Experimental investigation on static and dynamic mechanical properties of steel fiber reinforced ultra-high-strength concretes

Experimental investigation on static and dynamic mechanical properties of steel fiber reinforced ultra-high-strength concretes

Construction and Building Materials 178 (2018) 102–111 Contents lists available at ScienceDirect Construction and Building Materials journal homepag...

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Construction and Building Materials 178 (2018) 102–111

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Experimental investigation on static and dynamic mechanical properties of steel fiber reinforced ultra-high-strength concretes Liu Jin, Renbo Zhang ⇑, Yudong Tian, Guoqin Dou, Xiuli Du ⇑ Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China

h i g h l i g h t s  A SFR-UHSC produced with common materials and standard curing methods was studied.  Under static loadings, SFR-UHSC exhibits good ductility, toughness and plasticity.  Under dynamic loadings, SFR-UHSC cracks along various paths without fragmentation.  Mechanical properties of SFR-UHSC are improved by the addition of steel fibers.  SFR-UHSC has a slightly lower strain rate effect than ordinary concrete.

a r t i c l e

i n f o

Article history: Received 29 November 2017 Received in revised form 26 March 2018 Accepted 18 May 2018

Keywords: Steel fiber reinforcement Ultra-high strength concrete (UHSC) Static mechanical properties Dynamic compressive properties Split Hopkinson press bar (SHPB)

a b s t r a c t Nowadays, high-rise, long-span and complicated structures are springing up. Accordingly, there is an increasing need for concretes with high strength even ultra-high strength, low cost and low construction difficulties. In the present study, steel fiber reinforced ultra-high-strength concrete (SFR-UHSC) was designed and produced with common materials and standard curing methods. To obtain a good performance, a low water-to-binder ratio of 0.22, a superplasticizer and several readily available mineral admixtures were applied. Static mechanical and Split Hopkinson press bar tests were carried out to evaluate the mechanical performances of SFR-UHSC. It is found that under static loadings, SFR-UHSC exhibits good ductility, toughness and plasticity. In details, compared with cubic and prism compressive strengths as well as Young’s modulus of SFR-UHSC, much more increases of splitting tensile and flexural strengths are obtained by the introduction of steel fibers. When the volume fraction of steel fiber increases, the ratio between prism and cubic compressive strengths decreases while the ratio of tensile strength to compressive strength increases. On the other hand, in the scenario of high strain rate, SFR-UHSC has a good energy absorption capacity and compressive toughness. When subjected to impact loadings, SFRUHSC cracks along various paths without fragmentation. Moreover, dynamic compressive strength is increased by both increasing strain rate and steel fiber content while its strain rate effect is slightly lower than that of ordinary concrete. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Ordinary concrete can no longer meet the need due to the complexity of structures themselves and service environment for highrising buildings, bridges, offshore structures and hydraulic structures [1]. By employing a low water-to-binder ratio, fine and active admixtures (i.e., silica fume, fly ash and ground granulated blast furnace slag, etc.) as well as special curing technologies, high strength concrete (HSC) or ultra-high strength concrete (UHSC) ⇑ Corresponding authors. E-mail addresses: [email protected] (R. Zhang), [email protected] (X. Du). https://doi.org/10.1016/j.conbuildmat.2018.05.152 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

has been achieved [2]. It is well-known, however, the ratio between tensile strength and compressive strength of plain HSC and UHSC is quite low for their brittle nature. To overcome these drawbacks, various treatments have been taken by researchers, such as addition of discontinuous fibers, use of continuous textile reinforcements and external strengthening with fiber-reinforced polymer (FRP) [2]. Among these, it has been widely accepted that introduction of fibers into concrete is an effective way to enhance concrete tensile strength, fracture toughness and dynamic mechanical properties as well as durability [3]. During the last few decades, steel fiber is one of the most widely used fibers to reinforce the properties of concrete for its easiness to be obtained and to be included in concrete matrix [4,5]. Through

