Influence of silica fume on stress–strain behavior of FRP-confined HSC

Influence of silica fume on stress–strain behavior of FRP-confined HSC

Construction and Building Materials 63 (2014) 11–24 Contents lists available at ScienceDirect Construction and Building Materials journal homepage: ...

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Construction and Building Materials 63 (2014) 11–24

Contents lists available at ScienceDirect

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

Influence of silica fume on stress–strain behavior of FRP-confined HSC Jian C. Lim, Togay Ozbakkaloglu ⇑ School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia

h i g h l i g h t s  Influence of silica fume on compressive behavior of FRP-confined HSC was investigated.  Sufficiently confined HSC with and without silica fume exhibits highly ductile behavior.  For a given concrete strength, silica fume does not alter strength enhancement effects of confinement.  For a given concrete strength, silica fume increases ultimate axial strains of confined HSC.  Silica fume influences the behavior of confined HSC along transition regions of stress–strain curves.

a r t i c l e

i n f o

Article history: Received 7 February 2014 Accepted 27 March 2014

Keywords: High-strength concrete (HSC) Fiber reinforced polymer (FRP) Confinement Compression Silica fume Stress–strain relations

a b s t r a c t Confinement of high-strength concrete (HSC) columns with fiber reinforced polymer (FRP) composites has been receiving increasing research attention due to the advantageous engineering properties offered by the composite system. The use of silica fume as a concrete additive is a widely accepted practice in producing HSC. However, the influence of the presence and amount of silica fume on the efficiency of FRP confinement is not clearly understood. This paper presents the results of an experimental study on the influence of silica fume on the compressive behavior of FRP-confined HSC. 30 FRP-confined and 30 unconfined concrete cylinders containing different amounts of silica fume were tested under axial compression in two phases. In the first phase of the study, specimens with a constant water–cementitious binder ratio were tested. The results of this phase indicate that for a given water–cementitious binder ratio, the compressive strength of unconfined concrete increases with an increase in the amount of silica fume. It is found that this increase in strength leads to an increased concrete brittleness, which adversely affects the effectiveness of FRP confinement. In the second phase, water–cementitious binder ratios of the specimens were adjusted to attain a constant unconfined concrete strength for specimens containing different amounts of silica fume. The results of these tests indicate that for a given unconfined concrete strength, strength enhancement ratios of FRP-confined HSC specimens are not influenced by the silica fume content of the concrete mix. On the other hand, it is found that the silica fume content influences the axial strain enhancement ratios of these specimens. In addition, the transition zones of the stress–strain curves of FRP-confined HSC are observed to be sensitive to the amount of silica fume used in the mix. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The popularity of higher strength concretes in the construction industry has been on a steady incline during the last two decades due to the superior performance and economy offered by high-strength concrete (HSC) over normal-strength concrete (NSC) in a large number of structural engineering applications. The use of FRP for confinement of HSC leads to high-performance columns that exhibit very ductile behavior as was demonstrated ⇑ Corresponding author. Tel.: +61 8 8313 6477; fax: +61 8 8313 4359. E-mail address: [email protected] (T. Ozbakkaloglu). http://dx.doi.org/10.1016/j.conbuildmat.2014.03.044 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

in Ozbakkaloglu and Saatcioglu [1,2] and Idris and Ozbakkaloglu [3]. It has been reported in a number of studies that the efficiency of FRP confinement reduces with an increase in concrete strength [4,5]. However, the main contributors to this adverse effect of higher concrete strength have not been fully identified. Silica fume is one of the most popular pozzolans used to increase concrete strength [6–9], and it is known to have a significant effect on the compressive behavior of confined concrete [10–12]. Although several studies have reported that silica fume alters the brittleness of confined concrete [10,12,13], its influence on the behavior of confined concrete has been difficult to quantify due to the limited

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results and controversial experimental observations found from existing triaxial compression tests of HSC [10,12,14–18]. In FRP-confined HSC, the influence of silica fume is even less understood. Silica fume has been used in the existing experimental studies [4,5,19–27] to produce desirable concrete strengths. However, none of these studies attempted to establish the influence of silica fume on the behavior of confined concrete. This paper presents the results of the first-ever experimental study undertaken to address this gap, where the changes in the axial stress–strain behavior and ultimate conditions of FRP-confined HSC with silica fume were investigated. 2. Experimental program 2.1. Test specimens and materials 30 FRP-confined and 30 unconfined control concrete cylinders were manufactured and tested under monotonic axial compression. All of the specimens were 152.5 mm in diameter and 305 mm in height. The influence of silica fume on the mechanical properties of the confined and unconfined specimens was investigated using 10 separate batches of concrete mixes containing different percentage replacements of cement with silica fume and water–cementitious binder (w/c) ratios. The cementitious binder materials used were ordinary Portland cement and silica fume. Their chemical compositions and physical properties are given in Table 1. Detail of the mix proportions of each batch of concrete is given in Table 2. Crushed bluestone gravel of 7 mm maximum size and graded sand were used as the aggregates. Carboxylic ether polymer based superplasticiser was used in all batches. The superplasticiser contained 80% water by weight. The test results of the unconfined specimens are given in Table 3. The experimental program consisted of two phases. The first phase consisted of specimens fabricated from four different concrete batches containing different amounts of silica fume at designated w/c ratios. In Batches 1, 2A, and 3 that contain a fixed w/c ratio of 0.27, the percentages of silica fume that replaced cement were 0%, 8%, and 16% by weight. The w/c ratio was reduced to 0.24 in Batch 2B that contain 8% silica fume. As shown from Table 3, the unconfined concrete strengths (f’co) of specimens in this phase varied with the silica fume content and w/c ratios. The aim of Phase II of the experimental program was to attain a same unconfined strength among each specimen group having 0%, 8%, and 16% silica fume. The specimen groups in this phase were manufactured using two different concrete grades (i.e. a higher grade HSC with an average strength of 84.7 MPa in Batches 4–6 and a lower grade HSC with an average strength of 54.6 MPa in Batches 7–9). To establish the final w/c ratios used in Batches 4–9, a large number of trial batches were manufactured and tested. A total of 30 confined specimens was fabricated and tested in the two-phase experimental program. In Phase I, 12 specimens wrapped with Aramid FRP (AFRP) were prepared using a manual wet lay-up process by wrapping epoxy resin impregnated unidirectional fiber sheets around precast concrete cylinders in the hoop direction. The 18 specimens in Phase II were manufactured as tube-encased specimens using S-glass FRP (GFRP) tubes. The GFRP tubes were also prepared using the manual wet lay-up process, with the resin impregnated fiber sheets wrapped around precision-cut high-density Styrafoam templates, which were removed prior

