Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive behavior of ultra high performance concrete

Construction and Building Materials 153 (2017) 790–806

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Influence of steel fiber content and aspect ratio on the uniaxial tensile and compressive behavior of ultra high performance concrete An Le Hoang a,b,c,⇑, Ekkehard Fehling c a

Division of Construction Computation, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Faculty of Civil and Environmental Engineering, Institute of Structural Engineering, University of Kassel, Kurt-Wolters-Strabe 3, 34125 Kassel, Germany b

h i g h l i g h t s
There is no noticeable change in the compressive strength and elastic modulus of UHPFRC compared to those of UHPC in this study.
Steel fibers with higher aspect ratio result in a better improvement of post-peak behavior in compression.
The formulae for estimating the axial strain at the peak stress and the elastic modulus were proposed.
The fiber activation stage of the stress-crack opening relationship in tension is greatly affected by steel fiber content and aspect ratio.
A relationship between the fiber efficiency

a r t i c l e

rcf0 and the fiber factor K was established.

i n f o

Article history: Received 17 October 2016 Received in revised form 29 April 2017 Accepted 14 July 2017

Keywords: UHPC Steel fiber Fiber efficiency Aspect ratio Compressive strength Elastic modulus Post-peak behavior Direct tension tests

a b s t r a c t This study investigates the effect of steel fiber contents of 1.5% and 3% with different aspect ratios on the uniaxial tensile and compressive behavior of ultra high performance concrete (UHPC). Compressive tests on concrete cylinders of 150 mm  300 mm and direct tension tests on notched prisms of 40 mm  40 mm  80 mm were conducted. The test results indicated that there is no noticeable change in the compressive strength and elastic modulus with incorporation of steel fibers, however the postpeak behavior under compression is substantially affected by steel fiber content and aspect ratio. In terms of notched prisms under tension, there is no influence of steel fiber in the linear elastic stage, whereas the increase in steel fiber content results in not only a significant effect on the fiber activation stage but also higher values of fiber efficiency. Furthermore, the strain at the peak stress and the elastic modulus obtained from compressive tests were also evaluated by the comparison with some previous formulae. Finally, a relationship between the fiber efficiency rcf0 and the fiber factor K was proposed. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Ultra high performance concrete (UHPC) is well-known as one of the latest advances in concrete technology [15,26]. Moreover, UHPC is an emerging new family of concretes which exhibits superior mechanical and durability properties compared to conventional concrete such as normal strength concrete (NSC) and high strength concrete (HSC) [15]. Although there is currently no unique and widely accepted definition for UHPC, it can be classified as a cement-based material with a minimum compressive strength of

⇑ Corresponding author at: Division of Construction Computation, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail addresses: [email protected] (A. Le Hoang), [email protected] (E. Fehling). http://dx.doi.org/10.1016/j.conbuildmat.2017.07.130 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

150 MPa and a post-cracking tensile strength higher than 5 MPa [16]. On the other hand, it was also emphasized that depending on the composition and the temperature of heat – treatment, the compressive strength of UHPC can achieve between 200 MPa and up to 800 MPa [11,25]. Likewise, Fehling et al. [15] indicated that UHPC is characterized by a very dense matrix and compressive strength ranging from 150 MPa to 250 MPa. More importantly, Schmidt and Fehling [26] stated that in addition to the higher packing density of fines and compressive strength, which is defined for ultra high strength concrete (UHSC), the term ‘Ultra High Performance’ refers to the outstanding durability and low ratio water/cement. With numerous advantages offered by UHPC over NSC and HSC, the use of UHPC in a variety of structural constructions has been received a great deal of attention over the last two decades.

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However, brittle failure of UHPC accompanying with increased strength leads to some limitations for its applications in practice [13,35,43,47]. The incorporation of steel fibers in UHPC mixture can ensure ductile behavior in tension and transform brittle failure to ductile failure in compression [2]. For this reason, a large number of experimental studies have been conducted directly towards the evaluation on the effect of steel fibers on mechanical properties of UHPC. With regard to tensile properties of UHPC, three types of test methods including direct tension tests, splitting tests and flexural tests have been widely used [15,33]. Among these methods, the direct tension tests using prismatic and cylindrical specimens or dogbone shaped specimens are found to be the most suitable for observing the complete behavior of UHPC in tension [33],. According to Fehling et al. [15] and Wille et al. [33], direct tension tests on unnotched specimens are often preferred for determining the tensile strength, while tests on notched specimens are more relevant for determining the stress-crack width relationship of UHPC using fibers (UHPFRC). UHPC without fibers exhibits very brittle failure with tensile strength values ranging between 7 MPa and 10 MPa, while UHPFRC poses higher tensile strength varying from 7 MPa to 15 MPa and ductile behavior in the post-cracking stage with pronounced descending portion in the force-deformation diagram [15,26]. It has already been proven by many previous experimental studies that although the tensile performance of UHPFRC is affected by fiber characteristics including fiber type, content, shape, aspect ratio, orientation and distribution, the increase in amount of fibers results in the most significant improvement in the tensile strength, fracture energy capacity and post-cracking behavior [15,34]. Therefore, the influence of steel fiber content on the tensile performance needs further exploration to provide more fundamental knowledge. In addition, the direct tension tests on notched specimens should be adopted to fully characterize the post-cracking behavior and the fiber efficiency after cracking. In terms of compressive response of UHPC, Fehling et al. [15] concluded that the post-peak behavior is enhanced through the addition of steel fiber, but the descending portion of the stress– strain diagram is mainly influenced by some characteristics of fiber such as fiber stiffness, content, geometry, orientation, distribution, bond between fiber and matrix, and the combination of different fibers, whereas there is no significant influence on the ascending portion of the stress–strain diagram even increasing volume of steel fibers up to 2%. This conclusion was also drawn by many researchers (e.g., [13,16–18,20,28,34]). According to Tue et al. [31] and Fehling et al. [15], UHPC without fibers is observed to be linear elastic up to 70%–80% of the compressive strength, whereas Hassan et al. [18] reported that UHPFRC behaves elastically up to approximately 90%–95% of its compressive strength. Likewise, Graybeal [16] demonstrated that the linear range of UHPC under steam treatment could reach 80%–90% of the compressive strength. Yoo et al. [36] stated that the compressive strength and elastic modulus of UHPFRC cylinders are improved by a higher amount of fiber up to a volume fraction of 3%, while UHPFRC cylinders with volume of fiber up to 4% have the lowest compressive strength and elastic modulus due to poor fiber dispersion. Kazemi and Lubell [20] found that the addition of 2%–5% steel fibers results in an increase of cube compressive strength from 3.7% to 25% compared to UHPC without fibers; however, these authors suggested that additional vibration should be used for high fiber contents to achieve better mechanical characteristics. More recently, El-Helou et al. [12] have presented a series of compressive tests on UHPC with steel fiber contents of 0, 2 and 4% in order to capture the full compressive stress–strain curve. These test results show that steel fibers slightly increase the peak compressive strength by about 12% compared to that of UHPC without fibers but not so much difference in the peak compressive strength

