Behavior of High-Strength Fiber-Reinforced Concrete Beams under Cyclic Loading

This study investigated both the influence of longitudinal steel ratio and steel jiber length on high-strength concrete (HSC) beams' behavior under alternate cyclic bending. The evolution in both structural properties and cracking patterns was c?mpared with results from the monatonic bending test. To ~erve the mjl~e of jibers on deterioration of mechanical properties due to loadmg cycles, high-strength jiber-reinforced concrete (HSFR.C) bemn:' were tested using two jiber.lengths: 30 and 60 mm. Th1s analysis highlighted the positive effect of jibers on both the secant structural stiffness and the cracking patterns during the prepealc stage. For the postpeak stage, the ductility measurement did not reveal an! improvement. In seismic cases, however. the .measure~ of cycl1c dissipated energy is an important parameter m evaluating structural behavior. Within this framework, the positive effect of fibers ?n energy dissipation as well as on the cumulative damage capac1ty has been underscored.


INTRODUCTION
It is well-known that high-strength concrete (HSC) is a material featuring many favorable aspects, not o~y by ~e of its high compressive strength, but also through 1ts durability improvements. The mechanical tests in the literature, however, have revealed the brittleness of HSC and the low rate of increase in tensile strength. 1 • 2 These features reduced the use of HSC in earthquake-zones as a result of recommendations emphasizing the importance of obtaining a ductile material. 3 It is important, however, to mentio~ that, in the case of a high-strength reinforced concrete beam, the structural ductility4 of HSC can be similar to or better than that of ordinary reinfOI'Ced concrete beams if the failure mode occurs by steel failure. During an earthquake, however, structures are subjected to reverse loads, which ind~ce ~oth severe tensile damage of concrete and bond detenoration. Hence, the postpeak behavior is particularly influenced by the tensile and bond strength of the concrete. 5 Previous investigations have shown the effectiveness of fibers on the cracking propagation. 6 • 7 The greatest im~ve ment involved the increase of dissipated energy, charactenzed by the uniaxial compressive or tensile beha~or of a. soften~ postpeak slope. 8 This focus has served to gwde certain stu?ies on structural applications and has pointed out the effecti~e ness of fibers on cracking control and on shear and bending capacities. 9 The influence of fibers on the structural failure mode, however, depends on a structure's dimension, fiber type and concrete. Experimental results such as those re-' 10 . di dth . parted by Bspion, Devillers, and Halleux m cate e mefficiency of fibers in ductility increase, and can llf opposed to the results given by Chunxiang and Patnaikuni that revealed the good influence of fibers in ductility. These controversial results pointed out the qualified use of fibers under monotonic load, but few papers deal with the influence of fibers on structural behavior under cyclic load. The purpose of this paper is to examine the influence of fibers on cyclic beam-bending behavior (cyclic test). Two lengths of fibers are used: 30 and 60 mm. As a tradeoff between loss of workability and increase in structural strength, a reasonable level of steel fibers was chosen: 1% (by volume). To remain close to the structural dimensions used in civil engineering practice, a beam length of 2.75 m (0.11 ft) ~d a cross section of 150 x 300 mm (6 x 12 in.) are used. The mfluence. of tensile reinforcement is studied by including three different values for the tensile reinforcement ratio p.

RESEARCH SIGNIFICANCE
This study reports useful data on the app~cation. of ~gh strength fiber-reinforced concrete (HSFRC) m a se1sm1cally active zone. It has been shown that reverse loads involve severe bond deterioration. The control of macrocracks by fibers enhances not only the mechanical properties of high· strength concrete in tension and comp~ssion, but also thJ structural behavior. According to Lemmtre and Chaboche, mechanical properties of HSFRC, such as strength and ductility, are strongly influenced by length of fibers; consequen~y, this work brings some information about structural behavl<n: enhancement by fibers with respect to both the length of fibers and to the longitudinal reinforcement ratio used. These results broaden the application of fibers to reinforced concrete structures in seismically active zones.

