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Axial compressive behavior of confined steel fiber reinforced high strength concrete
Construction and Building Materials 230 (2020) 117043
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Axial compressive behavior of confined steel fiber reinforced high strength concrete Muhammad Usman a,⇑, Syed Hassan Farooq a, Mohammad Umair a, Asad Hanif b,⇑ a b
School of Civil and Environmental Engineering, National University of Science and Technology, Islamabad, Pakistan Joint Key laboratory of the Ministry of Education, Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da Universidade, Taipa, Macau
h i g h l i g h t s Effect of FRP confinement on steel fiber reinforced concrete (SFRC) is investigated. SFRC showed excellent behavior under axial compression. The properties were significantly enhanced with FRP confinement of SFRC. Improved ductility and enhanced stress-strain behavior of concrete is demonstrated.
a r t i c l e
i n f o
Article history: Received 22 May 2019 Received in revised form 26 July 2019 Accepted 18 September 2019
Keywords: Steel fiber Fiber reinforced concrete Compressive strength Stiffness Toughness
a b s t r a c t Concrete is brittle in nature which is why different materials have been used to improve this inherent behavior of concrete. In this experimental study, the effect of simultaneous use of steel fibers and confinement on high strength concrete and the corresponding post peak response of fiber reinforced concrete is investigated. A total of 39 high-strength concrete (incorporating varying amounts of steel fibers) cylinders were casted. The steel fiber volume fraction (Vf) was varied as 0.5%, 1.5% and 2.5%. 18 samples were confined with Carbon Fiber Reinforced Polymer (CFRP) sheet, and 9 samples were casted in steel pipe confinement, whereas 12 control specimens (without confinement) were also prepared. The samples were tested under axial compression. The results confirmed that the use of steel fiber had minute effect on the compressive strength, whereas it significantly improved the ductility and enhanced the post peak behavior of concrete. The confinement significantly contributed towards the compressive strength increase. The combined use of steel fibers and confinement in concrete columns can be viewed as extremely beneficial as it not only increases the concrete compressive strength but also solves the issue of brittle failure to an appreciable extent. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Increased interest in using High Strength Concrete (HSC) due to its superior strength, durability, and deflection control has led the researchers to explore ways of improving its brittle behavior through composite action. Addition of steel fibers in HSC and confinement with ductile materials exhibits great benefits to improve the performance concrete by reducing its brittleness [1–4]. The addition of discrete fibers into the concrete matrix helps reducing micro-cracking and localized macro-cracking, with improved postcracking strength and ductility [5–7]. The steel fibers act as crack arrestors not as crack inhibitors. They are known to improve ⇑ Corresponding authors. E-mail addresses: [email protected] (M. Usman), [email protected], [email protected] (A. Hanif). https://doi.org/10.1016/j.conbuildmat.2019.117043 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
post-cracking tensile response [8,9]. Steel fibers are discontinuous and are distributed randomly in the matrix [10] just like other fibers [11,12]. These characteristics allow cracks in any direction to be bridged by the fibers and permit improved stress transfer across all cracks, thereby improving post-cracking shear and flexural resistance [13,14]. In compression, similar to the tensile response, steel fibers incorporation primarily augments the toughness and post-peak ductility [6]. The fibers can act most effectively if aligned in the direction of the largest tensile stress. Fibers are the most beneficial when large strains occur in the cement matrix [2,11,15]. Fiber volume content is one of a major factor influencing the behavior of steel fiber reinforced concrete (SFRC). Many experimental tests have been conducted by researchers which focused different properties such as uniaxial direct shear test, flexural test and uniaxial tension test [14,16,17]. These tests show that
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M. Usman et al. / Construction and Building Materials 230 (2020) 117043
increases in fiber amounts will lead to enhanced strength, ductility, and toughness [5,18]. With increase in fiber content, more fibers are likely to intersect a crack, which enhances concrete matrix post crack behavior [19,20]. It was concluded that by increasing the fiber content, the relative flexural and tensile strength could be increased. The response for compressive loads is also enhanced by varying fiber volume content. With increasing fiber content, the pre-peak ascending branch of the compressive stress-strain relationship is marginally improved resulting in a slightly higher elastic modulus [21,22]. The addition of steel fibers only marginally improves the compressive strength only up to 15% [6,23]. As the fiber content is increased, the strain capacity is increased which leads to greater load absorption capacity of concrete in compression. Some tests conducted with varying aspect ratio (of fibers) showed that increasing the aspect ratio increased the strength of matrix to a low degree but increased the toughness of matrix to an even greater extent [5]. However, the improved tensile response from higher aspect ratios is only true up to an aspect ratio of 75; thereafter, the tensile response worsened for any further increase in the aspect ratio. Some research findings had also reported increase in shear strength with higher aspect ratio [18]. The length and shape of steel fiber used can also be an influential factor in behavior of SFRC. By incorporating small length fibers while maintaining the same aspect ratio, the number of fibers increase greatly, which leads to superior crack bridging and stress transfer through the cracks [16,21,24]. The efficiency of steel fibers in the matrix depends on the orientation of fibers in the concrete matrix. In the modeling of SFRC, many account for the effects of fiber orientation and its impact on the efficiency of fibers through a fiber orientation factor is studied [25–27]. It is shown that ‘‘the addition of steel fibers cause a slight increase in the compressive strength and result in an increase in peak axial strain”. It was further observed that the compressive strength and ultimate strains of the specimens generally increased with an increase in steel fiber volume fraction (Vf), and decreased slightly with an increase in steel fiber aspect ratio (As). The axial strength of concrete increased to a great extent with FRP confinement. The effect of confinement and steel fiber incorporation in concrete enhanced the properties of concrete as expected. The placement of reinforcing bars or meshes in structural members may, thus, be eliminated with the addition of steel fibers. However, SFRC has seen limited such applications, and had some early acceptance as primary reinforcement only in flexural-critical structural members [17]. Recently, SFRC has gained acceptance in design codes for shear-critical members but its use in such members, especially for seismic applications, is uncommon. This is likely attributable to the limited research and design recommendations on SFRC for these applications.