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between fiber volume of 2% and 4%. In contrast to these authors, Yan and Feng [35], and Liu et al. [22] maintained that it is not feasible to improve the compressive strength and ductility of UHPC by the incorporation of steel fibers even with the volume content exceeding 2%. It has been found that there is a large scatter of the measured descending portion of UHPFRC cylinders in compression reported by numerous researchers owing to many factors induced by fiber orientation, distribution, fiber alignment in formwork, concreting activities, measuring technique (e.g., [13,18,17,20,28]). Thus, the descending portion of stress–strain curve of UHPFRC cylinders seems to be hardly predicted by means of simple relationships using mathematical equations. It is necessary to conduct more tests on UHPFRC cylinders with various volumes of steel fibers to approach more accurate evaluations of the impact of the fiber volume on the post-peak behavior and the compressive strength, which remains to be continuously discussed among researchers. From the issues highlighted above, the purpose of this study is to examine the effect of steel fiber contents and aspect ratios on the stress–strain curve of UHPC and UHPFRC cylinders in compression, and the stress-cracking opening relationship of UHPFRC prisms in tension. Compressive tests on 20 cylinders of 150 mm  300 mm and direct tension tests on 36 notched prism of 40 mm  40 mm  80 mm were conducted. The steel fiber volumes of 1.5% and 3% (UHPFRC 1.5% and UHPFRC 3%) with different aspect ratios were used in this study in order to compare with UHPC without fibers. 2. Experimental program 2.1. Materials and mix proportions A fine-grained (maximum grain size of 0.5 mm) UHPC mixture named as M3Q that was developed at University of Kassel during the work on the priority program (SPP1182) of the German Research Foundation (Deutsche Forschungsgemeinschaft DFG) was used (SPP1182-DFG in Schmidt et al. [27]). The mechanical, chemical and physical properties of raw materials for M3Q were reported in Schmidt et al. [27]. It should be noted that the M3Q mixture was designed to provide a very high selfcompacting characteristic. The fine-grained UHPC and UHPFRC mixture have a water-binder ratio of 0.21 and a maximum grain size of 0.5 mm. The packing density of the M3Q mixture was optimized using the silica fume (SikaÒ Silicoll uncompacted) and the superplasticizer SikaÒ ViscoCrete 2810 was used. The composition of UHPC and UHPFRC mixtures following the recipe of M3Q are given in Table 1. To investigate the effect of fiber content, three types of micro steel fibers as shown in Table 2 and Fig. 1 were considered in two steel fiber volumes of 1.5% and 3% (UHPFRC 1.5% and UHPFRC 3%). The steel fiber type with diameter df = 0.15 mm and length lf = 9 mm was used only for the direct tension tests.

2.2. Mix procedure and sample preparation In total, seven different concrete mixes (UHPC; UHPFRC 1.5% and UHPFRC 3% using steel fibers with aspect ratios of lf/df = 13/0.175, lf/df = 20/0.25, lf/df = 9/0.15) were cast. A mixer for each batch of UHPC with capacity of 40 Liter was used. First, all of the dry components (cement, silica fume, quartz sand, ground quartz) were premixed to obtain a good dispersion. Then, water including the superplasticizer was poured into the dry mixture and continued mixing. Once the mixture had enough fluidity and viscosity, the steel fibers were dispersed and mixed together with the mixture. The mixing sequence and time for each step are shown in Table 3. It should be noted that, in the mixing procedure, steel fibers were added to the concrete mix through passing a sieve to insure that the fibers do not accumulate into bundles. When UHPC and UHPFRC mixtures were ready, for each batch of concrete, they were cast into 4 cylindrical moulds of 150  300 mm2 and 3 three-gang prism moulds of 40  40  160 mm3. The cylindrical moulds were filled with three layers of fresh concrete while on a vibrating table (see Fig. 2a) for about 120 s (each layer was individually vibrated for about 40 s). The fresh concrete was also cast into prism moulds on a small vibrating table (see Fig. 2c), which was set manually with frequency of 50 Hz, oscillation amplitude of 0.75 mm and compaction time of 120 s. The aim of additional vibration for casting concrete into the moulds is to further improve the mixture consolidation, especially with UHPFRC using relatively high volume of steel fibers. After casting, all specimens were covered by plastic sheets to prevent moisture loss until demolding and they were then kept in a room at the temperature of 20 °C for 48 h to harden, as depicted in Fig. 2b and d. In order to increase the strength and accelerate the strength development of UHPC as rec-

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Table 1 Composition of UHPC and UHPFRC mixtures. Mix composition

Unit 3

Water CEM I 52.5 R HS-NA Silica fume Superplasticizer Sika Viscorete 2810 Ground Quartz W12 Quartz sand 0.125/0.5 Steel fibers

kg/m kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

UHPC

UHPFRC 1.5%

UHPFRC 3%

187.98 795.40 168.60 24.10 198.40 971.00 –

185.16 783.47 166.07 23.74 195.42 956.44 117.78

182.34 771.53 163.54 23.38 192.45 941.86 235.61

Table 2 Properties of steel fibers. Type

Diameter df (mm)

Length lf (mm)

Aspect ratio (lf /df)

Density (g/cm3)

Tensile strength (MPa)

Elastic Modulus (GPa)

Characteristics

Smooth micro fiber

0.175 0.25 0.15

13 20 9

13/0.175 = 74.29 20/0.25 = 80 9/0.15 = 60

7.8 7.8 7.8

2500 2500 2500

200 200 200

Golden surface Silver surface Golden surface

lf/df =13/0.175

lf/df =20/0.25

lf/df =9/0.15

Fig. 1. Three types of steel fibers.

2.3. Specimen preparation and test setup Table 3 UHPC mixing plan. Process

Time

Materials filling Dry mixing (2 min) Water and superplasticizer (3 min) Break (2 min) Mixing Steel fibers filling Break (10 min) Final mixing

– 0 min–2 min 2 min–5 min 5 min–7 min 7 min–15 min 13 min 15 min–25 min 25 min–25.5 min

ommended by the results in Schmidt et al. [27] and Graybeal [16], after 48 h of hardening, the moulds were removed and the specimens were then heat treated at 90 °C for 48 h. After heat-treatment, the specimens were finally kept at laboratory temperature until testing day. The compression and tension tests were conducted at about two months after casting.

(a) Vibrating table for casting UHPC cylinders

(b) Cylinders

2.3.1. Flowability The flowability of the fresh concrete for each mixture was checked immediately after mixing, using a mini-slump cone on a flow table in accordance with DIN EN 12350–8: 2010–12 [9], as described in Fig. 3a. The slump-flow test includes two governing parameters: the slump flow and the flow time t500. The flow time t500 represented the time required for the fresh concrete to spread to a diameter of 500 mm. The slump flow was determined by the mean value of two diameters perpendicular to each other which were measured on the flow table after 3 min lifting the mini-slump cone. Fig. 3(b)-(d) illustrate the results of slump flow tests in three batches of UHPC, UHPFRC 1.5% and UHPFRC 3% using steel fibers with aspect ratio of lf/df = 13/0.175. Three tests on the flowability for each mixture were conducted. 2.3.2. Compression tests Prior to compression tests, all UHPC and UHPFRC cylinders were grinded to minimize uneven surfaces at each end as shown in Fig. 4. In accordance with the German standard DIN EN 12390–3:2009–07 [10], uniaxial compression tests were performed using a universal testing machine with maximum load capacity of 6000 kN at the laboratory of Structural Engineering Department of Kassel University. The details of the compression test setup are described in Fig. 5. To measure the vertical displacement before the peak stress,

(c) Vibrating table for casting UHPC prisms

Fig. 2. Placement of test specimens.

