Modified Disk-Shaped Compact Tension Test for Measuring Concrete Fracture Properties
International Journal of Concrete Structures and Materials
Modified Disk-Shaped Compact Tension Test for Measuring Concrete Fracture Properties
He´ ctor Cifuentes
Ta´nˇ a Holu sˇova´
Alfonso Ferna´ ndez-Canteli
A new approach for measuring the specific fracture energy of concrete denoted modified disk-shaped compact tension (MDCT) test is presented. The procedure is based on previous ideas regarding the use of compact tension specimens for studying the fracture behavior of concrete but implies significant modifications of the specimen morphology in order to avoid premature failures (such as the breakage of concrete around the pulling load holes). The manufacturing and test performance is improved and simplified, enhancing the reliability of the material characterization. MDCT specimens are particularly suitable when fracture properties of already casted concrete structures are required. To evaluate the applicability of the MDCT test to estimate the size-independent specific fracture energy of concrete (GF), the interaction between the fracture process zone of concrete and the boundary of the MDCTspecimens at the end of the test is properly analyzed. Further, the experimental results of GF obtained by MDCT tests for normal- and high-strength selfcompacting concrete mixes are compared with those obtained using the well-established three-point bending test. The procedure proposed furnishes promising results, and the GF values obtained are reliable enough for the specimen size range studied in this work.
concrete; fracture behavior; experimental techniques; specific fracture energy; compact tension
Compact tension (CT) tests have been widely and
successfully applied for measuring the fracture properties of
several materials, such as metals (ASTM Standard
E39912E3), asphalt-aggregate mixtures (ASTM Standard
D731313), plastics (ASTM Standard D5045-14) or even composite
materials with limited orthotropy (Pinho et al. 2006). The
compact tension fracture toughness test is essentially
performed to propagate an initial crack by applying equal and
opposite forces to the two holes previously made in the
specimen through tensile clevises and pins as shown in
Fig. 1. Its direct applicability in concrete, however, entails
some inconveniences, such as drilling the holes necessary to
apply the pulling forces and the hazard of a local fracture
originated at these holes. Wittmann et al. (1988) are the
pioneer in the application of CT tests in concrete but using
large specimens in order to avoid premature failures.
Wagoner et al. (2005), tried to apply this test methodology to
smaller and disk-shaped specimens of concrete (more
appropriated in case of specimens obtained from drill cores)
but they ran into troubles obtaining premature failures at the
pulling load holes in about 50% of the tests, thus evidencing
the disability of a direct application of the procedure.
The most usual experimental procedures for measuring the
specific fracture energy (GF) of concrete (Karihaloo 1995)
avoiding the problems associated with the CT tests are the
three-point bending test (TPB) and the wedge splitting test
(WS). The former, carried out on prismatic notched beams,
is the most widespread procedure due to its simplicity and
the satisfactory results it provides (Abdalla and Karihaloo
2003; Bazant 1996; Bazant and Kazemi 1991; RILEM
1985). The latter requires notched compact specimens,
usually cube or prismatic specimens, preventing the
mentioned disadvantages of the conventional CT specimens
Fig. 1 Round compact tensile test specimen and tensile
clevises and pins.
(Bruhwiler and Wittmann 1990; Cifuentes and Karihaloo
2013; Wittmann et al. 1988).
However, when the mechanical and fracture behavior of a
concrete in an already built structure is required, cylindrical
drilled cores are extracted from the concrete structure
allowing the compressive strength, the splitting tensile
strength and the Young’s modulus of concrete to be easily
determined (Abou El-Mal et al. 2015; Harkouss and Hamad
2015). In this case, the CT test seems to be the suitable test
for measurement of the specific fracture energy by using
slice shaped specimens cut off from the cylindrical cores, in
particular if the above mentioned disadvantages in testing
such specimen type are surmounted.
In spite of the CT test method being proposed by a RILEM
recommendation (RILEM 1985), only few papers in the
literature are related to the use of such a test for measuring
the specific fracture energy of concrete, most of them being
referred to specimens with rectangular shape as extracted
from cubic compression specimens (Issa et al. 2000; Pandey
et al. 2016; Van Mier 1991). The utilization of disk-shaped
compact tension (DCT) specimen geometry is common for
the analysis of fracture energy by asphalt materials (Kim
et al. 2009; Wagnoner et al. 2005; Wagoner et al. 2006;
Zofka and Braham 2009), whereas its use by plain concrete
is very limited (Amirkhanian et al. 2011, 2016) mainly due
to the mentioned premature failures originated at the
surrounding edge of the pulling holes.