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experimental means, the basic static mechanical properties of steel fiber reinforced high strength or ultra-high strength concretes (SFR-HSC and SFR-UHSC, respectively) were tested [6–10]. Considering the complicated stress state of concrete, Lu and Hsu [11] conducted a series of tests to evaluate the effect of steel fiber reinforcement on the behavior of HSC under triaxial compression. In light of that SFR-HSC and SFR-UHSC are most utilized in protective structures which may undertake dynamic loadings with high strain rate, the dynamic behaviors of SFR-HSC and SFR-UHSC were investigated. The effects of steel fiber shape, aspect ratio, distribution directions and hybrid steel fibers were often explored [6,9,12– 19]. Based on the available experimental data, Xu and Shi [3] carried out an investigation on correlations among compressive strength, splitting tensile strength and flexural strength of steel fiber reinforced concrete (SFRC). What’s more, some nonlinear numerical simulations have also been conducted on SFRC by modifying constitutive relationship of ordinary concrete [14] or employing direct tension force transfer model [20], multilevel computational model [21], computational fluid dynamics [22] and Delaunay triangulation to mesh the computation areas [23], etc. It can be viewed through the aforementioned studies that a relatively mature understanding of SFR-HSC and SFR-UHSC is forming currently. Nevertheless, a more comprehensive and thorough investigation is still in need to study both the static and dynamic mechanical properties of SFR-UHSC. Herein this work, the SFR-UHSC including gravel aggregate was designed and produced with common materials and standard curing methods. To guarantee its performances, a low water-to-binder ratio of 0.22, a superplasticizer and several readily available mineral admixtures (i.e., silica fume, fly ash and ground granulated blast furnace slag) were employed. After a brief introduction of the whole experimental process, test results on the basic static mechanical properties (compressive, splitting tensile and flexural strengths as well as Young’s modulus) of SFR-UHSC were reported and analyzed. Moreover, with SHPB experiments, the dynamic behavior of SFR-UHSC under high strain rate, namely, the failure patterns, stress-strain relationship, dynamic compressive strength, energy absorption capacity and compressive toughness were also described. The effects of steel fiber contents and strain rate on the mechanical performances of SFR-UHSC were discussed.

2. Experimental program 2.1. Materials and mixture proportion Four batches of SFR-UHSC specimens with different steel fiber contents were prepared for the experiment. As tabulated in Table 1, the following materials were used in the fabrication of concrete specimens. The cement was early-strength-type Portland cement (P II 52.5R) with measured compressive strengths of 41.0 MPa (3 d) and 53.2 MPa (28 d) while flexural strengths of 6.23 MPa (3 d)

and 7.63 MPa (28 d), respectively. The admixtures included silica fume (produced in Ningxia of China, SiO2: 97%, specific area: 2  104 m2/kg), fly ash (density: 2210 kg/m3, specific area: 550 m2/ kg) and GGBS (ground granulated blast furnace slag, density: 2850 kg/m3, specific area: 450 m2/kg). The river sand with diameter less than 5 mm, fineness modulus of 2.3 and density of 2650 kg/ m3 was utilized as fine aggregate. A superplasticizer based on poly carboxylic acid was used in all the concrete mixtures to guarantee their slump without loss of strength. The solid content of poly carboxylic acid water reducing agent was 40%, and when the content of superplasticizer is 0.5%, water reduction rate reaches to 30%. The final water-to-binder ratio was 0.22. It has been proved in Wu et al.’s [8] work that the incorporation of hook-end steel fiber can effectively increase the strength of concrete, especially the flexural strength. Thence, the hook-end steel fibers (shown in Fig. 1) were also selected to prepare the SFRUHSC in the present work and four different volume fractions of steel fibers, i.e., 0, 1%, 2% and 3%, were employed. The detailed physical properties of the steel fibers were defined in Table 2. As one of the main differences from others [6–10,14–17,19], mixtures of SFR-UHSC in the present work contains coarse aggregate and gravel with diameters of 5 mm–20 mm and density of 2740 kg/m3 was adopted. The detailed mix proportion for SFRUHSC with different steel fiber contents are listed in Table 1. 2.2. Mix procedure and specimen preparation To make the steel fiber distribute uniformly, a mix procedure as shown in Fig. 2 was employed. After the mixing process, the mixture was casted into steel molds. According to ‘‘Standard test methods for fiber reinforced concrete” of China [24], four batches of mold sizes were used: 100 mm  100 mm  100 mm for tests of cubic compressive strength and splitting tensile strength; 100 mm  100 mm  300 mm for measurements of prism compressive strength and Young’s modulus; 100 mm  100 mm  400 mm for evaluations of flexural strength and toughness; and 100 mm  100 mm  170 mm for the test of dynamic properties. In reality, the SHPB test was not directly carried out on the specimens of 100 mm  100 mm  170 mm while cylindrical samples (with diameter of 75 mm and height of 50 mm) taken from the cuboid specimens was employed. Freshly cast specimens were kept in molds for 24 h, and then demolded and cured in laboratory with relative humidity of 95% for 28 days at room temperature instead of in hot water. The ordinary curing condition for SFR-UHSC is also a main contribution of the present work. 2.3. Test methods According to Chinese Standard CECS 13: 2009 [24], an Instron 1343 servo pressure testing machine was adopted to test the static

