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Electrochemical immittance spectroscopy applied to a hybrid PVA/steel fiber engineeredcementitious compositeSuryanto, Benny; McCarter, William John; Starrs, Gerard; Ludford-Jones, Gregory Victor
Published in:Materials & Design
DOI:10.1016/j.matdes.2016.05.037
Publication date:2016
Document VersionPeer reviewed version
Link to publication in Heriot-Watt University Research Portal
Citation for published version (APA):Suryanto, B., McCarter, W. J., Starrs, G., & Ludford-Jones, G. V. (2016). Electrochemical immittancespectroscopy applied to a hybrid PVA/steel fiber engineered cementitious composite. Materials & Design, 105,179–189. DOI: 10.1016/j.matdes.2016.05.037
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Electrochemical immittance spectroscopy applied to a hybrid PVA/steel fiberengineered cementitious composite
B. Suryanto, W.J. McCarter, G. Starrs, G.V. Ludford-Jones
PII: S0264-1275(16)30638-4DOI: doi: 10.1016/j.matdes.2016.05.037Reference: JMADE 1785
To appear in:
Received date: 9 December 2015Revised date: 23 April 2016Accepted date: 11 May 2016
Please cite this article as: B. Suryanto, W.J. McCarter, G. Starrs, G.V. Ludford-Jones,Electrochemical immittance spectroscopy applied to a hybrid PVA/steel fiber engineeredcementitious composite, (2016), doi: 10.1016/j.matdes.2016.05.037
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Electrochemical immittance spectroscopy applied to
a hybrid PVA/steel fiber engineered cementitious composite
B. Suryanto#, W. J. McCarter, G. Starrs, G.V. Ludford-Jones
School of Energy, Geoscience, Infrastructure and Society,
Institute for Infrastructure and Environment,
Heriot Watt University,
Edinburgh, EH14 4AS, Scotland,
U.K.
# Corresponding Author:
E-mail: [email protected]
Tel: +44-131-451-3817
Fax: +44-131-451-4617
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Abstract
Alternating current (a.c.) electrical property measurements are presented on an Engineered
Cementitious Composite (ECC) reinforced with a hybrid mix of polyvinyl alcohol fibers
(fixed dosage) and straight steel fibers of varying dosages (0.15–1.0% by volume), with the
aim at elucidating the influence of conductive inclusions on the nature of conduction and
polarization processes within the composite. Measurements were undertaken over the
frequency range 1Hz–10MHz at 7, 14 and 28 days after casting and the data presented in a
range of formalisms to aid interpretation. When plotted in the frequency domain, the work
shows that steel fibers enhance the polarizability of the material, particularly within the
frequency range ~10Hz-10kHz. When presented in Nyquist format, this feature manifests
itself as an intermediate arc forming between a high frequency arc (>10kHz) and a low
frequency arc (<10Hz), the latter resulting from polarization processes at the
sample/electrode interface. The prominence of the intermediate arc was found to be
dependent upon steel fiber dosage and curing time. It is shown that the bulk electrical
conductivity conforms to the equivalent inclusion theory which is a variant on the effective
medium theory.
Keywords: Electrical properties; Immittance spectroscopy; Cement composite;
Multifunctional material; Effective medium theory.
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1. Introduction
Since its first application to cementitious systems [1], considerable advances have now
been made in the use of a.c. impedance spectroscopy (ACIS) to study this group of important
construction materials. Impedance measurements can be interpreted in terms of the
mechanisms of hydration, reaction kinetics and pore-structure development from initial
mixing through setting [2–14] and long-term hardening [15–17]. The influence of both
chemical admixtures, such as accelerators and retarders [18], and supplementary cementitious
materials, such as blast-furnace slag, fly-ash and silica fume [19–22], on the various stages of
hydration has also been investigated using ACIS techniques. These studies have also shown
that the impedance response can be linked to a number of material properties including pore-
water content, pore-water chemistry, and the porosity, connectivity and tortuosity of the
capillary pore network.
Studies on the electrical properties of fiber-reinforced cements are more limited and work
tends to be confined to d.c. or fixed-frequency, a.c. conductivity/resistivity measurements
[23–28]. In the main, these studies have explored the piezo-resistive properties of
cementitious materials containing short conductive fibers (i.e. carbon) and it is through these
properties the materials have self-monitoring capabilities with respect to deformation and
damage under static and dynamic loading. This has initiated the development of fiber-
reinforced cements as potentially smart materials. A multi-frequency impedance approach to
study cement-fiber composites is a relatively recent development [29–32] and has been used
to study the dispersion and orientation of steel fibers [33,34] and plant fibers [35] within
cement paste, with measurements obtained over the frequency range 0.1Hz-30MHz. When
plotted in Nyquist format, a dual-arc behavior has been observed for steel fibers and a
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frequency-switching fiber coating model has been proposed to explain the electrical
impedance spectrum. The dual arc behavior was absent for the plant fiber composite.
This current paper presents, for the first time, a detailed study on the a.c. electrical
properties of an advanced cement-based material termed an Engineered Cementitious
Composite (ECC), with a focus on the influence of conductive fibers, viz. steel, on
conduction and polarization processes. The distinctive engineering properties of an ECC are
its high tensile strain capacity, typically in excess of 3%, and a controllable crack width,
typically less than 0.1mm under service load [36,37]. It is these unique properties of ECC
that have attracted widespread interest from the engineering community, particularly for
applications where cracking, toughness and long-term durability are critical. Apart from
being viable as a durable construction material, the inclusion of conductive fibers could also
allow ECC to be further developed and exploited as a multi-functional material thereby
simultaneously fulfilling both structural and non-structural roles. Regarding the latter,
research to-date has primarily focused on developing a suitable ECC mixture for damage-
sensing applications [38–41].
As yet, there has been no systematic study on the electrical properties of ECCs. Research
findings from the present investigation into the influence of conductive steel fibers on the
nature of conduction and polarization processes will therefore be of considerable importance
in aiding the design of mixture compositions that give ECC multi-functional capabilities (e.g.
through the use of electrically conductive inclusions). Areas where conductive ECC could
find practical application in non-structural roles include, for example: electrically conductive
cementitious overlays for cathodic protection systems thereby providing a more uniform
current distribution; in structures where electromagnetic shielding or screening is required; in
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civil/military aviation applications where background static can cause problems; or self-
sensing applications in the detection and (real-time) monitoring of cracking, vibration or
fatigue in concrete structures (e.g. bridges, pressure vessels). Different applications may
require different mixture compositions, but the flexibility in ECC material design [36] would
allow the material to be tailored to suit the needs of any particular application.