MATERIAL PROPERTIES
· Three types of concrete were used for the purposes of this study: HSC, HSFRC with a fiber length of 30 JDID (HSFRC 30 ), and HSFRC with a fiber length of 60 JDID (HSFRC6Q). The mixture components for these concretes are given in Table 1.
A portland cement with low C 3 A content was used. Undensitied silica fume was added at a proportion of 10% of cement mass. The water-binder ratio was 0.32. To avoid a loss of workability due to the inclusion of fibers, the quantity of high-range water-reducing admixture was adjusted from 0.54 to 1% dry extract of cement mass The fibers were book-ended to enhance the anchorage in the matrix. The length diameter ratio of the fibers ltd 1 served as an efficiency factor, 4 and the optimum value used in the fibers' reinforced concrete production is ltd 1 = 80. This ratio has therefore been chosen for the two types of fibers. The fiber volume was constant at 1%. Fiber characteristics are displayed in Table 2.
Compressive tests were carried out on 110 x 220 mm ( 4.3 x 8.6 in.) cylindrical specimens after 28 days using a testing machine under load control at a loading rate of 0.5 MPals. The concrete specimens were kept at 20 ac and 95% relative humidity during the setting process, and then demolded 24 h after casting. Compressive tests were performed on three specimens for each type of concrete, and results are presented in Table 3. The compressive strength of HSC was approximately 95 MPa (13.8 ksi), with a strain at peak of2.4%o. The fibers accounted for a 15% increase in compressive strength, with an average value of 112 MPa (16.2 ksi) for HSFRC 30 and 118MPa(17.1 ksi)forHSFRC 60 . The strain at peak was also increased since it reached 3.1 %o for HSFRC3o and 2. 7%o for HSFRC 60 , and highlighted the ability of HSFRC to store a higher quantity of energy in the prepeak domain than HSC.

EXPERIMENTAL PROGRAM
The general test setup and beam cross section are described in Fig. 1(a). A dynamic actuator was used to apply reverse loads on beams 2.75 m in length and 150 x 300 mm in cross section. A positive and negative loading direction was introduced by means of a threaded rod system linked to the beam. The span-depth ratio aid was chosen to obtain bending failure. To generate failure between the loading points, stirrups (diameter of 8 mm, spacing of 20 cm) were arranged outside the pure bending zone. The influence of the reinforcement on beam behavior was analyzed by testing three different values fm the tensile reinforcement ratio (0.55, 0.97 and 1.52%) using longitudinal bars 12, 16, and 20 mm in diameter, respectively. The steel was Type FeE500 (tensile yield strength: 500 :MPa).
Each support was fitted with a swiveling frame that prevented vertical displacement but allowed rotation about the z-axis ( Fig. l(b)). The horizontal displacement was introduced by rollers arranged on one of the supports.
The cyclic tests were displacement controlled. A 0.5 Hz loading frequency was selected to reach the ultimate state of the beams. To measure strength deterioration at a given amplitude deflection, the loading sequence ( Fig. 2) was adjusted to 30 s. All of the test features related to the beams are given in Table 3.

BOND DETERIORATION UNDER REVERSE LOADS
A cyclic loading is the worst case of loading, as each concrete layer is alternately submitted to tension and compression stresses. Concrete and steel-concrete bonds are severely damaged. The bond deterioration mechanism observed by Popov 13 is described in Fig. 3(a) to (d) and relates to the typical cyclic load deflection curve presented in Fig. 4, which displays the following: • Before the peak load: During the positive loading ( Fig. 3(a)), the difference between the steel and concrete Young's moduli generates bond stresses. Once the limit tensile stress of the concrete has been reached, cracks   Dellec:llon (mm)
During unloading, the secant structural stiffness K on the load-deflection curve is regulated both by the strain of tensile bars and by the strain of the compressive zone. Once the load is close to zero, lugs and concrete are no longer connected, and compressive forces are used to close the tensile cracks ( Fig. 3(b)). This mechanism involves a decrease in secant structural stiffness up until the closure of the tensile cracks and the connection between lugs and concrete ( Fig. 3(c)). The secant stiffness can then be increased and new cracks generated due to compressive stresses of the bars, which may explain the pinching of the curves during the loading phases; and (a) static test: p = 1.52% (b) cyclic test: p = 1.52%