Table 1 Composition of SFR-UHSC matrix by weight. Materials

Portland cement (P II 52.5R) Silica fume Fly ash GGBS Water Superplasticizers River sand Gravel aggregate Steel fiber

Mix proportions (kg/m3) Vf = 0

Vf = 1%

Vf = 2%

Vf = 3%

413 32.5 65 130 143 9.75 730 1097 0

413 32.5 65 130 143 9.75 708 1041 78

413 32.5 65 130 143 9.75 686 985 156

413 32.5 65 130 143 9.75 664 929 234

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Fig. 1. Steel fibers utilized for ultra-high strength concrete.

mechanical properties (i.e., compressive strength, splitting tensile strength and flexural performance) of the SFR-UHSC. The experimental procedure for each parameter defined in Standard CECS 13: 2009 [24] were employed in these tests. Moreover, the dynamic mechanical properties of SFR-UHSC was tested on a SHPB device with a diameter of 75 mm in Artillery Academy of PLA of China. 3. Experimental results and discussion As mentioned before, the experimental tests were conducted in two parts: static mechanical tests and dynamical tests. The details are separately presented and discussed.

For the prism specimens after compressive loadings, diagonal cracks can be seen on the surfaces of specimens (Fig. 4) and it can be defined as a shearing-type failure. This is similar with those observed in Wu et al.’s [7] experiment. An explanation for this phenomenon is that prism specimens are under a tri-axial stress state due to the end constraint induced by friction when subjected to uniaxial compression. Thence, the plane of principal stress is not parallel to the axis of specimen, leading to failure along the oblique cross-section. For the case of plain UHSC, the specimen was even broken into two pieces (Fig. 4a) while the SFR-UHSC specimen can be kept as an integrity due to the connection of steel fibers, showing good ductility. Moreover, owing to the high strength of steel fibers, no failure of steel fibers was observed during the compression process for both cubic and prism specimens. It can be concluded obviously from Table 3 and Fig. 5 that, compressive strengths of SFR-UHSC obtained from both cubic and prism specimens increase linearly with an increasing volume fraction of steel fibers. When the volume fraction of steel fiber Vf = 3%, the strengths are increased by 12.14% and 15.23% compared with plain UHSC, respectively. These increase values are in the range of normal strength SFRC [26]. What’s more, it can be seen that the ratio between the prism strength (axial strength) fprism to cubic strength fcube is around 0.88 for SFR-UHSC while 0.85 for plain UHSC. However, this value is in the range of 0.7–0.8 for normal strength concrete [27]. The larger fprism/fcube ratio can be attributed to the fact that with the addition of steel fibers, the failure of SFRUHSC is not as brittle as that of normal strength concrete (Fig. 4). In fact, this is corresponding to the so-called size effect [28]. The more brittle the failure is, and the more significant size effect the materials exhibit.

