- Email: [email protected]
Damage mechanism of SCC under cyclic loading with different speed
Construction and Building Materials 101 (2015) 252–259
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Damage mechanism of SCC under cyclic loading with different speed Hamoon Fathi a,⇑, Hooshang Dabbagh b a b
Department of Civil Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran
h i g h l i g h t s The effect of loading rate on concrete behavior is greater before the peak. Changing cyclic loading rate would cause a corresponding change in SCC cracking. During creep cyclic loading, the stress–strain diagram undergoes great changes. Concrete demonstrates different behaviors under cyclic loading with different rate.
a r t i c l e
i n f o
Article history: Received 25 June 2015 Received in revised form 8 September 2015 Accepted 17 October 2015
Keywords: Self-compacting concrete Cyclic loading Loading rate Stress–strain curve Fracture mechanism
a b s t r a c t In this experimental research, the effects of cyclic loading at different frequencies on self-compacting concrete were studied. 108 standard cylindrical specimens and 120 cubic specimens were tested. The specimens had compressive strengths of approximately 25 MPa, 35 MPa and 45 MPa. The rate of loading was studied in the 0.05–250 KN/s range. The results showed that the behavior of concrete before and after peak loading depended on the number of loadings as well as the loading rate. Failure of concrete under periodic loading at high frequencies led to increased micro cracks in a direction perpendicular to that of the principal cracks. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Earthquakes reduce the bearing capacity of concrete. In order to model earthquakes and the amount of energy transferred to a structure, the loading rate or cyclic loading can be changed or the fatigue loading method can be used. The amount of energy transferred per unit time can alter the behavior of structural materials under the respective loading. The studies conducted by Sinha et al. [1] can be considered as the first experimental studies on concrete behavior under cyclic loading. They discussed concrete behavior under cyclic loading. They carried out their studies experimentally on 48 standard cylindrical specimens. Compressive strength of the cylindrical specimens ranged 20–28 MPa. The studies showed that a cyclic loading curve does not pass through monotonic loading curve. The curve was introduced as an envelope curve. Karsan and Jirsa [2], developed the earlier experimental results within the ⇑ Corresponding author. E-mail addresses: [email protected] (H. Fathi), [email protected] (H. Dabbagh). http://dx.doi.org/10.1016/j.conbuildmat.2015.10.103 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
compressive range. Their research was carried out on 46 short rectangular column specimens. Loading of the specimens was under the effect of a cyclic loading along the main axis of a column and column behavior was studied on the plate of the same axis. Finally, they presented a model for the envelope curve of concrete stress– strain diagram in a cyclic loading. Their study showed that the loading curve and re-unloading curve meet at some points, a series of which is called common points limit. There is almost a certain distance between this curve and the envelope curve. Buyukozturk and Tseng [3] developed the earlier studies on concrete behavior in a cyclic loading. These studies discussed the effects of increasing strain and energy level with respect to loading gradient. Yankelevsky and Reinhardt [4,5] presented a simple non-linear model for stress–strain diagram of concrete in a cyclic loading with respect to the effects of history of the previous loading. Their model is in two separate forms for compressive and tensile loadings states. Of course, these simple models are formed as a tangent line on the envelope curve in press section. Bahn and Hsu [6] carried out parametric and experimental studies on concrete under the effect of cyclic loading. The results led to overall control of cyclic stress–strain curve. The specimens
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
were tested as 76 * 152 cylinders. They used four loading models. The reverse relationship between plastic strain and mean of unloading and loading curve gradient is among the results of the studies, Vecchio and Collins [7] carried out an experimental study on concrete behavior under different loadings. Later, these studies were continued by Palermo and Vecchio [8] in the theoretical section. The models also point out the relationship between loading and unloading curve with the created cracks. They tested 30 reinforced concrete specimens and examined the cracks developed on the concrete surface. The studies indicated that concrete reloading provides an appropriate response in a linear manner and concrete loading within tensile range is non-linear. Sakai and Kawashima [9] studied behavior of reinforced concretes. The results obtained from the 28-day concrete specimens were used in these tests. In their research, they pointed out the monotony of the gradient of initial curve and the initial loading and showed that the unloading curve is concave from the initial point. Mander et al. [10] developed a stress–strain model of concrete in a uniaxial compressive loading. These loadings deal more with the range between tension and compression. Their experiments were carried out on beams and columns. Martinez and Elnashai [11] modified the reloading curve using a linear relation. This line was considered between the zero stress points and reloading strain; whereas, the unloading curve is placed between unloading strain and stress–strain curve in a monotonic loading. Mansour and Hsu [12] developed concrete behavior modeling with respect to a series of experimental results within the tensile and compressive range. These equations discuss linear models of reloading and curve models for loading. Elnashai and Martinez [11] and Sima et al. [13] were among those who presented cyclic loading models on concrete. Several studies have been conducted on the plastic behavior and the effects of cracks caused by cyclic loading on concrete models. Concrete, as a brittle non-homogenous material, is very sensitive under fatigue loading [14–18]. Examining the behavior of materials under cyclic loading is an approach to model the behavior of materials and structures during an earthquake. The behavior of materials under cyclic loading is studied using the stress–strain curves. Cyclic loading has a specific regime during an increase or a decrease in loading. However, in case of an earthquake where the cyclic loading is of variable rate, the situation is not similar. This study examines the simultaneous effects of cyclic loading and the variations in the loading rate. In fact, the concrete is subjected to a cyclic loading at different rates. Zheng et al. [19] examined the static behavior of concrete under different loading rates. The presented model complied with the experimental results. Their model aimed to establish a relationship between the dynamic strength and different levels of static stress. The model, however, was less consistent with the experimental results in low-rate loadings. Elias and Le modeled the fatigue crack growth under cyclic loading [20]. Their model addressed the compressive cyclic loading. Brittle non-homogenous materials undergo fatigue under cyclic loading, leading to crack growth in the material. Lots of studies are investigated and modeled the concrete behavior under cyclic loading at tension or compression area. But most of these studies are subjected cyclic loadings at quasi-static loading rate. In fact, uniaxial monotonic loadings have direct effects on test results. Compressive strength, cracks distribution, elastic modulus and Poisson ratio are dependent to loading rate. Test scales for loading rate are usually categorized with strain rate in a period of time. Fig. 1 defines a diagram for equivalent strain rates and loading simulation effects on the samples. According to the size of samples, these ranges can be categorized with loading rate from 10 8 m/s (0.05 KN/s for cylindrical samples) to 103 m/s. Many experimental researches are investigated the effect of loading rate on compressive strength, mechanical behavior and
253
Fig. 1. Diagram of strain rate and loading type.
