A magnetic method for non destructive monitoring of fiber dispersion and orientation in steel fiber...

$: A magnetic method for non destructive monitoring of fiber dispersion and orientation in steel fiber reinforced cementitious composites. Part 2: Correlation to tensile fracture toughness$
ORIGINAL ARTICLE

A magnetic method for non destructive monitoring of fiberdispersion and orientation in steel fiber reinforcedcementitious composites—part 1: method calibration

Liberato Ferrara • Marco Faifer • Sergio Toscani

Received: 11 April 2011 / Accepted: 26 September 2011 / Published online: 12 October 2011

� RILEM 2011

Abstract Steel fiber reinforced concrete (SFRC) is a

composite material which is becoming more and more

widely employed in building construction. The

mechanical behaviour of the material and the perfor-

mance of structural elements may significantly depend

on the fiber dispersion and orientation with respect to

the stress pattern. Non-destructive monitoring of fiber

dispersion related issues hence becomes of the fore-

most importance in order to reliably anticipate the

structural performance of elements made with fiber

reinforced cementitious composites (FRCCs), as well

as for quality control during manufacturing. In this

paper a new method for the detection of fiber density

and orientation is presented, which is based on the

employment of a probe sensitive to the magnetic

properties of the steel fibers. The presence and the

relative position of steel fibers modify the flux linked

by the winding of the probe thus resulting in an

impedance variation. The local average concentration

and orientation of the fibers can be thus assessed by

measuring the variation of the probe inductance. The

performance of the method has been analyzed with

reference to a self-consolidating high performance

FRCC slab and thoroughly verified by means of

comparison with destructive monitoring of fiber local

concentration and orientation. Besides its good sensi-

tivity, the method is also characterized by ease of use,

since it just requires to lean the probe on the surface of

the specimen, without any particular care about the

coupling. This guarantees a high degree of repeatabil-

ity and low uncertainty in the measurements, even,

e.g. on vertical elements or slabs accessible from the

bottom.

Keywords Fiber reinforced cementitious

composites � Flow-induced orientation �Non-destructive fiber monitoring �Magnetical inductance

1 Introduction

Fifty years of continuing research, since the early

pioneering studies by Romualdi and Batson [1], have

led to consolidated knowledge about the multifold

aspects of the physical and mechanical behaviour of

steel fiber reinforced concrete (SFRC) and fiber

reinforced cementitious composites (FRCCs) as well

L. Ferrara (&)

Politecnico di Milano, Department of Structural

Engineering, Piazza Leonardo da Vinci 32, 20133 Milan,

Italy

e-mail: [email protected]

M. Faifer � S. Toscani

Politecnico di Milano, Department of Electrical

Engineering, Piazza Leonardo da Vinci 32, 20133 Milan,

Italy


S. Toscani


Materials and Structures (2012) 45:575–589

DOI 10.1617/s11527-011-9793-y

as to the development of more and more advanced

theory and modelling tools able to describe such

behaviour and explain reinforcing mechanisms. As a

consequence, continuous developments have been

promoted in new advanced materials and improved

products for buildings and other structures, even

‘‘tailored’’ to the intended application, as well as in

terms of processing and standardization. In order to

guarantee the prescribed levels of performance,

multiple targets have to be met which include not just

merely mechanical properties, but also durability, fire

and extreme loading resistance, constructability

energy efficiency, life-cycle cost effectiveness: in

one word, which may broadly encompass all the

aforementioned requisites, sustainability.

The recently issued fib 2010 Model Code [2] has

finally made available to the world engineering

community a set of internationally recognized design

guidelines to confidently employ these materials to

build structures and infrastructures able to meet the

higher and higher needs and demands of our society.

The dispersion of fibers inside a structural element

has been long time recognized as a crucial issue to

design and achieve safe and reliable SFRC applica-

tions. As a matter of fact, a spotty dispersion, where

zones with a reduced or even nil amount of fibers may

stand side by side with zones richer in fiber content or

even where fibers have clumped, may, either the

former or the latter acting as defects, seriously affect

the element load bearing capacity as well as trigger

failure mechanisms which have not been anticipated in

the design stage.

Over the past years several researchers have

pointed out that the aforementioned spotty dispersion

of fibers most likely occurs due to the negative effects

which the addition of fibers has on the fresh state

performance of the material [3, 4]. This requires, for

successful casting, manual compaction and/or strong

mechanical vibration, which may most likely amplify

the somewhat unavoidable downward settlement of

the fibers, further contributing to an uneven spatial

distribution of material mechanical properties inside

the element.

