Self-compacting concrete incorporating steel and polypropylene fibers: Compressive and tensile strengths, moduli of elasticity and rupture, compressive stress–strain curve, and energy dissipated under compression

Composites: Part B 53 (2013) 121–133

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Self-compacting concrete incorporating steel and polypropylene fibers: Compressive and tensile strengths, moduli of elasticity and rupture, compressive stress–strain curve, and energy dissipated under compression Farhad Aslani ⇑, Shami Nejadi Centre for Built Infrastructure Research, School of Civil and Environmental Engineering, University of Technology, Sydney, Australia

a r t i c l e

i n f o

Article history: Received 6 August 2012 Received in revised form 12 March 2013 Accepted 7 April 2013 Available online 25 April 2013 Keywords: B. Mechanical properties A. Fibers C. Analytical modelling D. Mechanical testing

a b s t r a c t Fiber-reinforced self-compacting concrete (FRSCC) is a high-performance building material that combines positive aspects of fresh properties of self-compacting concrete (SCC) with improved characteristics of hardened concrete as a result of fiber addition. Considering these properties, the application ranges of both FRSCC and SCC can be covered. A test program is carried out to develop information about the mechanical properties of FRSCC. For this purpose, four SCC mixes – plain SCC, steel, polypropylene, and hybrid FRSCC – are considered in the test program. The properties include compressive and splitting tensile strengths, moduli of elasticity and rupture, compressive stress–strain curve, and energy dissipated under compression. These properties are tested at 3, 7, 14, 28, 56, and 91 days. Relationships are established to predict the compressive and splitting tensile strengths, moduli of elasticity and rupture, compressive stress–strain curve, and energy dissipated under compression. The models provide predictions matching the measurements. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Self-compacting concrete (SCC) can be placed and compacted under its own weight with little or no vibration and without segregation or bleeding. SCC is used to facilitate and ensure proper filling and good structural performance of restricted areas and heavily reinforced structural members. It has gained significant importance in recent years because of its advantages [1]. Recently, this concrete has gained wider use in many countries for different applications and structural configurations. SCC can also provide a better working environment by eliminating the vibration noise. Such concrete requires a high slump that can be achieved by superplasticizer addition to a concrete mix and special attention to the mix proportions. SCC often contains a large quantity of powder materials that are required to maintain sufficient yield value and viscosity of the fresh mix, thus reducing bleeding, segregation, and settlement. As the use of a large quantity of cement increases costs and results in higher temperatures, the use of mineral admixtures such as fly ash, blast furnace slag, or limestone filler could increase the slump of the concrete mix without increasing its cost [2].

⇑ Corresponding author. Tel.: +61 434419460. E-mail address: [email protected] (F. Aslani). 1359-8368/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2013.04.044

Fiber-reinforced self-compacting concrete (FRSCC) is a relatively recent composite material that combines the benefits of the SCC technology with the advantages of the fiber addition to a brittle cementitious matrix. It is a ductile material that in its fresh state flows into the interior of the formwork, filling it in a natural manner, passing through the obstacles, and flowing and consolidating under the action of its own weight. FRSCC can mitigate two opposing weaknesses: poor workability in fiber-reinforced concrete (FRC) and cracking resistance in plain concrete. A few studies have been carried out on optimization of the mix proportion for the addition of steel or polypropylene fibers to SCC. Meanwhile, there is insufficient research on the mechanical properties of FRSCC. In mechanical terms, the greatest disadvantage of cementitious material is its vulnerability to cracking, which generally occurs at an early age in concrete structures or members. Cracking may potentially reduce the lifetime of concrete structures and cause serious durability and serviceability problems. The most beneficial properties with the fiber addition to the concrete in the hardened state are the impact strength, the toughness, and the energy absorption capacity. A detailed description of the benefits provided by the fiber addition to concrete can be found elsewhere [3,4]. The fiber addition might also improve the fire resistance of cement-based materials, as well as their shear resistance. The possible applications of FRSCC include highways; industrial and airfield pavements; hydraulic structures; tunnel

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Table 1 Properties of cement, fly ash, and ground granulated blast furnace slag (GGBFS). Cement

Fly ash

Chemical properties CaO SiO2 Al2O3 Fe2O3 MgO SO3 K2O Na2O Cl LOI Physical properties Autoclave expansion Fineness index Mechanical properties Initial setting time Final setting time Soundness Drying shrinkage fc0 (3 days) fc0 (7 days) fc0 (28 days)

GGBFS

Chemical properties 64.5% 19.3% 5.2% 2.9% 1.1% 2.9% 0.56% <0.01% 0.02% 2.8% TiO2 405 m2/kg 90 min 135 min 1.0 mm 590 lstrain 37.2 MPa 47.3 MPa 60.8 MPa