3.1. Static mechanical properties Test results of compressive strength (both for cubic and prism specimens), Young’s modulus, and splitting tensile strength as well as flexural properties are summarized in Table 3. Moreover, failure patterns of specimens after the tests and the effects of steel fibers are illustrated in Figs. 3–9. 3.1.1. Compressive strength The failure patterns of both cubic and prism specimens after compressive test are described in Figs. 3 and 4. It can be observed from Fig. 3 that after compressive loading, the middle part of the plain UHSC specimen spalled, remaining two relatively complete pyramid at the two ends of the specimen. This is because, there is inevitably friction between the loading platens and the two end surfaces of the specimen in usual compression test, thus constraining the end surface from free expansion induced by Poisson effect. This phenomenon is usually called ‘‘end constraint” [25]. At the middle of the specimen, the constraint effect is weak due to the large distance to the end surfaces, thus concrete spalling. When it comes to the SFR-UHSC specimens under compression, the spalling of specimens is quite slight. This is because high bond strength exists between steel fibers and UHSC. Through the good bond performance, small pieces of concrete were connected by the web of steel fibers when cracks occurred within the matrix, thus preventing them from crushing. With the increasing of steel fiber dosage, the middle part of the cubic specimen was bulged under compressive loadings (Fig. 3b and c) and this indicates a better plastic deformation property.

3.1.2. Young’s modulus It can be known from Table 3 that Young’s modulus of SFRUHSC increases slightly when the volume fraction of steel fibers increases. Again the magnitude of increase is lower than that in publication [7]. However, the results in the present work is consistent with the findings for normal strength SFRC [26]. Therefore, within the scope of present study, it can be concluded that steel fiber has a negligible influence on Young’s modulus of SFR-UHSC. 3.1.3. Splitting tensile strength For the difficulties of direct tensile test, splitting tensile test was conducted to determine the tensile strength of SFR-UHSC. After splitting tensile loading, the failure patterns of specimens were described in Fig. 6. During the loading process, no visible changes were observed from the appearance of specimens when the loading increases from 0 to 80% of the ultimate load. The load can be increased further when some cracks appeared on the loading surfaces. This is since the splitting tensile load was transferred from concrete to steel fibers through the good bond and mechanical bite between the UHSC matrixes and hook-end steel fibers, resulting in a strengthen of SFR-UHSC’s strength. Once the ultimate load was reached, steel fibers were pulled out instead of broken themselves, forming obvious cracks on the surface of specimens, while the load decreases with the increasing deformation. Correspondingly, it can be seen from Table 3 and Fig. 7(a) that splitting strength of SFR-UHSC was increased significantly by the addition of steel fibers. For instance, compared with plain UHSC, a 140.6% higher splitting tensile strength was obtained for the

Table 2 Physical properties of the steel fibers. Length (mm)

Diameter (mm)

Aspect ratio

Tensile strength (MPa)

Density (kg/m3)

30

0.6

50

1100

7800

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f spt ¼ 0:3f c

ð4Þ

where f spt and f c are the splitting tensile strength and compressive strength of concrete, respectively. The comparison between the calculated results of Eqs. (2)–(4) and the test data is also made in Fig. 7(a). It can be seen that the three formulas seriously underestimate the splitting tensile strength of SFR-UHSC. This indicates that the tensile strength of SFR-UHSC is increased much more than compressive strength. The ratio between splitting tensile strength and cubic compressive strength increases from 0.096 to 0.125 when the volume fraction of steel fibers varies in the range of 1%–3%. With this higher tensile strength to compressive strength ratio, the brittleness of SFRUHSC decreases while its ductility increases significantly.

Fig. 2. Mix procedures for SFR-UHSC.

addition of 3 per cent by volume of steel fibers. To predict the tensile strength of SFRC (f ft ), an empirical formula was proposed in Chinese code ‘‘Steel fiber reinforced concrete” (JG/T 472-2015) [29],

f ft ¼ f t ð1 þ at V f lf =df Þ

ð1Þ

in which, f t is the tensile strength of plain UHSC matrix; V f is volume fraction of steel fibers; lf and df are the length and diameter of steel fibers, respectively; and at is a coefficient relative to the type and shape of steel fiber, here, at ¼ 1:03. One can note from Eq. (1) that the tensile strength of SFRC increases linearly with steel fiber dosage for a specific composition of concrete matrix and steel fiber type. The comparison between prediction of Eq. (1) and test results was illustrated in Fig. 7(a) and a good agreement can be observed. In other words, the splitting tensile strength of SFR-UHSC can be well predicted by Chinese code (JG/T 472-2015) [29]. What’s more, several concrete institutes have reported that splitting tensile strength can be estimated from compressive strength [3]. Among these, empirical formulae suggested by ACI 318-95 [30], ACI 363R-92 [31] and CEB-FIP [32] have the forms as Eqs. (2)–(4), respectively. 0:5

