ABSTRACT
Results are reported from a study aimed at investigating the correlation between the post-peak compressive response and the post-cracking behavior in tension and bending of various steel fiber reinforced concretes (FRC). The test program consisted of compressive, flexural, and tensile tests conducted on specimens from 24 batches of concrete. Four different types of hooked-end steel fibers were used in volume fractions of 0.5, 0.75, 1.0, and 1.5%. Concrete mixtures had a target compressive strength of either 41 or 69 MPa. Of the parameters investigated, it was found that the post-peak slope of FRC in compression was most correlated with the peak post-cracking flexural strength and the flexural strength measured at a mid-span deflection of approximately L/450 (1 mm) for an ASTM C1609-compliant specimen with a depth of 150 mm. Scatter in flexural and tensile test results decreased significantly when T50, a relative measure of viscosity, was greater than one second.

1. INTRODUCTION
Well distributed, discreet deformed steel fibers provide resistance to opening and propagation of cracks
in concrete. As a result, use of fiber reinforced concrete (FRC) usually leads to improved shear strength
and deformation capacity in reinforced concrete members [1, 2].
Despite the advantages of using FRC, there are also challenges that have slowed the widespread
adoption of FRC materials in practice [3]. One of these challenges is the difficulty of conducting the
multiple quality control tests required to characterize the load-deformation response of an FRC mixture.
In particular, engineers may be unable to use the post-peak compression response of FRC, which can
be similar to that of well confined concrete, in design without a consistent and readily available means
of specifying and verifying performance.
To potentially limit the scope of the test program required to characterize FRC behavior, the current
study examines correlations between the post-peak response of FRC under compression and postcracking
results from flexural and tensile tests. Results may lead to indirect means of qualifying FRC
mixtures for use in applications that benefit from the post-peak toughness of FRC.

2. RESEARCH SIGNIFICANCE
Results from tensile, compressive, and flexural tests are reported for FRC mixtures having four different
types of fibers in volume fractions of 0.5, 0.75, 1.0, and 1.5%. An effort has been made to quantify the
extent to which the results from different types of tests are correlated, with the aim of reducing the
number of types of tests required to characterize and qualify FRC mixtures for use in practice. Reported
results indicate that mixtures with T50 values less than one second are prone to exhibit a high amount
of scatter in tests of mechanical properties.

3. MATERIALS
3.1. Concrete Mixtures
Self-consolidating concrete was used as the base for the FRC used in this study to eliminate potential
workability problems associated with addition of large amounts of fibers. The result, which has been
called self-consolidating fiber reinforced concrete, is a highly workable concrete after addition of fibers
[4]. No vibration or rodding was therefore used when casting the specimens.
Concrete mixtures with target compressive strengths of 41 and 69 MPa were used in this study. The
mixture proportions prior to addition of fibers are listed in Table 1.

3.2. Fiber Types
The four types of hooked-end steel fibers used in this study are shown in Figure 1. These are the RC-
80/30-BP fiber, with a length of 30 mm, an aspect ratio of 80, and a tensile strength of 2300 MPa; the
RC-55/30-BG fiber, with a length of 30 mm, an aspect ratio of 55, and a tensile strength of 1350 MPa;
the 4D RC-65/60-BG fiber, with a length of 60 mm, an aspect ratio of 65, and a tensile strength of 1500
MPa; and the 5D RC-65/60-BG fiber, with a length of 60 mm, an aspect ratio of 65, and a tensile
strength of 2300 MPa. All four fibers are manufactured by Bekaert Corporation.

4. TEST PROGRAM
A series of tests were conducted on FRC mixtures having a target compressive strength of either 41 or
69 MPa. Except for two batches that did not have fibers, each batch of concrete had one of four types
of hooked steel fibers in volume fractions of 0.5, 0.75, 1.0, or 1.5%. Table 2 shows all combinations of
fiber type and volume fraction that were considered in this study. Specimens from each batch were
subjected to a test program consisting of compressive, flexural (un-notched beams), and tensile tests
conducted on five samples of each type.