Chemical properties

Al2O3 CaO Fe2O3 K2O MgO Mn2O3 Na2O P2O5 SiO2 SO3 SrO TiO2 Physical properties Moisture Fineness 45 lm Loss on ignition Sulfuric anhydride Alkali content Chloride ion Relative density Relative water requirement Relative strength 28 days

26.40% 2.40% 3.20% 1.55% 0.60% <0.1% 0.47% 0.20% 61.40% 0.20% <0.1% 1.00%

Al2O3 Fe2O3 MgO Mn2O3 SO3 Cl Insoluble residue LOI Physical properties Fineness index

14.30% 1.20% 5.40% 1.50% 0.20% 0.01% 0.50% 1.10% 435 m2/kg

<0.1% 78% Passed 2.30% 0.20% 0.50% <0.001% 2.02% 97% 88%

Table 2 Properties of crushed latite volcanic rock coarse aggregate, Nepean river gravel fine aggregate, and Kurnell natural river sand fine aggregate. Crushed latite volcanic rock coarse aggregate

Nepean river gravel fine aggregate

Kurnell natural river sand fine aggregate

Characteristics Sieve size

Results Passing (%)

Characteristics Sieve size

Results Passing (%)

Characteristics Sieve size

Results Passing (%)

13.2 mm 9.5 mm 6.7 mm 4.75 mm 2.36 mm 1.18 mm

100 89 40 7 1 1

6.7 mm 4.75 mm 2.36 mm 1.18 mm 600 lm 425 lm

100 99 83 64 42 28

100 98 87 46 1 Nil

Material finer than 75 lm (%) Mis-shapen particles (%) Ratio 2:1 Ratio 3:1 Flakiness index (%) Uncompacted bulk density (t/m3) Compacted bulk density (t/m3) Moisture condition of the aggregate (%) Particle density (Dry) (t/m3) Particle density (SSD) (t/m3) Apparent particle density (t/m3)

1

300 lm 150 lm Material finer than 75 lm (%) Uncompacted bulk density (t/m3) Compacted bulk density (t/m3) Particle density (Dry) (t/m3) Particle density (SSD) (t/m3) Apparent particle density (t/m3) Water absorption (%) Silt content (%) Degradation factor of fine aggregate the wash water after using permitted 500 ml was: CLEAR Moisture content (%) Method of determining voids content % Voids The mean flow time (s)

19 8 3 1.52 1.64 2.58 2.60 2.63 0.7 7 90

1.18 mm 600 lm 425 lm 300 lm 150 lm Material finer than 75 lm in aggregate by washing (%) Uncompacted bulk density (t/m3) Compacted bulk density (t/m3) Particle density (Dry) (t/m3) Particle density (SSD) (t/m3) Apparent particle density (t/m3) Water absorption (%) Silt content (%)

Water absorption (%) Ave. dry strength (kN) Ave. wet strength (kN) Wet/Dry strength variation (%) Test fraction (mm) The amount of significant breakdown (%) The size of testing cylinder = 150 mm diam. Los angeles value grd. ‘K’ (%Loss)

13 1 20 1.36 1.54 1.3 2.65 2.70 2.79

1.9 391 293 25 9.5 + 6.7 <0.2

1.39 1.54 2.58 2.59 2.62 0.6 4

5.5 41.7 26.5

13

segments; bridges components and concrete structures of complex geometry that present high difficulties in being reinforced by conventional steel bars, especially those that have a high degree of support redundancy. 2. Research significance It is vital to investigate that whether all the assumed hypotheses used to design structures of conventional and fiber reinforced

concretes are also valid for SCC and FRSCC structures. The research presented aims at finding experimentally and numerically the properties of SCC and FRSCC in the fresh and hardened stages. Therefore, an experimental program is carried out to investigate the mechanical properties of four mixes of SCC. The mechanical properties included in this study are compressive and splitting tensile strengths, modulus of elasticity, modulus of rupture, compressive stress–strain curve, and energy dissipated under compression. These properties are tested at 3, 7, 14, 28, 56, and 91 days. The

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F. Aslani, S. Nejadi / Composites: Part B 53 (2013) 121–133 Table 3 The physical and mechanical properties of fibers. Fiber type

Fiber name

Density (kg/ m3)

Length (l)

Diameter (d)

Aspect ratio (l/d)

Tensile strength (MPa)

Modulus of elasticity (GPa)

Cross-section form

Surface structure

Steel

Dramix RC-80/ 60-BN Synmix 65

7850

60

0.75

80.0

1050

200

Circular

Hooked end

905

65

0.85

76.5

250

3

Square

Rough

Polipropylene (PP)

Table 4 The proportions of the concrete mixtures (based on SSD condition). Constituents

N-SCC

D-SCC

S-SCC

DS-SCC

Cement (kg/m3) Fly ash (kg/m3) GGBFS (kg/m3) Cementitious content (kg/m3) Water (l/m3) Water cementitious ratio

160 130 110 400 208 0.52

160 130 110 400 208 0.52

160 130 110 400 208 0.52

160 130 110 400 208 0.52

3. Experimental study 3.1. Materials

Fine aggregate (kg/m3) Coarse sand Fine sand Coarse aggregate (kg/m3)