The synergy of the FRC with the Self Consolidating

Concrete (SCC) technology, which, thanks to the

higher deformability and rheological stability of the

latter, reduces or even eliminates the need for manual

compaction and mechanical vibration, has been

proved effective at guaranteeing a randomly uniform

dispersion of the fibers [4, 5]. This is also likely to have

positive outcomes in terms of experimental scattering

of material properties within the same casting. It has

been furthermore shown that, thanks to both a suitably

balanced set of fresh state properties and to a careful

design of the casting process, it is possible to

effectively orientate the fibers along the direction of

the casting flow [6–8]. All what said above paves the

way towards a challenging ‘‘holistic’’ approach to the

design of SFRC structural elements which tailors both

the material composition and the casting process to the

anticipated structural performance. This would require

the orientation of fibres to match as close as possible

with the direction of the principal tensile stress within

the structural element when in service, so to achieve a

more efficient structural use of the material [9–11]. In

this way a desirable closer correspondence between

the shape of an element and the function it performs in

a structure assembly could be pursued in the design.

A suitably balanced fresh-state performance of the

FRCC would allow to mould the shape of an element

and, thanks to a tailored casting process, to orient the

fibers along the direction of the principal tensile

stresses resulting from its structural function.

2 Non-destructive monitoring of fiber dispersion:

a literature survey

In the framework before discussed the assessment of

fiber dispersion and orientation related issues through

a non destructive both time- and cost-effective method

becomes a crucial need also in the sight of developing

‘‘ad-hoc’’ quality control procedures.

Research about not-destructive monitoring of fiber

dispersion and, in case, orientation in FRC elements,

dates back to the late 70s [12] but only in the very last

lustrum has undergone renewed interest and challeng-

ing advances have been made. This, besides the

evident progress in sensors and monitoring technolo-

gies, is due, in the authors’ opinion, to two peculiar

concurring issues. First of all, after about 50 years of

continuing research, a consensus has been achieved

about the feasibility and effectiveness of FRC struc-

tural applications and the knowledge thus garnered has

been transferred into reliable codified design

approaches, including the procedures for the identifi-

cation of relevant properties of the material. The issues

about quality control of the aforementioned

576 Materials and Structures (2012) 45:575–589

applications, including dispersion of the fibers, have

thus garnered renewed interest. This has been further-

more triggered by the ongoing tremendous develop-

ment in the SCC technology, the synergy of which

with FRC has been recognized, as above remarked, as

an effective tool to control the dispersion and orien-

tation of the fibers, thus providing added value to the

engineering applications.

In most of the so-far reported investigations, fiber

dispersion and orientation were (destructively) mon-

itored by manually counting the fibers on selected

‘‘specimen locations’’ (e.g. over fracture cross sec-

tions of specimens employed for toughness fracture

tests).

Manual counting is rather easy when low dosages

of longer fibers with average aspect ratios are

employed [13, 14] whereas image analysis techniques

are required for higher dosages of shorter fibers with

higher aspect ratios or whenever a quantitative infor-

mation on the orientation of fibers with respect to the

plane of the cut has to be sought [7, 15–17].

X-ray pictures of cores or of thin slices obtained by

sawing the specimens (the sample thickness is dictated

by the absorption properties of the material and power

of the equipment) were also taken in several investi-

gations [4, 12, 14] and can provide immediate and

effective visualization of the fiber orientation. Obtain-

ing quantitative information from X-ray pictures may

be cumbersome, either due to the loss of the third

dimension and, most of all, in the case of higher

percentages of short fibers.

A nice 3D visualization of the fiber arrangement

within a specimen can be obtained, as it was recently

shown, by means of Computed Axial Tomography

(CAT) scanning [6, 18]. The need of a dedicated

equipment (like in the case of X-rays) as well as of an

image analysis software for the quantitative process-

ing of the collected data, may be singled out, so far, as

a major drawback to a wider use of the method,

especially at an industrial scale.

Electrical methods, based on the effects of the fibers

on the resistivity/conductivity of the composite mate-

rial, has received lots of attention in the very last years.

