Steel Fiber Reinforced Concrete Characterization Bad on a Magnetic Probe
M. Faifer, R. Ottoboni, S. Toscani Dip. di Elettrotecnica, Politecnico di Milano Piazza Leonardo da Vinci 32 – 20133 Milano ITALY e-mail: marco.faifer@polimi.it
L.Ferrara
Dip. di Ingegneria Strutturale, Politecnico di Milano Piazza Leonardo da Vinci 32 – 20133 Milano ITALY e-mail: liberato.ferrara@polimi.it
Abstract—Steel fiber reinforced concrete (SFRC) is a composite material which is becoming more and more widely employed in building construction, due to its improved resistance to cracking and crack propagation with respect to plain concrete. Its mechanical behavior strongly depends on the choice of the properties of the fibers and their volume fraction in the concrete mixture. As any material employed in building construction, testing the material “on the site” reprents a very important task. Very often this requires employing non invasive and non destructive measurement methods which have to be implemented directly in-situ. In this paper a new method for the detection of fiber density and orientation is prented. It is bad on the employment of a probe nsitive to the magnetic properties of the steel fibers. The performances of the method have been theoretically and experimentally analyz
ed as well as a comparison with the results obtained with a previously developed capacitive method is also prented.
Keywords- magnetic measurement, materials behaviour.
I.I NTRODUCTION
As everybody knows, concrete is the most widely ud construction material worldwide, basically consisting of aggregates, cement and water. From a mechanical point of view, it is featured by good strength under compression but it is weak in tension.
This limit can be overcome incorporating into it different materials (such as wires, rods, cable etc) to take advantage of their composite action. When steel fibers are ud to this purpo, the resulting composite material is called Steel Fiber Reinforced Concrete (SFRC) or Steel Fiber Reinforced Cementitious Composite (SFRCC), which is becoming more and more widely employed, e.g. for slabs-on-ground floors and pavements, and other construction elements [1] [2] [3].
SFRC guarantees a crack opening toughness veral times greater than that of plain concrete, also resulting in a more time and cost-effective construction process with respect to conventional reinforc
ed concrete, due to reduced workmanship for detailing and hand-tying reinforcing bars. It is easy to understand that the geometrical characteristics of fibers (length and diameter), as well as their quantity and orientation with respect to the applied (tensile) stress play a fundamental role in determining the behavior of the composite. While the parameters can be easily checked during casting, their control reprents a much more complex task when it has to be performed on already cast elements.
On the other hand, the on-site monitoring of construction materials and elements reprents an important issue, since it is mandatory in order to provide a complete and correct structural and mechanical evaluation of the construction performance. In this ca, the critical aspect is very often reprented by the need to operate with non-destructive analysis, since it may be not possible to take (e.g. through core-drilling) any sample of the material. This requires performing the analysis in situ, having access only to the surface of the element to be monitored.
For this reason, some studies have been started on this field in the last decade. Their purpo is to develop methods and measurement systems able to detect the fiber density, and their shape and orientation in steel fiber reinforced concretes.
This rearch activity has been carrying out also by a team of rearchers of the Politecnico di Milano, involving experts both of the Department of Electrical Engineering and of the Department of Structural Engineering. In a previous work, the authors prented a measurement technique, bad on a capacitive method, able to give reliable information about the density and the orientation of the steel fiber.
In this paper, after a brief comparison of the state-of-art methods employed for non-destructive monitoring of fiber dispersion related issues in SFRCC, a new approach, bad on the ferromagnetic properties of the steel fibers, is prented. In particular, it will be prented how, using a simple and low-cost experimental tup, namely a magnetic probe, it is easily possible to discriminate the orientation and the density of the fibers. Another advantage of the propod method is reprented by its innsitivity to the aspects related to the coupling between the material surface and the probe. In fact this problem plays a fundamental role in the reliability of the measurement performed with resistive and capacitive methods.
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II.S TATE OF THE A RT
Many methods for the characterization of fibers dispersion in SFRCC have been prented in literature. The main challenge in this field is the achievement of a non-destructive method allowing the material analysis. Great part of the propod procedures is aimed to laboratory test: the complexity of the required t up makes them unsuitable for in situ analysis.