ð2Þ

0:5

ð3Þ

f spt ¼ 0:56f c f spt ¼ 0:59f c

3.1.4. Flexural strength and toughness Flexural test of SFR-UHSC was conducted on beam specimens of 100 mm  100 mm  400 mm. These beams have a span length of 300 mm while four-point loading was applied on the beams. During the loading process, cracks appear firstly in concrete of the pure-bending section. With the increase of loading, the cracks become larger and propagate upward, forming a main crack. For plain UHSC, the ultimate bearing capacity of beam was reached quickly and a brittle failure was observed while for SFR-UHSC, after the crack of concrete matrix, loading was transferred to steel fibers between the broken concrete pieces. When the loading increases further, some steel fibers were pulled out while the hook-ends of some fibers were even straightened. After the peak loading, more and more steel fibers lose their effect and the cracks developed further, reducing the height of compression zone on the cross-section of beam. Finally, the cracks at mid-span of SFR-UHSC beams were extended throughout the cross-section. As shown in Fig. 8, when the content of steel fibers was lower (e.g., Vf = 1% and 2%), a coarse crack throughout the specimen near the mid-span can be observed while for the case of a high amount of steel fibers (Vf = 3%), the crack is too fine to be visible. Corresponding to the failure process, only a very short decline can be observed on the load-deflection curves for the plain UHSC beams, indicating an instant brittle failure (Fig. 9a). For the counterparts of SFR-UHSC beams, however, there is a quite long decline after peak loading, charactering a typical ductile failure (Fig. 9b–d). Moreover, it can be found that the bearing capacity (i.e., the peak on the load-deflection curves) of SFR-UHSC beams increases with the increasing steel fiber dosage. As given in Table 3 and Fig. 7(b), the flexural-tensile strengths of SFR-UHSC were calculated according to the load when the first crack appeared and the bearing capacity was reached. One can note that the flexural strengths increase with the increasing steel fiber dosage. In addition, it can be seen that the differences between these two strengths are much larger for SFR-UHSC and this means that for SFR-UHSC after the first crack, the withstanding loading can be increased further. This difference is also larger for a higher volume fraction of steel fiber.

Table 3 Summary of the test results for static mechanical properties. Specimen size

Properties

Vf = 0

Vf = 1%

Vf = 2%

Vf = 3%

100 mm  100 mm  100 mm

Cubic compressive strength (MPa) Splitting tensile strength (MPa) Prism compressive strength (MPa) Young’s Modulus (GPa) First-crack strength (MPa) Flexural strength (MPa) Flexural toughness I5 Flexural toughness I10 Flexural toughness I20

114.5 6.67 97.2 49.7 8.26 8.94 – – –

118.5 11.42 105.4 50.6 8.62 9.67 4.77 9.47 19.02

123.7 15.82 109.4 51.2 9.23 12.14 5.05 10.71 22.11

128.4 16.05 112.0 53.2 11.67 17.38 5.15 11.23 24.06

100 mm  100 mm  300 mm 100 mm  100 mm  400 mm

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Fig. 3. Failure patterns of cubic specimens under compressive loading: (a) volume fraction of steel fibers Vf = 0; (b) Vf = 1%; (c) Vf = 2% and (d) Vf = 3%.

Fig. 4. Failure patterns of prism specimens under compressive loading: (a) volume fraction of steel fibers Vf = 0; (b) Vf = 1%; (c) Vf = 2% and (d) Vf = 3%.

Similar to the splitting tensile strength, some empirical relationships were established to predict the flexural strength of concrete. In Chinese code JG/T 472-2015 [29], flexural strength of SFRC (f ff ) is related to the flexural strength of plain concrete matrix and properties of steel fiber,

f ff ¼ f f ð1 þ af V f lf =df Þ

ð5Þ

in which, f f is the flexural strength of plain UHSC matrix; and af is a coefficient relative to the type and shape of steel fiber, herein, af ¼ 1:25. Flexural strength related to compressive strength of concrete is suggested by ACI 318-95 [30] and ACI 363R-92 [31] and the formulae have the forms as Eqs. (6) and (7), respectively. 0:5

ð6Þ

0:5

ð7Þ

f ff ¼ 0:62f c Fig. 5. Effect of steel fiber on compressive strength of SFR-UHSC.

f ff ¼ 0:94f c

Fig. 6. Failure patterns of cubic specimens after splitting tensile test: (a) volume fraction of steel fibers Vf = 1%; (b) Vf = 2%; (c) Vf = 3%.