660 221 820

660 221 820

660 221 820

660 221 820

Admixtures (l/m3) Superplasticiser VMA High range water reducing agent

4 1.3 1.6

4.86 1.3 1.6

4.73 1.3 1.6

4.5 1.3 1.6

Fiber content (kg/m3) Steel PP

– –

30 –

– 5

15 3

Table 5 The SCC mixes workability characteristics.

a

data to propose splitting tensile strength, moduli of elasticity and rupture, energy dissipated under compression models that on compressive strength and age of concrete. Also, compressive stress–strain relationships for SCC and FRSCC are compared with the test results.

Workability characteristics

N-SCC

D-SCC

S-SCC

DS-SCC

Average spreading diameter (mm) Flow time T50cm (s) Average J-Ring diameter (mm) Flow time T50cm J-Ring (s) L-box test Flow time V-funnel (s) V-funnel at T5min (s) Entrapped air (%) Specific gravity (kg/m3)

680 2.7 655 3.2 0.87 6 4 1.3 2340

670 3.8 580 5 Blockeda 7 5 1.2 2274

700 2.5 570 6 Blocked Blocked Blocked 1.2 2330

650 3.2 560 5 Blocked Blocked Blocked 1.0 2385

Fibers are the main reason for blockage.

developments of mechanical properties with time are investigated. Also, since only a few correlations among the mechanical properties of FRSCC have been reported and are unclear. In the presented study regression analyses are conducted on existing experimental

3.1.1. Cement In this experimental study, Shrinkage Limited Cement (SLC) corresponding to the ASTM C183-08 [5] (AS 3972 [6]) standard was used. SLC is manufactured from specially prepared portland cement clinker and gypsum. It may contain up to 5% of AS 3972 approved additions. The chemical, physical, and mechanical properties of the cement used in the experiments are shown in Table 1. The chemical, physical, and mechanical properties adhere to the limiting value or permissible limits specified in AS 2350.2, 3, 4, 5, 8, and 11 [7]. 3.1.2. Fly ash It is important to increase the amount of paste in SCC because fly ash is an agent to carry the aggregates. Eraring Fly Ash (EFA) is a natural pozzolan. It is a fine cream/grey powder that is low in lime content. The chemical and physical properties of EFA used in the experimental study are given in Table 1. The chemical, physical, and mechanical properties of the EFA used adhere to the limiting value or permissible limits specified in ASTM C311-11b [8] (ACI 232.2R-03 [9], AS 2350.2 [7], AS 3583.1, 2, 3, 5, 6, 12, and 13 [10]). 3.1.3. Ground granulated blast furnace slag Granulated Blast Furnace Slag (GGBFS) is another supplementary cementitious material that is used in combination with SLC. GGBFS used in the experiment originated in Boral, Sydney, and it conformed to ASTM C989-06 [11] (ACI 233R-95 [12] and AS 3582.2 [13]) specifications. The chemical and physical properties of GGBFS are given in Table 1.

Table 6 Compressive strength, tensile strength, modulus of elasticity, and modulus of rupture of SCC mixtures at different ages. Age (days)

N-SCC

Compressive strength (MPa) 3 12.45 7 21.80 14 29.05 28 33.30 56 40.60 91 46.40 Modulus of elasticity (GPa) 3 25.23 7 27.84 14 32.24 28 35.39 56 35.58 91 37.79

D-SCC

S-SCC

DS-SCC

18.50 25.30 34.30 38.00 50.50 51.15

13.65 22.50 32.45 38.10 42.90 47.65

14.30 26.30 38.10 45.00 50.75 52.00

24.45 26.57 29.14 35.76 36.44 37.58

25.36 27.87 29.68 35.76 36.32 37.47

26.78 30.13 31.26 36.10 37.03 38.12

Age (days)

N-SCC

Tensile strength (MPa) 3 1.65 7 2.26 14 2.80 28 3.60 56 4.17 91 4.57 Modulus of rupture (MPa) 3 2.50 7 3.35 14 4.66 28 5.00 56 5.87 91 7.13

D-SCC

S-SCC

DS-SCC

2.32 3.38 3.87 4.54 5.35 5.44

1.16 1.93 3.05 3.56 4.02 4.41

1.76 2.51 3.54 4.09 4.33 4.80

3.35 4.10 5.40 6.37 6.72 7.23

3.13 4.26 4.60 5.00 6.50 6.76

2.47 3.81 4.80 5.40 6.52 7.21

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Fig. 1. Flexural load–deflection curve of N-SCC mixture at different ages (a) 3 days, (b) 7 days, (c) 14 days, (d) 28 days, (e) 56 days, and (f) 91 days.

Fig. 2. Flexural load–deflection curve of D-SCC mixture at different ages (a) 3 days, (b) 7 days, (c) 14 days, (d) 28 days, (e) 56 days, and (f) 91 days.