stress–strain relationship of concrete. the results are showed, elastic modulus and Poisson ratio are grew when specimens were subjected with higher loading rate [21–23]. High speed loading, dynamic loading and earthquake loading effects on mechanical properties of concrete are simulated in these studies. Furthermore, some studies are tested different type of concrete under different strain rate’s level [24–26]. Most of experimental tests on concrete are performed in compressive area. Due to the increasing use of self-compacting concretes (SCC) and the need for more detailed studies on this type of concrete, SCC specimens are studied in this research. Continuous segments were examined for a detailed and step by step study of the SCC behavior under cyclic loading along with variations in the loading rate. The variations in the compressive strength of the SCC specimens were investigated. The SCC stress–strain curve under monotonic loading with different rates were extracted and compared. Finally, according to the results, the other batch of specimens was tested under a specific cyclic loading with different rates. The stress–strain curve of concrete under cyclic loading with different rates was compared in each step. Persistent strain, the angle of the tangent line on the reloading branch, and the shapes of hysteresis loops were compared. The main cause of behavioral changes in SCC under cyclic loading is the spread of cracks in the specimen. The crack depth, crack length, crack passage through the aggregates, and the crack angle are the main differences between the specimens under cyclic loading with different rates. 2. Experimental study This experimental study discusses the effect of cyclic loading with nine levels of loading rate on SCC. The experiment parameters are including cyclic loading rate and compressive strength. Stress–strain curves and compressive strength of SCC are studied under changing these tests’ parameters.
2.1. Materials The concrete mixes in the test consisted crushed aggregates, micro silica, plasticizer, cement and water. They were prepared from local sources with material properties as presented in Table 1.
2.2. Specimens One hundred and eight (diameter of crass section: 150 mm and height: 300 mm) standard cylindrical specimens and one hundred and twenty (100 * 100 * 100 mm) cubic specimens are tested. The compressive strength of the specimens which manufactured for respect to the different mixes was 25 MPa,
Table 1 Specifications of the materials used in the prepared concrete mix. Materials name
Materials type
Qualification
Aggregate Water Cement
Gravel Normal Type 1
Add materials
Micro silica Plasticizer
Bulk: 1750 kg/m3; maximum size: 19.5 mm PH: 7; low mineral Setting time: 135 min, compressive strength: 325 kg/cm2 Density: 2110 kg/m3 Density: 1200 kg/m3
254
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Table 2 The mix ratio used in SCC samples is in terms of percent by weight of the materials. Name
SCC 1 SCC 2 SCC 3
Cement weight ratio (375 kg in 1 m3) Plasticizer cement
Microsilica cement
Water cement
(%)
(%)
(%)
4 5 6
0 5 10
33 33 33
Slump flow (cm)
Compressive strength (MPa)
than bypassing the aggregates and passing the looser paths, given the power generated by the imposed force, the cracks break the aggregates and choose the shorter path. 3.1. Compressive strength
69 65 64
25 35 45
35 MPa and 45 MPa (Table 2). To compare the results of this research with those of previous studies, the concrete mixture ratios were selected from Tables 1 and 2 [27,28]. Specifications of the manufactured concrete mixes are categorized in three different groups. The amount of micro silica and plasticizer in these mixes are changed and other proportions of materials have fixed amounts. 2.3. Curing Aggregates were washed, dried and drowned in water for 24 h, aggregates were poured in a mixer, as Saturated Surface Dry (SSD) and cement and micro silica were added. The required water for concrete was added in two stages, before and after adding additive and lubricant in an equal volume. After 24 h mold were removed and samples were placed in a mixture of water and some lime to reducing alkaline condition for 26 days. The specimens were kept in laboratory temperature (23 °C) for one day, and then subjected to loading. 2.4. Loading In this study, the compressive monotonic and cyclic loadings were tested. Monotonic and cyclic loadings were applied under different rates. Monotonic loadings were continued until the failure in the specimens. Cyclic loadings were performed in 12 loading steps with different stress values (Fig. 2). Both cubic and cylindrical specimens were used for the study of mechanical properties of concrete. There are many relations for converting the results [29,30]. However, the results of previous studies were used for selecting the tests and the specimens thereof. In most previous research conducted on the effect of uniform load on concrete, cubic specimens were used [27,31]. For this reason, the authors also used cubic specimens for uniaxial load tests conducted to assess the difference between conventional and self-compacting concrete types. In most cyclic loading experiments, strains are calculated and stress–strain diagrams plotted. To this end, cylindrical samples are usually used for testing [27,32]. In the cyclic loading tests in the present study, cylindrical specimens were used to make possible comparison of test results with those obtained from conventional tests, and to compare the effects of velocity change on the behavior of concrete specimens and the failure images thereof [33–35]. Loading rates ranged from 0.05 kN/s to 250 kN/s (Table 3). The range included the creep, quasi-static, and dynamic behaviors (Fig. 1). SCC cubic specimens were tested under monotonic loads, and the stress–strain curves were extracted from the cylindrical specimens. Concrete specimen compressive strength changes with loading rate. Studies show that this change is proportional to the initial compressive strength of concrete, which can be selected on a relative basis. As in other uniform loading studies, the initial compressive strength of concrete in this study was assumed to be equal to that obtained at the start of quasi-static loading [24–27]. The three compressive strength ranges presented in Table 2 indicate increased maximum compressive strength with loading rate and, therefore, provide a wide range of compressive strength values for concrete.