Ozyurt et al. [19] and Woo et al. [20] employed the

Alternate Current Impedance Spectroscopy (AC-IS)

for the detection of fiber dispersion related issues and

demonstrated its reliability as well as its sensitivity to

fiber orientation, clumping, segregation etc. by means

of extensive comparison with results obtained from

destructive methods. Attempts were also made to

address the application of the aforementioned method

to industrial scale problems [21]. The method is based

on the frequency-dependant behaviour of cementitious

composites reinforced with conductive, such as steel

and carbon, fibers. These were in fact shown to be

practically insulating under Direct Current (DC) and

low frequency Alternate Current (AC) excitation

while they are conductive under high frequency AC.

The method consists of applying to the specimen a

voltage excitation over a range of frequencies (e.g.

10 MHz–1 Hz) and measuring the amplitude and

phase of the flowing current. When the real and

imaginary parts of the calculated impedance Z are

plotted on a Nyquist diagram, FRCCs exhibit the so

called dual-arc behaviour featured by a low-frequency

cusp (fibers are insulating), which gives the (higher)

resistance of the matrix, Rm, and a high frequency cusp

(fibers are conductive), which corresponds to the

(lower) resistance of the fiber reinforced composite R.

In order to overcome the drawback of the sensitivity to

moisture conditions of the resistivity of the concrete

matrix, the so-called matrix normalized conductivity

is used, from which information about local fiber

concentration should be easily obtained by means of a

simple mixture rule approach:

Rm

R¼ r

rm

¼ 1þ rfibers½ �Vf ð1Þ

where r and rm are the conductivity of the fiber

reinforced composite and of the matrix respectively,

[rfibers] is the intrinsic conductivity of the fibers which,

in the case of highly conductive fibers, only depends

on their geometrical properties (fiber aspect ratio) [22]

and Vf is the fiber volume fraction.

The method has been extensively employed to

assess the influence of the fresh state performance on

the dispersion of the fibers and their correlation with

the mechanical properties (e.g. fracture toughness) [5,

23]. Any direct quantitative comparison between, e.g.,

the concentration of fibers as evaluated from Eq. 1 and

data obtainable from destructive tests (e.g. crushing

samples, separating and weighing fibers) could hardly

be found in the literature. The need of a dedicated

expensive instrumentation, as required by the exten-

sion of the employed frequency range, and the

sensitivity of the method itself to the contact imped-

ance between the surface electrodes and the specimen/

structure surface, has led several researchers to

Materials and Structures (2012) 45:575–589 577

investigate different approaches and techniques in the

mainstream of electrical methods.

Lataste et al. [24] employed a method based on low

frequency resistance measurements, with a four elec-

trode arrangement, aimed at reducing the effects of the

poor electrical coupling. The method has been dem-

onstrated to be effective in detecting orientation

characteristics of fiber reinforcement, because of the

different resistance measured along the two directions

at right angle to each other; qualitative correlation

with mechanical properties measured according to the

same directions as above was also provided [25].

Anyway the method is not able to provide any

quantitative information about the local average

concentration of the fiber reinforcement, mainly due

to the uncertainty in the assessment of the concrete

matrix resistivity, because of its strong sensitivity to

aging, moisture content and presence of electrolytes in

the pores which also affect the measured resistivity

beside the effects of fiber concentration.

The effects of conductive fibers on the capacitive

properties of the fiber reinforced composite have led to

the development of another method, based on the

measurement of the effective permittivity through a

coaxial probe and microwave reflectometry tech-

niques [26]. The local average concentration of fibers

could be assessed by assuming a random orientation

and because of the known fiber geometry (aspect ratio)

which governs their capacitive behaviour: as a matter

of fact the method is unsuitable for FRCCs featured by

preferential fiber orientation.

In this paper a new method is proposed and validated

which employs a probe sensitive to the magnetic

properties of the steel fibers. The fundamentals of the

method rely on the fact that the presence and relative

position of the fibers in a fiber reinforced concrete

element modify the magnetic field lines due to the probe

winding, when leant on the element/structure surface,

thus resulting in a variation of the measured inductance.

Either fiber concentration can be quantitatively

assessed by calibrating the method and fibre preferen-

tial orientation can be estimated. As it will be further

elucidated, the method, besides its good sensitivity and

robustness, is also characterized by an intriguing ease of

use, due to the simple equipment which just needs to be

leant of the surface of a structural element, which can be

easily done even on vertical elements or slabs acces-

sible only from the bottom, without any dedicated care

about the electrical coupling.