3.1.4. Aggregate In this study, crushed volcanic rock (i.e., latite) coarse aggregate was used with a maximum aggregate size of 10 mm. Nepean river gravel with a maximum size of 5 mm and Kurnell natural river

sand fine aggregates were also used. The sampling and testing of aggregates were carried out in accordance with ASTM C1077-13 [14] (AS 1141 [15] and RTA [16]) and the results for coarse and fine aggregates are shown in Table 2, respectively.

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Fig. 3. Flexural load–deflection curve of S-SCC mixture at different ages (a) 3 days, (b) 7 days, (c) 14 days, (d) 28 days, (e) 56 days, and (f) 91 days.

Fig. 4. Flexural load–deflection curve of DS-SCC mixture at different ages (a) 3 days, (b) 7 days, (c) 14 days, (d) 28 days, (e) 56 days, and (f) 91 days.

3.1.5. Admixtures The superplasticiser, Viscosity-Modifying Admixture (VMA), and high-range water-reducing agent were used in this study. The new superplasticiser generation Glenium 27 complies with

AS 1478.1 [17] type High Range Water Reducer (HRWR) and ASTM C494 [18] types A and F are used. The Rheomac VMA 362 viscosity modifying admixture that used in this study is a readyto-use, liquid admixture that is specially developed for producing

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Fig. 5. Compressive stress–strain curve of (a) N-SCC, (b) D-SCC, (c) S-SCC, and (d) DS-SCC mixes at different ages.

concrete with enhanced viscosity and controlled rheological properties. Pozzolith 80 was used as a high-range water-reducing agent in the mixes. It meets AS 1478 [17] Type WRRe, requirements for admixtures. 3.1.6. Fibers In this study, two commercially available fibers, Dramix RC-80/ 60-BN type steel fibers and Synmix 65 type polypropylene (PP) fibers were used. The mechanical, elastic and surface structure properties of the steel and PP fibers are summarized in Table 3. 3.2. Mixture proportions One control SCC mixture (N-SCC) and three fiber-reinforced SCC mixtures were used in this study. Fiber-reinforced SCC mixtures contain steel (D-SCC), PP (S-SCC), and hybrid (steel + PP) (DS-SCC) fibers. The content proportions of these mixtures are given in Table 4. These contents were chosen to attempt to keep compressive strength to a level applicable to construction. As shown in Table 4, cement, fly ash, GGBFS, water, fine and coarse aggregates, VMA, and high range water reducing agent constituents amount are same for four mixes. But, fiber amount and superplasticiser that are used in the mixes are different. A forced pan type of mixer with a maximum capacity of 150 l was used. The volume of a batch with fibers was kept constant at

Table 7 The energy dissipated under compression. Mix

Gc (MPa) N-SCC D-SCC S-SCC DS-SCC

Age (days) 3

7

14

28

56

91

0.658 0.747 0.701 0.762

0.833 1.117 0.988 1.239

1.228 1.327 1.304 1.359

1.255 1.494 1.421 1.535

1.544 1.683 1.617 1.700

1.612 1.825 1.745 1.865

50 l. First, powders and sand are mixed for 10 s and water and superplasticiser are added and mixed for 110 s and the coarse aggregate is added and at the end fibers are added to the pan and mixed for 90 s. 3.3. Samples’ preparation and curing conditions We used six /150 mm  300 mm molds for the determination of compressive and splitting tensile strengths per each age, and three cylindrical molds /150 mm  300 mm are used for the determination of the modulus of elasticity per each age. Meanwhile, three 100 mm  100 mm  350 mm molds are used for the determination of modulus of rupture per each age. Specimens for testing the hardened properties are prepared by direct pouring of concrete into molds without compaction. The specimens are

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kept covered in a controlled chamber at 20 ± 2 °C for 24 h until demolding. Thereafter, the specimens are placed in water presaturated with lime at 20 °C. These specimens are tested at 3, 7, 14, 28, 56, and 91 days. For each test, separated specimens are used and surface of specimens are smoothed.

3.4. Samples’ test methods The compressive strength test, performed on /150 mm  300 mm cylinders, followed AS 1012.14 [19] and ASTM C39 [18] tests for compressive strength of cylindrical concrete specimens. The cylinders were loaded in a testing machine under load control at the rate of 0.3 MPa/s until failure. The splitting tensile test, run on /150 mm  300 mm cylinders, was in accordance with the AS 1012.10 [20] and ASTM C496 [18] tests for splitting tensile strength of cylindrical concrete specimens, although ACI committee 544.2R [4] hardly recommends the use of the test on fiber-reinforced concrete. The running arose because the ratio of fiber length to cylinder diameter took a low value of 0.23 in the work and because some investigators have shown that the ASTM C496 test is applicable to fiber-reinforced concrete specimens. The modulus of elasticity test that followed the AS 1012.17 [21] and ASTM C469 was done to /150 mm  300 mm cylinders. The flexural strength (modulus of rupture, MOR) test, conducted using 100 mm  100 mm  350 mm test beams under third-point loading, followed the AS 1012.11 [22] and ASTM C1018 test for flexural toughness and first-crack strength of fiber-reinforced concrete. The mid-span deflection was the average of the ones detected by the transducers through contact with brackets attached to the beam specimen.