3. Discussion and results Variations in the cyclic loading affect the opening and closure of cracks as well as the amount of energy transferred per unit time. The variations in the concrete stress–strain curve and the area of the hysteresis loops describe the extent of damage in concrete and as well as the absorbed energy. The amount of persistent strain in the curves indicates the cracks formed under a specific loading. Different rates affect the concrete compressive and tensile strengths. It also indirectly affects the elastic modulus and the Poisson’s ratio. The main difference between different loading rates is the amount of energy transferred to the specimen. An increased energy transferred per unit time to the concrete causes the cracks to choose a more direct path to break the concrete. In fact, rather
Results showed that by increasing the hardness of concrete, mortar compressive strength becomes more similar to that of the aggregates. The strength of mortar approaches to that of the aggregate, and when the concrete breaks, the crack passes through the aggregates and mortar. Accordingly, the impact of an increased loading rate is not significant and does not change the crack path in high-strength concretes, because the changes in the strength of high-strength concretes caused by an increased loading rate in less significant compared to that of the conventional concretes (Fig. 3). Fig. 3 compares the compressive strengths of the specimens Scc1, Scc2, and Scc3 under monotonic cyclic loading in the rate range of 0.5–45 KN/s. The compressive strengths of all three models slightly decreased at very low loading rates which may be due to the formation of initial cracks caused by shrinkage. The decrease continued to the limit specified for the creep behavior (This range is defined with due regard of loading rate.), confirming the effect of micro-cracks on the slight reduction in the compressive strength. Increase in the rate of the monotonic compressive loading increased the compressive strength of the concrete. 3.2. Stress–strain curve and monotonic loading The stress–strain curves under monotonic loading act like an envelope curve for the stress–strain curves under cyclic loading. Therefore, it can show the changes caused by the cyclic loading and the amount of damage and energy generated to crack the concrete under cyclic loading. However, variations in the loading rate affect the elastic modulus, strain, and strength. Therefore, the concrete specimens were tested under different rates. Fig. 4 shows the SCCL stress–strain curve under the monotonic loadings with rates of 0.05–25 KN/s. The SCCL elastic modulus concrete increases with increasing the loading. However, in low loading rates and in the creep behavior range, the variations are less significant, and the slope of the loading curve is strain-dependent. The slow loading rate (within the defined range for creep behavior), allows the concrete to fully undergo strain. The reason is that the calculated strain is greater under slowly applied uniaxial uniform loading [35]. 3.3. Stress–strain curve and cyclic loading The present study aimed at investigating the effects of compressive cyclic loading with different rates (0.05–250 KN/s) on the behavior of SCCs. For this purpose, the variations in the stress– strain curve were examined. The effect of cyclic loading is different pre and post-peak. Fig. 5 shows the pre-peak concrete stress–strain curve. In this section, each loading was repeated for three times. The loading stress was then increased to a higher range, where the loading was repeated for three more times. Results showed that, in lower loading rates, the reloading branch has a smaller curvature which decreases with increasing the rate of the cyclic loading. These variations indicate that the effect of micro-cracks on the stress–strain curve is less significant in high-rate cyclic loadings. The area of the hysteresis loops is greater in high-rate cyclic loadings. An increased area indicates an increased amount of absorbed energy. The changes in the persistent strain were also studied. The persistent strain is relatively greater in lower-rate loadings (Fig. 5).
255
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 2. The figure shows concrete sample loading machine and Method of cyclic loading. ((A) lateral strain gage; method of cyclic loading; (B) axial strain gage).
Table 3 Cyclic loading rate and specimens. Specimens shape
Cubic specimens
Cylindrical specimens
SCC type
SCC1 SCC2 SCC3 SCC1 SCC2 SCC3
Cyclic and monotonic loading rate KN/s 0.05
1
2.5
4
5
15
25
35
45
100
250
5 5 5 5 5 5
5 5 5 3 3 3
5 5 5 3 3 3
5 5 5 3 3 3
5 5 5 5 5 5
5 5 5 4 4 4
4 4 4 4 4 4
3 3 3 – – –
3 3 3 – – –
– – – 5 5 5
– – – 4 4 4
Samples
Fig. 3. Compressive strength of SCC under different loading rate and Cracks mechanism.
Fig. 4. Stress–strain curves of SCC1 under uniaxial monotonic compressive loading with different loading rates from 0.05 KN/s to 25 KN/s.
Increase in the number of loadings increases the amount of damaged concrete. The increased amount of concrete damage can be examined in the same loading rate, when the cyclic loading curves moves away from the monotonic loading curve. The slope of
the reloading branch is smaller in higher loading rates compared to that of the lower loading rates. However, this happens after the peak and after the stress–strain curve passes the maximum compressive strength of the concrete (Fig. 6).
256
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 5. Stress–strain curve of SCC under cyclic loading with 5 KN/s and 100 KN/s loading rate.
An opposite behavior is observed by comparing such behavior of the concrete and the state before the failure of the concrete. In fact, the variations in the reloading branch slope change as the concrete stress–strain curve passes the peak. This behavior may be caused by the release of the energy absorbed by the concrete at higher-rate cyclic loadings. The images of the crack and failure in the specimens can be examined to further investigate this finding.
The SCC stress–strain curves under cyclic compressive loading at two rates of 250 kN/s and 0.05 kN/s is compared in Fig. 7. The following differences were observed: (1) The maximum compressive strength of the SCC under cyclic loading is higher in higher rates. (2) The persistent strain under cyclic loading is higher in lower rates compared to the higher rates.
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
257
Fig. 6. Stress–strain curve of SCC under cyclic loading with 5 KN/s and 100 KN/s loading rate.
Fig. 7. SCC’s stress–strain curves under cyclic loading with two different loading rates.
(3) The area of the hysteresis loops after the stress–strain curve peak of concrete under cyclic loading in lower rates is smaller than that of the higher rates. This indicates that, after the main damage, concrete absorbs much more energy under cyclic loadings with lower rates. (4) The concrete damage under cyclic loading at higher rates is greater than that of the lower rates. This was examined by the stress–strain curve moving away from the envelope
curve. The sudden damage to the concrete was shown to be the cause of behavioral changes in concrete under highrate loadings. These differences in the behavior of the concrete stress–strain curve clearly occur in two pre- and post-peak areas. After the peak and the structural failure of the concrete, the energy stored in different parts and between the aggregate and mortar is released. In
258
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 8. Cracks mechanism of cylindrical SCC’s specimens under cyclic loading with different loading rate (5 KN/s, 100 KN/s and 250 KN/s).
cyclic loading, the amount of energy stored and dissipated is higher due to the opening and closure of cracks and the movement of crack dents on each other. This is the reason why behavioral changes are more significant in cyclic loading.
crete behaviors are different. Changes in the post-peak concrete behavior after the peak are affected by the pre-peak loading. In high-rate cyclic loadings, loading affects the pre-peak concrete behavior more that it does the post-peak concrete behavior.