L. Jin et al. / Construction and Building Materials 178 (2018) 102–111

107

Fig. 7. Comparison between the tested strengths and the empirical predictions: (a) Splitting tensile strength; (b) flexural strength.

Size: 100 mm × 100 mm × 400 mm Fig. 8. Failure patterns of SFR-UHSC beams after flexure test: (a) Volume fraction of steel fibers Vf = 1%; (b) Vf = 2%; (c) Vf = 3%.

The comparison between the calculated results predicted by Eqs. (5)–(7) and the test data is illustrated in Fig. 7(b). It can be noted that different from the splitting tensile strength, the flexural strength of SFR-UHSC is overestimated by JG/T 472-2015 [29]. The relationship in ACI 318-95 [30] again underestimate the parameter of SFR-UHSC. It seems that, however, flexural strength of SFR-UHSC with a lower steel fiber dosage (V f 6 2%) can be predicted well by American code ACI 363R-92 [31]. Due to the small amount of data, no modified empirical equations was recommended here. Nevertheless, it still can be concluded that the steel-fiber-caused increase of flexural strength is between those of tensile strength and compressive strength. To characterize the toughness of concrete, various calculation methods have been proposed in the technical codes [24,33,34]. Among these, the test method advised by ASTM code [33] was widely applied for its easiness to be operated and it was also employed in the present work. As suggested in ASTM code [33], the toughness index is calculated on the base of load-deflection curve (Fig. 10) of a beam-type specimen. The formulae are expressed as

8 > < I5 ¼ X3d =Xd I10 ¼ X5:5d =Xd > : I20 ¼ X10:5d =Xd

ð8Þ

in which, I5 , I10 and I20 are flexural toughness indexes; Xd , X3d , X5:5d and X10:5d are the areas of OAB, OACD, OAEF and OAEF, respectively (sketched in Fig. 10); moreover, d in Fig. 10 represents the midspan deflection when the first crack appears. As listed in Table 3, the flexural toughness indexes of SFR-UHSC were calculated based on the test data and Eq. (8). It can be seen that the flexural toughness of SFR-UHSC increases with an increasing steel fiber dosage. Moreover, flexural toughness indexes of SFRUHSC in the present work are in the ranges suggested by ASTM code [33] for SFRC (Table 4) and even reach those for ideal elasto-

plastic materials. This indicate that SFR-UHSC has good toughness and plasticity. 3.2. Dynamic mechanical properties After the SHPB experiment, the test results of dynamic compressive strength, strain at peak stress and energy absorption as well as compressive toughness index were reported in Table 5 while the failure patterns, stress-strain relationships as well as the effects of strain rate and steel fibers were demonstrated in Figs. 11–14. 3.2.1. Failure patterns It can be observed from Fig. 11 that under the strain rate of e_ = 25 s1, the plain UHSC specimens were broken into three pieces with a main crack throughout the specimen while for SFR-UHSC, the concrete spalling occurs at the edges of cylinder, preserving the core-area’s integrity. This illustrates the strengthen effect of steel fiber on the resistance of SFR-UHSC against dynamic loadings. However, more severe damage of SFR-UHSC was noted when the compressive strain rate increases. This phenomenon may be attributed to the fact that under high strain rates, the failure of bond between steel fibers and concrete increases due to the rupture of concrete matrix, leading to a loss of steel fiber reinforcement effect [26]. Nevertheless, it can be characterized that SFR-UHSC cracks along various paths without fragmentation when subjected to compressive loadings with high strain rate. 3.2.2. Dynamic stress-strain relationships One can note that from Fig. 12 that under impact loadings, the declines after peak stress on the stress-strain curves of plain UHSC are quite short, implying a typical brittle behavior. While, for the SFR-UHSC with different steel fiber dosages, the stress-strain curves with similar shapes were recorded. The longer decline, higher peak stress and fuller curve shape demonstrate the rein-