While using discontinuous fibers is one way to improve concrete properties, use of confinement for enhanced structural behavior of concrete has also been investigated for reinforced and composite structural members [24,28–32]. Although studies have been conducted in the past on FRP/steel confined concrete and SFRC as well, findings on the effects of such confinement on SFRC are sparse. This research work is, thus, conducted to fill the research gap by investigating the co-effects of steel fibers and confinement (by FRP and steel tube or sheet) on axial compressive behavior of HSC. Compressive stress, strain, toughness, ductility, and post cracking behavior were thought to be improved by such combined techniques which is, then, corroborated and presented in this study.
2. Experimental program Experimental program comprises of casting 39 (150 mm diameter 300 mm height) cylindrical specimens of High Strength Concrete (HSC) with varying volume fraction (Vf) of steel fibers. After the curing period of 28 days, 18 samples were confined with Fiber Reinforced Polymer (FRP) sheet, whereas 9 samples were directly casted in steel tube. 2.1. Materials All the material used in this research were obtained locally except steel fibers and CFRP sheet were imported from China. Detailed material properties are summarized in Table 1. Ordinary Portland cement of grade 53 (Type-I) and prepared according to Pakistan standard PS-232-2008 and conformity to AST C150-04, EN 116 was used in casting samples. Sikament-520BA super plasticizer and sand with 2.01 fineness modulus was used to prepare high strength concrete. Use of superplasticizer in improving the concrete properties has already been corroborated by the Authors [33]. The gradation and aggregate size was chosen as per mix design of HSC. The maximum size was restricted to 20 mm. Two sieve sizes – 20 mm and 10 mm – were used and the ratio was set to 1:0.8 respectively to ensure high packing density. Master Steel Fiber S65 (hooked end fiber with length 35 mm and aspect ratio 64) was used in this research, obtained from BASF, China. Nine steel tubes were prepared from hot rolled sheet with a thickness of 1.02 mm with a nominal yield stress of 300 kN. The steel tubes were formed by cold rolled sheets welding at the longitudinal seam. Concrete was poured directly in the steel tubes. Carbon Fiber Reinforced Polymer (CFRP) sheet was affixed using epoxy Master Brace P3500 and P4500 mixed at a ratio 1:0.5 for obtaining the final epoxy.
Table 1 Mechanical properties of materials. Super plasticizer
pH Value Bulk density
6.5–8.5 (at 20 °C) 300–600 kg/m3
Steel Fiber
Length Diameter Aspect Ratio Tensile Strength
35 mm 0.55 mm 64 1345 MPa
CFRP Sheet
Modulus of elasticity Tensile strength Thickness for static design weight/density
230 KN/mm2 4900 N/mm2 0.112 mm
Master Brace P3500
Adhesion strength on carbon MPa (ASTM D4541:95e1) Compressive strength, MPa (ASTM D695:96)
2.87 73
Master Brace P4500
Compressive Strength TS EN 196 (7 days) Bonding Strength to concrete (7 days)
>60 N/mm2 >3.0 N/mm2
3
M. Usman et al. / Construction and Building Materials 230 (2020) 117043 Table 2 Details of concrete mixes. Type
Cement (Kg/m3)
Sand (Kg/m3)
Gravel (<20 mm) (Kg/m3)
Gravel (<10 mm) (Kg/m3)
w/c Ratio
Steel Fiber % (Vf)
Mix Mix Mix Mix
460 460 460 460
621 621 621 621
706 706 706 706
578 578 578 578
0.35 0.35 0.35 0.35
0 0.5% = (39 Kg/m3) 1.5% = (117 Kg/m3) 2.5% = (195 Kg/m3)
1 2 3 4
2.2. Preparation of samples 39 samples were prepared with addition of varying volume fraction (Vf, 0.5%, 1.5% and 2.5%) of steel fibers. The mix design and percentage of steel fibers is summarized in Table 2. The steel fiber and super plasticizer was added in the mixture uniformly during the mixing for workability. The samples were casted in cylinders at standard room temperature of 25° C. The samples were cured for 28 days in water bath. Then, the samples were air dried and subsequently taken for wrapping of CFRP sheet. The surfaces of the samples were cleaned with brush and Master BraceÒ3500 was applied as a primer before the application of epoxy. MB3500 consisted of parts ‘‘A” and ‘‘B” which were mixed in ratio 1.67:1.0 before application. The primer was allowed to get absorbed in concrete surface for 24 h prior to the application of epoxy Master BraceÒ4500. MB4500 consisted of parts ‘‘A” and ‘‘B” which were mixed together in ratio 1:0.5 before application and applied to concrete samples and CFRP laminate as shown in Fig. 1. CFRP cloth was cut as 1200 2100 to give minimum 1.500 overlap at the ends. 2.3. Specimen designation The specimens were labeled for classification of data. Label/ nomenclature started with ‘C’ or ‘UC’ for confined and unconfined, respectively. Control specimens without steel fibers were denoted with ‘UR’. For reinforced specimens, the hyphen was followed by ‘R’, which was followed by hyphen and percentage of steel fiber (Vf). For steel tube confined samples, the letter ‘S’ was added after hyphen. For example, C-R-3F-2.5% denotes the specimen which is confined with three layer of CFRP and reinforced with steel fiber at 2.5% of volume fraction. The details of specimen tested are summarized in Table 3. 2.4. Testing of specimens The testing of specimens was carried out on strain controlled Universal Testing Machine IBMU4-2000. All specimens were ensured to be grounded at ends so that load could be distributed
Fig. 1. (a) Master BraceÒP3500/4500, and (b) CFRP sheet wrapped on concrete specimen.