(d) Prisms

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(a) Slump flow test

(b) UHPC

(c) UHPFRC 1.5%

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(d) UHPFRC 3%

Fig. 3. Slump flow tests of UHPC and UHPFRC using steel fibers with aspect ratio of 13/0.175.

(a) Grinding machine

(b) Specimen before grinding

(c) Specimen after grinding

Fig. 4. Grinding of UHPC and UHPFRC specimens.

Fig. 5. Uniaxial compression test setup.

three Linear Variable Differential Transducers (LVDTs) were mounted at 120 degree interval along the perimeter in the middle region of cylinder specimen (LVDTs-type 1). The base length of these LVDTs-type 1 was 100 mm. The vertical strains before the peak stresses were derived from the ratios of average values of vertical displacements obtained from 3 LVDTs-type 1 to the base length of 100mm. In terms of UHPFRC specimens, for capturing the vertical displacement after the peak stress, three more LVDTs were placed parallel to the specimen to measure the vertical movement of top steel plate (LVDTs-type 2). The vertical strains after the peak stresses were obtained by dividing the average values of vertical displacements from LVDTs-type 2 by the total specimen height. Therefore, the full compressive stress–strain response was then obtained by combining the two sets of results from LVDTs-type 1 and LVDTs-type 2. Besides, the elastic modulus was also derived from elastic stage of the compressive stress–strain curve in compliance with the German standard DIN 1048–5 [8]. The load was measured by a load cell attached to testing machine. The load rate applied to the cylindrical specimens was 0.01 mm/s until reaching the first peak load. It can be observed that, for UHPFRC cylindrical specimens under uniaxial compression, there is an abrupt load drop from the first peak load to the second peak load, thus the compression test was continued after the second peak load with increased load rate of 0.02 mm/s for capturing the post-peak stage. Finally, to end the test, the load rate was increased to 0.04 mm/s until failure. It should be mentioned that the use of displacement control for loading application allows the compressive response to be captured in the post-peak phase. A total of four cylindrical specimens for each batch of UHPC and UHPFRC were tested.

2.3.3. Direct tension tests on notched prisms The direct tension tests on notched prisms were carried out according to Leutbecher [21], as shown in Fig. 6. Fig. 6a describes the schematic view of notched prisms designed following Leutbecher [21]. The notched prisms have dimensions of 40 mm  40 mm  80 mm, which were cut from the casted prisms of 40 mm  40 mm  160 mm without notches after curing. In order to induce the failure in the middle of test specimen, the notches were created in the middle of two opposite sides of the prism and had a width and a depth of 5 mm. It should be mentioned that the prisms for the tension tests were casted perpendicular to the tensile loading direction, as depicted in Fig.6(a)–(c). The preparation for the notched prisms before testing was shown in Fig.6(c). Two steel blocks with internal thread M20 were glued to each end of the notched prism. The specimen was hold by two threaded rods M20 of the testing machine, which were connected with steel blocks at each end through the internal thread (Fig. 6(d)). Eight thin steel plates were also glued to the lateral surfaces of the notched prism for the installation of LVDTs and to avoid the failures outside the notch (Fig. 6(c)). The detail of direct tension test setup and instrumentation is described in Fig. 7. The values of crack opening were measured by four LVDTs, which were fastened at the thin steel plates on four sides of prisms by a device near to the notch edges. The gage lengths of four LVDTs were 40 mm. The direct tension tests were performed using tension testing machine (RBO 2000) having a load capacity of 2.0 MN. The prism specimen was loaded with a speed rate of 0.01 mm/s. When the crack opening exceeds 2 mm, the load rate was increased to 0.05 mm/s to speed up the test. A

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(a) Schematic view of notched prism (following Leutbecher [21])

(b) Notched prism of 40 x

(c) Preparation of notched prism

(d) Steel block

40 x 80 mm3 Fig. 6. Details of notched prism.

(a) Notched prism

(b) LVDTs

(c) Test machine

(d) At cracking

Fig. 7. Photos of direct tension test setup.

total of six prisms for each batch of UHPFRC were tested. The tensile stress was calculated by dividing the measured tensile load by the net area of the notched cross section. The crack width was computed by averaging the displacements recorded by four LVDTs.

3. Experimental results and discussion 3.1. Effects of steel fiber on the flowability Fig. 8 shows the effect of steel fiber content and aspect ratio on the flowability of fresh UHPC and UHPFRC mixtures. As can be seen in Fig. 8(a), the slump flow of UHPC batch without fibers was

approximately 1000 mm. In general, using higher steel fiber volumes led to a significant increase in the t500 time and a considerable decrease in the slump flow. With incorporation of 1.5% and 3% steel fibers, the slump flow gradually decreased as compared to that of UHPC. UHPFRC mixtures using fiber volume of 3% with highest aspect ratio 20/0.25 exhibited the lowest slump flow and the highest t500 time. The slump flow of mixtures using 1.5% steel fibers with aspect ratios of 13/0.175, 20/0.25 and 9/0.15 were decreased by 12%, 8% and 1%, respectively, as compared to those of UHPC mixture. Likewise, as also compared to UHPC mixture, the use of 3% steel fibers with aspect ratios of 13/0.175, 20/0.25 and 9/0.15 decreased the slump flow by 17%, 13% and 17%, respec-

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(b) t500 times

(a) Slump flows

Fig. 8. The effect of steel fiber content and aspect ratio on the flowability of fresh UHPC and UHPFRC mixture (M3Q).

tively. In addition, for the mixture with steel fiber volume of 1.5% using a lowest aspect ratio of lf/df = 9/0.15, there was a slight decrease in the slump flow and the t500 time, as compared to UHPC. Besides, it is evident from Fig. 2(d) that there is an increased risk of typical fiber balling in the mixtures using steel fiber volume of 3%, particularly with steel fibers having higher aspect ratios. Therefore, when higher steel fiber volume is used, smaller aspect ratio may lead to better flowability and prevent the appearance of fiber balling. This is due to the fact that the steel fibers with higher aspect ratio (longer length or larger diameter) increase the specific surface area with concrete matrix, thereby preventing the flow of fresh concrete (Wu et al. [37]).

3.2. Effects of steel fiber on the compressive response

Fig. 9. The effect of steel fiber content and aspect ratio on the compressive strength and the elastic modulus.

3.2.1. Compressive strength and elastic modulus The results of the compressive strengths, the elastic modulus, and the axial strain at the peak stress obtained from the individual compression tests of 4 cylindrical specimens for each concrete batch are given in Table 4.