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Fig. 9. Load-deflection curves of SFR-UHSC specimens under flexural performance test: (a) Volume fraction of steel fibers Vf = 0; (b) Vf = 1%; (c) Vf = 2%; (d) Vf = 3%.

an enhancement effect. However, the effect of steel fiber content on the strain at peak stress shows some irregular laws (Fig. 13). Furthermore, when the strain rate is fixed, a roughly increase trend can be found from the relationship of strain at peak stress and steel fiber dosage.

Fig. 10. Schematic diagram for the calculation of flexural toughness index.

Table 4 Suggested values for flexural toughness index.

I5 I10 I20

Ordinary concrete

Ideal elastoplastic material

Steel fiber reinforced concrete

1.0 1.0 1.0

5.0 10.0 20.0

1–6 1–12 1–25

forcement effect of steel fibers. For a specific volume fraction of steel fiber, the longer and steeper elastic stage on the stressstrain curve can be viewed with an increasing strain rate, denoting

3.2.3. Dynamic compressive strength It can be noted obviously from Fig. 13 that dynamic compressive strength of SFR-UHSC increases both when steel fiber contents and strain rate increase and a synergetic effect of steel fiber and strain rate is displayed. To quantitatively determine the effect of strain rate on dynamic compressive strength, the dynamic increasing factor (DIF, ratio between the dynamic compressive strength to quasi-static strength) was calculated as plotted in Fig. 14. It can be seen that almost all of the DIFs are in the range of 1–1.5. Some relationships between DIF and strain rate have been proposed for concrete in the past several decades. Among these, the CEB-FIP [32] formula for ordinary concrete is widely utilized and it can be expressed as 1=3 DIF ¼ 0:012ðe_ =e_ 0 Þ ;

ðe_ > 30s1 Þ

ð9Þ

where e_ and e_ 0 are strain rate and quasi-static strain rate, e_ 0 ¼ 30  106 . However, as shown in Fig. 14 that Eq. (9) overestimates the effect of strain rate on DIF of SFR-UHSC for the reason that SFRUHSC is more ductile than ordinary concrete [15]. Therefore, for a more accurate prediction, regressions of the test data were con-

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L. Jin et al. / Construction and Building Materials 178 (2018) 102–111 Table 5 Summary of the test results for dynamic mechanical properties. Volume fraction of steel fiber Vf

Strain rate (s1)

Dynamic strength (MPa)

Strain at peak stress

Energy absorption (MJ/m3)

Compressive toughness index

0

12 25 40 60 100 40 60 100 40 60 100

66.1 86.5 103 106 121 116 121 139 111 129 149

0.0027 0.0036 0.0037 0.0035 0.0058 0.0044 0.0051 0.0054 0.0059 0.0050 0.0056

0.192 0.453 0.705 0.973 1.822 0.923 1.231 1.979 0.941 1.619 2.752

1.64 2.12 3.46 4.57 4.23 3.30 3.06 4.23 2.23 3.63 4.74

1%

2%

3%

Fig. 11. Failure patterns of SFR-UHSC specimens after dynamic compressive loadings: (a) Volume fraction of steel fibers Vf = 0 and strain rate e_ = 25 s1; (b) Vf = 1%, e_ = 25 s1; (c) Vf = 1%, e_ = 60 s1; (d) Vf = 1%, e_ = 100 s1.

Fig. 12. Stress-strain responses of SFR-UHSC under different strain rates: (a) volume fraction of steel fibers Vf = 0; (b) Vf = 1%; (c) Vf = 2% (d) Vf = 3%.

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Fig. 13. Effect of steel fiber on dynamic compressive behavior of SFR-UHSC.