4.1. Uniaxial Compression Tests
Compression tests were conducted on 150 by 300 mm cylindrical concrete specimens in accordance
with ASTM C39 [5] using a 2670 kN hydraulic test frame. An infrared-based non-contact position
sensor system was used to record the position of 16 independent markers fixed to the specimen and test
frame (shown in Figure 2). Up to the peak load, longitudinal strains were calculated based on the
displacement of markers numbered 3, 4, 7, and 8. After the peak load, the relative displacement between

loading platens (recorded with markers numbered 15 and 16) was used to estimate longitudinal cylinder
strains because the location of markers fixed to the specimen became sensitive to localized damage.
The feature of the test results most relevant to the current study was the post-peak slope of the recorded
stress versus longitudinal strain curve. The post-peak slope was defined as the slope of a line from the
peak of the stress versus strain curve to a point representing a 50% loss of strength. This slope was then
divided by the peak compressive strength of the specimen to obtain a unitless measure of post-peak
slope, Z. This definition of Z has been applied previously to confined concrete [6].

4.2. Flexural Tests
Un-notched beams with dimensions of 150 by 150 by 510 mm were tested under four-point bending in
general accordance with ASTM C1609 [7]. One important change from the standard procedure was that
an infrared-based non-contact position sensor system was used instead of LVDTs to record beam
deflections. The position sensor system recorded the displacement of 16 markers attached to one side
of each specimen in the arrangement shown in Figure 3. Mid-span deflection was calculated using the
displacement of markers 1, 5, 6, and 9. Although not reported herein, the displacement data were also
used to calculate beam rotations at several sections and to estimate the width of the dominant crack at
the bottom face of the beam. More detailed results are reported in Reference [8].

4.3. Direct Tensile Tests
The relationship between tensile stress and crack width was evaluated using a tension test proposed in
Reference [9]. The specimens consist of a 150 by 150 by 510 mm concrete prism cast with a 16 mm
diameter reinforcing bar oriented along its centroidal longitudinal axis. The reinforcing bar is
discontinuous at the center of the specimen, where a 19 mm deep notch is cut around the perimeter of
the prism (Figure 4). Under load, a crack forms at the notched section. The width of the crack was
calculated using the recorded location of eight markers placed along the edges of the notch, accounting
for any rotation (reported crack widths represent an average width).

4.4. Tests of Fresh-State Properties
The fresh-state properties of each batch were documented using standard test methods (complete results
are presented in Reference [8]). Of most interest to this study were the results from tests for slump flow
and T50 performed in accordance with ASTM C1611 [10]. The T50 test is a non-mandatory and indirect
means of evaluating the viscosity of self-consolidating concrete. T50, measured during a slump flow
test, is the time it takes after lifting of the mold for the outer edge of the spreading concrete patty to
reach a diameter of 50 cm. Larger T50 values are correlated with higher concrete viscosity.

5. RESULTS
Typical results are shown in Figure 5 from tests of cylinders in compression (Figure 5a), un-notched
beams in bending (Figure 5b), and notched prisms under tension (Figure 5c) for one of the fibers
evaluated (RC-80/30-BP). Each of the curves in Figure 5 is the result of a single test selected from the
data recorded for mixtures having either no fibers or RC-80/30-BP fibers in a volume fraction of either
0.5 or 1.5%. As described below, the effects that use of fibers have on the post-peak response in
compression and the post-cracking response in bending and tension are evident in Figure 5.