Fig. 9 shows the effect of steel fiber content and aspect ratio on the average compressive strength and elastic modulus of UHPC and UHPFRC cylindrical specimens. It can be seen that there is no

Table 4 The compressive strengths and the elastic modulus. Vf (%)

lf/df

Measured values

Mean values

S.D

Measured values

Mean values

S.D

Measured values

Mean values

S.D

1 2 3 4

0

–

218.72 218.02 215.22 214.67

216.66

0.009

53.02 54.16 53.02 53.03

53.31

0.011

4.61 4.46 4.42 4.46

4.49

0.019

1 2 3 4

1.5

13/0.175

207.93 215.13 210.43 213.27

211.69

0.015

52.77 53.45 52.87 53.10

53.05

0.006

4.37 4.48 4.34 4.42

4.40

0.014

1 2 3 4

1.5

20/0.25

209.12 199.31 201.59 201.41

202.86

0.021

53.77 53.05 53.25 52.43

53.12

0.010

4.24 4.07 4.17 4.19

4.17

0.017

1 2 3 4

3

13/0.175

212.87 201.54 201.15 205.75

205.19

0.027

52.99 53.11 54.83 52.83

53.44

0.018

4.38 4.12 4.06 4.42

4.25

0.043

1 2 3 4

3

20/0.25

208.03 203.88 209.45 209.10

207.62

0.012

53.70 54.69 54.63 53.25

54.06

0.013

4.28 4.35 4.27 4.37

4.32

0.012

S.D: Standard deviation.

Compressive strength fc (MPa)

Strain at peak stress ec (‰)

No.

Elastic modulus Ec (GPa)

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noticeable difference in the elastic modulus when using higher volumes of steel fiber compared to UHPC without fibers. An average elastic modulus of approximately 53.4 GPa was found for UHPC and UHPFRC specimens. However, in contradiction with some previous studies (e.g., [20,18,36]), there is a relatively small reduction of compressive strength when using higher volumes of steel fibers compared to UHPC without fiber. For instance, an increase in fiber volume to 1.5% was found to decrease the compressive strength by 3% for steel fibers lf/df = 13/0.175 and by 7% for steel fibers lf/ df = 20/0.25, as compared to UHPC. A similar trend was observed for steel fiber volume of 3%, where a decrease by 5% and 6% was noted for UHPFRC specimens with steel fibers lf/df = 13/0.175 and lf/df = 20/0.25, respectively, as compared to UHPC without fibers. These results within typical scatter of material testing can demonstrate that the addition of steel fibers has a negative influence on the compressive strength of UHPFRC specimens.

3.2.2. Compressive stress – Strain curve The average stress–strain curves taken from four cylindrical specimens for UHPC and UHPFRC were illustrated in Fig. 10. As seen from Fig. 10(a), the slope of the ascending branch appears to be nearly linear up to the peak stress, regardless of the fiber content. On average, the measured strain at the peak stress of all UHPC and UHPFRC specimens ranged between 4.17‰ and 4.49‰. The linearity of stress–strain curves was investigated according to FIB Model Code 2010 [5], where the plasticity number k is defined by the ratio between the elastic modulus (Ec) and the secant modulus for the strain at the peak stress. The plasticity number k was found to be an average value of 1.09 for UHPC specimens and 1.1 for UHPFRC specimens, and was barely impacted by the fiber contents and aspect ratios. In addition, the linear range of compressive stress–strain curve was also determined based on the methods suggested by Graybeal [16] and Ma [23]. The test results in this study showed that the linear range can reach 79% and 80%–85% of the compressive strength for UHPC and UHPFRC, respectively. The complete stress–strain curve for all cylindrical specimens were shown in Fig. 11. It is indicated from Fig. 11 and Table 4 that there is a small scatter of the compression test results of four specimens in each concrete batch. UHPC without fibers exhibited extremely brittle failure with a very loud explosion at the peak stress, then followed by a fragmentation. Therefore, the post-peak branch could not be captured for UHPC without fibers. In contrast, as shown in Fig. 11(b), for UHPFRC specimens, the steel fibers had tremendous effects on the post-peak response. In general, there was a steep drop of compressive stress to a second peak stress after reaching the first peak stress, then the stress decreased slowly with

(a) Stress - strain curve before the peak stress

a progressive strain softening. Herein, the second peak stress is defined as the point at which the drop of stress stops and the stress–strain curve starts to show a large deformability. The steep drop of compressive stress occurs with the formation of critical crack in the specimen and then the steel fibers start to bridge the crack. The shape of stress–strain curve after the second peak stress is mainly dependent on the degree of bridging effect of steel fibers. In some specimens (UHPFRC 1.5%-20/0.25 and UHPFRC 3%13/0.175, as shown in Fig. 11b–c, there was a small strength recovery, this is due to the great bridging effect right after the stress drop but this effect is not well maintained. As seen in Fig. 10(b), the average values of the second peak stress of UHPFRC specimens using steel fibers with aspect ratio of 20/0.25 was higher than those of specimens with aspect ratio of 13/0.175. Furthermore, for the same fiber volumes of 1.5% and 3%, the specimens using steel fibers with higher aspect ratio 20/0.25 performed more ductile behavior in the descending branch as compared to the specimens using steel fibers with smaller aspect ratio 13/0.175. It is inferred from these observations that better interaction between steel fibers and concrete matrix can be achieved by using higher aspect ratios of steel fibers in comparison with smaller ones. This may be explained by the fact that steel fibers with smaller aspect ratio (shorter length or smaller diameter) result in a less efficiency in bridging macrocracks because more steel fibers may be pulled out from the matrix when the microcracks are transformed into macrocracks. This explanation was also drawn in Wu et al. [37]. The shape of descending branch in the compressive stress– strain curve for each steel fiber volume is hardly predicted using mathematical equations because there were discrepancies in the gradient of load drop and the second peak stress among specimens which have different aspect ratios. To get more consistent stress– strain curve of UHPFRC using various steel fiber volumes and aspect ratios, further experimental studies with accounting for the orientation and distribution of fibers or fiber characteristics are needed. After testing, some cylindrical specimens were cut into two parts in order to observe the fiber distribution. As seen from the Fig. 12, the steel fibers were distributed in random direction, but they were mostly oriented parallel to the longitudinal axis in the region near the edge of specimens. This observation was also presented by Kazemi and Lubell [23].

3.2.3. Failure pattern The typical failure patterns of UHPC and UHPFRC cylindrical specimens are shown in Fig. 13. As can be seen from this figure, UHPC without fibers fails in an extremely brittle manner with an

(b) Complete stress-strain curve

Fig. 10. The average stress–strain curve of UHPC and UHPFRC cylinders under uniaxial compression.

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(a) UHPFRC Vf =1.5%, lf /df =13/0.175

(b) UHPFRC Vf =3%, lf /d f =13/0.175

(c) UHPFRC V f =1.5%, l f /d f =20/0.25

(d) UHPFRC Vf =3%, lf /df =20/0.25

Fig. 11. Complete stress–strain curve of UHPFRC cylindrical specimens.