3.4. Fracture mechanism
Reference
The sudden changes can be investigated by examining the crack structure and its growth pattern in cyclic compressive loading. When the cyclic loading rate changes, the concrete behavior, stress–strain curve, and in fact, the crack growth pattern and its depth and angle change. Cyclic loadings with different rates create surface cracks as well as deep cracks (Fig. 8). In low-rate cyclic loadings, the cracks were first observed as micro-cracks in the surface, and by increasing the number of loadings, the surface of the concrete specimen was removed from the specimen. With increasing the loading intensity in the next cycles of the same loading, deeper cracks appeared, and the micro-cracks joined together, resulting in a reduced compressive strength and the failure of concrete (Fig. 8a). By increasing the rate of cyclic loadings, larger cracks in the concrete surface are observed. The cracks are longer and can dissipate the loading through consecutive opening and closing. At each loading, the crack chooses the weakest path. The behavior of concrete appears by the formation of continuous cracks in the opposite direction (Fig. 8b). With increase in the cyclic loading rate, cracks cannot change their path in the concrete, which results in a reduced crack length. In such loadings, crack penetrates the concrete depth, but it does not have enough time to change its path, resulting in multi-direction cracks. When the concrete fails in such loading, the damaged surface is wide which cannot be observed in a persistent strain (Fig. 8c). In this case, the concrete fails suddenly. In the case of high-rate loading, less energy is absorbed, and, due to the cyclic loading, some areas of powdered concrete can be observed on the fracture surface. 4. Conclusion Results showed that the loading rate affects the compressive and tensile strength, elastic modulus, and the strain of SCC. The extent of such effect is intensified in cyclic loading. By increasing the rate of cyclic loading, the behavior of concrete approaches to that of the monotonic loading due to the reduced time required for the opening and closure of cracks. These changes are small; however, the damage surface caused by the high-rate cyclic loading observed after the stress exceeds the concrete strength. High-strength concrete specimens are more sensitive to the changes caused by high-rate cyclic loading. At each cyclic loading, the loading branch acts as a monotonic loading with different rates. The total changes in every stage of loading causes many differences in the stress–strain curve. The pre- and post-peak con-
[1] B.P. Sinha, K.H. Gerstle, L.G. Tulin, Stress–strain relations for concrete under cyclic loading, ACI Struct. J. 61 (2) (1964) 195–211. [2] I.D. Karsan, J.O. Jirsa, Behavior of concrete under compressive loadings, ASCE Struct. Eng. J. 95 (12) (1969) 2543–2563. [3] O. Buyukozturk, T.M. Tesng, Concrete in biaxial cyclic compression, ASCE Struct. Eng. J. 110 (2) (1976) 355–369. [4] D.Z. Yankelevsky, H.W. Rainhardt, Model for cyclic compressive behavior of concrete, ASCE Struct. Eng. J. 113 (2) (1987) 228–240. [5] D.Z. Yankelevsky, H.W. Rainhardt, Uniaxial behavior of concrete in cyclic tension, ASCE Struct. Eng. J. 115 (1) (1989) 166–182. [6] B.Y. Bahn, C.T. Hsu, Stress-strain behavior of concrete under cyclic loading, ACI Mater. J. 95 (2) (1998) 178–193. [7] D. Palermo, F.J. Vecchio, Compression field modeling of reinforced concrete subjected to reversed loading: formulation, ACI Struct. J. 100 (5) (2003) 616– 625. [8] F.J. Vecchio, M.P. Collins, The modified compression field theory for reinforced concrete elements subjected to shear, ACI Struct. J. 83 (2) (1986) 219–231. [9] J. Sakai, K. Kawashima, Unloading and reloading stress–strain model for confined concrete, ASCE Struct. Eng. J. 132 (1) (2006) 112–122. [10] J.B. Mander, N.J.N. Priestley, R. Park, Theoretical stress–strain model for confined concrete, ASCE Struct. Eng. J. 114 (8) (1988) 1804–1826. [11] E. Martinez-Rueda, A.S. Elnashai, Confined concrete model under cyclic load, Mater. Struct. 30 (1997) 139–147. [12] M. Mansour, C.T. Hsu, Behavior of reinforced concrete elements under cyclic shear II: theoretical model, ASCE Struct. Eng. J. 131 (1) (2005) 54–65. [13] G.F. Sima, P. Roca, C. Molins, Cyclic constitutive model for concrete, J. Eng. Struct. 30 (2008) 695–706. [14] P. Grassl, R. Rempling, A damage-plasticity interface approach to the mesoscale modelling of concrete subjected to cyclic compressive loading, Eng. Fract. Mech. 75 (2008) 4804–4818. [15] B. Richard, F. Ragueneau, Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: formulation, numerical implementation and applications, Eng. Fract. Mech. 98 (2013) 383–406. [16] B. Richard et al., Isotropic continuum damage mechanics for concrete under cyclic loading: stiffness recovery, inelastic strains and frictional sliding, Eng. Fract. Mech. 77 (2010) 1203–1223. [17] S. Korte et al., Static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedge-splitting tests, Constr. Build. Mater. 57 (2014) 1–8. [18] I.M. Nikbin et al., Effect of coarse aggregate volume on fracture behavior of self-compacting concrete, Constr. Build. Mater. 15 (2014) 137–145. [19] D. Zheng et al., Rate effect of concrete strength under initial static loading, Eng. Fract. Mech. 74 (2007) 2311–2319. [20] L. Elias, J.L. Le, Modeling of mode-I fatigue crack growth in quasi-brittle structures under cyclic, Compression Eng. Fract. Mech. 96 (2012) 26–36. [21] G. Cusatis, Strain-rate effects on concrete behavior, Int. J. Impact Eng. 38 (2011) 162–170. [22] D. Wang, H.N. Li, G. Li, Experimental test on reinforced concrete columns under multi-dimensional dynamic loading, Constr. Build. Mater. 47 (2013) 1167–1181. [23] S. Wang, M. Zhang, S.T. Quek, Mechanical behavior of fiber-reinforced highstrength concrete subjected to high strain-rate compressive loading, Constr. Build Mater. 31 (2012) 1–11. [24] E.H. Yang, C.V. Li, Strain-rate effects on the tensile behavior of strain hardening cementation composites, Constr. Build Mater. 52 (15) (2014) 96–104. [25] Q. Fang, J. Zhang, Three-dimensional modelling of steel fiber reinforced concrete material under intense dynamic loading, Constr. Build Mater. 44 (2013) 118–132.
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259 [26] Y.S. Tai, Uniaxial compression tests various loading rates for reactive powder concrete, Theor. Appl. Fract. Mech. 55 (2009) 14–21. [27] H. Fathi, K. Farhang, Effect of cyclic loadings on heated self-compacting concrete, Constr. Build. Mater. 69 (2014) 26–31. [28] H. Fathi, K. Farhang, Behavior of reinforcement SCC beams under elevated temperatures, Int. J. Adv. Struct. Eng. 7 (3) (2015) 261–267. [29] S. Sinaie et al., Effect of size on the response of cylindrical concrete samples under cyclic loading, Constr. Build. Mater. 84 (2015) 399–408. [30] N.A. Brake, K. Chatti, Prediction of size effect and non-linear crack growth in plain concrete under fatigue loading, Eng. Fract. Mech. 109 (2013) 169–185. [31] G.B. Fonteboa et al., Structural recycled concrete: behaviour under low loading rate, Constr. Build. Mater. 28 (1) (2012) 111–116.