The validation of the method has been performed

with reference to slabs (1 m long 9 0.5 wide 9

25 mm thick) cast with a high performance fiber

reinforced cementitious composite (HPFRCC), con-

taining either 50 or 100 kg/m3 of steel fibers 13 mm

long and 0.16 mm in diameter. The slab casting

process was designed so to have, thanks to the self-

compacting fresh-state properties of the material, a

preferential orientation of the fibers parallel to the

longer edge of slabs. A thorough comparison with

fiber dispersion and orientation related issues as

detected by means of destructive techniques has been

also performed. In a companion paper [27] the tensile

fracture toughness of the material will be evaluated,

both along and at a right angle to the preferential fiber

orientation, and correlated to the previously garnered

information on fiber dispersion and orientation.

3 Research programme

In order to validate the proposed method for non-

destructive monitoring of fiber dispersion and to

further establish quantitative correlation with tensile

fracture toughness properties of the material, a

HPFRCC containing 100 kg/m3 short steel fibers,

already thoroughly investigated in a previous research

project [7], has been assumed as a reference. Its mix

design is shown in Table 1. Two further mixes, with

either 50 kg/m3 fibers or no fibers at all (plain matrix)

have been designed to the purpose of this study, the

compositions of which are also detailed in Table 1.

The plain matrix (mix HPFRCC0 in Table 1) has

been considered because of the need of a ‘‘zero

Table 1 Mix design of the employed FRCCs

Constituent Dosage (kg/m3)

HPFRCC

100

HPFRCC

50

HPFRCC

0

Cement type I 52.5 600 600 600

Slag 500 500 500

Water 200 200 200

Superplasticizer (l/m3) 33 33 33

Sand 0–2 mm 983 1,000 1,017

Straight steel fibres

(lf = 13 mm;

df = 0.16 mm)

100 50 0


reference point’’ for the calibration of the magnetic

test results, as it will be detailed in the forthcoming

sections.

The mixing protocol adopted for the mixes is

detailed in Table 2. As it clearly appears, the adopted

mix-design rationale when reducing the fiber content

was to replace them with an equivalent volume of

sand. This resulted in comparable fresh state perfor-

mance, as measured by means of the slump-flow and

V-funnel tests, irrespective of the fiber content, as

detailed in Table 3.

A thin slab 1 m long 9 0.5 m wide 9 25 mm

thick was cast with each of the three aforementioned

mixes: fresh concrete was poured at the center of one

short edge and, due to its self-levelling ability, after

having spread to the whole width of the slab,

completely filled the formwork flowing parallel to

the long side. A preferential orientation of the fibers

along the aforementioned direction was with high

probability obtained.

Fiber dispersion was monitored by means of the

magnetic method detailed in the following chapter and

according to the schematic shown in Fig. 1. A grid was

drawn on the slab surface dividing it into eighteen

cells: for each of the cells measurements were

garnered along four directions, i.e. parallel and

orthogonal to the flow direction and at ±45� with

respect to it (Fig. 1). In this way thorough information

on the orientation characteristics of the fiber rein-

forcement could be obtained. Along each direction

measures were repeated five times, for statistical

significance, and reference will be made hereafter to

their average.

After such a monitoring the slabs were cut into

square tiles according to the same schematic as the one

employed for the inductance measurements; the tile

specimens were employed to identify the tensile

stress-crack opening behaviour of the composite

according to a novel testing methodology called the

Double Edge Wedge Splitting test [28, 29], as

sketched in Fig. 2a. The groove and notch cutting

was done in such a way that the preordained fracture

plane resulted either parallel or perpendicular to the

preferential flow-induced fiber alignment. A detailed

scheme is provided in Fig. 2b, which shows as a

thorough characterization of the fiber orientation and

local concentration dependant tensile fracture tough-

ness was obtained from such a testing programme.

After mechanical tests, first fibers on the fracture

surface of each specimen were counted, for a ‘‘rough’’

evaluation of the fiber orientation factor [30], to be

correlated with information garnered either from

inductance measurements and fracture toughness

tests. Finally, some specimens were crushed (the ones

which are shadowed in Fig. 2b) and fibers were

separated and weighed, for a destructive evaluation of

local concentration, to be correlated once again with

non destructive predictions from the magnetic induc-

tance based method.