(a) The dispersion of steel fibers at

(b) Distribution of steel fibers inside the cylindrical specimen.

the top surface of specimen Fig. 12. The dispersion and distribution of steel fibers in the cylindrical specimen.

UHPC

UHPFRC Vf =1.5% lf /df =13/0.175

UHPFRC Vf =1.5% lf /df =20/0.25

UHPFRC Vf =3% lf /df =13/0.175

Fig. 13. The typical failure patterns of UHPC and UHPFRC cylindrical specimens.

UHPFRC Vf =3% lf /df =20/0.25

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(a) Relation betweenc and fc

(b) Relation between Ec and fc

Fig. 14. Comparison of the strain at the peak stress and the elastic modulus in this study with previous equations.

Table 5 Equations for the strain at the peak stress. Researchers

Equations for

Collins et al. [6]

ec ¼

De Nicolo et al. [7]

ec

CEB-FIB [3]

ec ec ec ec ec

Tasdemir et al. [29] CEB-FIB [4] EC2 [14] Wang et al. [32]

ec in ‰

Limitation

f c ð0:0588f c þ0:8Þ ð3320f 0:5 c þ6900Þð0:0588f c 0:2Þ

 103 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:76 þ ð0:626f c  4:33Þ  107  103 ¼ 0:7ðf c Þ

fc  110 MPa 10 MPa  fc  100 MPa fc  100 MPa

0:31 2

¼ 0:000067f c þ 0:029f c þ 1:053 c ¼ 1:7 þ 0:1f 7

0:53

¼ 2 þ 0:085ðf c  50Þ

¼ 0:5ð1:95 þ 0:01491f c þ 0:763 

ffiffiffiffiffi p 4 f cÞ

– fc  100 MPa 50 MPa  fc100 MPa fc  200 MPa

Table 6 The equations for the elastic modulus. Researchers

Graybeal [16]

Equations for Ec in MPa pffiffiffiffiffi Ec ¼ 4730 f c pffiffiffiffiffi Ec ¼ 3480 f c

Ma [23]

Ec ¼ 8800f c

ACI [1]

CEB-FIB [5] Heimann [19]

Ec ¼

 1=3

1=3 9350f c

UHPC without coarse aggregates Fine-grained UHPC

1=3

Ec ¼ 21500 

Limitation –

fc 10

Concrete with Quartzite aggregates Fine-grained UHPC

explosion at the peak stress accompanying with a fragmentation, while for UHPFRC specimens, the fragmentation is prevented by the presence of steel fibers. Furthermore, the sudden load drop right after the peak stress accompanying with a cracking noise was observed for all UHPFRC specimens. Generally, UHPFRC specimens show mostly vertical splitting failure or diagonal sliding failure in association with multiple cracks and localized failure. However, UHPFRC with steel fiber volume of 3% presented more multiple cracks and failed mainly in diagonal direction compared to UHPFRC with fiber volume of 1.5%. It should be mentioned that higher failure strain and higher residual strength can be achieved by the formation of multiple cracks (Prem et al. [24]). 3.2.4. Evaluation of the strain at the peak stress and the elastic modulus The strain ec at the peak stress fc and the elastic modulus Ec obtained from the compression test on each cylindrical specimen were evaluated by the comparison with the predictions of some previous studies, as illustrated in Fig. 14. The equations proposed by some previous researchers for estimating ec and Ec were given in Tables 5 and 6.

Fig. 15. The regression analysis of the relation between ec and fc.

The results of comparison in Fig.14(a) highlights that most equations do not accurately predict ec. Except for the equations in FIB Mode Code 1999 [4], which overestimated, the other equations tended to underestimate with large difference compared to the test results. However, the equations suggested by De Nicolo [7] presented the best fit with the test results. In an attempt to correct the prediction for ec, a formula was introduced using the regression analysis (Fig. 15) of the relation between ec and fc obtained from the test results of 20 cylindrical specimens in this study and 112 cylindrical specimens in other studies. The selected compression tests conducted by previous researchers were summarized in Table 7. The strain at the peak stress can be estimated using the following equation:

ec ¼ 0:0257  f 0:96 c

ð1Þ

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A. Le Hoang, E. Fehling / Construction and Building Materials 153 (2017) 790–806 Table 7 The selected compression tests on cylindrical specimens in other studies. Researchers

Number of specimens

Fiber volume (%)

Aspect ratios of fibers (lf/df)

Others

Sugano et al. [28]

11 15 4

0 2 3

– 15/0.2 (Smooth steel fibers) 15/0.3 (Organic PVA fibers)

Using fine aggregate

Kang et al. [45]

3 3 3 3 3 3

0 1 2 3 4 5

13/0.2 (Smooth steel fibers)

Using fine aggregate

Yoo et al. [36]

3 3 3 3

2 2 2 2

13/0.2 (Smooth steel fibers) 19.5/0.2 (Smooth steel fibers) 30/0.3 (Smooth steel fibers) 30/0.3 (Twisted steel fibers)

Using fine aggregate

Ma [23] Shin et al. [42]

34 6 6 6

0 0 1 1.5

– 30/0.5 (Bundled-type hooked-end steel fibers)

Using coarse aggregate (Basaltsplit) Using coarse aggregate

lf and df in mm, PVA = polyvinyl alcohol.

As seen in Fig. 14(a), the predictions by Eq. (1) are closer to the test results than those by previous models in Table 5. Within the limitation of this study, the regression analysis was based on the compression tests of cylindrical specimens which covering a relatively wide range of fiber aspect ratios, fiber volumes, fiber types and UHPC with fine and coarse aggregates. Therefore, the Eq. (1) can be used to predict the strain at the peak stress of UHPC and UHPFRC having the compressive strength of cylinders ranging between 150 MPa and 230 MPa. However, further investigations on the relation between ec and fc for various types of UHPC and UHPFRC should be carried out to improve the robustness of the design equation. With regard to the elastic modulus, from the observation of the results in Fig. 14(b), the equations proposed by ACI 1995 [1] and FIB Mode Code 2010 [5] gave the predictions of Ec much higher than the test results, whereas the predictions of Ec from the equation by Graybeal [16] were lower than the test results. However, the best fit with the test results was found for the equations proposed by Ma [23] and Heimann [19]. Interestingly, the values of Ec from the test results ranged between two estimations of Ma [23] and Heimann [19], thus the following formula for better prediction of Ec can be derived:

  1=3 1=3 1=3 Ec ¼ 0:5  8800f c þ 9350f c ¼ 9075  f c

ð2Þ

Fig. 16. Comparison between the predictions of Ec by Eq. (2) and previous test results in Table 7.