5.1. Compressive Test Results
The fibers used in this study had a negligible effect on concrete compression strength and initial
modulus (Figure 5a). However, the compression toughness, calculated as the area under the
compression stress versus longitudinal strain curve, increased as fiber amount increased.
The post-peak slope in compression, approximated as the slope of a line drawn from the peak stress to
a point representing a 50% loss of strength (Figure 5a), was significantly affected by both fiber type
and fiber volume fraction. The post-peak slope is represented herein as Z, which is defined as the slope
divided by the peak compressive strength. Values of Z are listed in Table 3 and plotted versus fiber
volume fraction in Figure 6.
Figure

Each point in the Figure 6 plots represents an average value for specimens tested for each batch. As
shown in Figure 6, Z became closer to zero as fiber volume fraction increased. At a volume fraction of
1.5%, most batches exhibited average Z values less than 300, with some as low as 70. At lower volume
fractions, caluclated values of Z were more sensitive to fiber type. Batches with a 0.5% volume fraction
of RC-80/30-BP fibers exhibited average Z values less than 400, whereas the batch with a 0.5% volume
fraction of 4D RC-65/60-BG fibers and a target compressive strength of 41 MPa had a calculated Z
value of approximately 800.
Although overall Figure 6 also shows a modest trend between Z and fiber type, scatter in results limits
the significance of observed differences. Specimens with fiber type RC-80/30-BP, with an aspect ratio
of 80, tended to perform better than other specimens for all volume fractions.

5.2. Flexural Test Results
The peak post-cracking equivalent flexural stress (?fp), divided by the stress on the bottom of the section
at first cracking (?fc), is shown in Table 3. Both ?fp and ?fc were calculated with Eq. 1:
???? =
????
???2 (1)
where: ?? is the force applied to the specimen, ?? is the clear span length, and ?? and ? are the width and
height of the specimen at the location of the governing crack. Note that ?fp is an equivalent stress
calculated assuming a linear distribution of stress about mid-depth. Batches with ?fp/?fc greater than 1.0
exhibited, on average, greater strength after first cracking, referred to as deflection hardening behavior.
The response plotted in Figure 5b for the mixture with a fiber volume fraction of 1.5% is an example
of deflection hardening behavior.
For a target compressive strength of 41 MPa, specimens with the RC-80/30-BP fiber in volume fractions
of 0.75% and greater exhibited deflection hardening behavior. For batches with both the 4D RC-65/60-
BG and 5D RC-65/60-BG fibers, a volume fraction of 1.5% was necessary for specimens to, on average,
exhibit deflection hardening behavior. Deflection hardening behavior was not exhibited by any
specimens with RC-55/30-BG fibers.
Values of ?fp/?fc tended to increase for all fiber types and volume fractions for batches with a target
compressive strength of 69 MPa relative to batches with a target compressive strength of 41 MPa.
Although the minimum volume fraction required to cause deflection hardening behavior for batches
with the RC-80/30-BP fiber remained 0.75%, the post-cracking strength increased by approximately
25% for volume fractions of 1 and 1.5%. The post-cracking behavior of specimens with both the 4D
RC-65/60-BG and 5D RC-65/60-BG fibers also improved, as a volume fraction of 0.75% was sufficient
to, on average, result in deflection hardening behavior. This would be consistent with concrete breakout
having an important role in the behavior of specimens with lower strength concrete.

5.3. Tensile Test Results
Similar to the flexural test results, the ratio of peak post-cracking tensile strength (?tp) to first cracking
tensile strength (?tc) was used as a measure of specimen performance (Table 3). Specimens with a ?tp/?tc
value greater than 1.0, which indicates the FRC had greater tensile strength after cracking than at
cracking, are said to exhibit strain-hardening behavior (illustrated in Figure 5c). This ?tp/?tc ratio was
sensitive to both fiber type and fiber volume fraction.
For target compressive strengths of 41 and 69 MPa, all batches with fiber volume fractions of 1.0 and
1.5% exhibited tensile strain hardening behavior, except for those with fiber type RC-55/30-BG. No
batch with the RC-55/30-BG fibers exhibited strain hardening behavior. Comparing batches with a
target compressive strength of 41 and 69 MPa, there is a slight trend towards smaller ?tp/?tc values as
concrete compressive strength increased. This trend is different from that observed in the flexural tests,
which generally showed increased ?fp/?fc values with increased concrete compressive strength.