Table 1 Chemical composition and physical properties of cementitious materials. Item

Cementitious materials (%) Ordinary Portland cement

Silica fume

SiO2 ZrO2 + HfO2 Al2O3 Fe2O3 P2O5 CaO MgO SO3 K2O Na20

21.46 – 5.55 3.46 – 63.95 1.86 1.42 0.54 0.26

92.5 5.5 0.35 0.4 0.3 0.02 – 0.9 0.02 0.02

C3S C2S C3A C4AF

Compounds 50.96 23.10 8.85 10.53

– – – –

Surface area (m2/kg)

Fineness 330

18,000

to concrete casting. The specimens tested in Phase I and the higher grade HSC specimens in Phase II had six layers of FRP, whereas the lower grade HSC specimens in Phase II had four layers of FRP. The specimens with four layers of FRP were wrapped with one continuous sheet with a single 150-mm long overlap zone, whereas the specimens with six layers were wrapped with two sheets creating two overlap zones of 150 mm terminating at the same location. The FRP epoxy adhesive used consisted of two parts: epoxy resin binder (MBrace Saturant) and thixotropic epoxy adhesive (MBrace Laminate Adhesive), which were mixed in the ratio of 3:1. The material properties of the unidirectional fiber sheets used to manufacture the FRP tubes and jackets are provided in Table 4. The table reports both the manufacturer-supplied fiber properties and the tensile tested FRP composite properties. The tensile properties of the FRP made from these fiber sheets and epoxy resin were determined from flat coupon tests undertaken in accordance with ASTM D3039 [28]. Three flat coupon specimens were made using the wet layout technique in a high-precision mold with 1 mm thickness and 25 mm width for each type of fiber. The coupons had a 138 mm clear span with each end bonded with two 0.5 mm by 85 mm aluminum tabs for stress transfer during tensile tests. Each coupon was instrumented with two 20 mm strain gauges at mid-height, with one on each side, for the measurement of the longitudinal strains. The coupons were allowed to cure in the laboratory environment for at least 7 days prior to testing. The tensile test specimens were tested using a screw-driven tensile test machine that had a peak capacity of 200 kN. The load was applied at a constant cross-head movement rate of 0.03 mm per second. The test results from the flat coupon specimens, calculated using nominal fiber thicknesses and actual coupon widths, are reported in Table 4. As evident from Table 4, the average rupture strains obtained from the tensile coupon tests were slightly lower than those reported by the manufacturer. Three nominally identical specimens were tested for each unique specimen configuration. The FRP-confined specimens were tested on the same day with their companion unconfined specimens, through which the test day unconfined concrete strengths (f0 co) reported in Table 3 were established. 2.2. Specimen designation The specimens in Tables 3 and 5 were labeled as follows: letters B, SF, WC, A or G, and W or T were used to represent the test parameters, namely the concrete batch, silica fume percentage, w/c ratio, type of FRP (i.e. AFRP or GFRP), followed by the number of layers and the confinement technique (i.e. wrapped or tubeencased), respectively. Each letter was followed by a number that was used to represent the value of that particular parameter for a given specimen. Finally, the last number in the specimen designation (i.e., 1, 2 or 3) was used to make the distinction between three nominally identical specimens. 2.3. Instrumentation and testing The specimens were tested under axial compression using a 5000-kN capacity universal testing machine. During the initial elastic stage of the behavior, the loading was applied with the load control set at 5 kN per second, whereas displacement control operated at 0.004 mm per second beyond the initiation of transition region until specimen failure. Prior to testing, all specimens were ground at both ends to ensure uniform distribution of the applied pressure, and load was applied directly to the concrete core using precision-cut high-strength steel plates. The hoop strains of the specimens were measured using a minimum of three unidirectional strain gauges placed at the mid-height around the circumference of specimens outside the overlap region. As illustrated in Fig. 1, the axial strains of the confined specimens were measured using three different methods: (i) four linear variable displacement transformers (LVDTs) mounted at each corner of the steel loading platens with a gauge length of 305 mm; (ii) four LVDTs placed at the mid-height at a gauge length of 175 mm at 90° spacing along the circumference of specimens; (iii) three axial strain gauges with a gauge length of 20 mm placed at the mid-height at 120° spacing along the circumference of specimens.

3. Test results and discussion 3.1. Failure mode The typical failure modes the unconfined HSC specimens tested in Phase I are illustrated in Fig. 2. As can be seen in Fig. 2(a), the formation of microcracks and the surface spalling of concrete were observed in the unconfined specimens containing 0% silica fume at failure. On the other hand, Fig. 2(b)–(d) shows that the unconfined specimens containing 8% and 16% silica fume failed due to concrete crushing after the formation of major macrocracks. The observed variations in the failure mode pattern suggest that the brittleness of the concrete increases with its strength in the presence of and with an increase in the amount of silica fume.

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J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24 Table 2 Mix proportions of concrete containing different levels of silica fume. Experimental program

Phase I

Phase II

AFRP-wrapped HSC Batch Cement (kg/m3) Silica fume (kg/m3) Sand (kg/m3) Gravel (kg/m3) Water (kg/m3) Superplasticiser (kg/m3) Water–cementitious binder ratio Superplasticiser–binder ratio Silica fume–binder ratio Slump height (m)

1 550 0.0 700 1050 124 30 0.270 0.055 0.000 0.240

2A 506 44 700 1050 124 30 0.270 0.055 0.080 0.215

2B 506 44 700 1050 108 30 0.240 0.055 0.080 0.130

3 462 88 700 1050 124 30 0.270 0.055 0.160 0.220

GFRP tube-encased higher grade HSC

GFRP tube-encased lower grade HSC

4 550 0 710 1065 130 20 0.265 0.036 0.000 >0.250

7 450 0 710 1065 205 2 0.460 0.004 0.000 0.230

5 506 44 710 1065 155 20 0.310 0.036 0.080 >0.250

6 462 88 710 1065 170 14 0.330 0.025 0.160 >0.250

8 414 36 710 1065 223 3 0.500 0.007 0.080 0.250

9 378 72 710 1065 235 1.5 0.525 0.003 0.160 0.095

Table 3 Compression test results of unconfined specimens. Phase

Specimen

Concrete batch

Silica fume percentage (%)

w/c ratio (%)