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3.5. Properties of fresh concrete The experiments required for the SCC are generally carried out worldwide under laboratory conditions. These experiments test the liquidity, segregation, placement, and compacting of fresh concrete. Conventional workability experiments are not sufficient for the evaluation of SCC. Some of the experiment methods developed to measure the liquidity, segregation, placement, and compaction of SCC are defined in the European guidelines [23] and ACI 237R-07 [24] for SCC, including specification, production and use as slump-flow, V-funnel, U-box, L-box and fill-box tests. This study performed slump flow, T50cm time, J-ring flow, V-funnel flow time, and L-box blocking ratio tests. In order to reduce the effect of loss of workability on the variability of test results, the fresh properties of the mixes were determined within 30 min after mixing. The order of testing is as follows: 1. Slump flow test and measurement of T50cm time; 2. J-ring flow test, measurement of difference in height of concrete inside and outside the J-ring and measurement of T50cm time; 3. V-funnel flow tests at 10 s T10s and 5 min T5min; and 4. L-box test [25]. 4. Experimental results 4.1. Properties of fresh concrete The results of various fresh properties tested by the slump flow test (slump flow diameter and T50cm); J-ring test (flow diameter); L-box test (time taken to reach 400 mm distance T400mm, time taken to reach 600 mm distance T600mm, time taken to reach

Fig. 6. Energy dissipated under compression (Gc) versus strain of (a) N-SCC, (b) D-SCC, (c) S-SCC, and (d) DS-SCC mixes at different ages.

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800 mm distance TL, and ratio of heights at the two edges of L-box [H2/H1]); V-funnel test (time taken by concrete to flow through Vfunnel after 10 s T10s); the amount of entrapped air; and the specific gravity of mixes are given in Table 5. The slump flow test judges the capability of concrete to deform under its own weight against the friction of the surface with no restraint present. A slump flow value ranging from 500 to 700 mm for self-compacting concrete was suggested [23]. At a slump flow >700 mm the concrete might segregate, and at <500 mm, the concrete might have insufficient flow to pass through highly congested reinforcements. All the mixes in the present study conform to the above range, because the slump flow of

SCC is in the range of 600–700 mm. The slump flow time for the concrete to reach a diameter of 500 mm for all mixes was less than 4.5 s. The J-ring diameters were in the range of 560–655 mm. In addition to the slump flow test, a V-funnel test was also performed to assess the flowability and stability of SCC. V-funnel flow time is the elapsed time in seconds between the opening of the bottom outlet, depending when it is opened (T10s and T5min), and the time when light becomes visible at the bottom when observed from the top. According to the European guidelines [23], a period ranging from 6 to 12 s is considered adequate for SCC. The V-funnel flow times in the experiment were in the range of 7–11 s. The test results of this

Fig. 7. Predicted time-related mechanical properties values versus experimented values (a) compressive strength, (b) tensile strength, (c) modulus of elasticity, (d) modulus of rupture, and (e) energy dissipated under compression.

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investigation indicated that all mixes met the requirements of allowable flow time. About V-funnel flow time test results for the N-SCC mix was 6 s and for the D-SCC was 7 s and for other fiber reinforced SCC mixes are blocked, obviously. The maximum size of coarse aggregate was restricted to 10 mm to avoid a blocking effect in the L-box for N-SCC mix. The gap between rebars in the L-box test was 35 mm. The L-box ratio H2/H1 for the N-SCC mix was above 0.8 which is, according to the European guidelines and, obviously, for other mixes is blocked. A total spread over 700 mm was measured and no sign of segregation or considerable bleeding in any of the mixtures was detected as the mixtures showed good homogeneity and cohesion. 4.2. Compressive strength Table 6 presents the compressive strength of N-SCC, D-SCC, SSCC, and DS-SCC mixes achieved at different ages. Compressive strength samples with fiber mixes are higher than N-SCC mix. Samples with the S-SCC mix have lower compressive strength unlike the D-SCC and DS-SCC mixes. The average compressive strength of the DS-SCC mix is 19%, 4%, and 13% higher than the N-SCC, D-SCC, and S-SCC mixes, respectively. The results show that the D-SCC mix at three days was 32%, 26%, and 22% higher than the N-SCC, S-SCC and DS-SCC mixes respectively. Furthermore, the results indicate that the compressive strength of the DS-SCC mix at 91 days is 11%, 1%, and 8% higher than the N-SCC, D-SCC, and SSCC mixes, respectively.