This work promotes the applicability of the so-called
modified disk-shaped compact tension (MDCT) test, as an
alternative and reliable pulling solution to the conventional
CT or DCT, using also cylindrical shape specimens for
measuring the specific fracture energy of concrete, in
particular when the fracture behavior of a concrete in an already
built structure must be assessed. Basically, the new
procedure consists in applying the pulling force by means of
reinforced bars already built in the specimen, either already
by the specimen concrete casting or by subsequent boring
and gluing, which are clamped in the machine during testing
(Nieto et al. 2014). In this way, outfitting holes in the
specimen is avoided thus lowering the ratio of invalid tests,
due to the local fracture in the pulling holes, practically to
In the following, a description of the proposed method, its
geometry, the way to prepare the specimens and the test set
up is thoroughly detailed. Additionally, an experimental
investigation is carried out to evaluate the applicability of the
method. MDCT tests are performed according to the
workof-fracture method for two different self-compacting
concrete (SCC) mixes (normal- and high-strength concrete). The
size of the specimen ligament area is varied in order to check
the size independency of the specific fracture energy
obtained. The results are compared with those obtained by
applying the well validated TPB tests, leading to the
conclusion that the proposed modified compact tension method
is accurate enough to estimate the specific fracture energy of
concrete in a simple way, representing an optimal alternative
for it to be applied in case of an existing concrete structure. It
should be noted that this MDCT tests can also be applied for
determining other additional fracture parameters, such us the
stress intensity factor or the critical mouth opening
displacement of concrete. Nevertheless, these parameters are
related with equivalent linear-elastic fracture models and this
work is focused on applicability of the fictitious crack
2. Background: Determination of the Size
Independent Specific Fracture Energy of Concrete
2.1 Work-of-Fracture Method
The work-of-fracture method was developed by Hillerborg
et al. (1976) for experimental determination of the specific
fracture energy in concrete The method, based on the
fictitious crack model, is included in a RILEM Standard
Recommendation (RILEM 1985) for measuring the fracture
energy of concrete, Gf. According to this method, the
specific fracture energy of concrete (energy per unit area
necessary to break the concrete) is obtained as follows:
Gf ¼ Alig
where Wf is the work-of-fracture supplied by the external
load (machine) and Alig is the ligament area of the specimen.
Although the main work-of-fracture test methods
traditionally applied to concrete are the TPB and the WS tests
due to their simplicity and their ability of complying with the
main hypothesis required, different kind of tests can be
proposed provided the external work can be easily measured,
the ligament area is localized, the cracking is only caused
due to tensile stresses and no energy dissipation takes place
outside the ligament area. All of these tests must have in
common their requirement of being applied on notched
specimens in order to guarantee the crack propagation being
localized in the ligament area.
The TPB test (Fig. 2a) is the most widely method used for
concrete fracture analysis due to the simple specimen
preparation and execution (Abdalla and Karihaloo 2003;
Bazant 1996; Bazant and Kazemi 1991; RILEM 1985), even
for fiber-reinforced concrete (Cifuentes et al. 2013;
Gopalaratnam and Shah 1987). However, the correct
execution of the TPB method is not exempted of complications
requiring some important aspects as to avoid energy
dissipations outside the ligament area and to reduce the influence
of the specimen geometry and loading type on the results.
Firstly, the supports and the tool employed for the
transmission of the vertical load to the beam have to be properly
designed. Further, the measuring system should be fixed to
the beam to avoid unrealistic vertical deflection
measurements caused by the torsional free-twist of the beam.
According to this, consideration of the vertical displacement
of the hydraulic actuator as the measurement of the vertical
deflection is not correct and a linear variable differential
transformer (LVDT) transducer has to be mounted on a
reference frame (Karihaloo 1995). Lastly, the specimen
Fig. 2 Schematic representation of several usual tests for
measuring the specific fracture energy of concrete.
a Three-point bending, b wedge splitting and c compact
weight, as influencing the experimental results, must be
compensated or taken into account for a correct
determination of the work-of-fracture during the test. As an example,
Guinea et al. propose the utilization of elastomeric springs to
avoid tensile stresses in the ligament area due to the
selfweight (Guinea et al. 1992).
Once the P–d curve is recorded for each specimen tested,
the work-of-fracture is determined as:
where du is the vertical deflection at the end of the test.
The WS test (Fig. 2b), as developed by Linsbauer and
Tschegg (1986) was subsequently modified by Bruhwiler
and Wittmann (1990) proving to be a very stable test for
determining the fracture energy of concrete. The specimens
used in this method are fairly compact requiring small
amounts of material as compared with the notched beams
employed in three-point bending tests. However, the
implementation of this test type requires a more
sophisticated fixture than that implied by the three-point bending test
so that the number of results available in the literature from
WS tests for concrete is scarce (Cifuentes and Karihaloo
2013; Korte et al. 2014; Merta and Tschegg 2013; Vesely´
et al. 2011). The fracture behavior is analyzed by wedging
out the starter notch. The testing has to be carried out using a
closed-loop testing machine and under displacement control
at a very low rate so that the specimen fracture occurs in a
stable manner (Abdalla and Karihaloo 2003; Cifuentes and
Karihaloo 2013). Since the direct application of two pulling
forces to stable split of the specimen entails a great difficulty,
the usual loading arrangement consists in a wedge made
from steel that is mounted between two bearings, which
transform the vertical applied load (F) into two horizontal
splitting loads (P) (Cifuentes and Karihaloo 2013).
Additionally, the specimen is usually placed on a linear support
(steel rod) fixed to the lower plate of the testing machine.
Some researchers have proposed placing two linear supports
in order to eliminate the weight effect of the specimens
(Abdalla and Karihaloo 2003). If bearing friction is
neglected, the splitting load can be calculated as:
where h is one-half of the wedge angle (Fig. 2b). According
to this, an equivalent P-CMOD curve can be obtained from
the recorded F-CMOD curve for each specimen tested, so
that the work-of-fracture is calculated as follows:
where CMODu, is in this case the crack mouth opening
displacement at the test completion.
In metallic materials, testing CT specimens represents a
usual procedure to determine fracture parameters, whereby
ASTM Standard E-399 specifies the geometry and general
configuration of this kind of tests. In such CT tests (Fig. 2c)
an eccentric tensile force has to be applied on the ligament
area of a previously notched sliced specimen with circular or
rectangular geometry. The crack opening displacement of the
notch lips at the level of the axis load must be recorded. In
this way, the load-COD (P-COD) curve is obtained and the
work-of-fracture is directly obtained as the area under the
curve. The tools necessary to perform the conventional CT
tests on concrete are difficult to be designed and their
implementation is not as easy as in case of the TPB test.