It must be emphasized that the presentation of impedance in the Nyquist format noted
previously, which has been generally used in a.c. electrical property measurements, is only
one of four connected parameters within the more general field of immittance spectroscopy.
These levels are impedance Z() and its reciprocal admittance Y(); relative permittivity
r() and its reciprocal electric modulus M() [42]. The work presented focuses on both the
impedance and permittivity levels.
2. Experimental Program
2.1. Materials
Table 1 presents the mix proportions of the ECCs used in the current study. The binder
comprised CEM I 52.5N cement to BS EN197-1:2011 [43] and a fine fly-ash (Superpozz
SV80 from ScotAsh), with a fly-ash-to-cement (FA/C) ratio of 1.7. The water/binder (w/b)
ratio was 0.28. A fine silica sand (RH110 from Minerals Marketing Ltd.) with an average
particle size of 120m was used in all mixes at a constant sand-to-cement ratio of 0.6 by
mass. The oxide analysis of the FA and silica sand is presented in Table 2. A
polycarboxylate high-range water-reducing admixture (Glenium C315 from BASF) was
added to the mix at a fixed dosage rate of 1% by weight of cement. Standard 12mm (long)
polyvinyl alcohol (PVA) fibers (REC15 from Kuraray) were used at a fixed dosage of 1.75%
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by volume. The PVA fibers had an average diameter of 39m and a tensile strength of
1.60GPa. The surface of the PVA fibers was coated with a proprietary oiling agent (1.2% by
weight) to reduce any excessive fiber-matrix chemical bond strength due to their hydrophilic
nature. In addition to the PVA fibers which, as a polymeric material is considered non-
conductive, 6mm steel fibers (Dramix OL6/.16 from Bekaert) were used at dosages in the
range 0.15–1.0% by volume. The steel fibers had a diameter of 160m (aspect ratio = 37.5)
and a tensile strength of 2.60GPa.
2.2. Test Specimens: Preparation, Casting and Curing
A 10-litre Hobart planetary motion mixer was used for preparing all the mixtures with a
total of six specimens cast for each ECC presented in Table 1: two, 40×40×160mm prisms
for electrical measurements, two, 20×40×170mm prisms for flexural strength testing, and
two, 50mm cubes for compressive strength tests. Specimens for each mixture were cast from
the same batch. With reference to Fig. 1(a), specimens for electrical measurements were cast
in polystyrene molds, each mold having two 45×65×2mm (thick) perforated stainless steel
electrodes placed 140mm apart. The perforations on the electrodes were 10mm in diameter
with a 15mm pitch, which ensured both intimate bonding between the electrode and the
specimen and that the ECC mixture flowed easily through the perforations.
After casting, all samples were covered with polythene sheeting and placed in a
temperature controlled laboratory (20±1oC, 55±5% RH). The samples were demolded after
24h and placed in a small curing tank in the same laboratory environment until required for
testing. The electrical measurements were conducted on the 7th
, 14th
and 28th
days of curing.
The mean 28-day compressive strengths of the mixtures are presented in Table 1.
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2.3. Test equipment and procedures
Electrical measurements were taken using a Solartron 1260 Frequency Response Analyser
connected in two-point mode, with the current-generator and potential-high leads coupled to
one electrode, and the current-input and potential-low leads to the other. A logarithmic
sweep at 20 points per decade was made over the frequency range 1Hz–10MHz at a voltage
of 350mV rms (matching the signal amplitude of previous studies, including field tests [15–
17,48]).
The flexural properties for each mixture were determined using a 100kN Instron 4206
testing machine under a cross head rate of 0.5 mm/min. The samples were loaded under a 4-
point bending configuration with central and shear spans of 40mm and 55mm, respectively
(see Fig. 1(b)). The load-deflection profiles of individual samples were recorded to failure.
The peak load and the corresponding deflection were then converted to tensile strength, ftu,
and tensile strain, tu, by assuming a uniform tensile stress distribution [44] and relating the
curvature and the average deflection at the two load points [45]. Axial compression tests
were carried out using a 3000kN Avery-Denison testing machine under a loading rate of
38kN/min.
3. Results and Discussion
3.1. Preliminaries
The impedance, of a cementitious system subjected to a sinusoidal electric field at
an angular frequency, can be written in rectangular form as,
(1)
where the real component is the resistance and the imaginary component is the
reactance. At any frequency, the electrical response of such a system will result from the
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superposed phenomena of conduction and polarization. These are quantified, respectively, by
the bulk conductivity, , and the real part of relative permittivity, , which are de-
embedded from the resistance and reactance by
(2)
(3)
where is the permittivity of a vacuum (8.854×1012
Farads/m); L/A is a factor which is
related to the electrode geometry and sample configuration. This was determined by
electrical measurements on solutions of known conductivity placed within the test-cell and
for the cell shown in Fig. 1(a), the L/A factor was determined as 94.7/m.
3.2. Flexural tests
Although the focus of this paper is the a.c. electrical properties of ECC, for completeness,
it was considered appropriate to include the mechanical properties of the composite. The
mean 28-day compressive strengths are presented in Table 1, whereas Fig. 2(a) presents the
flexural response under monotonically increasing displacement to failure. It is evident that
all samples displayed a deflection hardening response with notable fluctuations in load with
increasing vertical deflection. These fluctuations can be attributed primarily to progressive
development of micro-cracks on the tension face of each sample. Fig. 2(b) presents the
tensile strength, ftu, and tensile strain capacity, tu, determined using the procedure described
in Section 2.3, with the error bars on the markers representing the spread of results from the
mean value presented. It is evident that, within the scatter of the results, the tensile strength
and tensile strain capacity remain virtually unchanged, although the tensile strain capacity
appears to decrease slightly with increasing steel fiber dosage. The minor influence of the
steel fibers can be associated with the relatively low interfacial bond between the fibers and
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the matrix. The values of the tensile strength and tensile strain capacity obtained are in
general agreement with those obtained from direct tensile tests [46].
3.3 Impedance Response of ECC
The complex impedance spectra for Mix M1 specimens (no steel fibers) are presented in
Fig. 3(a) as a Nyquist plot (i.e. vs ), with frequency increasing from right-to-
left across the curve. Although measurements were obtained at 140 spot frequencies, for
clarity, only selected frequencies are highlighted with data markers. The results indicate
good repeatability and, at any stage during the hydration process, the impedance response can
be divided into three regions comprising,
(i) a spur at the low-frequency (right-hand) side of the curve;
(ii) a weakly developed intermediate plateau giving a U-shaped valley region; and,
(iii) a semicircular arc on the high-frequency (left-hand) side whose center is depressed
below the axis.