259
[32] P. Li, Y.F. Wu, Stress–strain model of FRP confined concrete under cyclic loading, Compos. Struct. 134 (2015) 60–71. [33] T. Yu et al., Unified cyclic stress–strain model for normal and high strength concrete confined with FRP, Eng. Struct. 102 (2015) 189–201. [34] V. Corinaldesi et al., Behaviour of beam–column joints made of recycledaggregate concrete under cyclic loading, Constr. Build. Mater. 25 (4) (2011) 1877–1882. [35] S. Korte, Experimental and numerical investigation of the fracture behaviour and fatigue resistance of self-compacting concrete Ph.D. thesis, Ghent University, 2015.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Damage mechanism of SCC under cyclic loading with different speed Hamoon Fathi a,⇑, Hooshang Dabbagh b a b
Department of Civil Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran
h i g h l i g h t s The effect of loading rate on concrete behavior is greater before the peak. Changing cyclic loading rate would cause a corresponding change in SCC cracking. During creep cyclic loading, the stress–strain diagram undergoes great changes. Concrete demonstrates different behaviors under cyclic loading with different rate.
a r t i c l e
i n f o
Article history: Received 25 June 2015 Received in revised form 8 September 2015 Accepted 17 October 2015
Keywords: Self-compacting concrete Cyclic loading Loading rate Stress–strain curve Fracture mechanism
a b s t r a c t In this experimental research, the effects of cyclic loading at different frequencies on self-compacting concrete were studied. 108 standard cylindrical specimens and 120 cubic specimens were tested. The specimens had compressive strengths of approximately 25 MPa, 35 MPa and 45 MPa. The rate of loading was studied in the 0.05–250 KN/s range. The results showed that the behavior of concrete before and after peak loading depended on the number of loadings as well as the loading rate. Failure of concrete under periodic loading at high frequencies led to increased micro cracks in a direction perpendicular to that of the principal cracks. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Earthquakes reduce the bearing capacity of concrete. In order to model earthquakes and the amount of energy transferred to a structure, the loading rate or cyclic loading can be changed or the fatigue loading method can be used. The amount of energy transferred per unit time can alter the behavior of structural materials under the respective loading. The studies conducted by Sinha et al. [1] can be considered as the first experimental studies on concrete behavior under cyclic loading. They discussed concrete behavior under cyclic loading. They carried out their studies experimentally on 48 standard cylindrical specimens. Compressive strength of the cylindrical specimens ranged 20–28 MPa. The studies showed that a cyclic loading curve does not pass through monotonic loading curve. The curve was introduced as an envelope curve. Karsan and Jirsa [2], developed the earlier experimental results within the ⇑ Corresponding author. E-mail addresses: [email protected] (H. Fathi), [email protected] (H. Dabbagh). http://dx.doi.org/10.1016/j.conbuildmat.2015.10.103 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
compressive range. Their research was carried out on 46 short rectangular column specimens. Loading of the specimens was under the effect of a cyclic loading along the main axis of a column and column behavior was studied on the plate of the same axis. Finally, they presented a model for the envelope curve of concrete stress– strain diagram in a cyclic loading. Their study showed that the loading curve and re-unloading curve meet at some points, a series of which is called common points limit. There is almost a certain distance between this curve and the envelope curve. Buyukozturk and Tseng [3] developed the earlier studies on concrete behavior in a cyclic loading. These studies discussed the effects of increasing strain and energy level with respect to loading gradient. Yankelevsky and Reinhardt [4,5] presented a simple non-linear model for stress–strain diagram of concrete in a cyclic loading with respect to the effects of history of the previous loading. Their model is in two separate forms for compressive and tensile loadings states. Of course, these simple models are formed as a tangent line on the envelope curve in press section. Bahn and Hsu [6] carried out parametric and experimental studies on concrete under the effect of cyclic loading. The results led to overall control of cyclic stress–strain curve. The specimens
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
were tested as 76 * 152 cylinders. They used four loading models. The reverse relationship between plastic strain and mean of unloading and loading curve gradient is among the results of the studies, Vecchio and Collins [7] carried out an experimental study on concrete behavior under different loadings. Later, these studies were continued by Palermo and Vecchio [8] in the theoretical section. The models also point out the relationship between loading and unloading curve with the created cracks. They tested 30 reinforced concrete specimens and examined the cracks developed on the concrete surface. The studies indicated that concrete reloading provides an appropriate response in a linear manner and concrete loading within tensile range is non-linear. Sakai and Kawashima [9] studied behavior of reinforced concretes. The results obtained from the 28-day concrete specimens were used in these tests. In their research, they pointed out the monotony of the gradient of initial curve and the initial loading and showed that the unloading curve is concave from the initial point. Mander et al. [10] developed a stress–strain model of concrete in a uniaxial compressive loading. These loadings deal more with the range between tension and compression. Their experiments were carried out on beams and columns. Martinez and Elnashai [11] modified the reloading curve using a linear relation. This line was considered between the zero stress points and reloading strain; whereas, the unloading curve is placed between unloading strain and stress–strain curve in a monotonic loading. Mansour and Hsu [12] developed concrete behavior modeling with respect to a series of experimental results within the tensile and compressive range. These equations discuss linear models of reloading and curve models for loading. Elnashai and Martinez [11] and Sima et al. [13] were among those who presented cyclic loading models on concrete. Several studies have been conducted on the plastic behavior and the effects of cracks caused by cyclic loading on concrete models. Concrete, as a brittle non-homogenous material, is very sensitive under fatigue loading [14–18]. Examining the behavior of materials under cyclic loading is an approach to model the behavior of materials and structures during an earthquake. The behavior of materials under cyclic loading is studied using the stress–strain curves. Cyclic loading has a specific regime during an increase or a decrease in loading. However, in case of an earthquake where the cyclic loading is of variable rate, the situation is not similar. This study examines the simultaneous effects of cyclic loading and the variations in the loading rate. In fact, the concrete is subjected to a cyclic loading at different rates. Zheng et al. [19] examined the static behavior of concrete under different loading rates. The presented model complied with the experimental results. Their model aimed to establish a relationship between the dynamic strength and different levels of static stress. The model, however, was less consistent with the experimental results in low-rate loadings. Elias and Le modeled the fatigue crack growth under cyclic loading [20]. Their model addressed the compressive cyclic loading. Brittle non-homogenous materials undergo fatigue under cyclic loading, leading to crack growth in the material. Lots of studies are investigated and modeled the concrete behavior under cyclic loading at tension or compression area. But most of these studies are subjected cyclic loadings at quasi-static loading rate. In fact, uniaxial monotonic loadings have direct effects on test results. Compressive strength, cracks distribution, elastic modulus and Poisson ratio are dependent to loading rate. Test scales for loading rate are usually categorized with strain rate in a period of time. Fig. 1 defines a diagram for equivalent strain rates and loading simulation effects on the samples. According to the size of samples, these ranges can be categorized with loading rate from 10 8 m/s (0.05 KN/s for cylindrical samples) to 103 m/s. Many experimental researches are investigated the effect of loading rate on compressive strength, mechanical behavior and
253
Fig. 1. Diagram of strain rate and loading type.
