Nowadays, high strength concrete is a common concrete type due to the demand of slender structural
elements subjected to increasing stress levels. Often, structural stresses have their origin in dynamic loading (i.e.
wind, railroad traffic, and more). This situation may result in changes in the structural response of concrete
elements. As a consequence, mechanical parameters of structural elements, stiffness mainly, changes throughout
the service life. These changes modify not only the structural response provoked by dynamic loads, but also the
one caused by static loads.
Many researchers [1-17] have studied the fatigue life of high strength concrete with and without the
addition of fibers. In most of these studies, specimens were tested under a predetermined stress level until they
break. The result is the number of cycles they are able to withstand. Few researchers analyzed the residual
modulus of elasticity and even fewer the maximum compressive strain of concrete elements after being subjected
to cyclic loading.
Early work in this field was carried out by Nelson et al. [6]. In 1988 they performed biaxial compression
tests on prismatic specimens. A small percentage of the test specimens reached the run-out value and were next
subjected to an uniaxial static testing until failure. An average increase of 4% in the residual modulus of
elasticity was observed; no information about the maximum compressive strain was presented. This phenomenon
was attributed to one or more of the following reasons: densification of the concrete at the micro-level,
rearrangement of the atomic structure towards a more stable orientation, reduction in localized stresses at the
aggregate-mortar interface and/or uniform redistribution of localized shrinkage stresses within the concrete.
Cachim et al. [7] carried out fatigue testing on concrete cylindrical specimens, with and without fibers. Similarly
to the previous case, a small percentage of the test specimens reached the run-out value and were next subjected
to static testing until failure. An increase of the modulus of elasticity of 10% for plain concrete and 16% for fiber
reinforced concrete was observed; no information about the maximum compressive strain was added.
The results of both these works are not representative, because only the specimens which had previously
reached the run-out condition were analyzed. In fact, only the strongest specimens fulfilled this condition. The
post-fatigue study was a secondary aspect in these researches.
It must be taken into account that real concrete structures are not subjected to constant amplitude cyclic
loading until failure. In fact, they are usually subjected to variable amplitude cyclic loading and occasionally to
high stress level loads. Cyclic loading usually does not cause the collapse of the concrete structure, but it causes
a variation of its mechanical parameters. Cyclic loading has a pronounced influence on the structural response
for both static and dynamic loading. Considering this fact, Urban et al. [18], studied the variation of the modulus
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variation of the structural response for static and dynamic loading. Furthermore, damage caused by cyclic
compressive loading appears to have no effect on the level of structural elements (i.e. no cracks are visible, etc.).
This phenomenon could also affect post-tensioned concrete beams. A variation of modulus of elasticity and
maximum compressive strain due to cyclic loading affects the structural response, especially under static loading
(instantaneous elastic deflection, deferred deflection, etc). Also the dynamic response of the structural element is
modified (natural frequency, maximum vertical acceleration, impact factor, etc).
2. EXPERIMENTAL PROGRAM
The experimental study consisted of on the analysis of the variation of the modulus of elasticity and
maximum compressive strain of C70/85 class concrete specimens according to Eurocode 2 [19], after having
been subjected to axial cyclic loading. Also, the effect of the addition of polypropylene and steel fibers is
analyzed. In all cases, the applied stress level and the number of load cycles did not provoke the collapse of the
specimens. Once the cyclic loading test was finished, the specimens were subjected to static testing until failure,
and both the residual modulus of elasticity and maximum compressive strain were measured. The maximum
compressive strain is defined as the compressive strain belonging to the maximum concrete compressive strength
(Figure 1). The values obtained are compared with the ones measured on the concrete specimens which had not
been previously subjected to cyclic loading. This test procedure had never been used previously by other
researchers, which is a significant aspect of this work.
The main testing parameters were:
1. Fiber dosage: a total of three concretes were tested. One without fibers (referred to as HSC),
another with 1 Vol. % polypropylene fibers (referred to as PPFRHSC) and the last one with 1 Vol.
% steel fibers (referred to as SFRHSC).
2. Cycle stress range: 35% - 50% of the characteristic compression strength, obtained at the
beginning of the cyclic testing. This range is usually considered the first stage of the “plastic
range” of concrete in the stress – strain diagram.