uniformly on the concrete surface. Precision cut high strength 150 mm steel disc were placed at top and bottom of specimens to transfer load to the concrete core. Initially the load was increased at 3 KN per second and upon initial softening of samples, the displacement control was set at 0.003 mm per second. 3. Results and discussions 3.1. Stress strain curves The stress – strain curves of the samples are shown in Fig. 2. The specimen UC-UR achieved the compression strength 50.67 MPa at 28 days. The stress-strain curves shows that the peak stress was achieved on average strain value (eco) 0.235%. The samples underwent brittle failure, and the stress curve fell immediately after failure. The increase in compressive strength due to addition of steel fibers was not very much effected. However, an increase of 10–15% in strain values were recorded. The increase in steel fiber content resulted in increase of peak strain as compared to control samples. However, it can be seen that after peak stress, the loss of concrete strength was not as sudden as for the control samples. It was also observed that the inherent abrupt failure property of concrete was diminished to an extent (Fig. 2(a)). Strain increased even after peak strain, and the fibers bridged the cracks and delayed the failure. The single layer FRP confined specimens showed up to 20% increase in compressive strength and up to 60–70% in strain values. Significant difference in post peak response of confined samples in comparison to unconfined containing similar was observed. The branch after peak value shows that the strain increased substantially further and resulted in increase in compressive stress. The specimen C-R-F-2.5% experienced premature bond failure. The samples yielded at an average strain value of 0.25% and were able to achieve failure strain ecu value of 0.483%. However, Fig. 2(b) shows that after peak stress the loss of concrete strength was quite mild, as for the control samples and the specimens showed better ductile behavior due to confinement. It was observed that the inherent abrupt failure property of concrete was diminished to an extent. Strain value increased even after peak strain and steel fibers bridged the cracks and delayed the failure. The specimens confined with 3-layers of FRP demonstrated good behavior and significant increase in compressive strength up to 70–90% was recorded while corresponding strain values also increased up to 40%. The higher yielding compression strength of 84.66 MPa was recorded at higher strain value of 0.34%. The specimens exhibited better post peak behavior and ductility due to efficient confinement provided by 3 layers of CFRP as shown in Fig. 2 (d). The post peak behavior also shows strain increase and does not show sudden failure as seen in control samples. Specimens C-R-3F1.5% experienced bonding failure, which is attributed to the improperly wrapped confinement on the specimens surface due to entrapped air bubbles in between. The strain value increased with increase in fiber content. The post peak behavior shows that the samples were taking stress even after peak stress point. Steel tube confined specimens with different steel fiber contents yielded at the average stress of 60 MPa with strain value of 0.228%. The post peak response is seen to be different from all other types of specimens and the stress-strain curves flattened
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Table 3 Details of specimens. S/No
Specimen designation
Vf (%)
Confinement
f’c (MPa)
eo (%)
f0 cc/f
1 2 3 4 5 6 7 8 9 10 11 12 13
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-F-0.5% C-R-F-1.5% C-R-F-2.5% C-R-S-0.5% C-R- S 1.5% C-R- S- 2.5% C-R-3F-0.5% C-R-3F-1.5% C-R-3F-2.5%
– 0.5 1.5 2.5 0.5 1.5 2.5 0.5 1.5 2.5 0.5 1.5 2.5
– – – – CFRP (1 Layer) CFRP (1 Layer) CFRP (1 Layer) Steel Sheet Steel Sheet Steel Sheet CFRP (3 Layer) CFRP (3 Layer) CFRP (3 Layer)
50.67 51.45 49.91 49.95 59.91 58.33 58.93 61.94 62.94 62.11 91.23 91.14 95.75
0.235 0.259 0.263 0.268 0.463 0.394 0.431 0.426 0.444 0.419 0.495 0.476 0.477
1 1.015 0.985 0.986 1.181 1.151 1.163 1.223 1.243 1.226 1.801 1.800 1.890
100
100 UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5%
(a) 60 40 20
60 40 20 0
0 0.2
Strain (%)
0.4
100
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-S-0.5% C-R-S-1.5% C-R-S-2.5%
(c)
80 60
0
0.6
40 20 0
0.2
0.4 Strain (%)
(d)
80 60
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-3F-0.5%" C-R-3F-1.5% C-R-3F-2.5%
40 20 0
0
0.2
Strain (%)
0.4
0.6
0.6
100
Stress (MPa)
0
Stress (MPa)
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-F-0.5% C-R-F-1.5% C-R-F-2.5%
(b)
80 Stress (MPa)
Stress (MPa)
80
UC
0
0.2
0.4 Strain (%)
0.6
Fig. 2. Stress strain curves for (a) unconfined SFRC samples, (b) Comparison of unconfined reinforced and single layer CFRP confined samples, (c) Comparison of unconfined reinforced and steel sheet confined samples, and (d) Comparison of unconfined reinforced and CFRP three layer confined samples.
after peak compressive strength with higher increase in strain values as shown in Fig. 2(c). The welding failures at steel tubes joint were observed closer to peak stress because of lateral expansion of concrete. Ductile behavior for steel tube confined specimens was observed and up to 30% increase in compressive strength was recorded and the strain values of specimens also increased up to 37%. It was observed that the peak stress is dependable on the strength of welded joints and not on the percentage of steel fibers. The confinement level becomes variable because of the difference in welding strength of steel sheets. 3.2. Failure modes The control samples failed, showing cracks propagation at surface of concrete and having sudden collapse after peak loads. The samples with steel fibers showed cracks with lesser crack widths at surface. Presence of steel fibers in concrete matrix stopped complete crushing of the specimens. The increase in steel fiber percent-
age led to increase in the stability of concrete at failure. Fig. 3 shows some of the sample at failure containing steel fibers. The failure mode of confined concrete specimens was quite ductile. For single layer CFRP confined concrete, the samples failed with debonding and CFRP sheet failure. 1.5 in. overlap proved to be insufficient. Samples with three Layer CFRP confinements showed different failure mode than single Layer CFRP confined samples. Three Layers CFRP sheet provided sufficient confinement to HSC. The samples failed with crushing of concrete. Unlike single layer CFRP, three layers CFRP remained intact even after failure. Due to this, the concrete achieved high strength enhancement and the samples failed with the failure of concrete matrix. Only one sample was seen to have debonding failure. The debonding may be attributed to the entrapped air while coating and wrapping which may weaken the confinement effect. Steel Tube filled SFR HSC experienced altogether different failure mode than other types of confined specimens. The welded joints failed with increase in compressive loads. The bulging of concrete led
M. Usman et al. / Construction and Building Materials 230 (2020) 117043
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Fig. 3. Failure patterns observed in (a–c) Unconfined SFRC specimens, (d–f) Single layer CFRP confined specimens, (g–i) Three layers CFRP confined specimens, and (j–l) Steel sheet confined specimens.
to the development of tensile forces at welded joints of confining steel sheet. The joints failed at stress levels of 9000 psi, this led to the failure of HSC as the confinement effect diminished. The specimen failed at the very same instant with the failure of HSC.