2.2 Size Dependency of the Specific Fracture Energy of Concrete
The values determined by the work-of-fracture method as
proposed in RILEM recommendation (RILEM 1985) are
dependent on the specimen size and shape used in the test, as
demonstrated and analyzed by several researchers in the past
(Hu and Wittmann 1992; Kwon et al. 2008; Muralidhara
et al. 2011; RILEM 2004; Vydra et al. 2012). The two most
popular models to obtain a size-independent specific fracture
energy of concrete (also called true fracture energy
(Karihaloo et al. 2003)) are the boundary effect model of Hu and
Wittmann (1992) and the experimental correction model to
avoid energy dissipations proposed by Guinea et al. (Elices
et al. 1992; Guinea et al. 1992; Planas et al. 1992). Although
these models are based on different fundamentals, they are
related to each other. Cifuentes et al. (2013) showed that if
the size-dependent Gf measured by the RILEM method is
corrected according to the method of Elices and co-workers
(Elices et al. 1992; Guinea et al. 1992; Planas et al. 1992) or
that of Hu and Wittmann (1992) (the latter admits a
simplification as proposed by Karihaloo et al. (2003) if the notch
to depth ratios are well apart from each other), then the
resulting specific fracture energy GF is very nearly the same
and independent of the size of the specimen.
The methodology of Hu and Wittmann (1992), based on
the local fracture energy concept as thoroughly detailed in
several papers (Cifuentes and Karihaloo 2013; Hu and
Wittmann 1992), states that the size effect on Gf (measured
specific fracture energy according to work-of-fracture
method) is caused by a variation of the fracture process zone
when the crack approaches the free boundary surface of the
specimen at test completion (Hu and Wittmann 1992). On
the other hand, among the several sources of experimental
errors analyzed by Guinea et al., the most significant proves
to be the influence of the non-measured fracture energy of
concrete due to the curtailment of the upper tail of the P–d
curve (Elices et al. 1992). Accordingly, the methodology
proposed by Guinea and co-workers (Elices et al. 1992;
Guinea et al. 1992; Planas et al. 1992) involves adding the
non-measured work-of-fracture due to the curtailment of the
tail of the load-central deflection (Q–d) curve recorded in the
three-point bend test.
Guinea et al. demonstrate that the non-measured
work-offracture (Wf nm) for a three-point bending test of a notched
beam with compensated self-weight, can be determined by
extrapolating the upper tail of the P–d curve beyond the
limits of the recorded test results using the expression:
where A is the fitting experimental coefficient of the tail of
the P’–d curve between d0 and du. d0 is usually considered
as the vertical displacement corresponding to a load of 5% of
the peak load (Pmax) (Lee and Lopez 2014; RILEM 2007)
and du is the last recorded mid-span deflection of the
specimen at the end of the test (Fig. 3). Once the
nonmeasured work-of-fracture is estimated, the size-independent
fracture energy of concrete is obtained as (Elices et al. 1992):
Fig. 3 P–d curve for a three-point bend test showing the
measured (Wf) and non-measured (Wf.nm)
3. Description of the MCT Specimens and Test
The MDCT specimens are based on the conventional DCT
test concept relative to a notched specimen with cylindrical
shape (Nieto et al. 2014), allowing the pulling force to be
applied in a simple way without the inconvenience of
possible material local fractures at the pulling holes due to stress
concentration, as would happen by conventional DCT
concrete specimens. Initially, the modified disk-shaped compact
tension test solution included sliced shape specimens cut off
from cylindrical specimens as used in standard compression
tests or from drill cores as extracted from real constructions
for evaluating age and conditions of the material. In such a
case, the pulling bars must be allocated and glued (e.g. by
using epoxy resin) into the holes drilled out into the
specimens in transversal direction to the notch milled, as shown in
Fig. 4. In the meantime, more simple and practical solutions,
here denoted ‘‘ad-hoc’’ specimens, are developed to facilitate
their preparation in the laboratory. In both MDCT solutions,
i.e. ‘‘drill-out’’ and ‘‘ad-hoc’’ specimens, the geometry is
apparently the same, consisting in notched cylinders of a
suitable thickness, B, furnished with the pulling bars, as
shown in Fig. 4, though requiring two different
manufacturing procedures. In this work ‘‘ad-hoc’’ specimens are
studied. /cs is the outside specimen diameter, /sb is the
pulling bar diameter, a is the initial notch depth measured
from load axis, B is the specimen thickness, e is the notch
width, Alig is the ligament area, and a is the relative notch
From these values, the ligament as the area of specimen to
be fractured, is calculated as the product of the length of the
Fig. 4 Characteristic geometry of the MCT specimens.
ligament times the thickness of the specimen, see Eq. (7).