3. Number of cycles: four cycles were analyzed: 2,000; 20,000; 200,000 and 2,000,000 cycles.
4. Number of specimens: Twenty-four specimens of each concrete type were tested. The specimens
were placed in a curing room with a constant relative humidity of 100% and an ambient
temperature of 20ºC. The specimens were stored there until testing at 120 days after casting.
Sixteen of them were subjected to cycling loading in a set of four specimens for each number of
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cycles. Four specimens were tested under static loading until failure immediately before cycling
testing began (Figure 2). The remaining four specimens were tested under static loading until
failure, at an age of 28 days.
Cyclic testing started when the specimens were 120 days old, in order to reduce the variation of the
modulus of elasticity due to age. In all cases the cyclic testing frequency was 6 Hz.
Figure 3 shows the theoretical variation of the modulus of elasticity due to age, according to Model Code
2010 [20]. The cyclic testing duration is approximately 25 days for each concrete. Cyclic testing started when
concrete specimens were 120 days old, and ended when concrete specimens were 145 days old.
According to Figure 3, during this time, the concretes exhibit a theoretical increase of the modulus of
elasticity of approximately 0.3%. Therefore, it is concluded that the variation of the modulus of elasticity due to
aging has a very small influence on the results.
3.1 Materials
Twenty-four cylindrical specimens (100 mm diameter, 200 mm height) were produced for each of the
concretes. PPFRHSC incorporated crimped polypropylene fibers (45 mm length, 0.95 mm diameter, tensile
strength 400 MPa). SFRHSC incorporated hooked-ended steel fibers (50 mm length, 1.05 mm diameter, tensile
strength 1000 MPa). Both fibers are specifically designed for the reinforcement of concrete. The mix proportions
of the concretes are shown in Table 1. The main mechanical parameters of the concretes are shown in Table 2.
In all cases, the characteristic compressive strength at 28 days is comparable. But there are significant
differences in the modulus of elasticity and the maximum strain depending on the concrete type. HSC shows the
lowest values for both the modulus of elasticity and the maximum strain; while SFRHSC shows the highest
values.
3.2 Specimens testing
Tests were carried out in the Laboratory of Large Civil Engineering Structures (LCESUBU), at the
University of Burgos, Spain. The concrete specimens were subjected to axial compression cycles using a
dynamic actuator model MTS 244.4, with a 500 kN traction and compression capacity. The actuator is equipped
with an MTS 661.23F-01 load cell with a range of 500 kN, for both traction and compression, the average error
of the load cell is below 1% in its range (Figure 4).
First, the static compressive strength of non-fatigued specimens was determined as the basis for
determining stress levels for the specimens to be tested under cyclic loading.
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In all cyclic tests, the stress function in time had a sine-wave form, and fluctuated between a constant
minimum of 35% and a maximum of 50% of the characteristic compressive strength (characteristic means a 95%
probability that the strength is higher) previously determined, from the start until the prefixed number of cycles
was reached. The same procedure was applied to each of the three concretes. Directly after the cyclic testing was
completed, the specimens were statically tested to determine the residual modulus of elasticity and the residual
maximum compressive strain. The static testing was carried out according to EN 12390-3:2009 [21] (Figure 5).
4. EXPERIMENTAL RESULTS AND DISCUSSION
Results on the static modulus of elasticity and the maximum compressive strain for the different number
of cycles and concretes are shown in Figures 6 and 7.
The characteristic value of the modulus of elasticity ,c kE is obtained using the following equation
(according to Gaussian distribution, the modulus of elasticity of concrete and a probability of 95% to be
exceeded) (Eq. 1).
, , 1.645·c k c m EE E s= − (1)
where:
,c mE is the average value of the modulus of elasticity.
Es is the standard deviation of the modulus of elasticity.
Analogously, the characteristic value of the maximum compressive strain ,c kε is obtained using the
following equation (according to Gaussian distribution, the maximum compressive strain of concrete and a
probability of 95% to be exceeded) (Eq. 2):
, , 1.645·c k c m sεε ε= − (2)
where:
,c mε is the average value of the maximum compressive strain.
sε is the standard deviation of the maximum compressive strain.