In this paper the fundamentals of the method will be

presented and the methodology which has been

adopted for the analysis of garnered measurements

and the obtainment of data in terms of fiber local

average concentration and orientation will be dis-

cussed. Validation through destructive assessment of

Table 2 Mixing protocol

Task Time

Mix raw cement and slag at 50 rpm 1 min

Add water and SP 1 min

Mix paste at 50 rpm 5 min

Add sand while mixing at 50 rpm 2 min

Mix mortar at 100 rpm 5 min

Add fibers while mixing at 100 rpm 2 min 30 s

Mix FRCC at 100 rpm 5 min

Table 3 Results of the fresh state characterization

Mix Slump flow test V-funnel test

Diameter (mm) T50 (s) Flow time TV (s)

HPFFRCC 100 750 6 30

HPFRCC 50 760 6 29

HPFRCC 0 775 5 25

Fig. 1 Scheme for the acquisition of magnetic measurements

on HPFRCC slabs (examples of measurement directions is given

for one cell, dimensions in mm)


the same quantities will finally demonstrate the

reliability of the method. Correlation with tensile

fracture toughness properties of the material will be

presented and analysed in a companion paper [27].

4 The proposed method: physics fundamentals

Low carbon steel fibers, employed in most of the

SFRC applications exhibit a ferromagnetic behaviour.

The FRCC hence consists of two phases with strongly

different magnetic properties: namely the cement-

based matrix, characterized by a magnetic permeabil-

ity l0, and the fibers, whose magnetic permeability lFe

is much higher than l0. Due to the generally quite low

volume fraction of fibers, the interactions between

inclusions may be neglected. Furthermore, both the

fiber length and the average fiber spacing are likely to

be much lower that the wavelength used for the

analyses.

Under the aforementioned assumptions the macro-

scopic magnetic properties of the composite material

and the effective magnetic permeability dyad leff of

the two-phase mixture can be defined [31]. It is

important to notice that the latter depends on the

volume fraction of the fibers, on their orientation, on

their aspect ratio but it does not depend on their size.

Therefore, it is evident that the measurement of a

parameter influenced by the effective permeability of

the SFRC can be used to asses both the concentration

and the orientation of the steel fibers. A possible

solution based on this approach consists in the

measurement of the equivalent inductance related to

a magnetic field which invests the SFRC specimen.

A C-shaped magnetic core with a N turn winding can

be used (Fig. 3) to this purpose. When the core is

placed on the surface of a SFRC element, the self-

inductance of the winding is influenced by the

concentration of the fibers: the higher the former, the

higher the latter. In addition, the inductance is also

influenced by the orientation of the magnetic core with

respect to the average direction of the fibers. When the

magnetic axis of the winding and the average direction

of the steel fibers are aligned the measured inductance

is maximum.

In Fig. 3 the permeances Kl, Kc, Kv assigned to the

various branches of the magnetic circuit and the

current iw flowing into the N-turn coil are shown.

Studying the equivalent circuit of the probe the

impedance evaluated at the terminals A–B of the coil

(Fig. 4) results:

ZAB ffi Rws þ jx Ll þLcLv

Lc þ Lv

� �ð2Þ

where Rws is the resistance of the coil.

(b)

(a)

Fig. 2 Scheme of the DEWS test specimen geometry and set-

up (a) and scheme of DEWS specimens cutting from the slab

with reference to casting flow lines (b—shadowed cells have

been crushed for destructive measurement of fiber concentra-

tion); dimensions in mm

Fig. 3 Schematic of the magnetic probe


As clearly indicated in Eq. 2, the real part of the

impedance does not depend on the presence of

the fibers, while the imaginary part may be affected

by the magnetic effects due to the fibers (inductance

Lv).

Since Lv can be split into two terms, Lv0 and DLv,

Eq. 2 can be re-written as:

ZAB ffi Rws þ jx Ll þLc Lv0 þ DLvð ÞLc þ Lv0 þ DLv

� �ð3Þ

Lv0 is the value assumed by Lv when the specimen

does not contain fibers. DLv is an additional term due

to presence of steel fibers.

Since the inductance Lc is surely much higher than

Lv, Eq. 3 can be approximated with the following

expression:

ZAB ffi Rws þ jx Ll þ Lv0 þ DLvð Þ ð4Þ

where DLv depends on the presence of fibers.

Equation 4 shows that the effect of the steel fibers

simply results in an increase of the probe inductance.

This increase can potentially be effective to assess

information about the concentration of the steel fibers.