The most widely discusd method is the AC impedance spectroscopy [4] [5]. This method consists in the employment of two electrodes placed on the specimen under test and the measurement of the imaginary and real part of the impedance over a very wide frequency range, from DC to veral MHz. The information about fiber clumping and orientation is assd through the analysis of the impedance Nyquist plot. However, the extension of the frequency range needs the employment of expensive instrumentation. Furthermore, this method is very nsitive to the contact impedance between the electrodes and the material. To overcome this problem, the two electrodes have to be casted into the concrete: however, this restricts the applicability of the method to laboratory tests only. Some authors have propod a modification of the measurement tup allowing in situ analysis. The contact impedance between the superficial electrode and the material under test is minimized becau of the employment of conductive solutions (generally water and NaCl) [6] [7] [8].
The spatial distribution of the steel fibers can be assd through low-frequency resistance measur
ements [9]. In order to reduce the effect of the poor electrical coupling, a four-electrode probe has been employed. However, this method cannot give information about the fiber concentration. This is becau the resistivity of the cement is highly affected by the aging, the humidity and the prence of electrolytes in the pores other than the amount of conductive fibers.
The inclusion of steel fibers in a homogeneous concrete matrix affects the effective permittivity of the mixture. Its value depends on the volume fraction of the fibers and their aspect ratio. The effective permittivity can be estimated employing a coaxial probe and microwave reflectometry techniques [10]. Assuming that the fibers are randomly oriented and their aspect ratio is known, it is possible to asss their concentration. This method has proven to be very effective; however, it is not applicable to SFRC featuring a preferential fiber direction.
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The authors have prented a method implementing a FFT-bad impedance measurement over frequency employing a two-electrode probe [11]. This technique allows the asssment of both the concentration of the fibers and their average direction. Furthermore, the required instrumentation is relatively inexpensive becau the involved frequencies are limited to a few hundred of kilohertz. However, the method is fairly nsitive to the coupling between the specimen under test and the electrodes. This led the authors to investigate a new method to estimate the properties of SFRC whi
ch does not suffer from this problem while maintaining the same cost effectiveness and the suitability to on-the-field measurement
III.T HE P ROPOSED M ETHOD
Different kinds of fiber featuring various shapes and cross ctions can be employed in order to enhance material and structural characteristics. Analyzing the phenomena it can be noticed that the most important geometric properties of the fibers are the length and the effective diameter: their ratio is called aspect ratio. Currently employed fibers are characterized by an aspect ratio ranging between 20 and 70: therefore the kinds of fibers are usually long and thin. Commonly, fibers are made of low carbon steel which shows a strong ferromagnetic behavior. Only in very specific applications, high carbon or stainless steel fibers (sometimes non ferromagnetic) are employed. Thus, generally speaking, SFRC is a composite consisting of two materials with very different magnetic properties parated by well defined boundaries.
Let’s consider a specimen of SFRC the dimensions of which are much greater than the fiber length; furthermore, let’s suppo that the fiber length and the distance between them are much smaller than the wavelength considered for the analysis. In this ca, it is possible to define the macroscopic
magnetic properties of the composite material and in particular the effective magnetic permeability [12]. It is clear that the measurement of a parameter influenced by the effective permeability can be ud to ass both the concentration and the orientation of the steel fibers in a specimen of SFRC. A possible solution bad on this approach consists in the measurement of the equivalent inductance due to a magnetic flux which invests the SFRC specimen. A C-shaped magnetic core with a N turn winding can be placed over the concrete slab in order to provide the magnetic field. It is clear that the winding lf inductance is influenced by the concentration of the fibers: the higher the concentration, the higher the inductance. Furthermore, it is also influenced by the orientation of the flux lines (thus the orientation of the magnetic core) with respect to the average direction of the fibers. When the magnetic core and the average direction of the steel fibers are aligned, the inductance is expected to be maximized.
It is quite simple to write a mathematical model of the system. The capacitive effects will be neglected becau frequencies up to some tenth of kilohertz will be considered. First of all, it is better to write down a simple magnetic circuit of the system. The winding can be reprented as a source of magnetomotive force Ni w, where i w is the current flowing through it. Some of the magnetic flux generated by the winding does not interest the concrete slab. A permeance Λl can be
assigned to this magnetic path. The other part of the magnetic flux flows into the magnetic core and pass through the SFRC specimen. In this ca, the path can be en as the ries connection between a (very big) permeance Λc which takes into account the drop of magnetic voltage due to the core and a permeance Λv which considers the path of the magnetic flux between the two pole pieces. Λv depends on the concentration of the steel fibers, on their distribution and on the angle between their average direction and that of the magnetic core. Thus, the magnetic circuit (Figure 1) consists in the parallel connection between the mmf source, the permeance Λl and the ries connection of the permeances Λv and Λc.
Figure 1: Magnetic circuit of the probe when the effect of the SFRC is taken
into account.