To evaluate the suitability of Eq. (2) for other types of UHPC, a comparison between the predictions of Ec using Eq. (2) and the test results reported by researchers in Table 7 was depicted in Fig. 16. The 10% and +10% error bounds of the predictions by Eq. (2) are also given in Fig. 16. As shown in Fig. 16, the Eq. (2) gave an overestimation of Ec as compared to the test results by most of researchers except for Ma [23]. The large difference (higher than 10%) in the predictions by Eq. (2) was found in the comparisons with the results of Ma [23] and Yoo et al. [36]. According to Ma et al. [44], the magnitude of Ec mainly depends on the type of aggregate and the paste volume fraction. Therefore, the Eq. (2) can not accurately predict the values of Ec for a wide range of different UHPC types. Within the limitation of this study, the Eq. (2) is believed to reliably estimate the values of Ec for fine-grained UHPC and UHPFRC following the recipe M3Q. However, the relevancy of the Eq. (2) for other types of UHPC and UHPFRC should be further checked. 3.3. Effects of steel fiber on the stress-crack opening relationship in tension 3.3.1. Background of the stress-crack opening relationship for UHPFRC under axial tensile load Based on the experimental studies at University of Kassel reported by Leutbecher [21], Fehling et al. [15] and Schmidt et al. [27], the idealized modeling approach for the stress-crack opening behavior of UHPFRC can be described in Fig. 11 and mainly distinguished into three parts as follows: - Part 1 is named as linear-elastic stage in uncracked state and determined by the overall tensile stiffness up to the cracking stress of the transformed cross section rcf,cr. - Part 2 is defined as fiber activation stage, which is characterized by the mobilization of load-carrying effect of fibers as the concrete matrix softens. In this stage, in some cases of UHPFRC prisms using higher fiber content, there is a severe increase in stresses for small crack widths due to fiber activation, leading to an increase in rcf,cr up to a higher stress ricf,cr before reaching the maximum load-carrying capacity rcf0 of the fibers in the cracked state (where ricf,cr is named as the imaginary cracking stress of the fiber-reinforced concrete andrcf0 is defined as the fiber efficiency). There are two possibilities of stress-crack opening behavior after crack formation depending on the values of ricf,cr and rcf0:

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The different embedded lengths of steel fibers on both sides of a crack cause the nonlinear curves for both fiber activation and pull out stages. It should be noted that the stress-crack opening relationship as modelled above is only valid for steel fibers which exclusively align in the tension direction (Fehling et al. [15]).

Fig. 17. Schematic view of stress-crack opening relationship of UHPFRC (following Leutbecher [21]).


UHPFRC with hardening behavior after crack formation when rcf0 > ricf,cr (noted by (1) in Fig. 17).
UHPFRC with softening behavior after crack formation when rcf0 < ricf,cr (noted by (2) in Fig. 17). According to Leutbecher [21], depending on the type of fiber and fiber content, the fiber efficiency rcf0 can be smaller or higher than the imaginary cracking stress of the fiber-reinforced concrete ricf,cr. - Part 3 is denoted by fiber pull-out, where the fiber efficiency rcf0 marks the transition from the phase of fiber activation to the phase of fiber pull-out. Accordingly, with further crack opening, all fibers are gradually pulled out from the concrete matrix, resulting in a softening curve after reaching the fiber efficiency rcf0. It can be seen that the progressive fiber pullout is significantly dependent on the length of the fibers and the bond between fibers and the concrete matrix. The limiting value of crack opening (w) at which the fibers no longer have any effect, is typically taken as a half the fiber length (lf/2).

(a) Complete stress-crack opening relationship

3.3.2. Observation of the stress-crack opening relationship from the test results For clarity of the differences among 6 direct tension test groups, Fig. 18 shows the average stress-crack opening relationship for UHPFRC prisms using fiber volume of 1.5% and 3% with three steel fiber aspect ratios of lf/df = 13/0.175, 9/0.15 and 20/0.25. In addition, the individual results of the stress-crack opening relationships for 36 prisms were plotted in Figs. 19–24. Table 8 provides the measured values of the cracking stress of the transformed cross section (rcf,cr) and its corresponding crack width (wcr), the fiber efficiency (rcf0) and its corresponding crack width (w0). Some prisms in Figs. 19–24 and Table 8 denoted by the signal ‘⁄’ indicates that there were an adhesive failure at the interface between the steel block and the notched prism, as described in Fig. 25. When the adhesive failure occurred before reaching the fiber efficiency, the prism was considered to provide no reportable values of the fiber efficiency, as also seen in Table 8. Moreover, with the appearance of the adhesive failure, the descending branch after reaching the fiber efficiency could not be well captured in some prisms, as seen in Figs. 22–24. Generally, there is a good match of the stress-crack opening relationship between the test results and the idealized model as mentioned above (see Fig. 17). In the linear-elastic stage (part 1), the contribution of steel fibers in the uncracked stated depends on their axial-stiffness to the overall stiffness of the prisms. However, it is apparent from Fig. 18 that there is no noticeable change in the initial tensile stiffness among UHPFRC prisms with different aspect ratios when using the same fiber volumes. This is due to the fact that there is no significant difference in the axial stiffness among three type of steel fibers used in this study. Before reaching the cracking stress rcf,cr, there is a high stress concentration at the tip of the notch, thus leading to the initiation and propagation of the crack plane. In this stage, the contribution of steel fibers can be more or less significant, mainly depending on the number and the geometry of fibers which cross the notched cross-section near the tip. Therefore, the values of rcf,cr and its corresponding crack width wcr considerably vary from the prim to the prism despite of having the same fiber volume and aspect ratio, as shown in Table 8. The

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 18. Representative stress-crack opening relationship of UHPFRC from the test results of notched prisms.

A. Le Hoang, E. Fehling / Construction and Building Materials 153 (2017) 790–806

(a) Complete stress-crack opening relationship

801

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 19. Stress-crack opening relationship of UHPFRC prisms with Vf = 1.5%, lf/df = 9/0.15.

(a) Complete stress-crack opening relationship

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 20. Stress-crack opening relationship of UHPFRC prisms with Vf = 3%, lf/df = 9/0.15.

(a) Complete stress-crack opening relationship

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 21. Stress-crack opening relationship of UHPFRC prisms with Vf = 1.5%, lf/df = 20/0.25.

activation of steel fibers starting in the incipient cracking stage prevents the softening of concrete matrix after reaching its maximum tensile stress (fct), thereby resulting in the cracking stress rcf,cr which is higher than the matrix tensile stress fct and a sharp increase in the tensile stress up to the values of the fiber efficiency rcf0. The steel fibers are found to be substantially decisive in the characteristic of the fiber activation stage (part 2). After achieving

the cracking stress, the tensile behavior was characterized by a more or less significant transient stress drop. For instance, right after the cracking stress, the UHPFRC prisms using 1.5% steel fibers with aspect ratio 13/0.175 performed a steep drop of stress, while a slight drop of stress was observed for most of the other types of UHPFRC prims. After the drop of stress, there is a stress recovery up to the fiber efficiency rcf0. It can be evident from Table 8 that

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(a) Complete stress-crack opening relationship

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 22. Stress-crack opening relationship of UHPFRC prisms with Vf = 3%, lf/df = 20/0.25.

(a) Complete stress-crack opening relationship

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 23. Stress-crack opening relationship of UHPFRC prisms with Vf = 1.5%, lf/df = 13/0.175.