3.3. Confinement effect on SFRC The comparison graphs of concrete specimens with different steel fibers are shown in Fig. 4. It can be seen that compressive
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M. Usman et al. / Construction and Building Materials 230 (2020) 117043
100 80 Stress (MPa)
(a)
UC-U R UC-R-0.5% C-R-F-0.5% C-R-S-0.5% C-R-3F-0.5%
60 40 20 0 0 100
Strain (%)
0.4
UC-U R UC-R-1.5% C-R-F-1.5% C-R-3F-1.5% C-R-S-1.5%
80 Stress (MPa)
0.2
0.6
(b)
3.4. Comparison of strain values
60 40 20 0 0 100
Strain (%)
0.4
UC-U R UC-R-2.5% C-R-F-2.5% C-R-3F-2.5% C-R-S-2.5%
80 Stress (MPa)
0.2
0.6
(c)
60 40 20 0 0
ing strain and ultimate strain. The post peak behavior is of great interest for HSC as it is of brittle nature. It can be seen from graph that confinement makes concrete more ductile. The strain ductility values are greatest for steel tube filled SFRC with an increase of 57%. The increase in compression strength of CFRP confined specimens was quite significant but increase in strain ductility was not significant and an increase of 16% was recorded. Results of specimen with 2.5% Vf indicated that the compressive stress value increases with increasing level of confinement. For three layer CFRP confinement, the axial strength increases 91.6% to unconfined. With single layer of CFRP confinement, the strength increases to almost 25%. The steel tube confined specimen failed to achieve appreciable strength enhancement but achieved greatest strains. Steel tube filled SFRC is tougher than unconfined SFRC and 1 layer CFRP confined specimen. Confinement increased the ultimate strain to a great extent. The post peak behavior is improved with level of confinement.
0.2
0.4
0.6
Strain (%) Fig. 4. Stress – strain curves of specimens with (a) 0.5% steel fiber, (b) 1.5% steel fiber, & (c) 2.5% steel fiber.
strength of specimens increases with increasing level of confinement. The compression strength increased 16.5% for C-R-F specimen as compared to UC-R specimen and 77.36% increase was observed in case of C-R-3F specimen. It can be observed that the peak strain and ultimate failure strain values are greatest for CR-3F specimen. Energy absorption is also enhanced by confinement. Confinement increases the toughness of concrete and steel tube filled SFRC is seen to be the toughest amongst all groups tested. In case of C-R-S specimen, an increase of 72.2% in strain ductility was recorded this was the highest amongst all groups. For 1.5% Vf of steel fibers, it can be observed that the compressive stress value increased with increasing level of confinement. For three layer CFRP confinement, the axial strength increases 82.7% in contrast to unconfined. The steel tube confined specimen failed to achieve appreciable strength enhancement (only 26%) but achieved greatest strains. Response of C-R-S specimens was better than C-R-1F specimens. The graph also shows the strain comparison of curves. Confinement increases the peak stress correspond-
A comparison is made to analyze the change in average strain values with the increase of Steel Fiber Content (Vf) in each type of specimen tested in this research. The effect of steel fiber content is different for each type of concrete composite. The values of yield strain (ey), peak strain (e0) and ultimate strain (ecu) of unconfined SFRC are shown in Fig. 5(a). The yield strain Ey values increased with increase in steel fiber content (Vf) values. The increase in yield strain for different steel fiber content was within 3.7–7.4% as compared to 0.5% steel content. The ultimate strains are also seen to increase for unconfined SFRC with increase in steel fiber content (Vf) values. For Vf = 2.5% there is an increase of 8.4% as compared to ultimate strain (ecu) values of Vf = 0.5%. This is because the role of steel fibers becomes predominant after failure as they act as crack binders. With higher fiber content, the values ultimate strains (ecu) increase to an appreciable extent. The comparison of strain values of specimens confined with single layer CFRP is shown in Fig. 5(b). The yield strain ey values are seen to increase with increase in steel fiber content (Vf) values. For Vf = 1.5% and Vf = 2.5% there is an increase of 5.26%, as compared to yield strain (ey) values of Vf = 0.5%. The ultimate strains are also seen to increase for unconfined specimen with increase in steel fiber content (Vf) values. For Vf = 2.5% there is an increase of 36.8% as compared to ultimate strain (ecu) values of Vf = 0.5%. This is because the role of steel fibers becomes predominant after failure as they act as crack binders. With higher fiber content, the values ultimate strains (ecu) increase to an appreciable extent. The failure mode for these specimens was mainly due to delamination of CFRP sheet. Therefore, after the peak point, the specimen behaved as partially confined with role of steel fiber predominant in post peak region. For higher fiber content the hold and toughness was greater. Therefore there is a huge increase in ecu values. Fig. 5(c) shows the comparison of strain value of specimens confined by three layer of CFRP. The values for ey are seen to be greatest for Vf = 0.5%. No significant increase in strain values is observed for ey and eo peak strain values. This can be explained based on the failure mode of three layer CFRP confined specimens. The failure is due to the crushing of concrete. CFRP confinement remains intact so the level of confinement is sufficient. Therefore, the role of steel fibers is not very predominant up to failure. There is an increase in ecu values with increase in steel fiber content (Vf). This could be due to the tensile forces which develop in steel fibers. Even after failure, concrete remains confined and steel fibers help concrete to remain intact. The values of strain values of steel confined specimens are shown in Fig. 5(d). The yield strain ey values are seen to increase with increase in steel fiber content (Vf) values. For Vf = 2.5% there
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M. Usman et al. / Construction and Building Materials 230 (2020) 117043
0.5
Yield Strain
Peak Strain
0.5
Ultimate Strain
Strain %
Strain %
0.3 0.2
Ultimate strain
0.3 0.2 0.1
0.1
0
0 0%
0.50%
Yield Strain
(a)
1.50%
Peak Strain
0%
2.50% 0.5
Ultimate Strain
0.4
Yield Strain
0.50%
(b)
1.50%
Peak Strain
2.50%
Ultimate strain
0.4
Strain %
Strain %
Peak Strain
0.4
0.4
0.5
Yield Strain
0.3 0.2 0.1
0.3 0.2 0.1
0
0 0%
0.50%
(c)
1.50%
2.50%
0%
0.50%
(d)
1.50%
2.50%
Fig. 5. Strain values for (a) Unconfined SFRC, (b) One layer CFRP confined SFRC, (c) Three layer CFRP confined SFRC, and (d) Steel confined SFRC.