The permeance Λv can be split in two terms:
v v v ΛΛΛΔ+=0 (1)
Where Λv0 is the value assumed by Λv when the specimen under measurement does not contain fibers. ΔΛv is an additional term due to prence of steel fibers in the concrete slab.
Having defined the magnetic circuit, it is possible to write down the electrical circuit shown in Figure 2. Becau of the relationship between electrical and magnetic parameters, the following inductances have been defined:
l l ΛN L 2= (2) c c ΛN L 2=
(3)
v v v v v ΛN ΛN L L L Δ+=Δ+=2020 (4)
自主学习Figure 2: Electrical model of the magnetic probe when the effect of the SFRC
东印度群岛is taken into account.
R
ws has been added in order to take into account the resistance of the coil, while the conductance G c reprents the core loss. Finally, the conductance G v schematizes the loss in the steel fibers due to the alternate induction field. On the other hand, since the thinness of the fiber is usually very small, the eddy currents are definetely negligible and hence G v can be neglected.
According to the model of Figure 2, the impedance evaluated at the terminals AB is:
c
v c v l c ws AB L L L L j L j G R +++
+
=ω
ω1
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Z (5)
Moreover, if the conductance G c can be neglected too, assuming that the employed magnetic core features low loss in the frequency considered range, the impedance measured at terminals AB is given by the following simplified expression:
⎟⎟⎠
⎞
⎜⎜⎝⎛+++≅v c v
c l ws AB L L L L L j R ωZ (6) As clearly indicate
d by eq. 6, th
e real part o
林森火f the impedance does not depends on the prence of the fibers, while the imaginary part may be affected by the magnetic effects due to the fibers (L v inductance).
Reminding that L v can be split into two terms, L v0 and ΔL v , eq. 7 can be written as follows:
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()⎥⎦
⎤
⎢⎣⎡Δ++Δ+++≅v v c v v c l ws AB L L L L L L L j R 00ωZ (7)
Since the inductance L c is sureley much higher than L v , eq.
(7) can be approximated with the following expression:
()v v l ws AB L L L j R Δ+++≅0ωZ (8)
where ΔL v depends on the prence of fibers.
As expected, eq. (8) shows that the effect of the steel fibers is simply an increa of the probe inductance. This increa can potentially be effective to asss information about the concentration of the steel fibers and their average direction. In fact by considering eq. (8) it can be written:
⎟⎠
⎞
⎜⎝⎛−=Δω0Im AB AB v L Z Z (9)
where Z AB0 is the impedance measured when the probe is
placed on a specimen without fibers.
IV. T HE E XPERIMENTAL S ETUP
Starting from the considerations reported in the previous paragraph, an experimental tup has been implemented. Its scheme is depicted in Figure 3.
As aforementioned, the magnetic probe ud to detect the steel fibers consists in a C-shaped ferrite core (Figure 4) on which a 79-turn coil has been wound. The core is 125 mm long, 90 mm high and has a rectangular ction of 20 x 30 mm. From the electrical point of view, the probe can be reprented by an inductance of about 1.855 mH and a resistance of about 2.8 Ω (at a frequency of 1kHz) when placed on a non-magnetic surface.
Figure 3: Setup scheme.
Figure 4: The magnetic probe.
The measurement system has been made-up by means of virtual instrument (VI) techniques. In particular the implemented VI allows performing automatic impedance versus frequency analysis. It provides the generation of the excitation signal producing the required magnetic field. Furthermore, it manages the measurement of the voltage applied to the magnetic probe and the flowing current.
The acquisition of the two signals has been performed by means of a National Instruments PCI 6143 DAQ board. This device features a 16bit resolution and a maximum sampling frequency of 250 kHz.
The generation of the excitation signal has been done by means of a digital signal waveform generator (DSWG) controlled through a GPIB interface. In order to avoid a ground loop between the generation and the acquisition ctions, the injection of the excitation signal has been done by means of a signal transformer (Figure 3).
The impedance measurement has been implemented through a vector analysis of the voltage and the current signals. This technique allows to reduce the requirements of low harmonic distortion of the generated stimulus signal and thus permits the employment of a wide bandwidth signal transformer to decouple the circuits.
V.E XPERIMENTAL R ESULTS
Some preliminary tests have been performed in order to asss the model and the hypothesis introduced in ssion III.