On its turn, the dimensionless relative notch length a as
defined in Eq. (8), is considered the reference parameter to
be studied in the modified compact tension tests of concrete,
the same as in the original compact tension tests (Harkouss
and Hamad 2015).
a ¼ a=W
Once the specimens are prepared, the execution of the test
is very simple using a universal machine equipped with two
clamps vertically aligned. This machine and the fixtures
needed are usually available in standard laboratories. The
procedure consists in clamping one of the ends of the pulling
bar to the lower grips, which stay fixed, while the other bar is
clamped to the upper grips, which move vertically up
transmitting the load to the specimen. Thus, as the
displacement of the upper grips increases, a crack is generated
in the specimen starting at the notch tip until achieving the
complete rupture of the specimen. Tests must be performed
by displacement control of the machine and the crack
opening displacement in the notch lips at the level of the
alignment of the pulling bars (COD) should be controlled
and recorded. Then, the P-COD curve is obtained and the
work-of-fracture, Wf, determined in a similar way as in the
TPB and WS tests as the area under the P-COD curve. The
specific fracture energy of concrete (probably
size-dependent), Gf, is then given by:
where CODu is the crack opening displacement at the test
completion. In this case, the load directly applied by the
testing machine is the load that produces the crack opening
without the need of any further transformation, as in case of
the original CT or DCT test. It should be noted that the crack
mouth opening displacement (CMOD) can be also measured
and the test can be alternatively controlled by this value.
Nevertheless, according to the procedure herein described
measurement of the CMOD is not necessary and the clip
gauge transducer can be located at the notch lips and aligned
with the steel bar axis to measure the COD.
4. Experimental Program
In order to confirm the applicability of the MDCT test for
measuring the specific fracture energy of concrete, a
comprehensive experimental investigation is carried out. Several
geometry configurations of the MDCT specimens with
varying size of the ligament area are tested in order to study
the influence of the specimen geometry on the results.
Moreover, TPB tests are also performed to obtain a reference
size-independent value of the specific fracture energy of
concrete GF with the aim of comparing and verifying the
results from the MDCT tests.
Table 1 Constituents and mix proportions for normal- and high-strength self-compacting concrete mixes.
Coarse aggregates (crushed
limestone) \ 10 mm
Sand \ 2 mm
Limestone powder (\2 mm)
Super-plasticizer (SIKA Viscocrete 20HE)
Flow spread (mm)
Both tests, MDCT and TPB, are performed for the same
concrete mixes. To extend the validity of the results, two
different self-compacting concrete mixes are designed. One
of the mixes is made of normal-strength concrete (NSC) and
the other mix, of high-strength concrete (HSC). In both
cases, an ordinary Portland cement CEMII/B-V 32.5R is
used with 10 mm maximum aggregate size. Their target
cube compressive strengths are 40 and 100 MPa,
respectively. The mix proportions and constituents are shown in
Table 1. In case of HSC mixes micro-silica has been used to
densified the concrete matrix.
The characteristic compressive strength (fc) is determined
from 100 mm3 cubes in accordance with UNE
EN129303:2009. The indirect tensile strength (fst) is obtained from
splitting tests (Brazilian tests) using 100 mm diameter by
200 mm long cylinders, according to UNE
EN129306:2010. The static elastic modulus of concrete (Ec) is
determined according to the UNE EN12390-13:2014 by
gradually loading a cylindrical specimen in compression to
approximately a third of its failure load and measuring the
corresponding strain from 30 mm strain gauges. The values
of the mean and coefficient of variation measured for the
mechanical properties of both concrete mixes are given in
4.2 Modified Disk-Shaped Compact Tension Tests
In this study, ‘‘ad hoc’’ MDCT rather than ‘‘drilled out’’
specimens are prepared for being tested in the laboratory,
allowing the same concrete to be employed in both MDCT
and TPB tests and the results to be conveniently compared.
The procedure of manufacturing of the MDCT specimens
is fairly simple. In order to obtain cylindrical shape
specimens, a PVC pipe with internal diameter of 153 mm is taken
as a mold, the outside diameter of specimens being
determined by this value (Fig. 5a). Next, the pulling steel bars,
which will be embedded in the concrete mass after casting,
are threaded through the molds at the prescribed position, W,
for the prospective specimen axis with respect to the
ligament back side, and at regular vertical axial distances. Usual
corrugated steel bars with 8 mm in diameter are
advantageously employed (Fig. 5b). At this time, the concrete mixes
are poured into the molds and cured in a water tank during
28 days. Thereafter, sliced shape specimens of 60 mm
thickness are cut off from the cylindrical molds so that the
steel bars remain in the mid-plane of the specimen (Fig. 5c).
To diminish the effect of segregation of aggregates because
of the height of the cylinder molds and the presence of the
steel bars, the bottom part of the filled cylinders is not
considered in obtaining the samples and specimens are
obtained from the central part of the cylinders. Lastly, the
notch is mechanized according to the prescribed notch depth
chosen (Fig. 5d). The final outlook of the notched sliced
specimens is shown in Fig. 6. In Table 3 the dimensions of
the different MDCT specimens tested are shown whereby
two different distances from the load axis (axis of the steel
pulling bars) to the ligament back side of the specimen and
three different relative notch depths are chosen. In that way,
six different sizes of the ligament area are tested for each
concrete mix and the influence of the specimen geometry
Table 2 Mechanical properties of NSC and HSC concrete mixes.
can be analyzed. As stated by different researchers, the size
effect on fracture energy can be accurately analyzed by
varying the relative notch depth (Cifuentes and Karihaloo
2013; Hu and Wittmann 1992). In this case, even if the
outside diameter of specimen remains the same, a variation
in the position of the axis of the steel pulling bars allows the
effective height (size) of the specimens to be varied. It
should be noted that the dimension of the outside diameter of
the specimen, in this case 153 mm, practically coincides
with that of the standard cylinder specimen used for
compressive strength determination and remains in the same
order of magnitude as the depth of 100 mm commonly
exhibited by the prismatic used for the GF determination in
the case of TPB tests.