stress–strain relationship of concrete. the results are showed, elastic modulus and Poisson ratio are grew when specimens were subjected with higher loading rate [21–23]. High speed loading, dynamic loading and earthquake loading effects on mechanical properties of concrete are simulated in these studies. Furthermore, some studies are tested different type of concrete under different strain rate’s level [24–26]. Most of experimental tests on concrete are performed in compressive area. Due to the increasing use of self-compacting concretes (SCC) and the need for more detailed studies on this type of concrete, SCC specimens are studied in this research. Continuous segments were examined for a detailed and step by step study of the SCC behavior under cyclic loading along with variations in the loading rate. The variations in the compressive strength of the SCC specimens were investigated. The SCC stress–strain curve under monotonic loading with different rates were extracted and compared. Finally, according to the results, the other batch of specimens was tested under a specific cyclic loading with different rates. The stress–strain curve of concrete under cyclic loading with different rates was compared in each step. Persistent strain, the angle of the tangent line on the reloading branch, and the shapes of hysteresis loops were compared. The main cause of behavioral changes in SCC under cyclic loading is the spread of cracks in the specimen. The crack depth, crack length, crack passage through the aggregates, and the crack angle are the main differences between the specimens under cyclic loading with different rates. 2. Experimental study This experimental study discusses the effect of cyclic loading with nine levels of loading rate on SCC. The experiment parameters are including cyclic loading rate and compressive strength. Stress–strain curves and compressive strength of SCC are studied under changing these tests’ parameters.
2.1. Materials The concrete mixes in the test consisted crushed aggregates, micro silica, plasticizer, cement and water. They were prepared from local sources with material properties as presented in Table 1.
2.2. Specimens One hundred and eight (diameter of crass section: 150 mm and height: 300 mm) standard cylindrical specimens and one hundred and twenty (100 * 100 * 100 mm) cubic specimens are tested. The compressive strength of the specimens which manufactured for respect to the different mixes was 25 MPa,
Table 1 Specifications of the materials used in the prepared concrete mix. Materials name
Materials type
Qualification
Aggregate Water Cement
Gravel Normal Type 1
Add materials
Micro silica Plasticizer
Bulk: 1750 kg/m3; maximum size: 19.5 mm PH: 7; low mineral Setting time: 135 min, compressive strength: 325 kg/cm2 Density: 2110 kg/m3 Density: 1200 kg/m3
254
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Table 2 The mix ratio used in SCC samples is in terms of percent by weight of the materials. Name
SCC 1 SCC 2 SCC 3
Cement weight ratio (375 kg in 1 m3) Plasticizer cement
Microsilica cement
Water cement
(%)
(%)
(%)
4 5 6
0 5 10
33 33 33
Slump flow (cm)
Compressive strength (MPa)
than bypassing the aggregates and passing the looser paths, given the power generated by the imposed force, the cracks break the aggregates and choose the shorter path. 3.1. Compressive strength
69 65 64
25 35 45
35 MPa and 45 MPa (Table 2). To compare the results of this research with those of previous studies, the concrete mixture ratios were selected from Tables 1 and 2 [27,28]. Specifications of the manufactured concrete mixes are categorized in three different groups. The amount of micro silica and plasticizer in these mixes are changed and other proportions of materials have fixed amounts. 2.3. Curing Aggregates were washed, dried and drowned in water for 24 h, aggregates were poured in a mixer, as Saturated Surface Dry (SSD) and cement and micro silica were added. The required water for concrete was added in two stages, before and after adding additive and lubricant in an equal volume. After 24 h mold were removed and samples were placed in a mixture of water and some lime to reducing alkaline condition for 26 days. The specimens were kept in laboratory temperature (23 °C) for one day, and then subjected to loading. 2.4. Loading In this study, the compressive monotonic and cyclic loadings were tested. Monotonic and cyclic loadings were applied under different rates. Monotonic loadings were continued until the failure in the specimens. Cyclic loadings were performed in 12 loading steps with different stress values (Fig. 2). Both cubic and cylindrical specimens were used for the study of mechanical properties of concrete. There are many relations for converting the results [29,30]. However, the results of previous studies were used for selecting the tests and the specimens thereof. In most previous research conducted on the effect of uniform load on concrete, cubic specimens were used [27,31]. For this reason, the authors also used cubic specimens for uniaxial load tests conducted to assess the difference between conventional and self-compacting concrete types. In most cyclic loading experiments, strains are calculated and stress–strain diagrams plotted. To this end, cylindrical samples are usually used for testing [27,32]. In the cyclic loading tests in the present study, cylindrical specimens were used to make possible comparison of test results with those obtained from conventional tests, and to compare the effects of velocity change on the behavior of concrete specimens and the failure images thereof [33–35]. Loading rates ranged from 0.05 kN/s to 250 kN/s (Table 3). The range included the creep, quasi-static, and dynamic behaviors (Fig. 1). SCC cubic specimens were tested under monotonic loads, and the stress–strain curves were extracted from the cylindrical specimens. Concrete specimen compressive strength changes with loading rate. Studies show that this change is proportional to the initial compressive strength of concrete, which can be selected on a relative basis. As in other uniform loading studies, the initial compressive strength of concrete in this study was assumed to be equal to that obtained at the start of quasi-static loading [24–27]. The three compressive strength ranges presented in Table 2 indicate increased maximum compressive strength with loading rate and, therefore, provide a wide range of compressive strength values for concrete.