Fig. 5-Cracking pattern of HSC beams under cyclic and monotonic loading.
• After the peak load: Bond deterioration is severe ( Fig. 3(d}}, and the residual steel strain is very high. Consequently, during a reverse load. the tensile steel strain remains and prevents the closure of previous tensile cracks. The secant stiffness cannot be increased, and the pinching disappears (Fig. 4).

COMPARISON BETWEEN MONOTONIC AND CYCLIC TESTS
To measure the influence of reverse loads on structural properties, two static tests were carried out on HSC beams with p = 0.97% and p = 1.52%, respectively. The analysis focused on both the cracking pattern and the load-deflection curves.

Cracking pattern
The expansion of the cracking zone can be observed in Fig. 5(a) and (b). The reverse loads prevent the concrete from crushing, but the cracks propagate throughout the depth over a wider zone. Moreover, a greater number of horizontal cracks are located at the level of the steel bars, thereby demonstrating the severity of steel-concrete bond deterioration.
The minimal and maximal spacings measured in static tests are close to those obtained by Maurel 14 on beams with a similar cross section and a shear span of 0.8 m (minimal spacing of 5 cm and maximal spacing of 12.5 cm). The longitudinal steel ratio seems to have little influence on the spacing of cracks. The cyclic tests, however, show an increase in the spacing of cracks within the shear zone, and thus, an increase in maximal spacing. This finding can be explained by the different stages of the cracking process. At first, bending cracks occur with low structural damage, and a similar cracking development to static test is denoted. Afterwards, under alternate loads, steel-concrete debonding reduces the rate of occurrence of transverse cracks wbile 1 inducing horizontal cracking.

Load-deflection curves
As a means of comparing tests under monotonic and cyclic loads, average envelope curves have been used in the cyclic' c~ses. One ex~ple of such an envelope curve is drawn in Fig. 4. A compan~on of different curves is provided in Fig. 6, and some mecharucal properties are given in Table 4. B~fore the peak load, it has been noted that alternate loading does no~ change the secant stiffness of the HSC beams, bu~ does mduce a decrease in maximal load capacity by approxunately 10%.
Beyond the peak load, the slope of the cyclic curve drops sh~ly ~~ a~ounts for the decrease in structural ductility. This ductili_ty IS defined as the ratio of ultimate deflection to the deflection .a! the peak load l>,jl>Fmax· A study of this structural ductthty was the topic of another paper 15 Th ultimate deflection corresponds to the deflection m~asure~ at 85% of the peak load. For p = 0.97%, the cyclic loading d~reases the ductility by 36%. For p = 1.52%, data acqui-Sition was not performed beyond the postpeak, but it was thought that the loss in ductility would not be so high as a ~esult of the greater brittleness of beams exhibited by the mcre~e of tensile reinforcement under monotonic loading. Cracking degrades the steel-concrete bond. As long as the anch~rage of bars and the force redistribution in the com-p~~sive zone are effective, the structural behavior remains SlDlllar. yn1~r alternate stresses, both the cyclic softening of matenals . and the time lag of the force redistribution in the compressive zone due to crack closure lead to a steep postpeak branch.