2.50
Ductility
2.00 1.50
0 0.50% 1.50% 2.50%
1.00 0.50 0.00 UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 6. Strain Ductility values Comparison for specimens.
is an increase of 5.03%, as compared to yield strain (ey) values of Vf = 0.5%. No visible trend is seen in peak strain (eo) values. This is because the failure mode depicts that the specimen failed with the welded joints rupture. The role of steel fibers is not predominant in this type. The values of ultimate strains are seen to increase with increase in steel fiber content (Vf). However, there is no clear trend as the failure mode depicted that the failure was due to the rupture of welds. The behavior was dependent on steel tube confinement and steel content had very less influence. 3.5. Strain ductility of concrete (m) A very important characteristic of any material is its strain ductility (m), which refers to the ability to deform after yield point. As concrete is a brittle material, special interest is paid to the ductility of composites. Ductility of different types of concretes tested in
this research was calculated, by dividing strain at 80% of peak load by Strain at yield. Fig. 6 shows the ductility values and comparison. The ductility (m) of control specimen was calculated to be 1.10 and ductility values for steel fiber reinforced specimen was about 1.3. The value of ductility (m) increased with increase in fiber content. This result is as expected because greater the fiber content, greater the energy absorption after peak hence greater the ductility. The C-R-3F specimens showed greater strain ductility (m) values ranged from 1.4 to 1.53. The trend line shows that the strain ductility increases as the fiber content increases in the concrete. It also shows that greater the level of confinement, the higher the values of strain ductility (m). For steel confined specimens, the strain ductility values (m) touched 1.9. This increase in ductility is caused by the ductility of steel sheets. The welds tend to elongate at joints, which increase the axial strains to a great extent. It can be seen that the inherent brittle nature of HSC can be made ductile through the use of composites. The use of CFRP not only increases the axial compressive strength to a double but also enhances the post peak behavior of HSC. It increases ductility to an appreciable extent. 3.6. Energy absorption and toughness index Toughness of a material can be defined as the ability to absorb energy before rupturing. It requires a balance of strength and ductility. In mathematics terms, it can be obtained by integrating the stress-strain curve. Energy absorbed for deformation per unit volume is known as the modulus of resilience of that material. ‘‘Precrack energy absorbed in compression (PEC) can be determined by calculating the area under the stress-strain curve up to the yield stress. Yield stress is taken as the stress at which first visual crack is observed during compressive strength test. The area under the stress-strain curve from yield stress to the peak stress is taken as
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0.10
PEC
0.08
6%
0 0.50% 1.50% 2.50%
(a)
5% 4% CEC
0.12
0.06
2%
0.02
1% 0%
0.00 UC-UR
0.10
UC-R
C-R-F
C-R-3F
UC-UR
C-R-S 0.25
0 0.50% 1.50% 2.50%
(c) 0.20 0.15
0.06
TEC
PCEC
0.08
(b)
3%
0.04
0.12
0% 0.50% 1.50% 2.50%
0.04
UC-R
C-R-F
C-R-3F
0 0.50% 1.50% 2.50%
C-R-S
(d)
0.10 0.05
0.02 0.00
0.00 UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 7. (a) PEC values Comparison for specimens, (b) CEC values Comparison for specimens, (c) PCEC values Comparison for specimens, and (d) TEC values Comparison for specimens 21.
cracked energy absorbed in compression (CEC). Post-crack energy absorbed in compression (PCEC) is taken as the area under the stress strain curve from peak stress to the ultimate stress. Ultimate stress is taken as the stress after the peak stress drops by 20%. Total energy absorbed in compression (TEC) is calculated as the area under the stress–strain curve from zero to ultimate stress” [34–37]. 3.6.1. Pre-Crack energy (PEC) The Energy absorbed by concrete specimens from start point up to yield point can be calculated from stress-strain graphs. The Fig. 7 (a) shows the values and comparison for different types of composites with different steel fiber content (Vf). The graph shows that PEC value increase slightly for UC-R specimens as steel fibers reinforce the concrete and bridge cracks. They absorb energy therefore PEC values are greater than control samples. For single layer CFRP, the values increase significantly because of the composite behavior. The confinement imparts toughness to concrete. PEC value is the highest for 3 layer CFRP due to its high confinement sustainability. It shows that as the confinement increases the toughness of concrete increases. Similar trend was observed for C-R-S specimens. 3.6.2. Cracked energy absorbed in compression (CEC) CEC is the energy absorbed from yield to the peak stress point. It shows the behavior of concrete after the cracks appear at yield point till peak stress is achieved. The Fig. 7(b) shows the comparison of CEC for all types of specimens. It can be observed that there is an appreciable difference in CEC values between control sample and unconfined specimens. The specimens with steel fibers have almost double values in comparison to unreinforced samples. This
is because of the presence of steel fibers and their ability to dissipate energy, which imparts toughness to concrete during this critical period. Samples with single layer CFRP showed greater values of CEC than control samples but were lower than unconfined specimens. Samples with three layers CFRP sheet gave the highest values of toughness in this period. Samples containing 2.5% steel fibers and 3 layer CFRP confinement showed the best results. This shows that best toughness in this region is achieved with 3 Layer CFRP confinement and 2.5% steel fibers by volume.