6. CORRELATIONS BETWEEN TEST RESULTS
An aim of this study was to determine the extent to which the behavior exhibited by FRC in tests of
mechanical behavior are correlated. Of particular interest was the correlation between the post-peak
slope of FRC tested in compression and the post-cracking results from flexural and tensile tests.
The analyses conducted do not explicitly consider differences between batches due to fiber type and
volume fraction. Rather, if a high degree of correlation is observed between results from compressive,
flexural, and tensile tests, it will be interpreted as an indication that differences in behavior resulting
from fiber type and volume fraction are implicitly included.
For these analyses, the degree to which two parameters are correlated was quantified using the Pearson
product-moment correlation coefficient, r. Values of r range from -1.0 to 1.0, where -1.0 indicates a
perfect negative correlation, 0.0 indicates no correlation, and 1.0 indicates a perfect positive correlation.
No definite threshold was selected to indicate a high degree of correlation. Instead, calculated r values
were interpreted as being relative, with r values closer to 1.0 indicative of higher correlation.

6.1. Correlations between Compressive and Flexural Test Results
Calculated values of Z were compared to several parameters derived from the flexural tests, including
the peak equivalent stress exhibited by the specimen after cracking and the equivalent stress resisted by
the beam at deflections of L/450, L/300, and L/150 (1, 2, and 3 mm).
It was observed that Z was most closely correlated with the maximum equivalent stress exhibited by
the specimen after cracking (?fp) and the equivalent stress resisted by the beam at a mid-span deflection
of L/450 (?? = L/450). These trends are plotted in Figure 7 as equivalent stress resisted by the flexural
specimen versus Z, where the coordinates for each point represent average values for all specimens
tested for each batch. The r values calculated for ?fp versus Z were -0.72 and -0.74 for the 41 and 69
MPa mixtures, respectively. For ?? = L/450 versus Z, calculated r values were -0.70 and -0.66 for the 41
and 69 MPa mixtures.
Two observations can be made. The calculated r values are relatively high given the scatter in the results
for both ?fp and ?? = L/450, indicating that, independent of the type and amount of hooked steel fiber used,
compression and flexural test results are correlated. It is also clear that compressive strength has an
important influence on the relationship.

6.2. Correlations between Compressive and Tensile Test Results
The peak post-cracking tensile stress (?tp) and the tensile stress at a crack width of 1.3 mm (?? = 1.3 mm)
are the tensile test parameters most closely correlated to Z. Figure 8 shows plots of ?tp and ?? = 1.3 mm
versus Z, where the coordinates for each point represent average values for all specimens tested for each
batch. The r values calculated for ?tp versus Z were -0.47 and -0.62 for the 41 and 69 MPa mixtures.
For ?? = 1.3 mm versus Z, calculated r values were -0.46 and -0.62 for the 41 and 69 MPa mixtures.
Although the calculated r values indicate a negative correlation, these tensile test parameters are not as
closely correlated to Z as the flexural test parameters plotted in Figure 7. Similar to Figure 7, Figure 8
shows that concrete compressive strength has an important influence on the relationships.

6.3. Correlations between Within-Batch Scatter (COV) and T50 Results
Figure 9 shows the coefficient of variation (COV) calculated for the peak post-cracking strength
recorded from flexural and tensile tests plotted versus T50. Both COV and T50 correspond to individual
batches of concrete. It is clear that specimens from batches with T50 values less than 1 second exhibited
higher scatter in post-cracking behavior (in terms of within-batch COV). This was more evident for the
peak post-cracking stress observed in flexural tests: for batches with T50 values less than 1.0 second,
the average COV calculated for the peak post-cracking loads was 40%, whereas batches with a T50
value of at least 1.0 second had an average COV of 13%. There was no correlation between T50 values
and the variation of the post-peak slope in compression.