First of all, resistance of the coil R ws has been measured, over the frequency range 1kHz – 40 kHz. For this purpo, a new winding having the same Litz wire, number of turns and turn area of tho of the probe has been arranged. This winding has been wound on a non-magnetic core in order to properly evaluate R ws. The experimental results clearly show that the resistance value is practically constant in the considered frequency range. Thus the R ws can be easily removed from the measurement of the impedance Z AB.
In particular, operating with the coil placed in free air, far away from the concrete slab and any other magnetic object, the compensation of R ws opens the way to the evaluation of the parameters G c, and L T= (L c//L v0) + L l. The knowledge of the two parameters allows us to verify the hypothesis done in ction III about G c.
Figure 5 shows the quantity ωL Tv G c, versus frequency (namely the ratio between the reactive and the dissipative effects of the compensated probe), measured following the above indicate procedure. It can be notice, that the dissipative effects are practically negligible in the considered frequency range. As a conquence, G c can be really neglected as hypothesized in ction III.
Figure 5: Plot of the quantity ωL Tv G c versus frequency.
The experimental activity has been then focud on three different specimens of concrete. The samples (1mx0.5m slabs, 30 mm thick) are characterized by different concentration of the steel fibers. The first one (S00) was cast without adding steel fibers, the cond (S50) features a steel fiber concentration of 50 kg/m3 while the last one (S100) has a steel fiber concentration of 100 kg/m3. Concrete mixtures were all lf-compacting, which allowed the slabs to be cast without any mechanical vibration, allowing the fresh concrete to flow parallel to the longer side. It has been shown that fibers tend to be preferentially oriented along the direction of the fresh concrete flow [13].
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The analysis has been performed by measuring the probe
impedance in the frequency range from 1 kHz to 40 kHz. The measurements on each specimen were done by placing the magnetic probe with its main axis of symmetry both in the orthogonal and in the parallel direction with respect to the suppod average fiber orientation.
The two measurements performed on each specimen have been achieved rotating the magnetic probe of 90° around its axis. In this manner the same volume of concrete has been analyzed in the two directions.
Each measurement has been repeated 5 times, by removing and replacing the probe in the same position each time. In this way, the standard deviation of the collected values reprents the evaluation of the repeatability uncertainty of the measurement.
During the test the transformer has been excited in order to achieve a constant current flowing in the coils and hence an almost rms constant magnetic flux. Moreover the test voltage has been chon so that the saturation of the magnetic core can be neglected. A SNR of at least 60dB was always achieved both for the current and the voltage measurement.
The measured probe inductance is shown in Figure 6. In this graph ven curves are reported: the measurement results in the two directions (orthogonal and along the average fiber orientation) for th
e three fiber concentrations (S00, S50 and S100). An additional measurement has been done placing the probe in free air, far away from the concrete slab and any other magnetic object.
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The obtained results show that, analyzing the inductance, it is possible to discriminate not only the steel fiber concentration but also their average orientation.
Figure 6: Probe inductance and its uncertainty bars (coverage factor k=3) over frequency. The curve label is made up by the relative direction between the magnetic probe and the fibers and the fiber concentration. From the top of the figure the following curves are plotted: along_S100, ortho_S100, along_S50, ortho_S50 and together along_S00, ortho_S00 and air.
Very good results can also be achieved by operating within a reduced frequency range (1 kHz to 10 kHz) as shown in Figure 7. From a practical point of view, this permits a great reduction of the measurement system requirements.
It can be noticed that the repeatability uncertainty is very low. In particular the uncertainties are lower than that obtained with the capacitive method prented by the authors in [11].
Figure 7: Detail of the probe inductance and its uncertainty bars (coverage
factor k=3) over frequency. The curve label is made up by the relative
direction between the magnetic probe and the fibers and the fiber concentration. From the top of the figure the following curves are plotted: along_S100, ortho_S100, along_S50, ortho_S50 and together along_S00,
ortho_S00 and air.
Now let’s consider the inductance measured in free air as the reference value, like described in Section III. Subtracting the values from tho measured placing the probe on the concrete slabs, it is possible to calculate the variable component due to the fiber reinforcement characteristics (quantity, dispersion and orientation). In Figure 8 the ratios between the computed inductance values are reported.
Figure 8: Ratios between compensated inductances.
It can be noticed that the greater the concentration of the fibers, the smaller the variation of inductance measured in the two directions (along the fibers and orthogonal to them). This happens becau, from a magnetic point of view, the concrete becomes more isotropic.
Comparing the results obtained applying this new approach with tho prented by the authors in [11], it can be noticed an improvement of the performances. In particular Figure 9 shows the ratios obtained between the capacitance values picked up
on the two directions, collected by analyzing the same