INFLUENCE OF FIBERS ON CYCLIC BEHAVIOR
The structural tests with fiber reinforced concrete (FRC) ha~e demonstrated the influence of the steel reinforcement ratio. on ~ber efficiency . 16 For this reason, three values of the longJ.tudinal steel ratio have been used: p = 0.55, 0.97 and 1.52%. Both the concentration and the 1/d ratio of fibe;s are also used as efficiency factors. It has therefore been decided to use a cons1a?t fiber volume of 1% with an 1/d ratio of 80. !t should be pomted out that the size of the structure is another 1Dlportant factor in regard to the structural efficiency of the ~C; however, the size effect has not been raised herein sm'7 all b~am specimens have the same height. In this paper the influence of fibers has focused on the cracking pattern' strength deterio~tion, the load-deflection envelope curves: and the cumulative damage capacity.
lnflue~ce on apparent cracking vi~e.mflu.enc~ of fibers on the apparent cracks can be fro ualized m Fig. 7(a)  !Dore sinuous when fibers are added ( Fig. 7(b) and (c)).lt is Important to note that this observation is made at the end of te~t. lnde~d, if fibers are often used to reduce the crack :-"Idth dunng service loads, their bridge effect allows an mcrease of the main crack width during the failure stage. The measure of the crack width, however, was not recorded due ~o the difficulties induced by both alternated loads and continuous measurement. Outsi~ l~ading points-The HSC beams displa~ some characte~stic. shear and horizontal cracking, which reveals the det~~oration of the steel-concrete bond (Fig. 7(a)). With the addition of fibers, both the number and length of cracks are reduced (Fig. 7(b) and (c)). The shear cracks seem to be effectively bridged by the fibers. Moreover, the horizontal cracks. are not located on the HSFRC beams and reflect the action of fibers on cracking induced by steel-concrete de~onding. Some isolated cracks can be noted, however, which sugge~ts the random bridging effect of fibers inside the cross sections.
lnfl!-lence on load-deflection envelope curves ~Igure 8 presents cycl~~ envelope curves that resulted by taking an a~erage ?f positive and negative envelope curves.
The deflection gam at the peak load is insignificant· the curv~s were thqs drawn with respect to a nonnalized defl~on relative to the peak deflection, and correspond to the definition of sn:uctural ductility. Three stages can be distinguished: the first IS a structural behavior without any damage, as char-  acterized by the secant initial stiffness Ki and the first cracking load F 1 ; the second stage is the damaged behavior up until the maximal load applied with a decreasing secant stiffness; and the last stage is the postpeak behavior that induces structural collapse. The specific values measured off of the curves are listed in Table 5.
Undamaged behavior (prepeak)-The initial secant stiffness, as shown in Table 5, is hardly increased by the presence of fibers; no real difference between HSFRC3o and HSFRC 60 can be observed. The beam's behavior is still elastic, it seems that only microcracking occurs inside the matrix. To enhance this initial stiffness, fibers would have to bridge these microcracks; consequently, the length of fibers needs to be shorter 17 (maximal length: 13 mm). With the length of fibers used in this work (that is, 30 and 60 mm), only macrocracks are bridged as the result of the improvements brought during material testing (increased strength and ductility of HSC).
When either the upper or lower concrete layer of the beam reaches the tensile stress limit, a macrocrack occurs. Should this crack not be bridged by the fibers, the tensile stress would suddenly be distributed in the tensile steel bars, and the secant structural stiffness of the beam would decrease. With HSFRC, as fiber length increases, the value ofF 1 also increases. This improvement is particularly distinct at the  low reinforcement ratio (p = 0.55%) since F1 increases by 77% with HSFRC 30 and by 170% with HSFRC60. This finding highlights the efficiency of fibers to delay the macrocracks' propagation. Due to the secant stiffness being controlled by the tensile bars, however, the value of F 1 rises less rapidly when the reinforcement ratio increases.
Damaged behavior (prepeak)-In this stage, bending and shear cracks occur and propagate but also bond cracks, as detailed previously. The bridging of cracks by fibers induces an increase in secant stiffness, accentuated by the length of the fibers. This improvement is effective throughout the loading stage up to the peak load. The yielding of reinforcement occurs prior to the peak, but no significant change of stiffness is observed. Table 5 displays an increase in the peak: load of HSFRC compared with that of HSC by 47, 30, and 5% for the L-30, M-30, and H-30 tests, respectively, and an increase of 59, 40, and 18% for the L-60, M-60, and H-60 tests. It can be noted that the increase in the tensile bar ratio reduces the gain contributed by the fibers, due to a wider crack opening for higher reinforcement ratio. Studies focusing on the steel-concrete bond with HSC 18 have indeed shown that the crack opening is related to the steel bar diameter. For the H-30 test, the crack opening at the peak: load seems to be too wide for the 30 nun fibers, which explains the negligible gain. Nevertheless, by preventing against the propagation of cracks, both HSFRC3o and HSFRC 60 contribute to the increase in secant stiffness and thereby to the slowing rate of beam damage. At this point, it is worth mentioning that for low longitudinal reinforcement ratios, fibers can replace some of the longitudinal bars (Fig. 9). This is important since this phenomenon has not been observed with big dimension beams under monotonic bending loads. 10 Only the replacement of stirrups with fibers has been foreseen according to certain studies.1•ll Collapse behavior (postpeak)-Many of the codes used to investigate structural performance during the failure stage are based on ductility measurements. Ductility has been defined as the ratio of the ultimate deflection to the deflection at the peak: load (8,j8pmax). In this paper, the ultimate deflection is assessed when the beam supports just 85% of the maximal load. This definition is based on the work of Park and Ang 19 that was then modified by Srinivas et al., 20 who considered that under cyclic and alternate loading, structures were too heavily damaged beyond this level of loading capacity. In Table 5, the ductility measurement indicates the inefficiency of the fibers. For each series, the concrete is severely degraded by tensile stresses at peak:, and the maximal load gain obtained by fibers actually induces a drop in ductility due to a severe bond deterioration between reinforcement bars and concrete.
Considering a support capacity of95% of Fmaxo the analysis conducted by Daniel and Loukili 21 indicates a similar ductility obtained with HSFRC 60 relative to HSC for the L-series and relative to HSFRC 30 for the M-series. This finding underscores the influence of long fibers with a low reinforcement ratio; however, the improvement is not substantial enough, and the small sample size only indicates some trends. More exploration should be realized to recommend the use of fibers for structural ductility-enhancement requests.