All tests are carried out in a servohydraulic test machine
MTS Bionix with 25 kN of load capacity, see Fig. 7. Tests
are performed under displacement control of the machine
with a rate of 0.2 mm/min. All deformations and
displacements of the specimens during the tests are measured by a
3-D digital image correlation equipment ARAMIS of GOM.
This technique is successfully used by different researchers
to study cracking and fracture behavior of concrete (De
Wilder et al. 2016; Nam and Lee 2015; Shah and Kishen
2011). Alternatively, a clip gauge transducer located at the
notch lips and aligned with the steel bar axis could be
additionally used. In that way, the full load-COD (P-COD)
curves for all specimens would be obtained after
post-processing of the digital images recorded during the test.
Accurate determination of such a load-COD is crucial for
assessing the work-of-fracture applied to split the specimen
into two halves.
4.3 Three-Point Bending Tests
With the aim of comparing the MDCT test results with
those using standard procedures, three-point bend tests with
prismatic notched specimens are performed according to the
experimental requirements of the work-of-fracture method
described in the RILEM recommendation (RILEM 1985).
The size-independent value of the specific fracture energy
GF is determined according to the procedure proposed by
Guinea et al. (Elices et al. 1992; Guinea et al. 1992; Planas
et al. 1992). Table 4 shows the geometrical dimensions of
the specimens as displayed in Fig. 8.
Four samples are tested for each mix of concrete, from
whose results the mean value and the coefficient of
variation for every analyzed parameter are obtained. The initial
tangent correction due to crushing of concrete at the
supports is applied for all specimens. Three-point bending tests
are performed with the indicated self-weight compensation.
All tests are carried out in a closed-loop servo-hydraulic
dynamic 25 kN MTS Bionix testing machine. The rate of
loading is controlled by a crack mouth opening
displacement (CMOD) gauge at a very low rate (0.001 mm/s) so
that the fracture occurs in a stable manner. The CMOD
displacement is measured with a clip gauge transducer
whereas a LVDT linear displacement transducer, fixed to
the bottom of the specimen by means of a reference frame,
is used to measure the vertical displacement at the midpoint
(Fig. 9). The load-CMOD (P-CMOD) and
load–displacement (P-d) curves are recorded for all specimens. The test
interruption is decided as a function of the last displacement
value being obtained by the fracture curve for any of these
Fig. 6 Final outlook of the MDCT specimens for different
notch depths: a a = 0.1, b a = 0.3 and c a = 0.5.
5.1 MDCT Tests
The recorded P-COD curves obtained from the MDCT
tests carried out for the different geometries, as indicated in
Table 3, are shown in Fig. 10. Although four samples of
Fig. 7 MDCT test of a cylindrical sliced shape specimen with
a = 0.1.
each relative notch depth are tested, only one representative
curve is just represented for each a in order to facilitate an
overview of the graphs.
Sometimes, due to the pulling bars stiffness and their rigid
build into the concrete, an affected part of the load-COD
curve may be observed at the upper tail of the curve when
the crack is approaching the ligament back free boundary
(see Fig. 10). At the test beginning, the crack opening
displacement necessary to break the concrete is relatively low
so that the moments arising by bending of the pulling bars
are negligible. Nevertheless, as the test progresses and the
necessary COD to further opening of the crack increases, the
pulling bar-concrete interaction acts against crack
propagation. As a result of such phenomenon, the observed behavior
evidences in the most cases a very long tail trending to a
constant value of the load, which does not tend
asymptotically to zero while in some few cases, an increase of the load
can be even observed. However, the fracture process of the
concrete seems to happen correctly as the crack path always
runs in perpendicular direction to the loading axis. Some
Table 3 Dimensions of the MDCT specimens tested in the experimental program.
Table 4 Geometrical parameter values of notched beams used in TPB tests.
a = a/D
Fig. 8 Geometrical shape parameters of notched specimens
used in the TPB tests.
Fig. 9 Three-point bend test of prismatic notched specimens
with weight compensation.
images of the crack propagation as captured by the 3D
Aramis equipment during one of the MDCT tests are shown
in Fig. 11. As can be observed, the crack propagation path is
that being expected for this kind of test and the opening
mode corresponds to pure mode I.
In order to amend this discordant behavior at the tail of the
curve, i.e. the end of the test, a curve processing, based on
the adjustment of the tail proposed by Guinea et al. in case of
TPB tests, is proposed. The P-COD curve corresponding to a
NSC-MDCT test with height W = 112.5 mm and relative
notch depth a = 0.5 is shown in Fig. 12a exhibiting, both in
the ascending part but also at the most part of the descending
branch until a certain small value of the load, a typical shape
as expected from the work-of-fracture method, while close to
which represents the area under the P-COD curve until the
CODu value. The size-independent specific fracture energy
of concrete can be now determined as follows:
Assuming the proposal is correct, its applicability can be
checked by comparing the specific fracture energy of
concrete just obtained with that from the TPB tests since the
concrete mixes for MDCT and TPB tests are the same and no
variation due to the material is expected.