Average f0 co (MPa)

Average eco (%)

I

B1-SF0-WC27-A0 B2A-SF8-WC27-A0 B2B-SF8-WC24-A0 B3-SF16-WC27-A0

1 2A 2B 3

0 8 8 16

0.27 0.27 0.24 0.27

85.7 112.4 120.9 113.5

0.24 0.27 0.26 0.26

II

B4-SF0-WC27-G0 B5-SF8-WC31-G0 B6-SF16-WC33-G0 B7-SF0-WC46-G0 B8-SF8-WC50-G0 B9-SF16-WC53-G0

4 5 6 7 8 9

0 8 16 0 8 16

0.27 0.31 0.33 0.46 0.50 0.53

84.7 84.8 84.5 57.3 52.1 54.4

0.28P 0.28P 0.28P 0.26P 0.25P 0.25P

P: Axial strains were not recorded experimentally. Theoretical values determined using expression given by Popovics [29].

Table 4 Material properties of fibers and FRP composites. Type

Aramid S-glass

Nominal thickness tf (mm/ply)

Provided by manufacturers Tensile strength ff (MPa)

Ultimate tensile strain ef (%)

Elastic modulus Ef (GPa)

Tensile strength ffrp (MPa)

Ultimate tensile strain efrp (%)

Elastic modulus Efrp (GPa)

0.200 0.200

2600 3040

2.20 3.50

118.2 86.9

2390 3055

1.86 3.21

128.5 95.3

Fig. 3 shows typical failure modes of the confined HSC specimens tested in Phase I. As can be seen from the figure, all of the AFRP-wrapped specimens of Phase I failed by the rupture of the FRP jackets. As evident from Fig. 3(a)–(c), the location of the rupture of the specimens containing 0% and 8% silica fume occurred at mid-height, with the height of the ruptures increasing with an increase in silica fume content. Full height ruptures, as illustrated in Fig. 3(d), were observed in two out of three nominally identical AFRP-wrapped specimens containing 16% silica fume. Fig. 3(b) and (c) shows specimens containing the same amount of silica fume of 8% but different w/c ratios of 0.27 and 0.24. Comparison of the figures shows that the specimen with the lower w/c ratio had a larger rupture region height. Figs. 4 and 5 show the typical failures of the GFRP tube-encased specimens tested in Phase II, which were composed of two different grades of HSC. As illustrated in Figs. 4 and 5, all of these specimens failed due to the rupture of the FRP tubes. As evident from Figs. 4 and 5, the heights of the rupture regions of the specimens were not significantly affected by the change in the silica fume content. Similar failure modes observed in specimens containing varying amounts of silica fume indicates that the influence of silica fume on the failure mode of FRP-confined concrete is minor, when the unconfined concrete strength remains constant. Further discussions on the influence of silica fume on the compressive behavior of FRP-confined HSC are presented in the following sections.

Obtained from flat FRP coupon tests

3.2. Ultimate conditions The ultimate condition of FRP-confined concrete is often characterized as the ultimate axial stress and strain of concrete recorded at the rupture of the FRP jacket. This makes the relationship between the ultimate axial stress (f0 cu), ultimate axial strain (ecu) and hoop rupture strain (eh,rup) an important one. The test results of the confined specimens are given in Table 5, which include: the silica fume percentage, compressive strength and ultimate axial strain of the specimens (f0 cc and ecu); hoop rupture strain (eh,rup); strength and strain enhancement ratios (f0 cc/f0 co and ecu/ eco); and hoop strain reduction factor (ke,f). The hoop strain reduction factor (ke,f) of the confined specimens was calculated as the ratio of the hoop rupture strain (eh,rup) to ultimate tensile strain of the fiber (ef). The summary of the test results of the companion unconfined specimens are shown in Table 3, which include the unconfined peak stress (f0 co) and the corresponding axial strain (eco). The unconfined concrete strain (eco) and ultimate axial strain of confined concrete (ecu) were averaged from the four steel platen mounted LVDTs. It should be noted that the unconfined concrete strains (eco) of specimens in Batches 4–9 were not recorded during the compression tests. The eco values for these specimens, reported in Table 3, were calculated using the expression given by Popovics [29].

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Table 5 Compression test results of confined specimens containing different levels of silica fume. Phase

Specimen

I

B1-SF0-WC27-A6W-1 B1-SF0-WC27-A6W-2 B1-SF0-WC27-A6W-3 B2A-SF8-WC27-A6W-1 B2A-SF8-WC27-A6W-2 B2A-SF8-WC27-A6W-3 B2B-SF8-WC24-A6W-1 B2B-SF8-WC24-A6W-2 B2B-SF8-WC24-A6W-3 B3-SF16-WC27-A6W-1 B3-SF16-WC27-A6W-2 B3-SF16-WC27-A6W-3

II

Silica fume percentage (%) 0

8

8

16

B4-SF0-WC27-G6T-1 B4-SF0-WC27-G6T-2 B4-SF0-WC27-G6T-3 B5-SF8-WC31-G6T-1 B5-SF8-WC31-G6T-2 B5-SF8-WC31-G6T-3 B6-SF16-WC33-G6T-1 B6-SF16-WC33-G6T-2 B6-SF16-WC33-G6T-3 B7-SF0-WC46-G4T-1 B7-SF0-WC46-G4T-2 B7-SF0-WC46-G4T-3 B8-SF8-WC50-G4T-1 B8-SF8-WC50-G4T-2 B8-SF8-WC50-G4T-3 B9-SF16-WC53-G4T-1 B9-SF16-WC53-G4T-2 B9-SF16-WC53-G4T-3