The low-frequency spur is associated with the polarization at the sample-electrode
interface [1,48,50] and would form part of a much larger arc that only develops at frequencies
lower than 1Hz. The intermediate U-shaped valley feature is more evident at longer
hydration times and has been reported as a feature typical of cementitious systems containing
fly-ash [20,21]. The prominence of this feature is dictated by the proportion of unburnt
carbon in the fly-ash which is quantified by the loss on ignition (LOI), with the feature
becoming more discernible as the LOI increases [21]. The fly-ash used in this work has a
relatively low LOI (<2%; Table 2) and would explain the U-shape rather than a more
distinctive plateau region. The high-frequency semi-circular arc represents the bulk response
from the sample, with the intercept of the low-frequency end of the arc with the real axis (i.e.
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) representing the bulk resistance of the ECC. It is evident from Fig. 3(a) that as curing
age increases, the sample impedance increases which results in a progressive displacement of
the response to the right-hand-side of the plot. This is due to the on-going hydration process
and resulting pore structure refinement which is well documented.
Figs. 3(b)–(d) present the complex impedance spectra for all mixes in Table 1. These
Figures show that the addition of steel fibers results in a marked transformation of the
impedance spectra which can now be separated into three, well-defined regions:
(i) a low-frequency spur on the right-hand-side of the plot representing electrode
polarization at the specimen/electrode interface. This arc would become more
pronounced at frequencies lower than those used in the current experimental
program;
(ii) a mid-frequency arc which arises as a direct result of the inclusion of the steel
fibers; and,
(iii) a high-frequency arc on the left hand side of the response.
The mid- and high-frequency arcs constitute the bulk response and it is apparent that the
relative contributions of these two arcs on the overall impedance are directly influenced by
steel fiber dosage. The double-arc feature has also been identified in a limited study using
carbon and steel fibers [29–31]. In general terms, at any stage in the hydration process, as the
fiber dosage increases,
(i) the radius of the high-frequency arc decreases and the high-frequency cusp point
(i.e. the junction between the high- and mid- frequency arcs) is progressively
displaced towards the origin;
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(ii) the radius of the mid-frequency arc increases and the low-frequency cusp point
(i.e. the junction between the right-hand electrode spur and the mid-frequency arc)
is progressively displaced away from the real impedance axis (Z'()) and merges
into the electrode spur.
Increasing hydration/curing time results in an overall increase in impedance over the test
period and in a displacement of the entire response to the right; in addition, over the
frequency range of the investigation, increasing the curing time results in a diminution in the
prominence of the right-hand spur.
With reference to Fig. 4(a), Figs 4(b)-(f) provide the summary of the frequency values at
which the two bulk arcs maximize (fp,m and fp,h on Fig. 4(a)) and at which the cusp-points
occurs (fc,l and fc,h on Fig. 4(a)). For Mix M1 (see Fig. 4 (b)), the frequency, fp , at which the
bulk arc maximizes is 6.3MHz at 7-days decreasing to 5.3MHz at 14-days and 3.5MHz at 28-
days hydration (these frequencies are also highlighted on Fig 4(c)); the cusp-point frequency,
fc , is 1.4kHz at 7-days, decreasing to 700Hz at 14-days and 400Hz at 28 days. Increasing
curing time results in an overall reduction of all salient frequencies reflecting on-going
hydration and microstructural changes within the cement paste. It is also interesting to note
that the frequency at which the high frequency arc maximizes, fp,h (Fig. 4(c)), is virtually
insensitive to fiber dosage, particularly at early curing times, as the values are similar to those
obtained for Mix M1 at the same stage of hydration (fp on Fig. 4(c)) suggesting that this
parameter is related to the cement paste component and not the inclusion of the steel fibers.
As steel fiber dosage increases, both fp,m (Fig. 4(d)) and fc,l (Fig. 4(f)) decrease whereas fc,h
(Fig, 4(e)) increases although it is evident that fp,m and fc,l are more sensitive to changes in
fiber dosage than fc,h. With reference to Fig. 4(a), the bulk resistance of the ECC (no fibers)
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can be obtained at the cusp-point frequency, fc, whereas when steel fibers are added to the
composite, at the frequency fc,h.
Regarding the Nyquist formalism, it is evident from Fig. 3 that the plots are dominated by
a single circular arc (Mix M1) or two circular arcs (Mixes M2-M6) whose centre is depressed
below the real (Z'()) axis. This feature results from dielectric dispersion within the system
and is discussed in section 3.4 below. In modelling the response in terms of resistive and
capacitive circuit elements, the capacitance is replaced by a pseudo-capacitance or constant
phase element (CPE) to account for the dispersive behaviour of the medium. The CPE is a
complex, frequency-dependent parameter defined by the relationship,
p
o
CPEiC
Z)(
1)(''
(4)
where i =√-1, Co is a coefficient and the exponent, p, has a value such that 0<p<1; if p equals
1, then the equation is identical to the reactive component of a pure capacitor of value Co with
units in farads (F). When a CPE with value of p<1 is placed in parallel with a resistor, a
circular arc is produced with its centre depressed below the real axis, with Co having units
Fs(p-1)
. The arc depression angle, (see Fig. 5(a)), is related to the exponent, p, in equation
(4) through the relationship,
= )p( 12
radians (5)
The responses presented in Fig. 3 can be represented by a number of parallel and/or series
connected circuit elements. With reference to Fig. 5(b), when the ECC is placed between a
pair of electrodes, it can be considered as comprising three electrical pathways: (i) the
continuous capillary pore network; (ii) the solid matrix comprising sand particles, products of
hydration, unhydrated cement, isolated water-filled capillary cavities and 'dead-end' capillary
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pores; and (iii) the fiber/fiber-matrix interface/solid matrix and continuous capillary pores
between the fibers. These can now be represented by the following circuit elements (see Fig.
5(c)):
(1) a circuit comprising a resistor, Rcp, in parallel with a constant phase element, CPEsm.