3. Discussion and results Variations in the cyclic loading affect the opening and closure of cracks as well as the amount of energy transferred per unit time. The variations in the concrete stress–strain curve and the area of the hysteresis loops describe the extent of damage in concrete and as well as the absorbed energy. The amount of persistent strain in the curves indicates the cracks formed under a specific loading. Different rates affect the concrete compressive and tensile strengths. It also indirectly affects the elastic modulus and the Poisson’s ratio. The main difference between different loading rates is the amount of energy transferred to the specimen. An increased energy transferred per unit time to the concrete causes the cracks to choose a more direct path to break the concrete. In fact, rather
Results showed that by increasing the hardness of concrete, mortar compressive strength becomes more similar to that of the aggregates. The strength of mortar approaches to that of the aggregate, and when the concrete breaks, the crack passes through the aggregates and mortar. Accordingly, the impact of an increased loading rate is not significant and does not change the crack path in high-strength concretes, because the changes in the strength of high-strength concretes caused by an increased loading rate in less significant compared to that of the conventional concretes (Fig. 3). Fig. 3 compares the compressive strengths of the specimens Scc1, Scc2, and Scc3 under monotonic cyclic loading in the rate range of 0.5–45 KN/s. The compressive strengths of all three models slightly decreased at very low loading rates which may be due to the formation of initial cracks caused by shrinkage. The decrease continued to the limit specified for the creep behavior (This range is defined with due regard of loading rate.), confirming the effect of micro-cracks on the slight reduction in the compressive strength. Increase in the rate of the monotonic compressive loading increased the compressive strength of the concrete. 3.2. Stress–strain curve and monotonic loading The stress–strain curves under monotonic loading act like an envelope curve for the stress–strain curves under cyclic loading. Therefore, it can show the changes caused by the cyclic loading and the amount of damage and energy generated to crack the concrete under cyclic loading. However, variations in the loading rate affect the elastic modulus, strain, and strength. Therefore, the concrete specimens were tested under different rates. Fig. 4 shows the SCCL stress–strain curve under the monotonic loadings with rates of 0.05–25 KN/s. The SCCL elastic modulus concrete increases with increasing the loading. However, in low loading rates and in the creep behavior range, the variations are less significant, and the slope of the loading curve is strain-dependent. The slow loading rate (within the defined range for creep behavior), allows the concrete to fully undergo strain. The reason is that the calculated strain is greater under slowly applied uniaxial uniform loading [35]. 3.3. Stress–strain curve and cyclic loading The present study aimed at investigating the effects of compressive cyclic loading with different rates (0.05–250 KN/s) on the behavior of SCCs. For this purpose, the variations in the stress– strain curve were examined. The effect of cyclic loading is different pre and post-peak. Fig. 5 shows the pre-peak concrete stress–strain curve. In this section, each loading was repeated for three times. The loading stress was then increased to a higher range, where the loading was repeated for three more times. Results showed that, in lower loading rates, the reloading branch has a smaller curvature which decreases with increasing the rate of the cyclic loading. These variations indicate that the effect of micro-cracks on the stress–strain curve is less significant in high-rate cyclic loadings. The area of the hysteresis loops is greater in high-rate cyclic loadings. An increased area indicates an increased amount of absorbed energy. The changes in the persistent strain were also studied. The persistent strain is relatively greater in lower-rate loadings (Fig. 5).
255
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 2. The figure shows concrete sample loading machine and Method of cyclic loading. ((A) lateral strain gage; method of cyclic loading; (B) axial strain gage).
Table 3 Cyclic loading rate and specimens. Specimens shape
Cubic specimens
Cylindrical specimens
SCC type
SCC1 SCC2 SCC3 SCC1 SCC2 SCC3
Cyclic and monotonic loading rate KN/s 0.05
1
2.5
4
5
15
25
35
45
100
250
5 5 5 5 5 5
5 5 5 3 3 3
5 5 5 3 3 3
5 5 5 3 3 3
5 5 5 5 5 5
5 5 5 4 4 4
4 4 4 4 4 4
3 3 3 – – –
3 3 3 – – –
– – – 5 5 5
– – – 4 4 4
Samples
Fig. 3. Compressive strength of SCC under different loading rate and Cracks mechanism.
Fig. 4. Stress–strain curves of SCC1 under uniaxial monotonic compressive loading with different loading rates from 0.05 KN/s to 25 KN/s.
Increase in the number of loadings increases the amount of damaged concrete. The increased amount of concrete damage can be examined in the same loading rate, when the cyclic loading curves moves away from the monotonic loading curve. The slope of
the reloading branch is smaller in higher loading rates compared to that of the lower loading rates. However, this happens after the peak and after the stress–strain curve passes the maximum compressive strength of the concrete (Fig. 6).
256
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 5. Stress–strain curve of SCC under cyclic loading with 5 KN/s and 100 KN/s loading rate.
An opposite behavior is observed by comparing such behavior of the concrete and the state before the failure of the concrete. In fact, the variations in the reloading branch slope change as the concrete stress–strain curve passes the peak. This behavior may be caused by the release of the energy absorbed by the concrete at higher-rate cyclic loadings. The images of the crack and failure in the specimens can be examined to further investigate this finding.
The SCC stress–strain curves under cyclic compressive loading at two rates of 250 kN/s and 0.05 kN/s is compared in Fig. 7. The following differences were observed: (1) The maximum compressive strength of the SCC under cyclic loading is higher in higher rates. (2) The persistent strain under cyclic loading is higher in lower rates compared to the higher rates.
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
257
Fig. 6. Stress–strain curve of SCC under cyclic loading with 5 KN/s and 100 KN/s loading rate.
Fig. 7. SCC’s stress–strain curves under cyclic loading with two different loading rates.
(3) The area of the hysteresis loops after the stress–strain curve peak of concrete under cyclic loading in lower rates is smaller than that of the higher rates. This indicates that, after the main damage, concrete absorbs much more energy under cyclic loadings with lower rates. (4) The concrete damage under cyclic loading at higher rates is greater than that of the lower rates. This was examined by the stress–strain curve moving away from the envelope
curve. The sudden damage to the concrete was shown to be the cause of behavioral changes in concrete under highrate loadings. These differences in the behavior of the concrete stress–strain curve clearly occur in two pre- and post-peak areas. After the peak and the structural failure of the concrete, the energy stored in different parts and between the aggregate and mortar is released. In
258
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259
Fig. 8. Cracks mechanism of cylindrical SCC’s specimens under cyclic loading with different loading rate (5 KN/s, 100 KN/s and 250 KN/s).
cyclic loading, the amount of energy stored and dissipated is higher due to the opening and closure of cracks and the movement of crack dents on each other. This is the reason why behavioral changes are more significant in cyclic loading.
crete behaviors are different. Changes in the post-peak concrete behavior after the peak are affected by the pre-peak loading. In high-rate cyclic loadings, loading affects the pre-peak concrete behavior more that it does the post-peak concrete behavior.