0

8

16

0

8

16

f0 cc (MPa)

ecu (%)

eh,rup (%)

f0 cc/f0 co

166.2 168.0 165.2 165.5 168.4 163.1 167.1 172.1 168.4 186.5 170.7 178.5

2.02 2.18 2.09 1.97 1.74 1.87 1.77 1.76 1.78 2.04 1.75 1.94

1.50 1.48 1.45 1.37 1.48 1.47 1.14 1.39 1.33 1.50 1.19 1.45

1.94 1.96 1.93 1.47 1.50 1.45 1.38 1.42 1.39 1.64 1.50 1.57

184.1 182.0 178.4 187.9 180.4 176.3 188.6 181.7 164.3 125.7 127.2 131.2 119.4 126.8 125.3 109.2 123.5 126.5

2.91 2.71 2.90 2.83 2.78 2.65 3.61 3.26 2.74 3.54 3.61 3.80 2.81 3.48 3.36 3.44 4.28 4.54

2.24 1.99 2.18 1.96 2.46 1.94 2.38 2.35 1.99 2.48 2.67 2.50 2.56 2.60 2.58 2.30 2.39 2.57

2.17 2.15 2.11 2.22 2.13 2.08 2.23 2.15 1.94 2.19 2.22 2.29 2.29 2.43 2.40 2.01 2.27 2.33

Steel platen Ø 150 mm Steel disc

LVDT 5

LVDT 2

LVDT 8

Axial SGs

LVDT 7 170 305 mm mm Lateral LVDT 3 SGs

LVDT 1

LVDT 4

500 mm Fig. 1. Test setup and instrumentation.

3.2.1. Strength enhancement ratio As shown in Table 3, the unconfined concrete strengths (f0 co) of specimens tested in Phase I increased from 85.7 MPa to 112.4 MPa with an increase in silica fume content from 0% to 8% for a constant w/c ratio of 0.27 (Batches 1 and 2A). Only a slight improvement in strength from 112.4 MPa to 113.5 MPa was observed with a further increase in silica fume content from 8% to 16% (Batches 2A and 3). These observations indicate that for a given w/c ratio, the presence of silica fume increases the unconfined concrete strength (f0 co), and this increase is not directly proportional to the amount of silica fume. To illustrate the influence of silica fume on the behavior of confined concrete, Fig. 6 shows the variation of strength enhancement ratios (f0 cc/f0 co) of the specimens with silica fume–cementitious binder ratio (sf/c). As shown by the trendline of the specimens in

Average f0 cc/f0 co

1.94

1.47

1.40

1.57

2.14

2.14

2.11

2.23

2.38

2.20

ecu/eco 8.25 8.89 8.54 7.38 6.51 7.01 6.72 6.68 6.76 7.89 6.77 7.47 10.24 9.53 10.20 9.95 9.78 9.32 12.71 11.48 9.64 13.73 14.00 14.74 11.16 13.82 13.35 13.52 16.82 17.84

Average ecu/eco

8.56

6.97

6.72

7.38

9.99

9.68

11.28

14.16

12.78

16.06

ke,f 0.68 0.67 0.66 0.62 0.68 0.67 0.52 0.63 0.60 0.68 0.54 0.66 0.64 0.57 0.62 0.56 0.70 0.55 0.68 0.67 0.57 0.71 0.76 0.71 0.73 0.74 0.74 0.66 0.68 0.73

Average ke,f

0.67

0.66

0.58

0.63

0.61

0.61

0.64

0.73

0.74

0.69

Phase I in Fig. 6 and the results in Table 5, the strength enhancement ratio (f0 cc/f0 co) reduced from 1.94 to 1.47 when the silica fume content was increased from 0% to 8% (Batches 1 and 2A). The reduction is a result of the significant improvement of unconfined concrete strength (f0 co) from 85.7 MPa to 112.4 MPa due to the silica fume addition. When the silica fume addition from 8% to 16% (Batches 2A and 3) resulted only a marginal improvement to the unconfined concrete strength (f0 co) from 112.4 MPa to 113.5 MPa, a minimal change in the strength enhancement ratio (f0 cc/f0 co) from 1.47 to 1.57 was observed. These observations indicate that the reduction in the strength enhancement ratio (f0 cc/f0 co) is primarily caused by the increase in the unconfined concrete strength (f0 co). This accords with the findings reported in Lim and Ozbakkaloglu [30] that the strength enhancement ratio (f0 cc/f0 co) decreases with an increase in the unconfined concrete strength (f0 co). Comparison of the results from specimen groups of Phase I containing 8% silica fume and different w/c ratios in Table 3 indicates that the unconfined concrete strength (f0 co) increased from 112.4 MPa to 120.9 MPa with a reduction in w/c ratio from 0.27 to 0.24 (Batches 2A and 2B). As illustrated in Table 5, the increased concrete strength (f0 co) resulted in a reduction in the strength enhancement ratios (f0 cc/f0 co) of the confined specimens from 1.47 to 1.40. This observation indicates that an increase in the unconfined concrete strength (f0 co) resulting from a reduction in the w/ c ratio leads to a decrease in the strength enhancement ratio (f0 cc/ f0 co), similar to that reported due to an increase in the silica fume content. To isolate the discrete influence of silica fume from the effects of concrete strength (f0 co), the GFRP tube-encased specimens tested in Phase II (Batches 4–9) were prepared to attain the same unconfined concrete strengths (f0 co) with different silica fume percentages. As shown by the trendlines of the higher grade (Batches 4–6) and the lower grade HSC specimens (Batches 7–9) in Fig. 6, for a given unconfined concrete strength, a change in silica fume

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

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Fig. 2. Failure modes of unconfined HSC specimens: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.27 w/c ratio; (c) 8% silica fume and 0.24 w/c ratio; and (d) 16% silica fume and 0.27 w/c ratio.

content from 0% to 16% had no significant influence on the strength enhancement ratios (f0 cc/f0 co) of companion specimens of Phase II. The slightly higher f0 cc/f0 co ratio of the specimen group with a silica fume content of 8% (Batch 8) can be attributed to the lower f0 co of this group compared to the companion groups with 0% and 16% silica fume contents. These observations indicate that silica fume content has no influence on the strength enhancement ratio (f0 cc/f0 co) provided that the unconfined strength of the concrete remains constant. These observations support the supposition that the change in the strength enhancement ratios (f0 cc/f0 co) of the specimens of Phase I was primarily caused by the change in their unconfined concrete strengths (f0 co).