Fig. 15. Experimental and fitting results on relationship of energy absorption with volume fraction of steel fiber and strain rate.

is tabulated in Table 5. It is noticed that the energy absorption of SFR-UHSC under impact loading increases with both increasing steel fiber content and strain rate. The influence of strain rate on energy absorption is stronger than that of steel fiber dosage. A bivariate polynomial relationship of energy absorption Ea with volume fraction of steel fiber and strain rate is fitted as

Ea ¼ 0:08  6:23V f þ 1:38  107 ðe_ =e_ 0 Þ þ 6:37  106 ðe_ =e_ 0 ÞV f

Fig. 14. Dynamic increase factors (DIFs) for compressive strength of SFR-UHSC.

Table 6 Fitting equation for DIF of SFR-UHSC’s compressive strength. Volume fraction of steel fiber Vf

1% 2% 3%

DIF ¼ aðe_ =e_ 0 Þ (e_ > 30 s1) b

a

b

R2

0.06882 0.06719 0.01476

0.19453 0.20222 0.30569

0.884 0.798 0.997

ducted adopting the form of CEB-FIP [32] formula as tabulated in Table 6. One can notice that the regression results vary with different volume fractions of steel fiber. For the fact the effect of steel fiber content on DIF is relatively small, a unified fitting equation irrespective to volume fraction of steel fiber was presented as 0:23686 DIF ¼ 0:03967ðe_ =e_ 0 Þ

R2 ¼ 0:783

ð10Þ

This equation is convenient for application and fits well with the experimental data within the scope of the present study as shown in Fig. 14. 3.2.4. Energy absorption and compressive toughness The energy absorption is often considered as a measurement of concrete toughness. Similar with that in [18], the energy absorption is calculated by integrating the stress-strain curve up and it

R2 ¼ 0:962

ð11Þ

Comparison of fitting results and experimental data is plotted in Fig. 15, showing a good consistence. Moreover, an index was defined to characterize the compressive toughness of SFR-UHSC and it was calculated as the ratio of the area under a stress-strain curve divided by that before the peak stress. This treatment is similar to that in [7]. One can note from Table 5 that compressive toughness indexes of SFR-UHSC are higher than the counterpart of plain UHSC in general. No regular laws, however, were shown in the relationships of compressive toughness index with volume fraction of steel fiber and strain rate. Moreover, compressive toughness indexes of SFR-UHSC within the present study are lower than those in the work [7] owing to the differences in composition, mixture and steel fiber type. Nevertheless, one can still conclude that SFR-UHSC is more ductile under impact loading than plain UHSC. 4. Conclusions A SFR-UHSC including gravel aggregate was designed and mixed with common materials and it was molded with standard curing procedures in the present work. Based on the experimental tests on the static and dynamic mechanical properties, some concluding remarks are drawn as follows: (1) Compared with the cubic and prism compressive strengths as well as Young’s modulus, the steel fiber reinforcement effect on splitting tensile and flexural strengths of SFRUHSC is much larger. With 3% steel fibers, the cubic and prism compressive strengths were increased by 12.14% and 15.23% while the splitting tensile and flexural strengths were increased by 140.63% and 94.41%, respectively;

L. Jin et al. / Construction and Building Materials 178 (2018) 102–111

(2) With 1%, 2% and 3% steel fibers, the ratio between prism and cubic compressive strengths decreases from 0.89 to 0.87 while the ratio of tensile strength to compressive strength increases from 0.096 to 0.125; (3) Compared with plain UHSC ones, SFR-UHSC specimens can kept as an integrity under loadings instead of breaking into pieces, exhibiting good ductility, toughness and plasticity; (4) SFR-UHSC cracks along various paths without fragmentation when subjected to compressive loadings with high strain rate; (5) Dynamic compressive strength of SFR-UHSC is influenced by both strain rate and steel fiber content while its strain rate effect is slightly lower than that of ordinary concrete. With strain rate varying from 20 to 100 s1, the DIF of SFRUHSC’s compressive strength increases from 1 to 1.5 while the counterpart for ordinary concrete is 1 to 1.8; (6) Under impact loadings, SFR-UHSC has a good energy absorption capacity and compressive toughness. The relationship between energy absorption and volume fraction of steel fibers as well as strain rate can be fitted as a bivariate polynomial.

[11]

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[14]

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[20]

Conflict of interest None.

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Acknowledgements

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This research was supported by the National Key Basic Research and Development Program of China (No. 2016YFC0701100, No. 2015CB058000). The support is gratefully acknowledged.

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