(a) Complete stress-crack opening relationship

(b) Stress-crack opening relationship up to crack width of 0.5 mm

Fig. 24. Stress-crack opening relationship of UHPFRC prisms with Vf = 3%, lf/df = 13/0.175.

the fiber efficiency rcf0 was reached at crack widths w0 ranging between 0.1 and 0.3 mm (which correspond to the strains ranging between 2.5 ‰ and 7.5‰) for UHPFRC prisms containing 3% fibers, and between 0.18 and 0.23 mm (which correspond to the strains ranging between 4.5 ‰ and 5.75‰) for UHPFRC prisms containing 1.5% fibers. The results of the cracking stresses rcf,cr given in Table 8 also revealed that at the same fiber volume, the UHPFRC using longer

length of steel fibers (lf/df = 20/0.25) gave an average values of rcf, cr smaller than those of UHPFRC using shorter length of steel fibers (lf/df = 13/0.175 and 9/0.15). This may be explained by the fact that the short steel fibers are more effective than the long steel fibers for resisting the small cracks. Fig. 18(b) described that, after crack formation, except for UHPFRC prisms using the fiber volume of 1.5% and aspect ratio of 13/0.175, which exhibited the softening behavior, the other types

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A. Le Hoang, E. Fehling / Construction and Building Materials 153 (2017) 790–806 Table 8 The results of cracking stressrcf,cr and fiber efficiency rcf0. Vf (%)

lf/df

Specimens

rcf,cr (MPa)

wcr (mm)

r cf0 (MPa)

w0 (mm)

3

9/0.15

1 2 3 4 5 6

9.64 10.33 10.00 8.640 11.280 14.30

0.041 0.019 0.028 0.030 0.061 0.055

10.15 12.58 10.46 9.71 11.45 14.93

0.206 0.110 0.058 0.303 0.124 0.130

Mean value 1.5

9/0.15

1 2 3 4 5 6

10.70 9.47 7.46 9.78 7.25 7.73 8.30

0.039 0.109 0.057 0.085 0.099 0.047 0.144

11.55 8.89 7.91 8.81 6.50 7.73 7.71

0.155 0.176 0.169 0.229 0.340 0.227 0.226

Mean value 3

20/0.25

1 2 3 4 5* 6*

8.33 13.53 12.34 9.27 8.68 9.88 14.46

0.090 0.111 0.037 0.076 0.062 0.019 0.079

7.92 12.60 15.69 10.96 12.15 – –

0.227 0.322 0.235 0.331 0.322 – –

Mean value 1.5

20/0.25

1 2 3 4 5 6

10.95 6.62 7.60 6.50 5.05 7.60 6.35

0.064 0.011 0.010 0.009 0.006 0.008 0.008

12.85 9.72 9.98 6.78 9.42 8.88 8.51

0.302 0.287 0.183 0.205 0.135 0.264 0.295

Mean value 3

13/0.175

1 2 3 4* 5 6

6.62 9.93 10.62 11.60 15.27 14.55 13.34

0.009 0.011 0.017 0.015 0.025 0.013 0.030

8.88 12.03 11.39 13.54 – 14.55 14.94

0.228 0.086 0.030 0.151 – 0.142 0.120

Mean value 1.5

13/0.175

1 2* 3 4 5 6

12.01 12.74 11.38 14.39 9.34 11.72 13.48

0.019 0.012 0.013 0.017 0.010 0.017 0.014

13.29 11.63 – 9.08 10.58 11.64 10.36

0.106 0.136 – 0.349 0.116 0.149 0.135

12.33

0.014

10.66

0.177

Mean value The bold values indicate the mean values for each group of fiber volume. * Adhesive failure.

(a) Failure of prisms

(b) Orientation of steel fibers

Fig. 25. The failure of prism (a) and the observation of the orientation of steel fibers at the crack surface (b).

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of UHPFRC prisms presented a hardening behavior (rcf0 < ricf,cr), the other UHPFRC prisms presented a hardening behavior (rcf0 > ricf,cr). In the fiber activation stage, in addition to the effects of type and the volume of steel fibers, the distribution and the orientation of steel fibers within the notched region, the interfacial bond between the fiber and the concrete matrix plays an important role in the decision of the softening or the hardening behavior. In fiber pull-out stage, obviously, Fig.18b shows that UHPFRC prisms using steel fibers with longer length (lf) have more extended descending branch, indicating that more dissipated energy is needed for longer length of steel fibers to extend the crack opening after reaching the fiber efficiency rcf0. In this stage, the steel fibers were observed to be gradually pulled out from the matrix at the side where the embedded lengths of fibers are shorter. In this study, in addition to the prims having rather small size, the placing direction of UHPFRC mixtures perpendicular to the loading direction could induce a random fiber distribution in the middle of the prisms. This placing method was also developed at University of Kassel for creating the notched prisms in the direct tension test in order to determine the tensile stress-crack opening relationship of UHPFRC. Furthermore, by adopting this placing method, the steel fibers are encouraged to align along the tensile direction to exploit the best contribution of steel fibers to the tensile performance. However, there is a rotation of steel fiber in different directions during the concrete pouring, thus leading to a variation in the fiber orientation. After testing, the distribution and orientation of steel fibers were visually observed on both opposite crack surfaces of the notched prisms, as shown in Fig. 25. The steel fibers were vertically or obliquely oriented to the crack surface. This visual observation is consistent with the same casting method in the studies by Choi et al. [38], Zhou and Uchida [39]. The fiber orientation coefficient (g) was introduced by most of the researchers to consider the influence of fiber orientations deviating from the tensile direction on the tensile performance of UHPFRC [27,38,33,46]. With the same casting method as mentioned above, the fiber orientation coefficient could be averagely determined as g = 0.8 from the optical analysis for the UHPFRC prisms using smooth steel fiber with the aspect ratios of 17/0.15 and 20/0.25 in the volumes varying from 0.3 to 1.5%, as reported in Schmidt et al. [27] and Stürwald [41]. 3.3.3. The fiber efficiency rcf0 Fig. 26 shows the mean values of the fiber efficiency for UHPFRC prisms with fiber volumes of 1.5% and 3% and using various aspect ratios. As can be seen, in the case of UHPFRC prisms with fiber volume of 1.5%, the highest fiber efficiency of 10.66 MPa was found for UHPFRC prism using steel fibers with aspect ratio of 13/0.175, while UHPFRC using steel fibers with aspect ratio of 9/0.15 had

Fig. 26. The fiber efficiency for UHPFRC prisms with various steel fibers type and volume.

the lowest fiber efficiency of 7.93 MPa. Among three aspect ratios of UHPFRC prisms with fiber volume of 3%, the prisms using steel fibers with aspect ratio of 13/0.175 had the highest fiber efficiency of 13.29 MPa, whereas the lowest fiber efficiency of 11.55 MPa was noted for the prisms using steel fibers with aspect ratio of 9/0.15. The increasing of fiber volume from 1.5% to 3% leads to the increase in the fiber efficiency by roughly 24.71%, 44.65% and 45.7% for the steel fibers with aspect ratios of 13/0.175, 20/0.25 and 9/0.15, respectively. From these observations, it can be concluded that, for both steel fiber volume of 1.5% and 3% in this study, the steel fibers with aspect ratio of 13/0.175 gave the most effective fiber activation. 3.3.4. The relationship between the fiber efficiency rcf0 and the fiber factor K According to Tue et al. [30], the effectiveness of fiber addition can be described using the fiber factor K, which reflects the combining influence of fiber volume (Vf) and fiber aspect ratio (lf/df) and given in the following equation:

K ¼ Vf 

lf df

ð3Þ

With an effort to establish a relationship between the fiber efficiency rcf0 and the fiber factor K, the database of the direct tension tests on the notched prisms (prism of 40  40  80 mm3 with notch of 5 mm  5 mm) obtained from this study (see Table 8) and from the similar studies reported by Schmidt et al. [27], Stürwald [41], and Thiemicke [40] were collected and analyzed. The selected database were summarized in Table 9. The recipes of M2Q and M3Q for producing UHPFRC were used for all the reference tests in Table 9. More details of these recipes can be found in Fehling et al. [15] and Schmidt et al. [27]. Basically, the M2Q and M3Q mixtures are rather similar. However, the water-binder ratio of 0.19, the silica fume Elkem MicrosilicaÒ Grade 983, and the superplasticizer FM 1254 were adopted in the M2Q, which marked the significant differences with the M3Q as described above. Besides, all notched prisms of the reference tests were produced and cast in the same method with this study. The regression coefficient R2 obtained from the relationship between rcf0 and K in Fig. 27 has a value of 0.81, indicating a strong correlation between rcf0 and K. Therefore, a formula for estimating the fiber efficiency rcf0 can be derived as follows:

rcf 0 ¼ 4:82  lnðKÞ þ 9:08

ð4Þ

Although the Eq. (4) was established without taking into account the fiber orientation, it can be simply used to mathematically reflect the increase in the fiber efficiency rcf0 as the fiber factor K increases. Because the regression analysis was based on the limited database as given in Table 9, the Eq. (4) may be applicable for UHPFRC prisms using smooth or hooked steel fibers with the aspect ratios lf/df ranging from 60 to 133.3 and the fiber factor K ranging from 0.24 to 2.4. Moreover, the validity of the Eq. (4) is only considered for the fine-grained UHPFRC mixtures using the recipes M2Q and M3Q and for the random distribution of steel fibers induced by placing concrete perpendicularly to the tensile direction. Note that the notched prisms in this study were rather small so that the variation in the distribution and the orientation of steel fibers throughout the whole prism was not large. Therefore, the Eq. (4) should be further checked and modified for the notched prisms with larger size because the larger variation in the fiber distribution and orientation can be induced by the larger ones as compared to smaller ones. Additional direct tension tests on notched prisms are required to develop a robust formula for predicting the fiber efficiency rcf0 of UHPFRC. Diverse test param-

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A. Le Hoang, E. Fehling / Construction and Building Materials 153 (2017) 790–806 Table 9 The selected database of direct tension tests on notched prisms. Researchers

Number of specimens

Fiber volume (%)

Aspect ratio (lf/df)

Type of fibers

Type concrete mixture

Schmidt et al. [27]

3 3 3 3 3

0.9 2.5 0.9 1.45 2.0

9/0.15

Smooth fibers

M2Q

6 6 6 6 6 6 6 6 6 6 6 6 6 6

0.3 0.5 0.9 1.5 0.3 0.5 0.7 0.3 0.5 0.9 1.5 0.3 0.5 0.7

20/0.25

Smooth fibers

M3Q

20/0.25

Smooth fiber

M2Q

30/0.385

Hooked fibers

M3Q

17/0.15

Smooth fibers

M2Q

17 10

1 0.5

13/0.175

Smooth fibers

M3Q

Stürwald [41]

Thiemicke [40]

17/0.15







Fig. 27. The relationship between the fiber efficiency rcf0 and the fiber factor K.

eters including concrete placing methods, UHPC mixtures, fiber types, fiber aspect ratios, fiber content and prisms in larger sizes should be further investigated.
4. Conclusions Based on the results of the experimental investigation presented in this study, the following conclusions can be drawn:
The incorporation of steel fiber reduces the flowability of UHPC. The increase in the fiber content results in a gradual decrease in slump flow. The fiber balling in fresh UHPFRC mixture is significantly dependent on the fiber characteristics, aspect ratios and fiber volume fractions and some factors from concreting activities. In this study, the fiber balling occurred with most of fresh UHPFRC mixtures using 3% volume of steel fibers.
There is no noticeable change in the compressive strength and the elastic modulus of UHPFRC compared to those of UHPC. However, the post-peak branch in the stress–strain curve is substantially influenced by the increase in the fiber content. For the same volume of steel fiber, higher aspect ratio may lead to a better improvement of post-peak behavior.
The linearity of stress–strain curve was found to be 79% and 80%–85% of the compressive strength for UHPC and UHPFRC, respectively. The plasticity number k was found to be on aver-




age of 1.09 for UHPC specimens and 1.1 for UHPFRC specimens, and was barely impacted by the fiber content and aspect ratio. The presence of steel fibers only prevents the fragmentation which occurs with UHPC without fibers through an explosion. After the peak load, regardless of steel fiber content, for UHPFRC cylindrical specimens, there is a sudden load drop before starting an excellent ductility with a large deformability. The strain at the peak stress and the elastic modulus in this study were evaluated by the comparison with some previous formulae. It is evident that, for the strain at the peak stress, the formula proposed by De Nicolo [7] enable a good prediction. Besides, the formulae suggested by Ma [23] and Heimann [19] can be used to estimate the elastic modulus with a good agreement. For the best fit with the test results, new formulae were introduced to estimate the strain at the peak stress and the elastic modulus. The Eq. (1) can be used for UHPC and UHPFRC with the compressive strengths of cylinders ranging between 150 and 230 MPa. The Eq. (2) is only valid for the specific type of fine-grained UHPC using the recipe M3Q. However, the relevancy of these equations should be further justified for other types of UHPC. Regarding the stress-crack opening relationship, there is no influence of steel fiber content to the linear elastic stage, whereas the fiber activation stage is greatly affected by steel fiber content and aspect ratio. The increasing fiber volume fraction from 1.5% to 3% leads to a significant increase in the fiber efficiency rcf0. In this study, steel fibers with aspect ratio of 13/0.175 showed the highest value of the fiber efficiency rcf0. A relationship between the fiber efficiency rcf0 and the fiber factor K was established in the Eq. (4) by a very strong correlation obtained from the regression analysis, thereby mathematically describing the increase in the fiber efficiency rcf0 as the fiber factor K increases. Further direct tension tests on notched prisms is needed to evaluate the fiber efficiency rcf0 with consideration of a wide range of the fiber factor K, various fiber types, the fiber orientation induced by different concrete placing methods, prisms in larger sizes, and other types of UHPC mixtures.

The above conclusions were drawn based on the limited test results of UHPC and UHPFRC following the specific type of M3Q. The authors recommend that a more systematic investigation should be further conducted to have a deeper insight into the effect

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