3.2.2. Strain enhancement ratio Fig. 7 shows the variation of the strain enhancement ratio (ecu/ eco) of the FRP-confined specimens with silica fume–cementitious binder ratio (sf/c). As shown by the trendline of specimens in Phase I in Fig. 7 and results in Table 5, the increase in the concrete strength (f0 co) due to silica fume addition from 0% to 8% (Batches 1 and 2A) resulted in a reduction in the strain enhancement ratio (ecu/eco) from 8.56 to 6.97. The additional increase in silica fume content from 8% to 16% (Batches 2A and 3), which resulted in only a marginal increase in the unconfined concrete strength, led to a slight increase in the strain enhancement ratio (ecu/eco) from 6.97 to 7.38 was observed. Comparison of the specimens with

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Fig. 3. Failure modes of AFRP-wrapped HSC specimens: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.27 w/c ratio; (c) 8% silica fume and 0.24 w/c ratio; and (d) 16% silica fume and 0.27 w/c ratio.

8% silica fume and different w/c ratios of 0.27 and 0.24 (Batches 2A and 2B) in Table 5 indicates that the increase in unconfined strength (f0 co) as a result of the w/c ratio reduction decreased the strain enhancement ratio (ecu/eco) from 6.97 to 6.72. These observations indicate that an increase in unconfined concrete strength resulting from either the silica fume addition or w/c ratio reduction also leads to a reduction in the strain enhancement ratio (ecu/eco). As illustrated by the trendline of higher grade HSC specimens of Phase II in Fig. 7, an increase in the silica fume content from 0% to 8% resulted in a slight reduction in the strain enhancement ratio (ecu/eco) from 9.99 to 9.68 (Batches 4 and 5). A further increase in the silica fume content from 8% to 16%, however,

resulted in an increase in the strain enhancement ratio from 9.68 to 11.28 (Batches 5 and 6). Similarly, the lower grade HSC specimens of Phase II exhibited a reduction in strain enhancement ratio (ecu/eco) from 14.16 to 12.78 with an increase in silica fume content from 0% to 8% (Batches 7 and 8), which is followed by an increase in strain enhancement ratio (ecu/eco) from 12.78 to 16.06 with an increase in silica fume content from 8% to 16% (Batches 8 and 9). These observations suggest that specimens with silica fume content above a certain threshold exhibits a higher strain enhancement ratio (ecu/eco) than the companion specimens with the same unconfined strength (f0 co) and lower or no silica fume content. Additional studies are required to gain further insight into this interesting influence.

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Fig. 4. Failure modes of GFRP tube-encased high-grade HSC specimens: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.31 w/c ratio; and (c) 16% silica fume and 0.33 w/c ratio.

3.2.3. Hoop strain reduction factor It has been discussed previously in a number of studies [5,31– 36] that the ultimate hoop strain (eh,rup) reached in the FRP jacket is often smaller than the ultimate tensile strain of the fibers (ef), which necessitates the use of a strain reduction factor (ke,f) in the determination of the actual confining pressures. The recorded hoop rupture strains (eh,rup) and calculated strain reduction factors (ke,f = eh,rup/ef) of the specimens in the present study are provided in Table 5. The results reveal that the ke,f values recorded in Phase I decrease slightly with an increase in unconfined concrete strength (f0 co), resulting from either an increase in silica fume content or a reduction in w/c ratio. The influence of the concrete strength on

the strain reduction factor was previously reported in Lim and Ozbakkaloglu [30] and findings of the present study are in agreement with those observations. On the other hand, no clear influence of silica fume on the strain reduction factor (ke,f) can be observed from the results of specimen groups in Phase II within a given concrete strength grade. These observations indicate that amount of silica fume does not have direct influence on the strain reduction factor (ke,f). 3.3. Axial stress–strain behavior Figs. 8 and 9, respectively, illustrate the different stages observed on a typical axial stress–strain curve and the corresponding

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J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

Fig. 5. Failure modes of GFRP tube-encased low-grade HSC specimens: (a) 0% silica fume and 0.46 w/c ratio; (b) 8% silica fume and 0.50 w/c ratio; and (c) 16% silica fume and 0.53 w/c ratio.

lateral strain–axial strain curve of the specimens exhibiting stress–strain behaviors with and without post-peak strength softening regions. The different stages marked on these curves were established based on the observed changes in the concrete expansion behavior, which is indicated by different tangential slopes of the corresponding regions shown in Figs. 8(b) and 9(b), namely: linear elastic region, rapid expansion region, and the stabilized dilation region. The axial stress–strain and lateral strain–axial strain curves of the specimens of Phase I are shown in Figs. 10 and 11, respectively. Those of the specimens of Phase II are shown in Figs. 12–15. In Figs. 10–15, the curves of the three companion specimens in each

group are represented through the use of three different line styles. As evident from the axial stress–strain curves in Figs. 10, 12 and 14, FRP-confined HSC can exhibit highly ductile compressive behavior. It is well established that sufficiently confined concrete exhibits a monotonically ascending curve, which consists of a parabolic first ascending branch and a nearly straight-line second branch (e.g., Specimen B1-SF0-WC27-A6W in Fig. 10(a) and specimens in Figs. 12 and 14). On the other hand, when the confinement level is below a certain threshold, the first ascending branch is followed by a second branch that exhibits a post-peak strength softening region [37,38] (e.g., Specimens B2A-SF8-WC27-A6W, B2B-SF8WC24-A6W and B3-SF16-WC27-A6W in Fig. 10(b)–(d)). The

19

Strength Enhancement Ratio (f'cc /f'co)

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

3.0 Constant f'co (Phase II)

2.5

B7 - B9

2.0

B4 - B6

1.5

B1 - B3

1.0

Varying f'co, constant w/c (Phase I)

0.5 0.0 0.00

GFRP tube-encased lower grade HSC GFRP tube-encased higher grade HSC AFRP-wrapped HSC

0.04

0.08

0.12

0.16

Silica Fume-Cementitious Binder Ratio (sf/c)

Strain Enhancement Ratio (εcu/εco)

Fig. 6. Variation of strength enhancement ratio (f0 cc/f0 co) with silica fume–cementitious binder ratio (sf/c).