Influence on cumulative dissipated energy
Measuring ductility is not the only motivation for investigating behavior during the postpeak: phase. When earthquakes occur, energy gets injected into the structure and then has to be dissipated for safety reasons. According to this setup, the behavior of fibers inside the matrix acts as a dissipative mechanism. The measurement of dissipated energy could thus become a good efficiency index independently from structural ductility considerations.
During cyclic tests on structures, dissipative mechanisms are frequently encountered and must be distinguished to determine the action of fibers on the dissipated energy (Eq. (1)) .
In fact, a principal energy ET is injected into the structure, composed of a beam or column and supports. One component of this energy is redistributed into the soil E 1 , while the other is used b~ the structure over the elastic Ee and inelastic E domains. The first component Ee represents the energ; necessary both for beam displacement (kinematics energy Ec) and for elastic strain Ees· The latter component E includes The dissipated energy during a loading cycle was determined by computing the hysteretic area of the loop. The increase of dissipated energy during cycles at similar displacement amplitudes is low. It was thereby assumed that the contribution of fibers is concentrated during the first cycle of each displacement amplitude. The computation of primary dissipated energy was carried out up until total collapse (Fig. 1 0).
For L-series-Fibers increase the dissipation of energy up until collapse. The gain provided by the longest fibers, compared with the shorter ones, is observed at the end of the test for a normalized deflection of greater than 1.4. The maximal dissipated energy increases by 45% for HSFRC 60 (1490 kNmm) with respect to HSC, while for HSFRC 30 it increases by only 13%.
For M-series-Only the HSFRC 60 increases the dissipation of energy up until collapse, with an increase in ultimate dissipation (2240 kNmm) of 41 % with respect to HSC. The behavior of HSFRC 30 is similar to that of HSC, with a low increase in dissipated energy over the postpeak: zone. Furthermore, the maximal value is 26% less than HSC, which highlights the low effectiveness of shorter fibers.
For H-series-A reduction in the improvement of long fibers is noted since the maximal energy with respect to HSC increases by 28%. HSFRC 30 does not show good behavior, as the level of energy dissipation remains less than that of the HSC beam during the entire postpeak: stage.
There were not enough repetitive tests to draw firm conclusions, but some trends could be mentioned. It seems that the inclusion of fibers leads to an improvement in energy dissipation, which is particularly efficient at low longitudinal steel reinforcement ratios. As the tensile bar ratio increases, the maximal dissipation rate drops. The postpeak behavior of the HSFRC 60 beam can be considered as good for all series.
Only the L-series, however, exhibits an efficient dissipation of the HSFRC 30 beam.  The use of this index is not straightforward for structures subjected to many cycles during the postpeak phase. Moreover, some results must be derived from tests under monotonic loading, which would increase the number of tests required overall. To overcome this constraint, a new damage index (Eq. (8)), based on the expression of Sadeghi's index (Eq. (6)), has been developed. A strain factor a.i (Eq. (9)) is introduced for the dissipated energy of each first cycle Epi to stand for the secant stiffness deterioration with respect to the peak load. The damage induced by successive cycles of similar displacement amplitude is attenuated by a fatigue factor A.i (Eq. (10)) related to the strength deterioration with respect to the first cycle. The energy summation is normalized by the total amount of energy dissipated_ by each first cycle I:.Epi· The tensile reinforcement ratio p is introduced to take into account the difference m energy behavior with increasing tensile reinforcement. The power number is computed to yield an index value close to that for the HSC beams where KFmax = secant stiffness at peak load; ~~-· = secant stiffness of primary cycles; K = maximal load of primary cycles; and 1,; = maximal load of successive cycles.