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4.3. Tensile strength Table 6 presents the splitting tensile strengths of N-SCC, D-SCC, S-SCC, and DS-SCC mixes determined at different ages. The tensile strengths of the D-SCC and DS-SCC samples are higher than those of the N-SCC and S-SCC. The S-SCC mix has a lower tensile strength than N-SCC. The average tensile strength of the D-SCC mix is 23%, 27%, and 15% higher than that of the N-SCC, S-SCC, and DS-SCC mixes, respectively. Moreover, the results indicate that the tensile strength of the D-SCC mix at 91 days is 16%, 19%, and 12% higher than that of the N-SCC, S-SCC, and DS-SCC mixes, respectively. 4.4. Modulus of elasticity Table 6 presents the modulus of elasticity of N-SCC, D-SCC, SSCC, and DS-SCC mixes attained at different ages. The average modulus of elasticity of DS-SCC mix is 2%, 4% and 3%, higher than that of the N-SCC, D-SCC, and S-SCC mixes, respectively. The results show that the N-SCC mix at 14 days age is 9%, 8%, and 3% higher than D-SCC, S-SCC, and DS-SCC mixes, respectively. Additionally, the results indicate that the tensile strength of the DS-SCC mix at 91 days is 0.8%, 1%, and 1% higher than that of the N-SCC, D-SCC, and S-SCC mixes, respectively. 4.5. Modulus of rupture (flexural tensile strength) Table 6 and Figs. 1–4 present the flexural tensile strengths and flexural load–deflection curve of N-SCC, D-SCC, S-SCC, and DS-SCC

Fig. 8. Predicted compressive strength-related mechanical properties values versus experimented values (a) tensile strength, (b) modulus of elasticity, and (c) modulus of rupture.

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Fig. 9. Comparison between experimented (a) N-SCC, (b) D-SCC, (c) S-SCC, and (d) DS-SCC mixes compressive stress–strain curve results with proposed relationship.

mixes determined at different ages. The average flexural tensile strength of the D-SCC mix is 14%, 9%, and 9% higher than that of the N-SCC, S-SCC, and DS-SCC mixes, respectively. The results show that the S-SCC mix at seven days is 21%, 4% and 10% higher than the N-SCC, D-SCC, and DS-SCC mixes, respectively. Also, the results indicate that flexural tensile strength of D-SCC mix at 91 days is 1%, 6%, and 0.2% higher than that of the N-SCC, S-SCC, and DSSCC mixes, respectively. 4.6. Compressive stress–strain curve Complete stress–strain curves of the concrete of specimens were obtained from the compression tests of the cylinders with a controlled displacement rate. For each mix, three cylinders were tested. As the test results reproduced well, each stress–strain curves shown in Fig. 5 represents the average results of the three tests. It should be noted that the axial strains of the concrete in compression were obtained from the full height shortening of the cylinders using LVDTs. To assure stable tests in the softening phase the testing equipment should have enough stiffness and sophisticated PID control should be available. During the test, the strains were obtained from the relative displacement of the loading platens. For this purpose three LVDT’s were disposed around the test sample forming an angle of 120° between consecutive LVDT’s. This test set up avoids that the deformation of the test equipment is added to the displacements read by the LVDT’s. This arrangement of the transducers also allows that the specimen deformation in the longitudinal axis, can be computed simply by the average readouts of the three transducers. There is no need to attend to the rotation of the upper loading paten, since the computed deforma-

tion is at the longitudinal axis of the specimen. The strain was calculated from the average displacement readings divided by the height of the specimen. The used testing rig has these features and the tests were carried out in displacement control. The compression stress–strain curves at increasing ages of N-SCC, D-SCC, S-SCC, and DS-SCC mixes are shown in Fig. 5. All the fibrous SCC mixes verified more substantial ductility than the corresponding N-SCC mix. Commonly, the nature of failure in compression for the N-SCC mix tended to be more sudden and brittle as the age of the concrete increased. On the other hand, with the increasing age, the majority of the fibrous SCC mixes maintained their ductility and gradual failure mechanism. 4.7. Energy dissipated under compression The energy absorption per unit volume under compression was determined as the area under the stress (r)/strain (e) curve, the value can be calculated using Eq. (1):

Gc ¼

Z

eu

r de

ð1Þ

0

The Gc value was always determined until a ultimate deformation,

eu, of 0.05, where it was expected that the residual strength would be small. Table 7 includes the average values of Gc. In general, the concrete energy absorption increased with age. The major part of the energy is released in the softening phase that is too dependent on the fiber reinforcement mechanisms provided by fibers crossing the cracks. The efficiency of those mechanisms depend considerably on the fiber bond length and fiber orientation towards the cracks

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they bridge, whose homogeneity cannot be assumed between two, apparently, equal batches. The variation of the energy dissipated under compression with the strain is represented in Fig. 6. In general, Gc increased with strain more quickly for the older specimens, 56 and 91 days than for the specimens with 3, 7, 14 and 28 days. 5. Analytical relationships for the mechanical properties