Table 5 shows the main results necessary to calculate the
specific fracture energy of concrete according to the
workof-fracture method applied to MDCT specimens, where
COD0 is the crack opening displacement at the level of the
loading axis considered for fitting the P-COD curve, CODu
is the ultimate crack opening displacement considered to
avoid the affected part of the curve at the end of the test, A is
the coefficient for fitting the tail of the P-COD curve, Wf.nm
is the non-measured work-of-fracture as indicated in
the end of the test the curve behavior becomes affected. The
proposal suggests removing the affected part for each of the
specimens tested what implies part of the P-COD curve not
being included as an area under the curve contributing to the
total work-of-fracture being involved in the concrete fracture
of the ligament. Accordingly, this area should be estimated
in order to obtain this non-measured work-of-fracture as
explained by Guinea et al. for TPB tests (Kwon et al. 2008).
The same concept can be here applied once the tail of the
remaining curve is fitted using the following expression:
where P0 = 0 for CODu. The non-measured
work-offracture can be estimated as:
According to Fig. 11b, the COD0 is the initial crack
opening displacement considered for fitting the tail of the
curve, CODu is the ultimate crack opening displacement
until the P-COD is found to be correct and A is the
coefficient for fitting the tail of the curve between COD0 and
CODu as shown in Fig. 11b.Once the curve is amended, the
measured work-of-fracture is given by:
Fig. 10 Load-COD curves obtained from MDCT tests: a, b for normal-strength concrete and c, d for high-strength concrete.
Eq. (12), Wf m is the measured work-of-fracture under the
PCOD curve, Wf T is the total work-of-fracture, Alig is the
ligament area of the different specimens and GF is the
sizeindependent specific fracture energy of concrete.
The values considered for CODu in this work are those
corresponding to a load of about the 15% of the peak load in
the softening branch of the P-COD diagram. In case of
COD0, the values adopted are 0.55CODu approximately.
As may be observed in the results shown in Table 5, the
values of the specific fracture energy of concrete obtained as
indicated above (i.e. fitting the tail of the curve after
eliminating the affected part of the curve due to the interaction
between pulling bar and concrete) are roughly the same,
independently of the relative notch depth and height of the
pulling bars. In case of NS concrete, the minimum mean
obtained value is 155.2 N/m for W = 112.5 mm and
a = 0.3 and the maximum obtained value is 164.4 N/m for
W = 112.5 mm and a = 0.5. The maximum coefficient of
variation of results is 15%, which means that values of GF
obtained for the different NSC-MDCT tests are statistically
the same. A similar analysis, with the same conclusion, can
be made for the HSC-MDCT test results. In that way,
according to the proposed procedure, the GF values obtained
are not dependent of the specimen geometry in the range of
the sizes tested, as required for a parameter to be considered
as a material property. It should be noted, that to reduce the
effect of the rigid union between steel bars and concrete on
the tail of the behavior curve of concrete another fixture
system, allowing the rotation between the pulling bars and
concrete, could be also employed.
5.2 TPB Tests
In Table 6, the mean value and the coefficient of variation of
the material parameters corresponding to both mixes of
concrete used to obtain the specific fracture energy of concrete are
presented, where m is the mass of the specimen, d0, the initial
value of the displacement considered by fitting the tail of the
curve, du, the displacement when the test is stopped, Wf.m, the
measured work-of-fracture under the load–displacement
curve, A, the coefficient of fitting the upper tail of the curve,
Wf nm, the non-measured work-of-fracture according to
Eq. (11), Alig, the real ligament area measured in the
specimens, and GF, the specific fracture energy of concrete, which is
size-independent according to Guinea et al.
This procedure is repeatedly validated by different
researchers, and the value of GF so determined is
demonstrated to be correct and claimed as being the
size-independent specific fracture energy of concrete.
6. Analysis of Results
Table 7 summarizes the GF results obtained for the two
different concrete mixes studied in the present work using
Fig. 11 a–f Crack path evolution during the MDCT test for one of the specimens tested.
the TPB and MDCT tests. In case of MDCT test, the result
represents the mean value obtained for the different heights
W and relative notch depths a considered in this work.
As can be seen, the results from the MCT tests are slightly
higher than those from TPB (less than 7% in the worst case).
This can be attributed to the bending stiffness of the steel
Concrete W (mm)
Table 5 Results from MDCT tests.
A (Nmm2) Wf NM (Nmm) Wf M (Nmm)
pulling bars stiffness and the necessary compatibility
between them and the concrete specimen, which implies
slightly higher energy consumption. However, from a
statistical point of view, considering the difference between the
mean values of each test geometry and concrete and with the
obtained coefficient of variation the values obtained in case
of MDCT are roughly the same as those obtained in case of
TPB and the estimation of GF, according to the proposed
Modified Disk-Shaped Compact Tension test method, is
considered to be reliable.
The principal conclusions derived from this work are the
– Enforced bending of the pulling bars as the crack opens,
due to the bar stiffness and the necessary compatibility
between the latter and the concrete, influences the stress
distribution along the specimen ligament. As a result, an
affected course is noticed at the upper tail of the P-COD
curve, i.e. at the end of the test. However, in the
remaining zones of the curve, in particular till the
immediate post-peak part, this effect is negligible and the
specimen behavior is entirely satisfactory.
The affected part of the curve course is amended by using a
similar procedure to that proposed by Guinea et al., which
provides a size-independent specific fracture energy of
concrete, GF, assessed and compared with that resulting
from well validated TPB tests for the same concrete. The
results prove that the MDCT test provide reliable results
within the range of variation of those for the TPB test, at
least for the specimen sizes considered in this work.
Future work is envisaged to define analytically the
correction of the P-COD curve at the end of the test as a
function of the interaction between steel bar and
Authors would like to acknowledge the partial financial
supports from the following research projects:
BIA201348352-P (Ministry of Economy and Competitiveness of
Spain), SV-PA-11-012 (Department of Education and
Sciences of the Asturian Regional Government) and
16-18702S (Czech science foundation).