The average values are useful to understand the mechanical response of the concrete, although the
characteristic values are used in design of concrete elements.
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www.ernst-und-sohn.de Page 7 Structural Concrete 4.1 Modulus of elasticity
Figure 6 shows that there is an initial reduction of both the residual average and characteristic modulus of
elasticity, and then, an increase follows. Usually this increment reaches a maximum value, and then it starts
decreasing again. In all concretes, the minimum value is reached at 2,000 cycles ( ( )log 3.3N = ), and then it
starts increasing up to 20,000 cycles ( ( )log 4.3N = ), with more cycles the values dropped again.
The residual characteristic modulus of elasticity of HSC, between 0 and 2,000 cycles, of HSC shows an
insignificant decrease, of about 2%; PPFRHSC shows a decrease of approximately 8%. SFRHSC has a greater
decrease, of approximately 14%. The residual average modulus of elasticity shows smaller percentages of
decrease (0%, 1% and 7% for HSC, PPFRHSC and SFRHSC, respectively). After this initial decrease, between
2,000 and 20,000 cycles, the HSC shows a moderate increase of its residual characteristic modulus of elasticity,
of approximately 6%. PPFRHSC has a higher increase, of approximately 9%; SFRHSC has a smaller increase, of
about 5%. The residual average modulus of elasticity of the three concretes shows similar percentages of change
at increasing number of cycles (11%, 10% and 6%, respectively). Finally, between 20,000 and 2,000,000 cycles (
( )log 6.3N = ), the residual characteristic modulus of elasticity of HSC decreases again with approximately
19%. In this case, the decrease of PPFRHSC and SFRHSC was about 9% and 10%, respectively. The residual
average modulus of elasticity shows smaller percentages of change (12%, 9% and 5%, respectively).
Between 0 and 2,000,000 cycles, the decrease of the residual characteristic modulus of elasticity of HSC,
PPFRHSC and SFRHSC is about 16%, 9% and 18%, respectively; the decrease of the residual average modulus
of elasticity is about 2%, 1% and 7%, respectively.
4.2 Maximum compressive strain
Figure 7 shows the variation of the residual maximum compressive strain of the three concretes. In all
cases, no uniform variation of this parameter can be observed up to 20,000 cycles. Then, the maximum strain
increases.
In the case of HSC, the residual characteristic maximum compressive strain shows a decrease of 22%
between 0 and 20,000 cycles. The residual average maximum compressive strain shows a decrease of
approximately 13%. In the case of PPFRHSC, the residual characteristic maximum compressive strain shows an
increase, between 0 and 20,000 cycles, of about 8%. The residual average maximum compressive strain shows
an increase of approximately 12%. In the case of SFRHSC, the residual characteristic maximum compressive
strain shows a decrease, between 0 and 20,000 cycles, of about 7%. However, the residual average maximum
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characteristic maximum compressive strain of HSC increased by approximately 32%. PPFRHSC has a smaller
increase, of approximately 13%; the increase of SFRHSC was approximately 11%. The residual average
maximum compressive strain shows similar percentages of change (20%, 7% and 10%, respectively).
Between 0 and 2,000,000 cycles, the residual characteristic maximum compressive strain of HSC,
PPFRHSC and SFRHSC increased by 6%, 23% and 4%, respectively; the increase of their residual average
maximum compressive strain was about 6%, 20% and 12%, respectively.
Figures 8 and 9 compare the results of the three concretes concerning the modulus of elasticity and the
maximum compressive strain, both for average and characteristic values. Relative values are defined as the ratio
of the modulus of elasticity or the maximum compressive strain to "N" cycles and the initial modulus of
elasticity or maximum compressive strain (static testing). These figures show graphically the above explained.
5. ANALYSIS OF RESULTS
Decreases and increases of the residual characteristic modulus of elasticity and the maximum
compressive strain can be explained with the occurrence of two internal phenomena in concrete occurring at the
same time. The first one is microcracking and fracture of the interface between the aggregates and the mortar,
and also between the mortar and the fibers. The result is a decrease of the modulus of elasticity and,
subsequently, an increase of the maximum compressive strain. This phenomenon occurs in two stages. The first
stage occurs within a few cycles, and it may be due to a reduction in localized internal stresses. The second stage
is less intensive and requires more cycles. It may be due to micro-cracking propagation, caused by the fatigue
process. The results are consistent with those obtained by [22], who showed that there is a relationship between
the variation of diffuse damage (porosity variation) and the variation of the mechanical parameters of concrete.