STRUCTURAL DAMAGE INDEXES
The cumulative damage capacity of the beams is computed using the index in Eq. (8); results are showninFig. ll(a) to (c). The HSFRC beams reveal two phases: 1) the rate of damage is reduced during the first successive cycles in comparison with the HSC beam, with this distinction being particularly strong for the lower tensile reinforcement; and 2) damage related to the loss of ductility in the beams speeds up. For p = 0.55%, however, both HSFRC 30 and HSFRC 60 successfully increase the cumulative damage capacity with values of greater than one, yet 60 mm fibers appear to reveal a faster damage growth than the others. For p = 0.97%, only the HSFRC 60 manages to enhance the cumulative damage index with respect to HSC with a value similar to that from the previous test. This fmding may suggest that 60 mm fibers are not being used up to their maximal efficiency . For p = 1.52%, the HSFRC exhibits no increase in the damage index, which underscores the inefficiency of fibers with the higher longitudinal reinforcement ratio.

CONCLUSIONS
The aim of this study has been to investigate the influence of fibers on the behavior of HSFRC beams under cyclic bending. The severe concrete damage due to alternate loading induces a loss in both maximal load capacity and ductility.
This degradation suggests that the use of fibers can be efficient to prevent an early emergence of macrocracks during the prepeak stage. Fibers induce an increase in beam structural stiffness up to the peak load. For a tensile reinforcement ratio of 0.55%, HSFRC exhibits behavior similar to that of an HSC beam with a tensile reinforcement ratio of 0.97%. Nevertheless, the fibers have no influence on strength deterioration during loading cycles at a given displacement. In the Within an energy-based framework, however, and particularly so in the case of earthquake zones, the insertion of long fibers enhances the energy dissipation over both the elastic and inelastic domains for all longitudinal reinforcement ratios; with regard to the 30 mm fibers, however, enhanced energy dissipation only occurs for lower ratios. With respect to energy dissipation alone, however, 30 mm fibers may be recommended for lower reinforcement ratios. The effect on the cumulative damage capacity is positive for 60 mm fibers, with an efficiency limit for p = 1.52%.
These findings have raised the possibility of using the HSFRC 60 in small-sized structures (low heights or low reinforcement ratios) in earthquake zones to increase the mechanical postpeak properties and energy dissipation in the inelastic domain.