Rcp represents ionic conduction through the continuous, interstitial pore solution within
the capillary network and CPEsm represents the response from the solid matrix;
(2) a circuit comprising a resistor, Rf, and two, series connected, parallel elements Rfi/CPEfi
and Rf-cp/CPEf-sm. This pathway represents that fraction of the composite whereby the
fibers and cement matrix are considered to be in series with each other as the fiber
dosages in Table 1 are below the electrical percolation threshold. Accordingly, it is
expected that there is no continuous steel fiber pathway between the electrodes. In this
circuit, Rf represents electronic conduction through the steel fibers; the interface
between the steel fibers and the cement matrix is represented by Rfi/CPEfi, and the
cement matrix between the fibers associated with this pathway is represented by
Rf-cp/CPEf-sm.
In addition to these elements, the following are also present,
(3) a circuit comprising Rel/CPEel representing the response from the electrode/sample
interface; and,
(4) a resistor Rs representing the projected intercept of the high-frequency end of the high
frequency arc with the real axis.
For illustrative purposes, Fig. 6 presents the measured and simulated responses for Mixes
M1, M3 and M6 at 7-days curing with the simulation parameters presented in Table 3,
together with those for Mixes M2, M4 and M5. The measured and simulated responses
presented in Fig. 6 show good agreement over the frequency range, being slightly degraded at
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the high frequency end of the response. The most important finding from these simulations is
that the fiber-matrix interface plays a significant role in the response. As the steel-fiber
dosage is increased from 0.15% to 1.0%, the Rfi increases markedly, increasing by over two
orders of magnitude. Further refinement is required to determine the contribution of fly-ash
which causes the development of the U-shaped valley in the impedance response of Mix M1.
3.4. Relative Permittivity and Conductivity of ECC
Fig. 7(a) displays the relative permittivity, , for Mix M1 which has been de-
embedded from the impedance spectra using equation (3) above. The relative permittivity at
any frequency provides a quantitative measure of the sum of all polarization mechanisms
operative at that frequency and by plotting this parameter in the frequency domain allows
identification of the dominant polarization process(es). Fig. 7(a) indicates that dispersion in
permittivity (i.e. the decrease in permittivity with increasing frequency) is detected across the
entire frequency range which extends over seven decades; if there existed a single, dominant
relaxation process the region of dispersion would, typically, be contained within one decade
of frequency [49]. This Figure clearly shows that the permittivity decreases by
approximately six to seven orders of magnitude over this frequency range and would indicate
that more than one polarization process is operative. Consider, for example, the response at
7-days hydration where the permittivity attains an anomalously high value of ~6×108 at 1Hz
and attributable to polarization processes at the sample-electrode interface; at 1.5kHz this
value has been reduced to 1.6×104. It is also interesting to note that the rate of change of
dispersion reduces at this frequency thereafter attaining values of ~440 at 100kHz, 150 at
1MHz and ~90 at 10MHz. The frequencies indicated (by arrows) on the dispersion curves in
Fig. 7(a) occur at the minimum point within the U-shaped valley region of the impedance
response presented in Fig. 3(a).
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It is proposed that the dispersion in permittivity presented for Mix M1 in Fig. 7(a) is a
result of three possible polarization mechanisms: a polarization process at the
electrode/specimen interface dominant in the range 1Hz-1kHz together with a superimposed
electrochemical double-layer polarization process and a Maxwell-Wagner interfacial
polarization process operative over the range ~1kHz-10MHz. Both double-layer and
interfacial processes relax in this frequency range, although double-layer polarization is a
low-frequency mechanism relaxing within the low kHz region [50] whereas interfacial
polarization is a mid-frequency mechanism relaxing within the MHz region [49]. Regarding
double-layer processes, porous materials saturated with conductive liquids have been shown
to exhibit high dielectric permittivity [51] and in ECCs this would result from polarization of
charges electrostatically held onto the cement gel surfaces. Interfacial processes, on the other
hand, would result from charge separation at pore-fluid/crystal boundary interfaces. Under
the application of an electric field, charged carriers can be blocked by internal crystal
boundaries leading to a separation of charge which will contribute to the polarizability of the
sample.
Fig. 7(a) would indicate that double-layer processes dominate over the range 1kHz-
100kHz, whereas interfacial effects are operative over the range 100kHz-10MHz, with the
tilde indicating that processes will overlap at the delineating frequencies viz. 1kHz
(electrode/double-layer) and 100kHz (double-layer/interfacial). Fig. 7(a) also highlights the
influence of curing time on relative permittivity, which is seen as a gradual downward
displacement of the curves. As the ECC hydrates, the capillary pore network becomes more
tortuous, constricted and disconnected, with free-water consumed in the hydration reactions
resulting in an irrotational binding of charges/water. These physico-chemical processes result
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in an overall reduction in bulk polarization, hence dielectric permittivity, across the entire
frequency range.
Fig. 7(b) displays the conductivity, which has been de-embedded from the impedance
spectra using equation (2). The conductivity increases with frequency across the entire
frequency range and decreases with increasing curing time. The overall decrease in
conductivity with time will be due to continual refinement of pore-structure as a result of on-
going hydration and pozzolanic reaction. Conductivity can be regarded as a measure of all
loss processes operative within the material and quantifies the energy dissipated by the
motion of charges in an applied electric field. For the ECC, this would include the movement
of ions in the continuous, water-filled capillary pore network (i.e. ionic conduction process),
together with losses associated with relaxation/dispersion of the polarization process (i.e.
double-layer and interfacial). The cumulative effect of these losses would result in an
increase in conductivity with increasing frequency hence the conductivity, , at angular
frequency, , can be written as,
(4)
where is the low-frequency, ionic conductivity and is the dielectric conductivity
resulting from dissipative polarization processes. With reference to Fig. 7(b), within the
frequency range ∼100Hz-1MHz, conduction will be dominated by ionic transfer through the
continuous water-filled capillary pores. Superimposed on this loss mechanism will be
contributions from double-layer relaxation processes over the range 100Hz-100kHz (albeit a
very weak contribution) and a stronger contribution from interfacial processes at frequencies
>1MHz.