The second phenomenon is reconsolidation of the concrete, and a loss of pores, causing an increase of the
modulus of elasticity and, subsequently, a decrease of the maximum compressive strain. This process occurs
with increasing number of cycles, although it seems to be more intense in the early cycles. That agrees with the
results obtained by [6, 7 and 23]. Figures 10 and 11 show graphically the above explanation.
Comparing the different concretes, it can be concluded that steel fibers provoke the highest decrease of
the modulus of elasticity, while polypropylene fibers provoke the lowest decrease. Similarly, it also can be
concluded that steel fibers provoke the lowest increase of the maximum compressive strain compared to the
reference HSC, while polypropylene fibers provokes the highest increase.
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www.ernst-und-sohn.de Page 9 Structural Concrete 5.1 Correlation between residual modulus of elasticity and residual maximum compressive strain
Figure 12 displays the residual modulus of elasticity versus residual maximum compressive strain for all
tests. Each dot represents one test specimen. Figure 12 indicates a trend of decreasing modulus of elasticity with
increasing maximum compressive strain. This trend is clear, although it is not a very strong correlation and a
wide dispersion of the results can be observed. An effort was then made to extract this relation. The following
general equation describes this relation.
21·c cE αα ε −= (3)
where cE is the modulus of elasticity (in MPa) as defined earlier, cε is the maximum compressive strain, and
1α and 2α are model coefficients. For higher fidelity, the model coefficients are identified respectively for
each of the three concretes included in the test program, using statistical regression. The results are shown in
Table 3, with respective R2 values.
5.2 Scanning electron microscope analysis
Once static testing was done, an analysis of the microstructure of the concretes was carried out on some
samples using scanning electron microscope. Specifically, the presence of microcracking at the interface of
fibers and mortar was studied. Specimens with no-cyclic loading were analyzed, and also specimens that were
subjected to a cyclic loading of 2,000,000 cycles. Figures 13 to 16 show some of the images obtained by
scanning electron microscope. These figures show that the specimens that had not been previously subjected to
cyclic loading showed no microcracking at the interface fiber - mortar. However, the specimens subjected to
2,000,000 cycles of cyclic loads show microcracking in the interface fiber - mortar. It can be concluded that
cyclic loading cause microcracking at the interface fiber - mortar. As a consequence, internal stresses are
reduced and the stiffness of the fibers begins to influence the structural response of the specimen.
International workshop Ann Arbor, Michigan, June 16-18, 2003" Cement & Concrete Composites, vol.
26, pp. 757-759, 2004.
[9]. Zanuy C., Albajar L., De la Fuente P. “The fatigue process of concrete and its structural influence,"
Materiales de Construcción, vol. 61, no 303, pp. 385-399 2011.
[10]. Zhang B., Wu K. “Residual fatigue strength and stiffness of ordinary concrete under bending” Cement
and Concrete Research, vol. 27, no 1, pp. 115-126, 1997.
[11]. CEB-FIB "Constitutive modeling of high strength/high performance concrete," Fib Bulletin 42, 2008.
[12]. ACI Committee 544 "State-of-the-Art Report on Fiber Reinforced Concrete," American Concrete
Institute, ACI 544.1R-96 (Reapproved 2009)
[13]. ACI Committee 363 “State of the art on High Strength Concrete” American Concrete Institute, ACI
363R-92 (Reapproved 1997)
[14]. Hsu, T.T.C. “Fatigue of plain concrete”. ACI J., vol. 78, no 4, pp 292-305, 1981.
[15]. Zanuy, C.; Albajar, L.; de la Fuente, P. “Sectional analysis of concrete structures under fatigue loading”,
ACI Struct. J., vol. 106, no 5, pp. 667-677, 2009.
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www.ernst-und-sohn.de Page 12 Structural Concrete [16]. Gao L. and Hsu C.T. "Fatigue of concrete under uniaxial compression cyclic loading", ACI Material
Journal, vol. 95, no 5, pp. 575-581, 1998.