20 B7 - B9

Constant f'co (Phase II)

15 B4 - B6

10

B1 - B3

5

0 0.00

GFRP tube-encased lower grade HSC GFRP tube-encased higher grade HSC AFRP-wrapped HSC

0.04

0.08

Varying f'co, constant w/c (Phase I)

0.12

0.16

Silica Fume-Cementitious Binder Ratio (sf/c) Fig. 7. Variation of strain enhancement ratio (ecu/eco) with silica fume–cementitious binder ratio (sf/c).

confinement requirements and the threshold conditions for distinguishing the curves with or without post-peak strength softening are discussed in detail in Lim and Ozbakkaloglu [30]. This section of the present study presents a discussion on the influence of silica fume on the transition region that connects the first ascending branch to the second branch of the stress–strain curves of FRP-confined concrete. The specimens with 8% and 16% silica fume shown in Fig. 10(b)– (d) experienced a sudden drop in strength starting at the initial peak of their stress–strain curves. This post-peak strength softening phenomenon can be attributed to the increased concrete brittleness with increasing concrete strength, which alters the concrete crack patterns from heterogenic microcracks to localized macrocracks [25]. The failure modes of the unconfined specimens shown in Fig. 2 illustrates the larger crack formations observed in the specimens with 8% and 16% silica fume contents compared to those of the specimens containing no silica fume. As illustrated by the lateral strain–axial strain curves shown in Fig. 11, the rate of lateral expansion of concrete (i.e. dilation rate) along the post-peak strength softening region was larger for specimens with 8% and 16% silica fume contents compared to that of the specimens containing no silica fume. The more rapid lateral expansion of the former specimens results in their sustaining a significant amount of damage before the full activation of the confinement mechanism that marks the initiation of strength recovery shown in Fig. 8(a). This is evident from Fig. 10(a)–(d), which illustrate that the magnitude of the strength loss observed along the post-peak strength softening region was more significant for the specimens with higher unconfined strengths resulting from either an addition of silica fume or a reduction in w/c ratio.

Ultimate

f'cc

Ultimate Initial peak Initiation of transition region

Linear Transition portion of region of the 1st the 1st ascending ascending branch branch

Initiation of strength recovery

Axial Stress (fc)

Axial Stress (fc)

f'cc

Post-peak strength loss

Initial strength softening region of the 2nd branch

Final portion of the 2nd branch

Transition region

Termination of transition region Initiation of transition region

2nd ascending branch

Transition region

Linear portion of the 1st ascending branch

Axial Strain (εc)

Axial Strain (εc)

(a)

(a) Ultimate

Ultimate

h,rup Region Region Region correscorrescorresponding ponding to ponding to the postthe linear to the peak strength portion of transition softening the 1st region of region of the ascending the 1st 2nd branch branch ascending branch

Region corresponding to the final portion of the 2nd branch (stabilized dilation)

Transition region (rapid concrete expansion)

Lateral Strain (εl)

Lateral Strain (εl)

h,rup

Region corresponding to the linear portion of the 1st ascending branch

Region corresponding to the 2nd ascending branch (stabilized dilation)

Transition region (rapid concrete expansion)

Axial Strain (εc)

Axial Strain (εc)

(b)

(b)

Fig. 8. Illustration of different stages of: (a) axial stress–strain; and (b) lateral strain–axial strain curves of specimen with initial strength softening behavior.

Fig. 9. Illustration of different stages of: (a) axial stress–strain; and (b) lateral strain–axial strain curves of specimen without initial strength softening behavior.

20

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

200

160 B1-SF0-WC27-A6W

120

No initial strength loss

80

B1-SF0-WC27-A0

40

Axial Stress (fc) (MPa)

Axial Stress (fc) (MPa)

200

160 B2A-SF8-WC27-A6W

120

Small initial strength loss

80

B2A-SF8-WC27-A0

40 0

0 0

0.005

0.01

0.015

0.02

0.025

0

0.005

Axial Strain (εc)

0.015

0.02

0.025

200

160 B2B-SF8-WC24-A6W

120 Large initial strength loss

80 B2B-SF8-WC24-A0

40

Axial Stress (fc) (MPa)

200

Axial Stress (fc) (MPa)

0.01

Axial Strain (εc)

0

160 B3-SF16-WC27-A6W

120 Large initial strength loss

80

B3-SF16-WC27-A0

40 0

0

0.005

0.01

0.015

0.02

0.025

0

0.005

Axial Strain (εc)

0.01

0.015

0.02

0.025

Axial Strain (εc)

Fig. 10. Axial stress–strain curves of: AFRP-wrapped HSC specimens with: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.27 w/c ratio; (c) 8% silica fume and 0.24 w/c ratio; and (d) 16% silica fume and 0.27 w/c ratio.

0.020 B1-SF0-WC27-A6W

0.015 Small tangential slope

0.010 0.005

Lateral Strain (εl)

Lateral Strain (εl)

0.020

B1-SF0-WC27-A0

0.000 0

0.005

0.01

B2A-SF8-WC27-A6W

0.015 0.010 Large tangential slope

0.005 B2A-SF8-WC27-A0

0.000

0.015

0.02

0.025

0

0.005

Axial Strain (εc)

0.015

0.02

0.025

0.020 B2B-SF8-WC24-A6W

0.015 0.010

Large tangential 0.005 slope B2B-SF8-WC24-A0

0.000 0

0.005

0.01

0.015

Lateral Strain (εl)

0.020

Lateral Strain (εl)

0.01

Axial Strain (εc)

B3-SF16-WC27-A6W

0.015 0.010

Large tangential slope

0.005

B3-SF16-WC27-A0

0.000 0.02

0.025

Axial Strain (εc)

0

0.005

0.01

0.015

0.02

0.025

Axial Strain (εc)

Fig. 11. Lateral strain–axial strain curves of: AFRP-wrapped HSC specimens with: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.27 w/c ratio; (c) 8% silica fume and 0.24 w/c ratio; and (d) 16% silica fume and 0.27 w/c ratio.