3.4. Fracture mechanism
Reference
The sudden changes can be investigated by examining the crack structure and its growth pattern in cyclic compressive loading. When the cyclic loading rate changes, the concrete behavior, stress–strain curve, and in fact, the crack growth pattern and its depth and angle change. Cyclic loadings with different rates create surface cracks as well as deep cracks (Fig. 8). In low-rate cyclic loadings, the cracks were first observed as micro-cracks in the surface, and by increasing the number of loadings, the surface of the concrete specimen was removed from the specimen. With increasing the loading intensity in the next cycles of the same loading, deeper cracks appeared, and the micro-cracks joined together, resulting in a reduced compressive strength and the failure of concrete (Fig. 8a). By increasing the rate of cyclic loadings, larger cracks in the concrete surface are observed. The cracks are longer and can dissipate the loading through consecutive opening and closing. At each loading, the crack chooses the weakest path. The behavior of concrete appears by the formation of continuous cracks in the opposite direction (Fig. 8b). With increase in the cyclic loading rate, cracks cannot change their path in the concrete, which results in a reduced crack length. In such loadings, crack penetrates the concrete depth, but it does not have enough time to change its path, resulting in multi-direction cracks. When the concrete fails in such loading, the damaged surface is wide which cannot be observed in a persistent strain (Fig. 8c). In this case, the concrete fails suddenly. In the case of high-rate loading, less energy is absorbed, and, due to the cyclic loading, some areas of powdered concrete can be observed on the fracture surface. 4. Conclusion Results showed that the loading rate affects the compressive and tensile strength, elastic modulus, and the strain of SCC. The extent of such effect is intensified in cyclic loading. By increasing the rate of cyclic loading, the behavior of concrete approaches to that of the monotonic loading due to the reduced time required for the opening and closure of cracks. These changes are small; however, the damage surface caused by the high-rate cyclic loading observed after the stress exceeds the concrete strength. High-strength concrete specimens are more sensitive to the changes caused by high-rate cyclic loading. At each cyclic loading, the loading branch acts as a monotonic loading with different rates. The total changes in every stage of loading causes many differences in the stress–strain curve. The pre- and post-peak con-
[1] B.P. Sinha, K.H. Gerstle, L.G. Tulin, Stress–strain relations for concrete under cyclic loading, ACI Struct. J. 61 (2) (1964) 195–211. [2] I.D. Karsan, J.O. Jirsa, Behavior of concrete under compressive loadings, ASCE Struct. Eng. J. 95 (12) (1969) 2543–2563. [3] O. Buyukozturk, T.M. Tesng, Concrete in biaxial cyclic compression, ASCE Struct. Eng. J. 110 (2) (1976) 355–369. [4] D.Z. Yankelevsky, H.W. Rainhardt, Model for cyclic compressive behavior of concrete, ASCE Struct. Eng. J. 113 (2) (1987) 228–240. [5] D.Z. Yankelevsky, H.W. Rainhardt, Uniaxial behavior of concrete in cyclic tension, ASCE Struct. Eng. J. 115 (1) (1989) 166–182. [6] B.Y. Bahn, C.T. Hsu, Stress-strain behavior of concrete under cyclic loading, ACI Mater. J. 95 (2) (1998) 178–193. [7] D. Palermo, F.J. Vecchio, Compression field modeling of reinforced concrete subjected to reversed loading: formulation, ACI Struct. J. 100 (5) (2003) 616– 625. [8] F.J. Vecchio, M.P. Collins, The modified compression field theory for reinforced concrete elements subjected to shear, ACI Struct. J. 83 (2) (1986) 219–231. [9] J. Sakai, K. Kawashima, Unloading and reloading stress–strain model for confined concrete, ASCE Struct. Eng. J. 132 (1) (2006) 112–122. [10] J.B. Mander, N.J.N. Priestley, R. Park, Theoretical stress–strain model for confined concrete, ASCE Struct. Eng. J. 114 (8) (1988) 1804–1826. [11] E. Martinez-Rueda, A.S. Elnashai, Confined concrete model under cyclic load, Mater. Struct. 30 (1997) 139–147. [12] M. Mansour, C.T. Hsu, Behavior of reinforced concrete elements under cyclic shear II: theoretical model, ASCE Struct. Eng. J. 131 (1) (2005) 54–65. [13] G.F. Sima, P. Roca, C. Molins, Cyclic constitutive model for concrete, J. Eng. Struct. 30 (2008) 695–706. [14] P. Grassl, R. Rempling, A damage-plasticity interface approach to the mesoscale modelling of concrete subjected to cyclic compressive loading, Eng. Fract. Mech. 75 (2008) 4804–4818. [15] B. Richard, F. Ragueneau, Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: formulation, numerical implementation and applications, Eng. Fract. Mech. 98 (2013) 383–406. [16] B. Richard et al., Isotropic continuum damage mechanics for concrete under cyclic loading: stiffness recovery, inelastic strains and frictional sliding, Eng. Fract. Mech. 77 (2010) 1203–1223. [17] S. Korte et al., Static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedge-splitting tests, Constr. Build. Mater. 57 (2014) 1–8. [18] I.M. Nikbin et al., Effect of coarse aggregate volume on fracture behavior of self-compacting concrete, Constr. Build. Mater. 15 (2014) 137–145. [19] D. Zheng et al., Rate effect of concrete strength under initial static loading, Eng. Fract. Mech. 74 (2007) 2311–2319. [20] L. Elias, J.L. Le, Modeling of mode-I fatigue crack growth in quasi-brittle structures under cyclic, Compression Eng. Fract. Mech. 96 (2012) 26–36. [21] G. Cusatis, Strain-rate effects on concrete behavior, Int. J. Impact Eng. 38 (2011) 162–170. [22] D. Wang, H.N. Li, G. Li, Experimental test on reinforced concrete columns under multi-dimensional dynamic loading, Constr. Build. Mater. 47 (2013) 1167–1181. [23] S. Wang, M. Zhang, S.T. Quek, Mechanical behavior of fiber-reinforced highstrength concrete subjected to high strain-rate compressive loading, Constr. Build Mater. 31 (2012) 1–11. [24] E.H. Yang, C.V. Li, Strain-rate effects on the tensile behavior of strain hardening cementation composites, Constr. Build Mater. 52 (15) (2014) 96–104. [25] Q. Fang, J. Zhang, Three-dimensional modelling of steel fiber reinforced concrete material under intense dynamic loading, Constr. Build Mater. 44 (2013) 118–132.
H. Fathi, H. Dabbagh / Construction and Building Materials 101 (2015) 252–259 [26] Y.S. Tai, Uniaxial compression tests various loading rates for reactive powder concrete, Theor. Appl. Fract. Mech. 55 (2009) 14–21. [27] H. Fathi, K. Farhang, Effect of cyclic loadings on heated self-compacting concrete, Constr. Build. Mater. 69 (2014) 26–31. [28] H. Fathi, K. Farhang, Behavior of reinforcement SCC beams under elevated temperatures, Int. J. Adv. Struct. Eng. 7 (3) (2015) 261–267. [29] S. Sinaie et al., Effect of size on the response of cylindrical concrete samples under cyclic loading, Constr. Build. Mater. 84 (2015) 399–408. [30] N.A. Brake, K. Chatti, Prediction of size effect and non-linear crack growth in plain concrete under fatigue loading, Eng. Fract. Mech. 109 (2013) 169–185. [31] G.B. Fonteboa et al., Structural recycled concrete: behaviour under low loading rate, Constr. Build. Mater. 28 (1) (2012) 111–116.
259
[32] P. Li, Y.F. Wu, Stress–strain model of FRP confined concrete under cyclic loading, Compos. Struct. 134 (2015) 60–71. [33] T. Yu et al., Unified cyclic stress–strain model for normal and high strength concrete confined with FRP, Eng. Struct. 102 (2015) 189–201. [34] V. Corinaldesi et al., Behaviour of beam–column joints made of recycledaggregate concrete under cyclic loading, Constr. Build. Mater. 25 (4) (2011) 1877–1882. [35] S. Korte, Experimental and numerical investigation of the fracture behaviour and fatigue resistance of self-compacting concrete Ph.D. thesis, Ghent University, 2015.