In fact by considering Eq. 4 it can be written:

DLv ¼ ImZAB � ZAB0

x

� �ð5Þ

where ZAB0 is the impedance measured when the

probe is placed on a specimen without fibers. At the

same time, the average direction of the fiber can be

detected by rotating the magnetic probe around its axis

of symmetry and by finding the angular position where

the quantity Im(ZAB/x) becomes maximum.

Starting from the theoretical formulation of the

problem the experimental set-up shown in Fig. 5 has

been developed. The magnetic probe used to detect the

steel fiber reinforcement inside SFRC elements con-

sists of a C-shaped N87 ferrite core. The excitation is

provided by a 100 mA current flowing through a

78-turn coil. 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. In

fact, it provides the generation of the excitation signal

producing the required magnetomotive force. Further-

more, it permits to measure the voltage applied to the

magnetic probe and the consequent current.

The acquisition of the two signals has been

performed by means of a National Instruments PCI

6143 DAQ board featuring a 16-bit resolution and a

maximum sampling frequency of 250 kHz. The exci-

tation signal has been provided by a digital signal

waveform generator (DSWG) controlled through a

GPIB interface. In order to avoid a ground loop

between the generation and the acquisition sections,

the excitation signal has been injected through a wide

bandwidth signal transformer.

The impedance measurement consists in a FFT

analysis of the voltage and the current signals. This

technique allows to reduce the requirements of low

harmonic distortion of the stimulus signal, thus

strongly relaxing the linearity requirement of the

decoupling transformer.

By means of a comparison with a high precision

LCR meter (Agilent E4980A) it has been estimated

that the system features a resolution better than

0.3 lH, which complies with the requirements

assessed through the finite element validation of the

set-up [31].

Fig. 4 Electrical model of the magnetic probe when the effect

of the steel fibre reinforced cementitious composite is taken into

account

Fig. 5 Schematics of the experimental setup


5 Data acquisition and analysis: assessing local

fiber concentration and orientation from

non-destructive magnetic measurements

As briefly recalled above in Sect. 2, for each, either

plain or fiber reinforced slab (respectively containing

50 and 100 kg/m3 of fibers), measurements of the

probe magnetic inductance were garnered with refer-

ence to the eighteen cells the slab was virtually

divided into and along four different directions as

sketched in Fig. 1. Measurements were taken in the

frequency range between 1 and 10.2 kHz. Figure 6

shows the measured inductance versus frequency

trends. As an example measurements have been done

on the same cell for each of the tested slab (No. 8 in

the schematic shown in Fig. 1). Measured trends

resulted similar everywhere else. The sensitivity of

the measured inductance to both the nominal fiber

content and to the local concentration and most likely

alignment of the fibers clearly appears. Furthermore, it

can be observed a certain frequency dependence of the

measurements, which is by the way insensitive to

either the fiber content and orientation, as highlighted

by the parallel curve trends. This depends on the

frequency dependent behaviour of the ferromagnetic

material the employed probe is made of. Significantly,

in fact, the same trend has also been detected for the

inductance of the plain matrix, showing no anisotropy

as expectable, which also coincided with the one

measured in free air.

By considering the latter value as the reference one,

the so called ‘‘compensated inductances’’ can be

calculated as the differences between the inductance

measured for each of the investigated cells and

directions and the reference free air value itself.

Because of the aforementioned statements, the com-

pensated inductances turned out independent of the

frequency (Fig. 7a). The ratios between compensated

inductances along two directions, respectively parallel

and perpendicular to the flow direction, confirm the

guessed orientation of the fibers. It can be also

observed (Fig. 7b) that the higher the nominal content

of the fibers, the smaller the aforementioned ratio. This

may be most likely attributed to the fact that because

of their higher number, fibers are supposed to form a

more isotropic network. The ratio between compen-

sated inductances along the same direction but for two

different fiber contents results significantly coherent

with the nominal fiber content itself. The aforemen-

tioned statement, illustrated in Fig. 7 with reference to

a single monitored cell and confirmed all over the slab

specimens, has hence dictated the criteria for further

processing the whole set of garnered data (as summa-

rized in detail in Fig. 8) in order to obtain a more

meaningful quantitative information about both the

local concentration and orientation of the fibers.

Fig. 6 Measured probe inductance for different fiber concentrations and both parallel (along) and orthogonal to fiber orientation (data

are referred to cell 8 in Fig. 1)


As for the latter, Fig. 9 shows the direction along

which the maximum value of the compensated induc-

tance has been measured, for each cell, which most

likely coincided with the preferential alignment of the

fibers. Results appear to be coherent with the hypoth-

esized casting flow kinematics as well as with the wall

effects due to the formwork boundaries.