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Figs. 8(a)-(c) present the relative permittivity and Figs. 9(a)-(c) the conductivity for all
ECC mixes. With reference to the permittivity results presented in Figs. 8(a)–(c), it is
immediately evident that when compared with Mix M1, the addition of steel fibers results in
a significant enhancement in relative permittivity - hence polarizability of the composite -
across the entire frequency range with the permittivity increasing with increasing fiber
dosage. The increase in permittivity is particularly prominent in the range 50Hz-5kHz
causing a shoulder to occur in the frequency-domain response. The permittivity is
progressively reduced with increasing curing time as a result of the hydration and pozzolanic
processes (causing, for example, pore structure refinement and irrotational binding of
charges), however, the enhanced permittivity due to steel fiber additions is still prominent
across the bandwidth. It is also evident from Figs 9(a)-(c) that over the frequency range
50Hz-5kHz the conductivity increases rapidly although this feature decreases with
decreasing fiber dosage. Increasing hydration time also has a marked effect on the
conductivity of the ECC: at 7-days hydration (Fig. 9(a)), at frequencies < 50Hz, the addition
of steel fibers does not result in any significant change in the conductivity of the composite
relative to Mix M1 which has no steel fibers. As hydration time increases (Figs. 9(b) and
(c)), relative to Mix M1, the conductivity of Mixes M2-M4 increased across the entire
frequency range of the investigation. However, at frequencies < 50Hz, Mixes M5 and M6,
with higher steel fiber contents, display a reduced conductivity relative to Mix M1 attributed
to the development of a non-conductive barrier at the steel fiber-matrix interface (i.e. the
circuit element Rfi/CPEfi discussed above); whereas at frequencies >50Hz the enhancement in
conductivity becomes increasingly more evident. For illustrative purposes, the salient
frequencies identified from the impedance spectra for Mixes M1 and M6 at 7-days curing
(see Fig. 4(a)) are presented in Figs. 10(a) and (b) on the respective relative permittivity and
conductivity curves.
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In order to explain these features, the ECC can be considered as comprising highly
conductive steel fibers randomly dispersed in a lossy dielectric medium (i.e. the cementitious
mortar). On application of an a.c. electrical field between the electrodes, electric current must
pass across the interface between the cement-paste and the embedded steel fibres. There will
be a change in conduction processes – ionic conduction through the cement paste and
electronic conduction through the steel fibers. The ECC thus has a mixed ionic-electronic
conduction process with the result that charges can accumulate at the interface and result in
the development of an electrochemical over-potential. This will result in polarization at the
interface which is quantified by enhancement of capacitance, hence permittivity, of the
composite. This effect is shown schematically in Fig. 11 and would be similar to induced
polarization phenomena that can develop in rocks containing metallic minerals [52]. As the
steel-fiber dosage increases, the fiber-electrolyte contact area increases, resulting in an
increase in polarizable surfaces and consequent increase in permittivity. This effect
diminishes with increasing frequency although it is evident that it persists across the entire
frequency range, and would be in addition to those polarization processes present in the ECC
without steel fibers.
3.5 Composite Mixing Laws
Fig. 12 presents the measured conductivity of the ECC after 7, 14 and 28 days curing. The
bulk conductivity, bulk, of the specimens was obtained at the cusp-point within the valley
region for mix M1 (at frequency fc as depicted on Fig. 4(a)) and at the cusp point between the
mid-frequency arc and high-frequency arc in the case of Mixes M2-M6 (i.e. at frequency fc,h
as depicted on Fig. 4(a)). It is evident that the conductivity increases in a linear fashion over
the range of steel fiber dosages considered in this investigation (0.15%-1.0%). Fig. 12 would
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also indicate that the highest fiber dosage is still below the fiber percolation threshold, with
percolation occurring at a dosage which would create a continuous fiber pathway between the
electrodes. To explain the increase in bulk conductivity of the composite with increasing
steel fiber dosage, the Equivalent Inclusion Method (EIM) is used. The EIM was originally
developed for studying heat conduction problems [53] and is based on the Effective Medium
Theory. This mathematical model was chosen as it was derived primarily for short fiber
inclusions. In this model, the predicted bulk conductivity, c , of a composite reinforced with
3-D randomly oriented fibers is related to the matrix conductivity, m , the fiber conductivity,
f , and the fiber volume fraction, through the following relationship:
2
3311
2
3311
313
321
mmfmmf
mmffm
mcRSS
SS
(5)
where
33113311 23 SSSSR (6)
d
L
d
L
d
L
dL
LdSS 1
5.0
2
2
5.122
2
2211 cosh12
(7)
2233 21 SS (8)
The same relationships have recently been used by [54] to study the electrical resistivity of
steel fiber reinforced concrete. When fibers become preferentially aligned in one direction,
thereby forming a cosine fiber orientation distribution [53] and equivalent to a 2-D random
orientation, the equation becomes
2
3311
2
3311
2'12
21
mmfmmf
mmfmf
mcRSS
SS
(9)
where
33112' SSR (10)
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In equation (7), L is the fiber length and d is the fiber diameter. In the calculations, the
matrix conductivity (i.e the cement mortar and PVA fibers) was determined from the
impedance response of the control mix M1; from Fig. 3(a) these values are determined at the
cusp-point frequency fc as: m = 0.0975 S/m, 0.0525 S/m and 0.0265 S/m at 7, 14 and 28
days, respectively. The conductivity of the steel fibers, f, was taken as 107 S/m and the
geometrical properties of the fibers were L = 6mm and d = 0.16mm.
Figs. 13(a)-(c) present the predicted bulk conductivity using equations (5) and (9) above
together with the measured values for samples cured for 7, 14 and 28 days, respectively. It is
apparent from Fig. 13 that, within the range of fiber volumes studied, the EIM 3-D random
model (equation (5)) under-predicts the bulk conductivity, whereas the EIM 3-D cos
(equation (9)) better fits the measured values, suggesting that the actual fiber orientation was
not completely random and that a certain degree of fiber alignment occurred along one axis.
This is not entirely unexpected and could be attributed to the wall effect [55] occurring during
the casting process as fibers close to the side-walls of the mold will tend to align themselves
parallel to the walls (i.e. parallel to the direction of the applied current), leading to a higher
percentage of fibers aligned longitudinally. The underestimation of the predicted bulk
conductivity for randomly oriented fibers could also be attributed to the fact that, although
the fiber dosage is still below the percolation threshold, some fibers might be in direct contact
with each other thereby increasing their effective length. It should be noted, however, in
reality non-uniform fiber orientation and partial inter-fiber contacts occur concurrently and
therefore it could be argued that the effective length should be closer to the actual fiber
length.
4.0 Conclusions
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The following conclusions can be drawn from the work presented:
1. The inclusion of steel fibers in the ECC (up to 1% by volume) resulted in a
transformation of the Nyquist plot from a single-arc response to a dual-arc response.
The prominence of the new arc was found to be dependent upon steel fiber dosage
and curing time, the latter resulting from on-going hydration of the cementitious
component.
2. An electrical model comprising resistive and constant phase circuit elements was
developed which could simulate the response for the ECC containing conductive steel
fibers. It was observed that the fiber-matrix interface plays a significant influence on
the impedance response. As the fiber dosage is increased from 0.15% to 1.0%, the
resistance representing the fiber-matrix interface increases significantly by two orders
of magnitude.