[17]. Do M., Schaller I., de Larrard F. and Aïtcin P.-C. "Fatigue des bétons à hautes performances", Annales
ITBTP, vol. 536, pp. 2-27, 1995.
[18]. Urban, S.; Strauss, A.; Macho, W.; Bergmeister, K.; Dehlinger, C. and Reiterer, M. “Zyklisch belastete
Betonstrukturen. Robustheits- und Redundanzbetrachtungen zur Optimierung der Restnutzungsdauer
(Concrete structures under cyclic loading. Robustness and redundancy considerations for residual lifetime
optimization) (In German)”. Bautechnik, vol. 89, no 11, 2012,
[19]. European Committee for Standardization “EUROCODE 2, Design of concrete structures”, 2004.
[20]. International Federation for Structural Concrete (FIB) “Model Code 2010”, 2010 Fib Bulletin 65.
[21]. EN 12390-3:2009 “Testing hardened concrete - Part 3: Compressive strength of test specimens”.
AEN/CTN 83: 478.
[22]. Zhang, B. (1998) “Relationship between pore structure and mechanical properties of ordinary concrete
under bending fatigue”. Cement and Concrete Research, vol. 28, no 5, pp 688-711.
[23]. Pons, G., and Maso, J. C. "Microstructure evolution of concrete under low-frequency cyclic loading:
determination of the porosity variations" Pergamon Press, 2817-2824.
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www.ernst-und-sohn.de Page 13 Structural Concrete TABLES AND FIGURES.
List of Tables:
Table 1 – Mix proportions.
Table 2 – Main mechanical parameters at 28-days age.
Table 3 1α and 2α coefficients found for equation 3.
List of Figures:
Figure 1: Typical stress-strain curve for concrete.
Figure 2: Testing procedure.
Figure 3: Variation of modulus of elasticity with age [20].
Figure 4: Dynamic testing facility.
Figure 5: Testing specimen subjected to static testing until failure, once cyclic loading was applied.
Figure 6: Residual modulus of elasticity versus number of cycles.
Figure 7: Residual maximum compressive strain versus number of cycles.
Figure 8: Residual relative modulus of elasticity versus number of cycles. Average (left) and characteristic
values (right).
Figure 9: Residual relative maximum strain versus number of cycles. Average (left) and characteristic values
(right).
Figure 10: Theoretical explanation of the variation of the modulus of elasticity, as a combination of
microcracking and reconsolidation phenomena.
Figure 11: Theoretical explanation of the variation of the maximum compressive strain, as a combination of
microcracking and reconsolidation phenomena.
Figure 12: Correlation between residual modulus of elasticity and residual maximum compressive strain.
Figure 13: Scanning Electron Microscopy. Fiber – mortar interface. PPFRHSC 0 cycles. (a) General View. (b) Detail.
Figure 14: Scanning Electron Microscopy. Fiber – mortar interface. PPFRHSC 2,000,000 cycles. (a) General
View. (b) Detail.
Figure 15: Scanning Electron Microscopy. Fiber – mortar interface. SFRHSC 0 cycles. (a) General View. (b)
Detail.
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View. (b) Detail.
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Table 1 Mix proportions
Concrete Cement (kg/m3)
Water (kg/m3)
Superplasticizer(kg/m3)
Silica fume
(kg/m3)
Fine aggregates
(kg/m3)
Coarse aggregate (kg/m3)
Fibers
HSC 400 125 14 6 800 1080
PPFRHSC 400 125 14 6 800 1080 1 Vol. %
SFRHSC 400 125 14 6 800 1080 1 Vol. %
Table 2 Main mechanical parameters at 28-days age.
Type of concrete
Characteristic compressive
cylinder strength (MPa)
Characteristic modulus of
elasticity (MPa)
Standard deviation of
the modulus of elasticity
(MPa)
Characteristic maximum
compressive strain (m/m)
Standard deviation of the
maximum compressive strain (m/m)
HSC 73.4 31,334 1,525 0.0030 0.0002
PPFRHSC 75.9 37,441 1,731 0.0027 0.0002
SFRHSC 78.8 39,871 1,380 0.0034 0.0001
Table 3 1α and 2α coefficients found for Equation 3.