Compensated inductances may be further pro-

cessed in order to calculate, coherently with a

procedure already adopted by Ozyurt et al. [19] with

reference to fiber dispersion monitoring through

AC-IS, the so-called ‘‘fractional compensated induc-

tance’’. This, as it has been shown for the fractional

impedance in AC-IS through comparison with image

analysis [19], can be thought to be correlated to the

fiber orientation factor [30]. In Fig. 10 the fractional

inductances are shown, calculated as:

f== ¼DL==

0:5 DL== þ DL?� � ð6aÞ

(a)

(b)

Fig. 7 Compensated inductance versus frequency (a) and ratios between compensated inductances (b) for different fiber dosages and

alignment (plotted data refer to cell 8 in Fig. 1)


f? ¼DL?

0:5 DL== þ DL?� � ð6bÞ

where subscripts //and \ are meant as parallel and

orthogonal to the supposed flow direction and 0.5 is

the expected value in the case of an in-plane isotropic

dispersion. The thus calculated values of the fractional

inductances are interestingly coherent, for either the

fiber content investigated, with fiber orientation fac-

tors evaluated in a previous investigation [7] by means

of image analysis for similar specimens similarly cast

with the same material.

As for the quantitative assessment of the local

concentration of fibers, the following approach has

been followed. First of all it has been assumed that, in

the average, the slab as a whole contains a specific

amount of fibers equal to the nominal fiber content in

the mix. This assumption reasonably holds if one

considers that an amount of material was cast just

slightly larger than the one necessary to fill the slab

moulds and that fiber losses, if any, in the mixer and

during casting may be neglected. Such a guessed

nominal reference fiber content has been plot versus a

‘‘nominal average compensated inductance’’ value,

(a) (b)

Fig. 8 a Compensated inductances as from measured induc-

tances along four directions for each cell of HPFRCC50 slab

(values refer to inductances measured at a frequency equal to

4 kHz; angles refer to the casting flow direction, positive if

clockwise; compensated inductances have been calculated to an

average inductance of the reference plain matrix equal to

Lv0 = 1,856,347 mH). b Compensated inductances as from

measured inductances along four directions for each cell of

HPFRCC100 slab (values refer to inductances measured at a

frequency equal to 4 kHz; angles refer to the casting flow

direction, positive if clockwise; compensated inductances have

been calculated to an average inductance of the reference plain

matrix equal to Lv0 = 185,635 mH)


defined as the average, over the whole slab, of the

averages of the values measured along the four

directions for each cell (see Fig. 8). The calibration

of the ‘‘nominal average compensated inductance’’

versus nominal fiber content correlation is shown in

Fig. 11. A linear dependence on the fiber content has

been hypothesized because of the low fiber volume

fraction and the consequently negligible interactions

between fibers, as from the physics fundamentals of

the approach. By means of such a calibrated law, the

average values of compensated inductance for each

cell could be processed to assess whether and to what

extent the local concentration of fibers differed from

the assumed nominal value. Results are shown in

Fig. 12. The detected dispersion of the fibers inside

the slabs appears to be featured by an acceptable

degree of homogeneity and once again coherently

understandable on the basis of the casting flow

kinematics. It can be observed that the initial higher

peak in the fiber content, which is most likely due to

the onset of the laminar casting flow after the

turbulence which occurs where the fresh cementitious

composite is poured, is followed by a slight progres-

sive impoverishment of the fibers (anyway lower than

20%) along the flow, as a result of a dynamic

segregation, which to some extent seems to be

unavoidable.

6 Verification: non-destructive versus destructive

measurements

Data about fiber concentration and orientation

assessed through the analysis of non-destructively

garnered measurements, as detailed in the previous

paragraph, have been finally validated through

destructive evaluation.

As already explained above, after magnetic survey,

each HPFRCC slab was cut into eighteen tiles and

tensile fracture toughness tests were performed on

those specimens with a notch-preordained fracture

plane either orthogonal or parallel (respectively odd

and even numbered cells in Fig. 2) to the casting flow

direction and hence to the preferential orientation of

the fibres.

After the aforementioned tests had been completed,

specimens were broken along the ligament and, also

through the aid of micro-imaging, fibers protruding

from either side of the fracture surface were counted.