Figs. 12 and 14 show the stress–strain curves of the specimens of Phase II, which all exhibited monotonically ascending curves. Figs. 13 and 15 show the corresponding lateral strain–axial strain curves of these specimens. Although no post-peak strength loss was observed from the stress–strain curve of specimens in Phase II, the changes in their transition radii and second branches are

nevertheless evident in the comparisons of Figs. 12(a)–(c) and 14(a)–(c). The transition radii are the radii of the curved segments that form the transition regions marked in Figs. 12 and 14, which connect the first and second branches of the axial stress–strain curves. Smaller transition radii and longer second branches of the axial stress–strain curves of specimens containing 16% silica fume

21

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

0.03

160

Lateral Strain (εl)

Axial Stress (fc) (MPa)

200

B4-SF0-WC27-G6T

120 Large transition radius

80 40 0

0.02

0.01

0 0

0.01

0.02

0.03

0.04

0

0.01

(a)

(a) 0.03

Lateral Strain (εl)

160 B5-SF8-WC31-G6T

120 Large transition radius

80 40

0

0.01

0.03

Axial Strain (εc)

0 0.02

0.03

0.04

B5-SF8-WC31-G6T

0.02

0.01

0

0.04

0

0.01

Axial Strain (εc)

0.02

0.03

0.04

Axial Strain (εc)

(b)

(b)

200

0.03 B6-SF16-WC33-G6T

160 B6-SF16-WC33-G6T

120 80

Small transition radius

40 0 0

0.01

0.02

0.03

0.04

Axial Strain (εc)

(c)

Lateral Strain (εl)

Axial Stress (fc) (MPa)

0.02

Axial Strain (εc)

200

Axial Stress (fc) (MPa)

B4-SF0-WC27-G6T

0.02

0.01

0 0

0.01

0.02

0.03

0.04

Axial Strain (εc)

(c)

Fig. 12. Axial stress–strain curves of GFRP tube-encased high-grade HSC specimens with: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.31 w/c ratio; and (c) 16% silica fume and 0.33 w/c ratio.

Fig. 13. Lateral strain–axial strain curves of GFRP tube-encased high-grade HSC specimens with: (a) 0% silica fume and 0.27 w/c ratio; (b) 8% silica fume and 0.31 w/ c ratio; and (c) 16% silica fume and 0.33 w/c ratio.

shown are evident in Figs. 12 and 14, when compared to those of their companions with 0% and 8% silica fume content. These changes can be attributed to the differences in the dilation behavior of these specimens, as illustrated by their lateral strain–axial strain curves shown in Figs. 13 and 15. To enable an easier observation of these differences, the segments corresponding to the transition regions on the axial stress–strain curves are also marked on the companion lateral strain–axial strain curves in Figs. 13 and 15. As evident from these figures, the lateral strain–axial strain curves of the specimens with 16% silica fume content exhibit lower tangential slopes along the marked segments and stabilized dilation regions of the second branch, compared to those of their counterparts containing 0% and 8% silica fume. The lower tangential slopes observed along the second branches of the specimens with 16% silica fume content led to longer second branches on the axial stress–strain curves of these specimens, resulting in higher ultimate axial strains. Comparison of the specimens of Phase I with similar unconfined concrete strengths (i.e. Specimen groups B2A-SF8-WC27-A6W and B3-SF16-WC27-A6W) further supports this observation, with the specimens containing 16% silica fume

exhibiting longer second branches compared to those of the specimens with 8% silica fume content as shown in Fig. 10. These observations indicate that the addition of silica fume above a certain threshold increases the axial deformation capacity of confined concrete by reducing its dilation rate along the second branch of the stress–strain relationship. 3.3.1. Influence of axial strain measurement method As was previously discussed in Ozbakkaloglu and Lim [36], the recorded ultimate axial strains (ecu) are highly sensitive to the type of instrumentation used in their measurement. Based on a large database of experimental results, it was shown that LVDTs mounted along the entire height of the specimens gave higher axial strains than those measured by LVDTs mounted at mid-height of the specimens and by axial strain gauges [36]. In the present study, factors causing discrepancies between the axial strains obtained from these three instrumentation arrangements were experimentally investigated. An example comparison is shown in Fig. 16, which illustrates the stress–strain curves of one of the test specimens obtained using the three different

22

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24

0.03

Lateral Strain (εl)

Axial Stress (fc) (MPa)

160

120 B7-SF0-WC46-G4T

80 Large transition radius

40

0

B7-SF0-WC46-G4T

0.01

0 0

0.01

0.02

0.03

0.04

0.05

0

0.01

0.02

Axial Strain (εc)

(a)

(a)

Lateral Strain (εl)

0.03

120 B8-SF8-WC50-G4T

80 Large transition radius

40

0 0

0.01

0.02

0.03

0.04

0.04

0.05

B8-SF8-WC50-G4T

0.02

0.01

0

0.05

0

0.01

0.02

Axial Strain (εc)

0.03

0.04

0.05

Axial Strain (εc)

(b)

(b)

160

0.03 B9-SF16-WC53-G4T

120

Lateral Strain (εl)

Axial Stress (fc) (MPa)

0.03

Axial Strain (εc)

160

Axial Stress (fc) (MPa)

0.02

B9-SF16-WC53-G4T

80 Small transition radius

40

0 0

0.01

0.02

0.03

0.04

0.02

0.01

0

0.05

0

0.01

0.02

Axial Strain (εc)

(c)

measurement methods. As evident from the figure, significant differences exist among the axial strains measured by these methods beyond the initial peak of the stress–strain curves. Table 6 presents the comparison of ultimate axial strains (ecu) of all specimens recorded using the three different measurement methods, including the ultimate axial strains recorded by the axial strain gauges (ASG), the LVDTs mounted at the mid-height of the specimens (AML), and the LVDTs mounted along the entire height of the specimens (AFL). Fig. 17 shows the comparison of the difference between AML and AFL, defined by the ratios of AML/AFL, with a change in unconfined concrete strength (f0 co). This accords with the observation reported in Ozbakkaloglu and Lim [36] that the difference in axial strain recorded by AML and AFL increases with an increase in unconfined concrete strength (f0 co). The increased discrepancies between AML and AFL were attributed to the change in the concrete cracking pattern from microcracks to macrocracks as a result of the increased concrete brittleness with an increase in concrete strength [36]. Closer investigation of the result of the present study indicates that, for a given concrete strength, the difference between AML and

0.04

0.05

(c) Fig. 15. Lateral strain–axial strain curves of GFRP tube-encased low-grade HSC specimens with: (a) 0% silica fume and 0.46 w/c ratio; (b) 8% silica fume and 0.50 w/ c ratio; and (c) 16% silica fume and 0.53 w/c ratio.