7. SUMMARY AND CONCLUSIONS
Results are reported from an experimental study aimed at investigating the correlation between results
from flexural, tensile, and compressive tests of various fiber reinforced concrete (FRC) materials. Four
different types of hooked-end steel fibers were used in volume fractions of 0.5, 0.75, 1.0, and 1.5%.
Concrete mixtures had a target compressive strength of either 41 or 69 MPa. Findings include:
? The post-peak slope of FRC in compression (represented as Z) was more closely correlated to
results from un-notched flexural tests (tested per ASTM C1609) than direct tensile tests. Values
of Z were most correlated with the peak post-cracking equivalent stress (?? ? 0.73) and the
equivalent stress resisted by the beam at a deflection of L/450 (?? ? 0.68).
? The coefficient of variation calculated for the peak post-cracking strength in both tension and
bending decreased significantly when T50 was greater than one second. This was particularly
evident for results from flexural tests, which had a COV of 40% when T50 was less than one
second and 13% when T50 was greater than 1 second.
? The ratio of peak post-cracking equivalent stress to the stress associated with cracking increased
for all fiber types and volume fractions when the target compressive strength increased from
41 to 69 MPa. This is consistent with local concrete breakout caused by fibers having an
important role in the behavior of specimens with lower strength concrete.

ACKNOWLEDGMENTS
Materials used for this study were donated by Bekaert Corporation, Midwest Concrete Materials, Inc.,
W.R. Grace and Company, and Gerdau Ameristeel Corporation. The opinions expressed in this article
are those of the authors and do not necessarily represent the views of the sponsors.

REFERENCES
[1] ACI Committee 544. (1996, Reapproved 2009). 544.1R-09: Report on Fiber Reinforced Concrete.
Farmington Hills, MI: American Concrete Institute.
[2] Parra-Montesinos, G. J. (2005). High-Performance Fiber-Reinforced Cement Composites: An
Alternative for Seismic Design of Structures, ACI Structural Journal, 102(5), 668-675.
[3] Mindess, S. (2014). FRC in Structural Applications, Proceedings: FRC 2014 Joint ACI-fib
International Workshop: Fiber Reinforced Concrete: from Design to Structural Applications,
Montreal, Canada, July 24-25.
[4] Liao, W.-C., Chao, S.-H., Park, S.-Y., and Naaman, A. E. (2006). Self-Consolidating High
Performance Fiber Reinforced Concrete (SCHPFRC) - Preliminary Investigation. Ann Arbor,
USA: University of Michigan.
[5] ASTM Standard C39. (2015). Standard Test Method for Compressive Strength of Cylindrical
Concrete Specimens, West Conshohocken, Pennsylvania, ASTM International.
[6] Kent, D.C. and Park, R. (1971). Flexural Members with Confined Concrete, Journal of the
Structural Division, 97(7), 1969-1990.
[7] ASTM Standard C1609. (2012). Standard Test Method for Flexural Performance of Fiber-
Reinforced Concrete (Using Beam With Third-Point Loading), West Conshohocken, Pennsylvania,
ASTM International.
[8] Tameemi, W., and Lequesne, R. (2015). SM Report No. 114: Correlations between Compressive,
Flexural, and Tensile Behavior of Self-Consolidating Fiber Reinforced Concrete. Lawrence,
Kansas: University of Kansas Center for Research.
[9] Parra-Montesinos, G. J., Wight, J. K., Kopczynski, C., Lequesne, R. D., Setkit, M., Conforti, A.,
and Ferzli, J. (2014). Earthquake-Resistant Fiber Reinforced Concrete Coupling Beams Without
Diagonal Bars. Proceedings: FRC 2014 Joint ACI-fib International Workshop: Fiber Reinforced
Concrete: from Design to Structural Applications, Montreal, Canada, July 24-25.
[10] ASTM Standard C1611. (2014). Standard Test Method for Slump Flow of Self-Consolidating
Concrete, West Conshohocken, Pennsylvania, ASTM International.