Fig. 9 Directions of measured maximum inductance in

HPFRCC-50 (a) and HPFRCC-100 (b) slabs

(a)

(b)

Fig. 10 Fractional compensated inductances parallel and

orthogonal to the flow direction for HPFFRCC-50 (a) and

HPFRCC-100 (b) slabs

Fig. 11 Average compensated inductance versus nominal fiber

content


Fig. 12 Estimated

dispersion of local

concentration of fibers in

HPFRCC-50 (a) and

HPFRCC-100 (b) slabs

(coordinates x and y are

referred to the centroids of

the measuring cells

highlighted in Fig. 1)


This allowed the fiber orientation factor to be calcu-

lated according to the well known formula:

a ¼ nfibers

Af

Vf

ð7Þ

with nfibers specific number of fibers on the fracture

surface, Af cross section area of a single fiber and Vf

fiber volume fraction. With reference to the latter,

calculations have been made either assuming the

nominal fiber dosage (50 kg/m3—Vf = 0.64%;

100 kg/m3—Vf = 1.27%) or the actual one for each

single cell, as either assessed through the analysis of

non-destructively garnered measurements or quanti-

fied by means of destructive testing as it will be further

explained in details.

The acceptable correlation between the fiber ori-

entation factors calculated as above and the fractional

compensated inductances, along the same direction,

calculated according to Eq. 5 (Fig. 13) supports by

evidence the method reliability, at least with reference

to its sensitivity to fiber orientation.

Finally destructive evaluation of fiber concentra-

tion was performed by crushing specimens into a cast-

iron mortar, separating fibers with a magnet and

weighing them; weight was then referred to the

measured dimensions of each specimen. Such an

operation, because of its time consumption and labor

intensiveness, was performed for a limited number of

specimens (actually 10 out of 18 for each slab) and

namely the ones which appear shadowed in Fig. 2.

The data shown in Fig. 14 highlight once again the

reliability of the method which has been hence proved

to be able to detect with sharp sensitivity both fiber

orientation and local average concentration.

7 Conclusions

A new methodology for non-destructive monitoring of

fiber dispersion and orientation in steel fiber rein-

forced cementitious composites has been presented in

this paper. The method is based on ferromagnetic

properties of steel fibers commonly employed in most

of SFRC applications and hence on the modification

which results, as a function of the fiber concentration

and orientation, on the magnetic field path generated

by a probe when leant on the specimen/structure

surface. The main features of the method which are

worth being highlighted for its potential use in quality

control and monitoring of SFRC structural applica-

tions are its ease of use and its insensitiveness to

moisture content and gradients inside the specimen as

well as to the specimen/probe coupling.

The method has been thoroughly and successfully

validated through comparison with destructively mea-

sured dispersion and orientation of the fibers in thin

slabs (25 mm thickness) cast with a self-consolidating

Fig. 13 Correlation between fiber orientation factor and

fractional compensated inductance

(a)

(b)

Fig. 14 Fiber concentration (kg/m3): destructive (D) measure-

ments versus not-destructive (ND) estimates for HPFRCC-50

(a) and HPFRCC-100 (b) slabs


High Performance Fiber Reinforced Cementitious

Composite containing different amounts of fiber

reinforcement. Due to the self compactability of the

mixtures and to an ad-hoc designed casting process,

preferential orientation of the fibers was obtained,

which has been reasonably captured by the method.

Actually the method can work also with thicker slabs,

because, as it has been shown in [31], the probe

generates a significant magnetic flux density also at

depths greater than 25 mm, which allow the detection

of ferromagnetic materials in thicker elements. More-

over it is possible to further increase this capability by

suitably modifying the distance between the pole

pieces.

In a companion paper [27], the effects of the

aforementioned flow-induced orientation as well as of

fiber dispersion on the tensile fracture toughness of the

fiber reinforced composites will be thoroughly exper-

imentally analyzed and correlation with the measure-

ments garnered through the proposed non-destructive

method will be established. This will be also instru-

mental at paving the way to effectively incorporate

non-destructive testing methods into design oriented

procedures for the identification of relevant material

properties.

Work is also ongoing to address the applicability of

the proposed method and set-up to real scale precast

elements and correlate the results to their structural

performance.

Acknowledgments The authors wish to acknowledge the

help of Mr. Stefano Bufalino in performing experimental

measurements and tests and reducing data, in partial fulfilment

of the requirements for his BSc in Civil and Environmental

Engineering.

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