200

Axial Stress (fc) (MPa)

Fig. 14. Axial stress–strain curves of GFRP tube-encased low-grade HSC specimens with: (a) 0% silica fume and 0.46 w/c ratio; (b) 8% silica fume and 0.50 w/c ratio; and (c) 16% silica fume and 0.53 w/c ratio.

0.03

Axial Strain (εc)

(iii) ASG

160

(i) AFL

(ii) AML

120 B2B-SF8-WC24-A6T-1

80

AFL: axial strains determined from LVDTs mounted along the entire height of the specimens AML: axial strains determined from LVDTs mounted at the mid-height of the specimens ASG: axial strains determined from strain gauges attached on the surface of specimens

40 0 0

0.005

0.01

0.015

0.02

Axial Strain (εc) Fig. 16. Influence of instrumentation arrangement on axial stress–strain curves.

AFL becomes less significant with an increase in the silica fume content. This is evident from the comparison of the AML/AFL ratios of specimens in Batches 4–6 and Batches 7–9 in Table 6. As discussed previously, the reduced discrepancy between AML and

23

J.C. Lim, T. Ozbakkaloglu / Construction and Building Materials 63 (2014) 11–24 Table 6 Comparison of axial strains measured by different methods. Specimen

Average f0 co (MPa)

B1-SF0-WC27-A6W B2A-SF8-WC27-A6W B2B-SF8-WC24-A6W B3-SF16-WC27-A6W B4-SF0-WC27-G6T B5-SF8-WC31-G6T B6-SF16-WC33-G6T B7-SF0-WC46-G4T B8-SF8-WC50-G4T B9-SF16-WC53-G4T

85.7 112.4 120.9 113.5 84.70 84.80 84.50 57.30 52.10 54.40

Average ecu (%)

Differences

AFL

AML

ASG

AML/AFL

ASG/AFL

2.10 1.86 1.77 1.91 2.84 2.75 3.20 3.65 3.22 4.09

1.19 0.97 0.80 1.00 1.27 1.53 2.07 2.88 2.61 3.74

1.02 0.86 0.61 0.89 – – – – – –

0.57 0.52 0.45 0.52 0.45 0.56 0.65 0.79 0.81 0.91

0.49 0.46 0.35 0.47 – – – – – –

AFL: axial strains determined from LVDTs mounted along the entire height of the specimens. AML: axial strains determined from LVDTs mounted at the mid-height of the specimens. ASG: axial strains determined from strain gauges attached on the surface of specimens.

1.2

AML/AFL

1.0

AML/AFL = 1.10-0.0056f'co Test Results = 30 R² = 0.690

0.8 0.6 0.4

GFRP tube-encased low-grade HSC GFRP tube-encased high-grade HSC AFRP-wrapped HSC

0.2 0.0 40

60

80

100

120

140

Unconfined Concrete Strength ( f'co) Fig. 17. Variation of AML/AFL ratio with unconfined concrete strength (f0 co).

AFL can be attributed to the smaller concrete crack size. These observations, therefore, indicate that, for a given unconfined concrete strength, FRP-confined concrete specimens with higher silica fume content develop smaller cracks than their counterparts with a lower or no silica fume content. This in turn leads to a more favorable dilation behavior and, as was noted previously, results in higher axial deformation capacities of specimens with higher silica fume content. Based on the significant differences observed in the axial strains obtained from different measurement methods as outlined herein, it is recommended that in future studies due consideration be given to the influence of instrumentation method in the interpretation of the results of FRP-confined HSC specimens, with or without silica fume. 4. Conclusions This paper has presented the results of an experimental study on the influence of silica fume on the axial compressive behavior of FRP-confined HSC. Based on the results and discussions presented in the paper, the following conclusions can be drawn: 1. Sufficiently confined HSC with and without silica fume can exhibit highly ductile compressive behavior. 2. An increase in the unconfined concrete strength resulting from a reduction in the w/c ratio or an increase in silica fume content leads to reductions in the strength and strain enhancement ratios. 3. For a given unconfined concrete strength, the presence and change in silica fume content do not significantly alter the strength enhancement effect of FRP confinement.

4. For a given unconfined concrete strength, specimens with silica fume content above a certain threshold exhibits a higher strain enhancement than the companion specimens with lower or no silica fume content. 5. FRP-confined concrete can exhibit a monotonically ascending stress–strain curve or a curve with a post-peak strength loss at the transition region. Due to the resulting increase in concrete strength and its associated brittleness, the silica fume addition or w/c ratio reduction in the concrete mix leads to a more significant post-peak strength loss on the stress–strain relationships. 6. Transition regions of stress–strain curves of FRP-confined concrete are observed to be sensitive to the silica fume content of the concrete mix, with mixes having higher silica fume content exhibiting curves with smaller transition radii. 7. The hoop strain reduction factor (ke,f) is observed to decrease slightly with an increase in concrete strength (f0 co) resulting from the addition of silica fume to the mix or reduction of w/c ratio of the mix. 8. The discrepancy between the axial strains measured using LVDTs mounted on FRP-confined HSC specimens at their midheight (AML) and LVDTs mounted along the full-height of specimens (AFL) increases with either an increase in the concrete strength (f0 co). However the discrepancy reduces with an increase in silica fume content at a given concrete strength. 5. Notations Ef Efrp f0 cc f0 co ke,f sf/c tf w/c

eco ecu ef efrp eh,rup

elastic modulus of fibers (MPa) elastic modulus of FRP material (MPa) peak axial compressive stress of FRP-confined concrete (MPa) peak axial compressive stress of unconfined concrete (MPa) hoop strain reduction factor of fibers silica fume–cementitious binder ratio total nominal thickness of fibers (mm) water-to-cementitious binder ratio axial strain at peak axial compressive stress of unconfined concrete ultimate axial strain of FRP-confined concrete ultimate tensile strain of fibers ultimate tensile strain of FRP material hoop rupture strain of FRP shell

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