3.6.3. Post-Crack energy absorbed in compression (PCEC) PCEC is the energy absorbed after peak stress till failure and comparison is shown in Fig. 7(c). It can be observed that the control samples show very less energy absorption values. This was expected as High Strength Concrete shows brittle behavior as expected. HSC is inherently of brittle nature and is shown by the PCEC values obtained from test data. The specimens with steel fibers showed much greater values than control samples. This elaborates the effect of steel fibers in concrete matrix. It imparts toughness to concrete even after peak stress is achieved. For unconfined specimens with steel fibers, the greatest values are obtained for 2.5% fiber content because as the fiber content increases, the resistance to crack increases. Single Layer CFRP confined specimens showed much greater values than unconfined specimens. The use of confinement holds the concrete even after peak stress. Therefore, PCEC values show significant increase. The values for three layers CFRP confined specimens are slightly greater than single layer CFRP specimens of similar type. It could be because the presence of three layers CFRP increase the compressive strength but do not impart greater toughness after peak stress. Steel Tube filled specimens shows the greatest values of PCEC. This is because the
M. Usman et al. / Construction and Building Materials 230 (2020) 117043
3.75
Toughness Index
concrete (HSC) to investigate its properties under axial compression (strength, modulus, and post peak behavior), for civil engineering applications. Specimens reinforced with steel fibers were then confined with three variable confinements (1 layer CFRP, 3 Layer CFRP and Steel tube). The stress strain curves for all the specimens were analyzed and following conclusions are made:
0 0.50%
3.00
1.50% 2.50%
2.25 1.50 0.75 0.00 0
9
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 8. Toughness index of the specimens.
steel confinement provided sufficient ductility. The welds elongate to an appreciable extent, absorbing the energy before failure. 3.6.4. Total energy absorbed in compression (TEC) TEC value refers to the total energy absorbed by the specimens before ultimate failure as shown in Fig. 7(d). The control specimen achieved TEC value of 0.061. When HSC specimens were reinforced with steel fibers, TEC values increased to 0.078 for 0.5% steel fiber content and increased with increase in fiber content. This is in line with previous research results that as the percentage increase, the energy absorption also increases. For single layer CFRP wrapping on SFRC, TEC values increased substantially. This is the combined effect of fibers and confinement that the energy absorption increases to an appreciable extent. Specimens with 3 layer CFRP wrapping, showed the highest TEC values. The specimens with 2.5% steel fibers were the toughest amongst all the specimens. The specimens confined with steel also dissipated energy much greater than control specimens. It absorbed energy greater than single Layer CFRP samples. This is as expected due to the high tensile strength of steel confining sheet. The value would had been greater if the weld would not had failed at slightly lower loads than expected. 3.6.5. Toughness index (TI) Toughness of a material can be defined as the ability to absorb energy before rupturing. It requires a balance of strength and ductility. In mathematics terms, it can be obtained by integrating the stress-strain curve. Toughness index in compression (TIC) is ‘‘the ratio of total energy absorbed in compression to the pre-crack energy absorbed in compression” [34] (i.e. TEC/PEC). Fig. 8 shows the comparison of TI values of all concrete specimens. The values for control samples are 1.21, which are the lowest of all specimen groups. For specimens reinforced with steel fibers, the values are 24% greater than the control specimen. This is due to the fact that steel fibers make the concrete tougher by bridging the cracks. For 1 Layer confined specimens, TI values increase by 66.6% as compared to control samples due to presence of steel fibers and CFRP confinement. This type of composite imparts toughness to concrete to an appreciable level. TI values for three layer CFRP confined specimens are same as single layer CFRP confined specimens indicating that the additional layers of CFRP do not have considerable effect on the toughness. Steel confined specimens shows the highest TI values and an increase of 247% was recorded as compared to control specimen. 4. Conclusions In this study, steel fibers were added at variable contents ((Vf = 0.5%, 1.5% and 2.5% by volume of sample) to high strength
i. Three layer CFRP wrapping provides efficient confinement at which the concrete crushes but confinement does not fail. It enhances axial compressive strength by 70–80% of unconfined strength. 1 layer CFRP confinement also shows strain enhancement but with much less increase in compressive strength (20–25%). ii. The addition of Steel Fiber has little effect on the axial compressive strength but make HSC tougher and ductile. With increase in steel fiber content (Vf) the Post Peak behavior is affected predominantly and causes increase in the ultimate strains Eu. iii. Steel Filled SFRC exhibit highest toughness and ductility, but endure failure at lower loads due to failure of welded joints. In can be concluded that the strength and behavior of this type of composite depends on the strength of welded joints as steel sheet poses much greater tensile strength for confinement. iv. The use of steel fiber and confinement simultaneously in compression members leads to increased compressive strength, energy absorption, increased strain values, enhanced post peak response; thus can reduce the brittleness and defects of HSC.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Funding support from China National Key R&D Program – Intergovernmental International Scientific and Technological Innovation Cooperation Key Project, ‘‘Research on the application and demonstration of the green construction materials for the postdisaster reconstruction in Pakistan and Nepal”, Grant No. 2018YFE0106300, 2019.07-2022.06, is gratefully acknowledged. References [1] S.Y.N. Chan, N.Q. Feng, M.K.C. Tsang, Durability of high-strength concrete incorporating carrier fluidifying agent, Mag. Concr. Res. 52 (2009) 235–242, https://doi.org/10.1680/macr.2000.52.4.235. [2] H.P. Behbahani, B. Nematollahi, M. Farasatpour, Steel Fiber Reinforced Concrete : A Review, in: ICSECM 2011 – Kandy – Sri Lanka – 15th to 17th December 2011, 2011. [3] A. Gholampour, T. Ozbakkaloglu, Fiber-reinforced concrete containing ultra high-strength micro steel fibers under active confinement, Constr. Build. Mater. 187 (2018) 299–306, https://doi.org/10.1016/ j.conbuildmat.2018.07.042. [4] H. Farooq, M. Usman, K. Mehmood, M.S. Malik, A. Hanif, Effect of steel confinement on axially loaded short concrete columns, IOP Conf. Ser. Mater. Sci. Eng. 414 (2018), https://doi.org/10.1088/1757-899X/414/1/012026 012026. [5] S.P.S. and B.V. Rangan, Fiber Reinforced Concrete Properties, J. Proc. 68 (n.d.). doi: 10.14359/11299. [6] P.R. Tadepalli, Y.L. Mo, T.T.C. Hsu, Mechanical properties of steel fibre concrete, Mag. Concr. Res. 65 (2013) 462–474, https://doi.org/10.1680/macr.12.00077. [7] M. Grzybowski, S.P. Shah, Shrinkage cracking of fiber reinforced concrete, ACI Mater. J. 87 (1990), https://doi.org/10.14359/1951. [8] J.C. Lim, T. Ozbakkaloglu, Confinement model for FRP-confined high-strength concrete, J. Compos. Constr. 18 (2013) 04013058, https://doi.org/10.1061/ (asce)cc.1943-5614.0000376.