3. When presented in the frequency domain, the addition of steel fibers manifests itself
as a dielectric enhancement over the entire frequency range under study, most notably
in the frequency range 50Hz-5kHz causing a shoulder to occur in the frequency-
domain response. The enhancement was attributed to an induced polarization effect
whereby charges accumulate at the fiber/matrix interface thereby increasing the
polarizability of the composite. Furthermore, it is shown that the permittivity is
progressively reduced with increasing curing time as a result of hydration.
4. It was also found that the addition of steel fibers increases the conductivity of the
composite at mid to high frequencies, with conductivity increasing with steel fiber
dosage. A distinct increase in conductivity occurs within the frequency range 10Hz-
500Hz indicating dispersion in fiber-matrix interfacial polarization and the emergence
of a new conduction pathway through the steel fibers and cement matrix in series.
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5. The bulk electrical conductivity of the composite was found to conform to the
Equivalent Inclusion Method. It was shown that the composite bulk conductivity
increases as the fiber dosage increases although it was found that the highest fiber
dosage (1% by volume) was still below the percolation threshold for the composite.
Acknowledgements
The authors wish to acknowledge the support of Kuraray Japan and Kuraray Europe GmbH
for providing the PVA fibers, Bekaert for providing the steel fibers and BASF UK for
providing the admixtures. Financial support from the School of Energy, Geoscience,
Infrastructure and Environment, Heriot Watt University, is gratefully acknowledged. Thanks
also expressed to Mr. D. Stone and Mr. K. Chronopoulos for assistance in the experimental
work.
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Graphical abstract
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
Increasing
frequency
Mix 1
Mix with
steel fibres
fc,h
10MHz
1 Hz
fp,h
fp,m
fc,l
fp
fc
Z'() ohm
Z''(
) o
hm
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
Increasing
frequency
Mix 1
Mix with
steel fibres
fc,h
10MHz
1 Hz
fp,h
fp,m
fc,l
fp
fc
Z'() ohm
Z''(
) o
hm
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
Increasing
frequency
Mix 1
Mix with
steel fibres
fc,h
10MHz
1 Hz
fp,h
fp,m
fc,l
fp
fc
Z'() ohm
Z''(
) o
hm
0.01
0.1
1
100
102
104
106
Mix 1
Mix 6
fpf
c
fc,h
fc,l
fp,h
fp,m
Frequency (Hz)
()
S/m
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)f c
,l (
Hz)
0.01
0.1
1
100
102
104
106
Mix 1
Mix 6
fpf
c
fc,h
fc,l
fp,h
fp,m
Frequency (Hz)
()
S/m
0.01
0.1
1
100
102
104
106
Mix 1
Mix 6
fpf
c
fc,h
fc,l
fp,h
fp,m
Frequency (Hz)
(
) S
/m10
1
103
105
107
109
100
102
104
106
fc,h
fp,h
fc,l f
p,m
fc
fp
Frequency (Hz)
r' (
)
101
103
105
107
109
100
102
104
106
fc,h
fp,h
fc,l f
p,m
fc
fp
Frequency (Hz)
r' (
)
0.01
0.1
1
100
102
104
106
Mix 1
Mix 6
fpf
c
fc,h
fc,l
fp,h
fp,m
Frequency (Hz)
(
) S
/m
Impedance Response Permittivity Response
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Figure captions
Fig. 1. Schematic diagram of test samples for: (a) electrical property measurements; and (b)
flexural tests (all dimensions in mm).
Fig. 2. Results of flexural tests: (a) load-deflection response for all samples; and (b)
computed tensile stress and strain capacity (error bars indicate the spread of measurements
from the mean value presented).
Fig. 3. (a) Impedance response for Mix 1 at 7, 14 and 28-days curing, with the arrows
indicating the minimum point within the U-shaped valley region. Impedance response for all
mixes after (b) 7-days curing; (c) 14-days curing and (d) 28-days curing.
Fig. 4. (a) Schematic showing salient frequencies on Nyquist plot for ECC with and without
steel fibers; (b) observed peak, fp, and cusp, fc, frequencies for Mix 1. Influence of steel fiber
dosage and curing time on (c) fp,h - peak on high frequency arc; (d) fp,m - peak on mid-
frequency arc; (e), fc,h - cusp on high frequency arc, and (f), fc,l - cusp on low-frequency arc.
Fig. 5. (a) Schematic diagram of Nyquist plot showing arc depression angle, , with centre,
O; (b) diagrammatic representation of electrical pathways in the cementitious composite
placed between a pair of electrodes, and, (c) Electrical model for the cementitious composite
represented in (b). Refer to text for circuit element notation.
Fig. 6. Measured and simulated impedance responses for Mixes 1, 3 and 6 at 7-days curing.
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Fig. 7. (a) Relative permittivity and (b) conductivity of Mix 1 at 7, 14 and 28 days curing.
The arrows indicate the permittivity/conductivity responses corresponding to the minimum
point within the U-shaped valley region of the impedance response presented in Fig. 3(a).
Fig. 8. Relative permittivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.
Fig. 9. Conductivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.
Fig. 10. Salient frequencies (refer also to Fig. 4(a)) for Mixes 1 and 6 on their respective
dispersion curves: (a) conductivity; and (b) relative permittivity.
Fig. 11. Schematic showing induced polarization at steel fiber–pore solution interface.
Fig. 12. Bulk conductivity of Mixes 1–6 at 7, 14 and 28(d)ays curing.
Fig. 13. Measured conductivity (bulk) and simulated conductivity (c) using equations (5)
(3D random) and (9) (3D cos) at (a) 7; (b) 14; and (c) 28(d)ays curing.
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Fig. 1. Schematic diagram of test samples for: (a) electrical property measurements; and (b)
flexural tests (all dimensions in mm).
(a)
(b)
40
40
electrode
1.6 mm rod
sample
10 40 55 10
170 40
20
55
sample
10
160
10 140
sample
polystyrene
0.5P 0.5P
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Fig. 2. Results of flexural tests: (a) load-deflection response for all samples; and (b)
computed tensile stress and strain capacity (error bars indicate the spread of measurements
from the mean value presented).