This article is distributed under the terms of the Creative
C o m m o n s A t t r i b u t i o n 4 . 0 I n t e r n a t i o n a l L i c e n s e
permits unrestricted use, distribution, and reproduction in any
medium, provided you give appropriate credit to the original
author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Abdalla , H. M. , & Karihaloo , B. L. ( 2003 ). Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests . Magazine of Concrete Research , 55 ( 2 ), 133 - 141 .
Abou El-Mal , H. S. S. , Sherbini , A. S. , & Sallam , H. E. M. ( 2015 ). Mode II fracture toughness of hybrid FRCs . International Journal of Concrete Structures and Materials , 9 ( 4 ), 475 - 486 . doi:10.1007/s40069- 015 - 0117 -4.
Amirkhanian , A. , Spring , D. , Roesler , J. , Park , K. , & Paulino , G. ( 2011 ). Disk-Shaped Compact Tension Test for Plain Concrete . In Transportation and Development Institute Congress 2011 (pp. 688 - 698 ). American Society of Civil Engineers. doi:10.1061/41167(398)66
Amirkhanian , A. , Spring , D. , Roesler , J. , & Paulino , G. ( 2016 ). Forward and inverse analysis of concrete fracture using the disk-shaped compact tension test . ASTM Journal of Testing and Evaluation , 44 , 625 - 634 .
Bazant , Z. P. ( 1996 ). Analysis of work-of-fracture method for measuring fracture energy of concrete . Journal of Engineering Mechanics , ASCE, 122 ( 2 ), 138 - 144 .
Bazant , Z. P. , & Kazemi , M. T. ( 1991 ). Size dependence of concrete fracture energy determined by RILEM work-offracture method . International Journal of Fracture , 51 , 121 - 138 .
Bruhwiler , E. , & Wittmann , F. H. ( 1990 ). The wedge splitting test: A method of performing stable fracture mechanics tests . Engineering Fracture Mechanics , 35 ( 1-3 ), 117 - 125 .
Cifuentes , H. , Alcalde , M. , & Medina , F. ( 2013a ). Measuring the size-independent fracture energy of concrete . Strain , 49 ( 1 ), 54 - 59 .
Cifuentes , H. , Garc´ıa , F. , Maeso , O. , & Medina , F. ( 2013b ). Influence of the properties of polypropylene fibres on the fracture behaviour of low-, normal- and high-strength FRC . Construction and Building Materials , 45 , 130 - 137 .
Cifuentes , H. , & Karihaloo , B. L. ( 2013 ). Determination of sizeindependent specific fracture energy of normal- and highstrength self-compacting concrete from wedge splitting tests . Construction and Building Materials , 48 , 548 - 553 .
De Wilder , K. , De Roeck , G. , & Vandewalle , L. ( 2016 ). The use of advanced optical measurement methods for the mechanical analysis of shear deficient prestressed concrete members . International Journal of Concrete Structures and Materials , 10 ( 2 ), 189 - 203 . doi:10.1007/s40069- 016 - 0135 -x.
Elices , M. , Guinea , G. V. , & Planas , J. ( 1992 ). Measurement of the fracture energy using three-point bend tests: Part 3- Influence of cutting the P-d tail . Materials and Structures , 25 , 327 - 334 .
Gopalaratnam , V. S. , & Shah , S. P. ( 1987 ). SP105-01 Failure mechanisms and fracture of fiber reinforced concrete . ACI Special Publication , 105 , 1 - 26 .
Guinea , G. V. , Planas , J. , & Elices , M. ( 1992 ). Measurement of the fracture energy using three-point bend tests: Part 1- Influence of experimental procedures . Materials and Structures , 25 ( 4 ), 212 - 218 .
Harkouss , R. H. , & Hamad , B. S. ( 2015 ). Performance of high strength self-compacting concrete beams under different modes of failure . International Journal of Concrete Structures and Materials , 9 ( 1 ), 69 - 88 . doi:10.1007/s40069- 014 - 0088 -x.
Hillerborg , A. , Mode´er, M. , & Petersson , P. E. ( 1976 ). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements . Cement and Concrete Research , 6 , 773 - 782 .
Hu , X. Z. , & Wittmann , F. H. ( 1992 ). Fracture energy and fracture process zone . Materials and Structures , 25 ( 6 ), 319 - 326 .
Issa , M. , Issa , M. , Islam , M. , & Chudnovsky , A. ( 2000 ). Size effects in concrete fracture-Part II: Analysis of test results . International Journal of Fracture , 102 ( 1 ), 25 - 42 . doi: 10.1023/A:1007677705861.
Karihaloo , B. L. ( 1995 ). Fracture mechanics and structural concrete . USA: Longman Scientific and Technical Publishers.
Karihaloo , B. L. , Abdalla , H. M. , & Imjai , T. ( 2003 ). A simple method for determining the true specific fracture energy of concrete . Magazine of Concrete Research , 55 ( 5 ), 471 - 481 .
Kim , M. , Buttlar , W. , Baek , J. , & Al-Qadi , I. ( 2009 ). Field and laboratory evaluation of fracture resistance of Illinois hotmix asphalt overlay mixtures . Transportation Research Record: Journal of the Transportation Research Board , 2127 , 146 - 154 . doi:10.3141/ 2127 - 17 .