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Axial compressive behavior of confined steel fiber reinforced high strength concrete Muhammad Usman a,⇑, Syed Hassan Farooq a, Mohammad Umair a, Asad Hanif b,⇑ a b
School of Civil and Environmental Engineering, National University of Science and Technology, Islamabad, Pakistan Joint Key laboratory of the Ministry of Education, Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da Universidade, Taipa, Macau
h i g h l i g h t s Effect of FRP confinement on steel fiber reinforced concrete (SFRC) is investigated. SFRC showed excellent behavior under axial compression. The properties were significantly enhanced with FRP confinement of SFRC. Improved ductility and enhanced stress-strain behavior of concrete is demonstrated.
a r t i c l e
i n f o
Article history: Received 22 May 2019 Received in revised form 26 July 2019 Accepted 18 September 2019
Keywords: Steel fiber Fiber reinforced concrete Compressive strength Stiffness Toughness
a b s t r a c t Concrete is brittle in nature which is why different materials have been used to improve this inherent behavior of concrete. In this experimental study, the effect of simultaneous use of steel fibers and confinement on high strength concrete and the corresponding post peak response of fiber reinforced concrete is investigated. A total of 39 high-strength concrete (incorporating varying amounts of steel fibers) cylinders were casted. The steel fiber volume fraction (Vf) was varied as 0.5%, 1.5% and 2.5%. 18 samples were confined with Carbon Fiber Reinforced Polymer (CFRP) sheet, and 9 samples were casted in steel pipe confinement, whereas 12 control specimens (without confinement) were also prepared. The samples were tested under axial compression. The results confirmed that the use of steel fiber had minute effect on the compressive strength, whereas it significantly improved the ductility and enhanced the post peak behavior of concrete. The confinement significantly contributed towards the compressive strength increase. The combined use of steel fibers and confinement in concrete columns can be viewed as extremely beneficial as it not only increases the concrete compressive strength but also solves the issue of brittle failure to an appreciable extent. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Increased interest in using High Strength Concrete (HSC) due to its superior strength, durability, and deflection control has led the researchers to explore ways of improving its brittle behavior through composite action. Addition of steel fibers in HSC and confinement with ductile materials exhibits great benefits to improve the performance concrete by reducing its brittleness [1–4]. The addition of discrete fibers into the concrete matrix helps reducing micro-cracking and localized macro-cracking, with improved postcracking strength and ductility [5–7]. The steel fibers act as crack arrestors not as crack inhibitors. They are known to improve ⇑ Corresponding authors. E-mail addresses: [email protected] (M. Usman), [email protected], [email protected] (A. Hanif). https://doi.org/10.1016/j.conbuildmat.2019.117043 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
post-cracking tensile response [8,9]. Steel fibers are discontinuous and are distributed randomly in the matrix [10] just like other fibers [11,12]. These characteristics allow cracks in any direction to be bridged by the fibers and permit improved stress transfer across all cracks, thereby improving post-cracking shear and flexural resistance [13,14]. In compression, similar to the tensile response, steel fibers incorporation primarily augments the toughness and post-peak ductility [6]. The fibers can act most effectively if aligned in the direction of the largest tensile stress. Fibers are the most beneficial when large strains occur in the cement matrix [2,11,15]. Fiber volume content is one of a major factor influencing the behavior of steel fiber reinforced concrete (SFRC). Many experimental tests have been conducted by researchers which focused different properties such as uniaxial direct shear test, flexural test and uniaxial tension test [14,16,17]. These tests show that
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increases in fiber amounts will lead to enhanced strength, ductility, and toughness [5,18]. With increase in fiber content, more fibers are likely to intersect a crack, which enhances concrete matrix post crack behavior [19,20]. It was concluded that by increasing the fiber content, the relative flexural and tensile strength could be increased. The response for compressive loads is also enhanced by varying fiber volume content. With increasing fiber content, the pre-peak ascending branch of the compressive stress-strain relationship is marginally improved resulting in a slightly higher elastic modulus [21,22]. The addition of steel fibers only marginally improves the compressive strength only up to 15% [6,23]. As the fiber content is increased, the strain capacity is increased which leads to greater load absorption capacity of concrete in compression. Some tests conducted with varying aspect ratio (of fibers) showed that increasing the aspect ratio increased the strength of matrix to a low degree but increased the toughness of matrix to an even greater extent [5]. However, the improved tensile response from higher aspect ratios is only true up to an aspect ratio of 75; thereafter, the tensile response worsened for any further increase in the aspect ratio. Some research findings had also reported increase in shear strength with higher aspect ratio [18]. The length and shape of steel fiber used can also be an influential factor in behavior of SFRC. By incorporating small length fibers while maintaining the same aspect ratio, the number of fibers increase greatly, which leads to superior crack bridging and stress transfer through the cracks [16,21,24]. The efficiency of steel fibers in the matrix depends on the orientation of fibers in the concrete matrix. In the modeling of SFRC, many account for the effects of fiber orientation and its impact on the efficiency of fibers through a fiber orientation factor is studied [25–27]. It is shown that ‘‘the addition of steel fibers cause a slight increase in the compressive strength and result in an increase in peak axial strain”. It was further observed that the compressive strength and ultimate strains of the specimens generally increased with an increase in steel fiber volume fraction (Vf), and decreased slightly with an increase in steel fiber aspect ratio (As). The axial strength of concrete increased to a great extent with FRP confinement. The effect of confinement and steel fiber incorporation in concrete enhanced the properties of concrete as expected. The placement of reinforcing bars or meshes in structural members may, thus, be eliminated with the addition of steel fibers. However, SFRC has seen limited such applications, and had some early acceptance as primary reinforcement only in flexural-critical structural members [17]. Recently, SFRC has gained acceptance in design codes for shear-critical members but its use in such members, especially for seismic applications, is uncommon. This is likely attributable to the limited research and design recommendations on SFRC for these applications.