0
0.5
1.0
1.5
0 2.5 5.0 7.5
M6-2
M6-1
M5-2
M5-1
M4-2
M4-1
M3-2
M3-1
M2-2
M2-1
M1-2
M1-1
(a)
Deflection (mm)
Lo
ad
(k
N)
0
0.5
1.0
1.5
0 2.5 5.0 7.5
M1-1
M1-2
M2-1
M2-2
M3-1
M3-2
M4-1
M4-2
M5-1
M5-2
M6-1
M6-2
(a)
Deflection (mm)
Lo
ad
(k
N)
0
0.5
1.0
1.5
0 2.5 5.0 7.5
M1-1
M1-2
M2-1
M2-2
M3-1
M3-2
M4-1
M4-2
M5-1
M5-2
M6-1
M6-2
(a)
Deflection (mm)
Lo
ad
(k
N)
0
0.5
1.0
1.5
0 2.5 5.0 7.5
M1-1
M1-2
M2-1
M2-2
M3-1
M3-2
M4-1
M4-2
M5-1
M5-2
M6-1
M6-2
(a)
Deflection (mm)
Lo
ad
(k
N)
2
3
4
5
0 0.25 0.50 0.75 1.002
3
4
5
6
7
8
(b)
Steel fiber volume (%)
f tu (
MP
a)
tu (
%)
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Fig. 3. (a) Impedance response for Mix 1 at 7, 14 and 28-days curing, with the arrows
indicating the minimum point within the U-shaped valley region. Impedance response for all
mixes after (b) 7-days curing; (c) 14-days curing and (d) 28-days curing.
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
M1
M2
M3
M4
M5
M6
(a) 7d
Z'() ohm
Z''(
) o
hm
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
M1
M2
M3
M4
M5
M6
(a) 7d
Z'() ohm
Z''(
) o
hm
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
M1
M2
M3
M4
M5
M6
(a) 7d
Z'() ohm
Z''(
) o
hm
(b) 7d
-1250
-1000
-750
-500
-250
00 500 1000 1500 2000 2500
(b) 14d
Z'() ohm
Z''(
) o
hm
(c) 14d
-2500
-2000
-1500
-1000
-500
00 1000 2000 3000 4000 5000
(c) 28d
Z'() ohm
Z''(
) o
hm
(d) 28d
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
-1800
-1500
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-2-28d
M1-1-28d
M1-2-14d
M1-1-14d
M1-2-7d
M1-1-7d
(a)
Z'() ohm
Z''(
) o
hm
ACC
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Fig. 4. (a) Schematic showing salient frequencies on Nyquist plot for ECC with and without
steel fibers; (b) observed peak, fp, and cusp, fc, frequencies for Mix 1. Influence of steel fiber
dosage and curing time on (c) fp,h - peak on high frequency arc; (d) fp,m - peak on mid-
frequency arc; (e), fc,h - cusp on high frequency arc, and (f), fc,l. - cusp on low-frequency arc.
5
10
15
20
25
0 0.25 0.50 0.75 1.00
28d
14d
7d
Steel fiber volume (%)
f c,l (
Hz)
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
0
30
60
90
120
0 0.25 0.50 0.75 1.00
28d
14d
7d
Steel fiber volume (%)
f c,h
(k
Hz)
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
0
30
60
90
120
0 0.2 0.4 0.6 0.8 1.0
28d
14d
7d
Steel fiber volume (%)
f p,m
(H
z)
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
5
10
20
50
100
0 0.2 0.4 0.6 0.8 1.0
28d
14d
7d
Steel fibre volume (%)
f p,m
(H
z)
2
4
6
8
0 0.25 0.50 0.75 1.00
28d
14d
7d
fp
fp
fp
Steel fiber volume (%)
f p,h
(M
Hz)
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
2
4
6
8
0 0.25 0.50 0.75 1.00
28d
14d
7d
fp
fp
fp
Steel fibre volume (%)
f p,h
(M
Hz)
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
Increasing
frequency
Mix 1
Mix with
steel fibres
fc,h
10MHz
1 Hz
fp,h
fp,m
fc,l
fp
fc
Z'() ohm
Z''(
) o
hm
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
0
0.5
1.0
1.5
0 7 14 21 283
4
5
6
7
(b)
Curing time (days)
f c
(kH
z)
f p
(MH
z)
ACC
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(a)
(b)
(c)
Fig. 5. (a) Schematic diagram of Nyquist plot showing arc depression angle, , with centre,
O(b) diagrammatic representation of electrical pathways in the cementitious composite
placed between a pair of electrodes, and, (c) electrical model for the cementitious composite
represented in (b). Refer to text for circuit element notation.
O
Z'()
-iZ
''(
)
Increasing frequency
CPEfi
Rfi Rf Rf-cp
Rel
CPEf-sm
CPEel
Rcp
CPEsm Rs
(i)
(ii)
(iii)
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Fig. 6 Measured and simulated responses for Mixes 1, 3 and 6 at 7-days curing.
-625
-500
-375
-250
-125
00 250 500 750 1000 1250
M1: measuredM3: measuredM6: measuredM1: simulatedM3: simulatedM6: simulated
Z'() ohm
Z''(
) o
hm
ACC
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Fig. 7. (a) Relative permittivity and (b) conductivity of Mix 1 at 7, 14 and 28 days curing.
The arrows indicate the permittivity/conductivity responses corresponding to the minimum
point within the U-shaped valley region of the impedance response presented in Fig. 3(a).
0.01
0.02
0.05
0.1
0.2
100
102
104
106
(c)
Frequency (Hz)
(
) S
/m
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
(b)
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rel
ativ
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rel
ativ
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rel
ativ
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
(b)
Frequency (Hz)
Rel
ativ
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Frequency (Hz)
r' (
)-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
-1200
-900
-600
-300
0400 1000 1600 2200 2800 3400 4000
M1-1-7dM1-2-7dM1-1-14dM1-2-14dM1-1-28dM1-2-28d
(a)
Z'() ohm
Z''(
) ohm
ACC
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101
103
105
107
109
100
102
104
106
(b) 14d
Frequency (Hz)
r' (
)
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
Fig. 8. Relative permittivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)R
ela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
r' (
)
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
r' (
)
101
103
105
107
109
100
102
104
106
(c) 28d
Frequency (Hz)
r' (
)
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
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Fig. 9. Conductivity for all Mixes at (a) 7; (b) 14; and (c) 28 days.