Mix

Ec

g

l

N-SCC D-SCC S-SCC DS-SCC

EcN EcfD EcfS EcfDS

9.47 8.40 9.30 10.47

21.42 19.20 20.83 23.15

5.1. Time-related mechanical properties relationships To estimate the SCC mixes’ compressive strength, tensile strength, modulus of elasticity, modulus of rupture, and energy dissipated under compression at various ages, Eqs. (2)–(6) are proposed based on regression analyses of the experimental data. Fig. 7 shows that the proposed time-related relationships of compressive strength, tensile strength, modulus of elasticity, modulus of rupture, and energy dissipated under compression are in good agreement with the experimental results. Also, R2 (correlation coefficient) of proposed models in comparison with experimental results is shown in Fig. 7. 5.1.1. Compressive strength

fcm ðtÞ ¼

fc0

a

lnðtÞ þ b

ð2Þ

Mix

fc0

a

b

N-SCC D-SCC

0 fcN 0 fcfD 0 fcfS 0 fcfDS

3.47 3.75

2.54 6.66

3.84

3.87

3.96

4.54

S-SCC DS-SCC

where EcN is the N-SCC mix modulus of elasticity, EcfD is the D-SCC mix modulus of elasticity, EcfS is the S-SCC mix modulus of elasticity, EcfDS is the DS-SCC mix modulus of elasticity, and g and l are the empirical constants. 5.1.4. Modulus of rupture

fcrm ðtÞ ¼

fcr lnðtÞ þ u w

ð5Þ

Mix

fcr

w

/

N-SCC D-SCC S-SCC DS-SCC

fcrN fcrfD fcrfS fcrfDS

3.89 5.39 4.75 3.99

1.00 2.07 1.96 1.08

where fcrN is the N-SCC mix modulus of rupture, fcrfD is the D-SCC mix modulus of rupture, fcrfS is the S-SCC mix modulus of rupture, fcrfDS is the DS-SCC mix modulus of rupture, and w and / are the empirical constants. 5.1.5. Energy dissipated under compression

0 fcN

0 fcfD

where is the N-SCC mix compressive strength, is the D-SCC 0 mix compressive strength, fcfS is the S-SCC mix compressive 0 strength, fcfDS is the DS-SCC mix compressive strength, and a and b are the empirical constants. 5.1.2. Tensile strength

fctm ðtÞ ¼

fct

c

lnðtÞ þ k

ð3Þ

Mix

fct

c

k

N-SCC D-SCC S-SCC DS-SCC

fctN fctfD fctfS fctfDS

4.09 4.87 3.69 4.60

0.60 1.43 0.19 0.91

Gcm ðtÞ ¼

Gc

x

lnðtÞ þ q

ð6Þ

Mix

Gc

x

q

N-SCC D-SCC S-SCC DS-SCC

GcN GcfD GcfS GcfDS

4.33 4.91 4.69 5.16

0.340 0.476 0.411 0.541

where GcN is the N-SCC mix energy dissipated under compression, GcfD is the D-SCC mix energy dissipated under compression, GcfS is the S-SCC mix energy dissipated under compression, and GcfDS is the DS-SCC mix energy dissipated under compression. 5.2. Compressive strength-related mechanical properties relationships

where fctN is the N-SCC mix tensile strength, fctfD is the D-SCC mix 0 0 tensile strength, fctfS is the S-SCC mix tensile strength, fctfDS is the DS-SCC mix tensile strength, and c and k are the empirical constants. 5.1.3. Modulus of elasticity

Ecm ðtÞ ¼

Ec

g

lnðtÞ þ l

ð4Þ

Eqs. (5)–(7) are proposed based on regression analyses of the experimental data to predict the SCC mixes’ tensile strength, modulus of elasticity, and modulus of rupture based on the compressive strength. The bases of the proposed relationships are captured from Aslani and Nejadi’s [1] study. Fig. 8 indicates the proposed compressive strength-related relationships of tensile strength, modulus of elasticity, and modulus of rupture are in good agreement with the experimental results. Moreover, R2 (correlation coefficient) of proposed models in comparison with experimental results is shown in Fig. 8.

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5.2.1. Tensile strength

fct ¼ g1 ðfc0 Þg2

ð7Þ

Mix

fct

fc0

g1

g2

N-SCC D-SCC

fctN fctfD

0 fcN 0 fcfD

0.204 0.237

0.8047 0.7999

S-SCC

fctfS

0 fcfS

0.067

1.0889

DS-SCC

fctfDS

0 fcfDS

0.226

0.7585

where rc is concrete stress, fc0 maximum compressive strength of concrete, n material parameter that depends on the shape of the stress–strain curve, e concrete strain, e0c strain corresponding with the maximum stress fc0 , n1 modified material parameter at the ascending branch, n2 modified material parameter at the descending branch, Ec modulus of elasticity, Esec secant modulus of elasticity, n1 modified material parameter at the ascending branch, n2 modified material parameter at the descending branch, and q, x coefficients of linear equation.