Korte , S. , Boel , V. , De Corte , W. , & De Schutter , G. ( 2014 ). Static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedge-splitting tests . Construction and Building Materials , 57 , 1 - 8 . doi:10.1016/j.conbuildmat. 2014 .01.090.
Kwon , S. , Zhao , Z. , & Shah , S. ( 2008 ). Effect of specimen size on fracture energy and softening curve of concrete: Part II. Inverse analysis and softening curve . Cement and Concrete Research , 38 ( 8-9 ), 1061 - 1069 . doi:10.1016/j.cemconres. 2008 .03.014.
Lee , J. , & Lopez , M. M. ( 2014 ). An experimental study on fracture energy of plain concrete . International Journal of Concrete Structures and Materials , 8 ( 2 ), 129 - 139 . doi: 10.1007/s40069- 014 - 0068 -1.
Linsbauer , H. N. , & Tschegg , E. K. ( 1986 ). Fracture energy determination of concrete with cube-shaped specimens . Zement und Beton , 31 , 38 - 40 .
Merta , I. , & Tschegg , E. K. ( 2013 ). Fracture energy of natural fibre reinforced concrete . Construction and Building Materials , 40 , 991 - 997 . doi:10.1016/j.conbuildmat. 2012 .11.060.
Muralidhara , S. , Raghu Prasad , B. K. , Karihaloo , B. L. , & Singh , R. K. ( 2011 ). Size-independent fracture energy in plain concrete beams using tri-linear model . Construction and Building Materials , 25 ( 7 ), 3051 - 3058 . doi: 10.1016/j.conbuildmat. 2011 .01.003.
Nam , I. W. , & Lee , H. K. ( 2015 ). Image analysis and DC conductivity measurement for the evaluation of carbon nanotube distribution in cement matrix . International Journal of Concrete Structures and Materials , 9 ( 4 ), 427 - 438 . doi:10.1007/s40069- 015 - 0121 -8.
Nieto , B. , Lozano , M. , & Seitl , S. ( 2014 ). Determining fracture energy parameters of concrete from the modified compact tension test . Frattura ed Integrita` Strutturale, 30 , 383 - 393 . doi:10.3221/IGF-ESIS. 30 .46.
Pandey , S. R. , Kumar , S. , & Srivastava , A. K. L. ( 2016 ). Determination of double-K fracture parameters of concrete using split-tension cube: A revised procedure . International Journal of Concrete Structures and Materials . doi: 10.1007/s40069- 016 - 0139 -6.
Pinho , S. T. , Robinson , P. , & Iannucci , L. ( 2006 ). Fracture toughness of the tensile and compressive fibre failure modes in laminated composites . Composites Science and Technology , 66 ( 13 ), 2069 - 2079 . doi:10.1016/j.comp scitech. 2005 .12.023.
Planas , J. , Elices , M. , & Guinea , G. V. ( 1992 ). Measurement of the fracture energy using three-point bend tests: Part 2- Influence of bulk energy dissipation . Materials and Structures , 25 , 305 - 312 .
RILEM. ( 1985 ). TCM-85: Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams . Materials and Structures , 18 ( 106 ), 287 - 290 .
RILEM. ( 2004 ). TC QFS: ''Quasibrittle fracture scaling and size effect''- Final report. Materials and Structures , 37 ( 8 ), 547 - 568 .
RILEM. ( 2007 ). TC 187-SOC: Experimental determination of the stress-crack opening curve for concrete in tension . Final Report of RILEM Technical Committee.
Shah , S. G. , & Kishen , J. M. C. ( 2011 ). Fracture properties of concrete-concrete interfaces using digital image correlation . Experimental Mechanics , 51 ( 3 ), 303 - 313 . doi: 10.1007/s11340- 010 - 9358 -y.
Van Mier , J. G. M. ( 1991 ). Mode I fracture of concrete: Discontinuous crack growth and crack interface grain bridging . Cement and Concrete Research , 21 ( 1 ), 1 - 15 . doi: 10.1016/ 0008 -8846(91) 90025 - D .
Vesely ´ , V. , Routil , L. , & Seitl , S. ( 2011 ). Wedge-splitting testdetermination of minimal starting notch length for various cement based composites part I: Cohesive crack modelling . Key Engineering Materials , 452 - 453 , 77 - 80 .
Vydra , V. , Trt´ık , K. , & Voda´k, F. ( 2012 ). Size independent fracture energy of concrete . Construction and Building Materials , 26 ( 1 ), 357 - 361 .
Wagnoner , M. P. , Buttlar , W. G. , & Paulino , G. H. ( 2005 ). Diskshaped compact tension test for asphalt concrete fracture . Experimental Mechanics , 45 ( 3 ), 270 - 277 . doi:10.1007/ BF02427951.
Wagoner , M. , Buttlar , W. , Paulino , G. , & Blankenship , P. ( 2006 ). Laboratory testing suite for characterization of asphalt concrete mixtures obtained from field cores . Asphalt Paving Technology , 75 , 815 - 852 .
Wittmann , F. H. , Rokugo , K. , Br u¨hwiler, E. , Mihashi , H. , & Simonin , P. ( 1988 ). Fracture energy and strain softening of concrete as determined by means of compact tension specimens . Materials and Structures , 21 , 21 - 32 .
Zofka , A. , & Braham , A. ( 2009 ). Comparison of low-temperature field performance and laboratory testing of 10 test sections in the Midwestern United States . Transportation Research Record: Journal of the Transportation Research Board , 2127 , 107 - 114 . doi:10.3141/ 2127 - 13 .