0.01
0.1
1
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
(
) S
/m
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y10
1
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
0.01
0.1
1
100
102
104
106
M1
M2
M3
M4
M5
M6
(a)
Frequency (Hz)
Co
nd
ucti
vit
y (
S/m
)
0.01
0.1
1
100
102
104
106
M1
M2
M3
M4
M5
M6
(a)
Frequency (Hz)
Co
nd
ucti
vit
y (
S/m
)
0.01
0.1
1
100
102
104
106
(b) 14d
Frequency (Hz)
(
) S
/m
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
0.01
0.1
1
100
102
104
106
(c) 28d
Frequency (Hz)
(
) S
/m
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
101
103
105
107
109
100
102
104
106
M1
M2
M3
M4
M5
M6
(a) 7d
Frequency (Hz)
Rela
tiv
e p
erm
itti
vit
y
ACC
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Fig. 10. Salient frequencies (refer also to Fig. 4(a)) for Mixes 1 and 6 at 7-days curing on
their respective dispersion curves: (a) conductivity; and (b) relative permittivity.
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
101
103
105
107
109
100
102
104
106
fc,h
fp,h
fc,l f
p,m
fc
fp
Frequency (Hz)
r' (
)
0.01
0.1
1
100
102
104
106
Mix 1
Mix 6
fpf
c
fc,h
fc,l
fp,h
fp,m
Frequency (Hz)
(
) S
/m
1
2
5
10
20
0 0.25 0.50 0.75 1.00
(a) (b) (c) (d) (e) (f)
Steel fibre volume (%)
f c,l (
Hz)
M1-7d
M6-7d
ACC
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Fig. 11. Schematic showing induced polarization at steel fiber–pore solution interface.
Steel fibre
(electronic
conduction)
+
__
_
_
_
e-
+
+
+
+
+
+
+
_____
_
_
_+++++
Electrolyte
(ionic
conduction)
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Fig. 12. Bulk conductivity of Mixes 1–6 at 7, 14 and 28(d)ays curing.
0
0.1
0.2
0.3
0.4
0 0.25 0.50 0.75 1.00
28d
14d
7d
Steel fiber volume (%)
b
ulk
(
) S
/m
ACC
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Fig. 13. Measured conductivity (bulk) and simulated conductivity (c) using equations (5)
(3D random) and (9) (3D cos) at (a) 7; (b) 14; and (c) 28(d)ays curing.
0
0.1
0.2
0.3
0.4
0 0.25 0.50 0.75 1.00
simulated (3D cos)simulated (3D random)measured
(a) 7d
Steel fiber volume (%)
b
ulk
;
c (S
/m)
0
0.1
0.2
0.3
0.4
0 0.25 0.50 0.75 1.00
measured
simulated (3D random)
simulated (3D cos)
(a) 7d
Steel fibre volume (%)
b
ulk
;
c (S
/m)
0
0.05
0.10
0.15
0.20
0 0.25 0.50 0.75 1.00
(b) 14d
Steel fiber volume (%)
b
ulk
;
c (S
/m)
0
0.02
0.04
0.06
0.08
0.10
0 0.25 0.50 0.75 1.00
(c) 28d
Steel fiber volume (%)
b
ulk
;
c (S
/m)
ACC
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Table captions
Table 1 Materials mix proportions and mechanical property.
Table 2 Oxide analysis and physical properties of fly-ash and silica sand (wt%).
Table 3 Equivalent circuit simulation parameters for all mixes at 7-days curing.
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Table 1 Materials mix proportions and mechanical property.
Mix CEM I FA Silica sand w/b HRWR PVA Steel F28
(kg/m3) (kg/m
3) (kg/m
3) (kg/m
3) (kg/m
3) (kg/m
3) (MPa)
M1 471 801 284 0.28 4.7 22.8 – 44.6
M2 471 800 283 0.28 4.7 22.8 11.8 +
M3 470 799 283 0.28 4.7 22.8 19.6 48.4
M4 469 797 282 0.28 4.7 22.8 39.3 +
M5 468 796 281 0.28 4.7 22.8 58.9 49.7
M6 467 793 280 0.28 4.7 22.8 78.5 49.0
Notes: binder includes cement and fly-ash; + means not available; F28: 28-day compressive
strength determined on 50mm cubes.
Table 2 Oxide analysis and physical properties of fly-ash and silica sand (wt%).
Fly-ash Silica sand
Chemical analysis
SiO2
52.7
98.8 Al2O3 26.6 0.21
Fe2O3 5.6 0.09
K2O – 0.03
CaO 2.4 –
MgO 1.2 –
Na2O equivalent 1.7 –
SO3 0.3
3
–
Free CaO 0.03 –
Total phosphate 0.5 –
Loss on Ignition (LOI) <2.0 0.14
Physical properties
Specific gravity
Surface area (m2/kg)
Fineness (% retained on 25 m)
2.20
1300
<25
2.65
–
–
Size distribution (m) and cumulative retained (%)
500 – 0.1
355 – 0.5
250 – 1.5
180 – 6.0
125 – 46.0
90 – 83.0
63 – 96.5
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Table 3 Equivalent circuit simulation parameters for all mixes at 7-days curing.
Mix M1 M2 M3 M4 M5 M6
Fibre dosage (%) 0 0.15 0.25 0.50 0.75 1.0
Rs () 450 345 300 235 185 170
Rcp () 510 840 870 925 950 980
CPEsm 3.0×10-9
1.0 ×10-9
1.0×10-9
1.0×10-9
2.5×10-9
2.5×10-9
CPEsm (p 0.80 0.83 0.83 0.84 0.81 0.84
Rf () + 10-3
10-3
10-3
10-3
10-3
Rfi (k) + 2.4 3.0 14 100 500
CPEfi + 7.0×10-6
7.0×10-6
7.0×10-6
1.0×10-5
1.0×10-5
CPEfi (p) + 0.77 0.80 0.80 0.78 0.80
Rf-cp () + 550 420 320 200 150
CPEf-sm + 1.0×10-9
1.0×10-9
1.0×10-9
2.0×10-9
2.5×10-9
CPEf-sm (p + 0.83 0.83 0.84 0.81 0.84
Rel (k) 10 10 10 10 10 10
CPEel 3.5×10-4
3.5×10-4
3.0×10-4
4.0×10-4
3.0×10-4
3.3×10-4
CPEel (p 0.90 0.94 0.94 0.90 0.97 0.95
+ = not determined
ACC
EPTE
D M
ANU
SCR
IPT
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Research Highlights
- AC electrical properties of a hybrid PVA/steel fiber ECC presented for the first time.
- A dual bulk-arc response observed in the Nyquist format.
- A dielectric enhancement observed in the frequency-domain response.
- Charges at the steel fiber-ECC matrix interface give rise to the polarizability of the
composite system.
- The bulk electrical conductivity conforms to the equivalent inclusion theory.
