27.89σε′′r19.24 37.75 68.08Rel. variances large probe (%)Variance S00 S20 S40σε′r1.66 4.20 4.94σε′′r1.69 4.20 4.93Table 3: Comparison of the relative variances onthe permittivities measured with both probes.6 COMPARISON OF THE TWOPROBESWhen comparing the results for the two differentprobes, the following conclusions can be drawn.The global average permittivity values over the to-tal grids are comparable for both probes, as canbe seen from Tables 1 and 2, but local spatialvariations are more important with the moderatesized probe than with the large probe. The vari-ance relative to the mean value (in %) is shown inTabel 3. It follows that for both probes the vari-ance grows larger with increasing fiber volume frac-tion. However, the variances for the larger probeare much smaller than those for the moderate sizedprobe. The active area of an open-eded coaxialprobe roughly is given by the aperture area withinthe outer conductor. The active area of the largesized probe (≈ 314 cm2) is approximately 25 timeslarger than that of the moderate sized probe (≈ 12cm2), such that there is no need to perform a spatialaveraging. It is concluded that the large probe ismore suited to measure the fiber content in SFRC.7 CONCLUSIONSRecently, a non-destructive measurement techniquewas introduced by the authors [2]. The techniquerelies on the use of an open-ended coaxial probemeasurement method. In previous work, a moder-ate sized probe was used. This probe showed rela-tively large spatial variations in the measured per-mittivity. In this paper, a large probe was build.The results with this probe showed significantlysmaller spatial permittivity variations. This is dueto the larger active area of the probe. It can beconcluded that this larger probe is more suited formeasuring permittivities of SFRC.AcknowledgmentsThis work was sponsored by the Fund for ScientificResearch - Flanders. The authors are grateful toL. Haentjens for constructing the large open-endedcoaxial probe.References[1] L. Taerwe, A. van Gysel, G. de Schutter andJ. Vyncke, “Experimental determination of thesteel fibre content in fresh and hardened con-crete used for concrete slabs on grade,” Proceed-ings of the Asian-Pacific Specialty Conferenceon Fibre Reinforced Concrete Ed. T.S. Lok,pp. 255–261, Aug. 1997.[2] S. Van Damme, A. Franchois, D. De Zutter, andL. Taerwe, “Nondestructive Determination ofthe Steel Fiber Content in Concrete Slabs Withan Open-Ended Coaxial Probe,” IEEE Trans.Geoscience Remote Sens., Vol. 42, pp. 2511–2521, Nov. 2004.[3] P. De Langhe, K. Blomme, L. Martensand D. De Zutter, “Measurement of low-permittivity materials based on a spectral-domain analysis for the open-ended coaxialprobe,” IEEE Trans. Instrum. Meas., Vol. 42,pp. 879–886, Oct. 1993.[4] S.S. Stuchly, C.L. Sibbald and J.M. Anderson,“A new aperture admittance model for open-ended waveguides”, IEEE Trans. MicrowaveTheory Tech., Vol. 42, pp. 192–198, Feb. 1994.[5] P. De Langhe, L. Martens and D. De Zutter,“Design Rules for an Experimental Setup Us-ing an Open-Ended Coaxial Probe Based onTheoretical Modelling,” IEEE Trans. Instrum.Meas., Vol. 43, pp. 810–817, 1994.[6] A. Kraszewski, M.A. Stuchly, and S.S. Stuchly,“ANA Calibration Method for Measurementsof Dielectric Properties,” IEEE Trans. Instrum.Meas., Vol. 32, pp. 385–387, 1983.

Comparison of two coaxial probes for measuring the steel fiber content in fiber reinforced concrete slabs

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Comparison of two coaxial probes for measuring the steel fiber content in fiber reinforced concrete slabs

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