6. Conclusions 5.2.2. Modulus of elasticity

The following conclusions can be drawn from this study:

0 j2 1 ðfc Þ

Ec ¼ j

ð8Þ

Ec

fc0

j1

j2

N-SCC D-SCC

EcN EcfD

10.913 6.649

0.3226 0.4383

S-SCC

EcfS

10.395

0.3271

DS-SCC

EcfDS

0 fcN 0 fcfD 0 fcfS 0 fcfDS

12.895

0.2651

Mix

5.2.3. Modulus of rupture

fcr ¼ d1 ðfc0 Þd2

ð9Þ

fcr

fc0

d1

d2

N-SCC D-SCC

fcrN fcrfD

0.325 0.376

0.7871 0.7511

S-SCC

fcrfS

0.670

0.5818

DS-SCC

fcrfDS

0 fcN 0 fcfD 0 fcfS 0 fcfDS

0.309

0.7714

Mix

5.3. Compressive stress–strain relationship In this study, a compressive stress–strain relationship (Eqs. (10)–(17)) for SCC mixes that is based on authors’ [1,26] model was developed by using the proposed compressive strength (Eq. (2)) and elastic modulus (Eqs. (4), (8)) relationships. Fig. 9 shows that the proposed stress–strain relationship fits the experimental results well. In Fig. 9, typical 91 days age compressive stress–strain curve results are selected to compare with the proposed compressive stress–strain relationship.

  n eec0 c ¼  n fc0 n  1 þ eec0

rc

Acknowledgements This work was supported by Centre for Built Infrastructure Research, School of Civil and Environmental Engineering, University of Technology Sydney, Australia. The authors would like to express their sincere gratitude and appreciation to Boral, BOSFA, and Concrite companies.

ð10Þ References

c

n ¼ n1 ¼ ½1:02  1:17ðEsec =Ec Þ0:74 n ¼ n2 ¼ n1 þ ð- þ 28  fÞ if

 Experimental investigation and analytical study were performed to develop a simple and rational mathematical model for the prediction of mechanical properties and complete stress–strain curves of concrete under compressive load. Four different SCC mixes were used in the experiment. These mixes include N-SCC (normal SCC), D-SCC (steel fiber-reinforced SCC), S-SCC (PP fiber-reinforced SCC), and DS-SCC (hybrid fiber-reinforced SCC).  Based on the experimental results: (a) the average compressive strength and modulus of elasticity of the DSSCC mix is higher than that of the N-SCC, D-SCC, and SSCC mixes, respectively; (b) the average tensile strength of the D-SCC mix is higher than that of the DS-SCC, NSCC, and S-SCC mixes, respectively; (c) the average modulus of rupture of the D-SCC mix is higher than that of the N-SCC, S-SCC, and DS-SCC mixes, respectively.  The proposed analytical expressions to predict the most significant mechanical properties (i.e., compressive strength, tensile strength, modulus of elasticity, modulus of rupture, and energy dissipated under compression) of the developed SCC mixes are in a good agreement compare to experimental results.  The proposed compressive stress–strain model based on the author’s model with several modifications (i.e., changing the ascending and descending portions) is developed by using the proposed compressive strength and elastic modulus models that are in good agreement with the experimental results for the developed SCC mixes.

if

ec P e0c

ec 6 e0c

ð11Þ ð12Þ

- ¼ ð135:16  0:1744fc0 Þ0:46

ð13Þ

f ¼ 0:83 expð911=fc0 Þ

ð14Þ

Esec ¼ fc0 =e0c  0  f m  e0c ¼ c Ec m  1 fc0 m ¼ þ 0:8 17

ð15Þ ð16Þ ð17Þ

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[17] AS 1478.1. Chemical admixtures for concrete, mortar and grout – admixtures for concrete. Standards Australia; 2000. [18] Annual book of ASTM standards 2000. Volume 04.02, Concrete and aggregates; 2000. [19] AS 1012.14. Method for securing and testing from hardened concrete for compressive strength; 1991. [20] AS 1012.10. Determination of indirect tensile strength of concrete cylinders; 2000. [21] AS 1012.17. Determination of the static chord modulus of elasticity and Poisson’s ratio of concrete specimens; 1997. [22] AS 1012.11. Determination of modulus of rupture; 2000. [23] EFNARC. The European guidelines for self-compacting concrete. Specification, Production and Use; 2005. [24] ACI 237R-07. Self-consolidating concrete. ACI Committee 237; 2007. [25] Maia L, Azenha M, Geiker M, Figueiras J. E-modulus evolution and its relation to solids formation of pastes from commercial cements. Cem Concr Res 2012;42:928–36. [26] Aslani F, Jowkarmeimandi R. Stress–strain model for concrete under cyclic loading. Mag Concr Res 2012;64(8):673–85.