While using discontinuous fibers is one way to improve concrete properties, use of confinement for enhanced structural behavior of concrete has also been investigated for reinforced and composite structural members [24,28–32]. Although studies have been conducted in the past on FRP/steel confined concrete and SFRC as well, findings on the effects of such confinement on SFRC are sparse. This research work is, thus, conducted to fill the research gap by investigating the co-effects of steel fibers and confinement (by FRP and steel tube or sheet) on axial compressive behavior of HSC. Compressive stress, strain, toughness, ductility, and post cracking behavior were thought to be improved by such combined techniques which is, then, corroborated and presented in this study.
2. Experimental program Experimental program comprises of casting 39 (150 mm diameter 300 mm height) cylindrical specimens of High Strength Concrete (HSC) with varying volume fraction (Vf) of steel fibers. After the curing period of 28 days, 18 samples were confined with Fiber Reinforced Polymer (FRP) sheet, whereas 9 samples were directly casted in steel tube. 2.1. Materials All the material used in this research were obtained locally except steel fibers and CFRP sheet were imported from China. Detailed material properties are summarized in Table 1. Ordinary Portland cement of grade 53 (Type-I) and prepared according to Pakistan standard PS-232-2008 and conformity to AST C150-04, EN 116 was used in casting samples. Sikament-520BA super plasticizer and sand with 2.01 fineness modulus was used to prepare high strength concrete. Use of superplasticizer in improving the concrete properties has already been corroborated by the Authors [33]. The gradation and aggregate size was chosen as per mix design of HSC. The maximum size was restricted to 20 mm. Two sieve sizes – 20 mm and 10 mm – were used and the ratio was set to 1:0.8 respectively to ensure high packing density. Master Steel Fiber S65 (hooked end fiber with length 35 mm and aspect ratio 64) was used in this research, obtained from BASF, China. Nine steel tubes were prepared from hot rolled sheet with a thickness of 1.02 mm with a nominal yield stress of 300 kN. The steel tubes were formed by cold rolled sheets welding at the longitudinal seam. Concrete was poured directly in the steel tubes. Carbon Fiber Reinforced Polymer (CFRP) sheet was affixed using epoxy Master Brace P3500 and P4500 mixed at a ratio 1:0.5 for obtaining the final epoxy.
Table 1 Mechanical properties of materials. Super plasticizer
pH Value Bulk density
6.5–8.5 (at 20 °C) 300–600 kg/m3
Steel Fiber
Length Diameter Aspect Ratio Tensile Strength
35 mm 0.55 mm 64 1345 MPa
CFRP Sheet
Modulus of elasticity Tensile strength Thickness for static design weight/density
230 KN/mm2 4900 N/mm2 0.112 mm
Master Brace P3500
Adhesion strength on carbon MPa (ASTM D4541:95e1) Compressive strength, MPa (ASTM D695:96)
2.87 73
Master Brace P4500
Compressive Strength TS EN 196 (7 days) Bonding Strength to concrete (7 days)
>60 N/mm2 >3.0 N/mm2
3
M. Usman et al. / Construction and Building Materials 230 (2020) 117043 Table 2 Details of concrete mixes. Type
Cement (Kg/m3)
Sand (Kg/m3)
Gravel (<20 mm) (Kg/m3)
Gravel (<10 mm) (Kg/m3)
w/c Ratio
Steel Fiber % (Vf)
Mix Mix Mix Mix
460 460 460 460
621 621 621 621
706 706 706 706
578 578 578 578
0.35 0.35 0.35 0.35
0 0.5% = (39 Kg/m3) 1.5% = (117 Kg/m3) 2.5% = (195 Kg/m3)
1 2 3 4
2.2. Preparation of samples 39 samples were prepared with addition of varying volume fraction (Vf, 0.5%, 1.5% and 2.5%) of steel fibers. The mix design and percentage of steel fibers is summarized in Table 2. The steel fiber and super plasticizer was added in the mixture uniformly during the mixing for workability. The samples were casted in cylinders at standard room temperature of 25° C. The samples were cured for 28 days in water bath. Then, the samples were air dried and subsequently taken for wrapping of CFRP sheet. The surfaces of the samples were cleaned with brush and Master BraceÒ3500 was applied as a primer before the application of epoxy. MB3500 consisted of parts ‘‘A” and ‘‘B” which were mixed in ratio 1.67:1.0 before application. The primer was allowed to get absorbed in concrete surface for 24 h prior to the application of epoxy Master BraceÒ4500. MB4500 consisted of parts ‘‘A” and ‘‘B” which were mixed together in ratio 1:0.5 before application and applied to concrete samples and CFRP laminate as shown in Fig. 1. CFRP cloth was cut as 1200 2100 to give minimum 1.500 overlap at the ends. 2.3. Specimen designation The specimens were labeled for classification of data. Label/ nomenclature started with ‘C’ or ‘UC’ for confined and unconfined, respectively. Control specimens without steel fibers were denoted with ‘UR’. For reinforced specimens, the hyphen was followed by ‘R’, which was followed by hyphen and percentage of steel fiber (Vf). For steel tube confined samples, the letter ‘S’ was added after hyphen. For example, C-R-3F-2.5% denotes the specimen which is confined with three layer of CFRP and reinforced with steel fiber at 2.5% of volume fraction. The details of specimen tested are summarized in Table 3. 2.4. Testing of specimens The testing of specimens was carried out on strain controlled Universal Testing Machine IBMU4-2000. All specimens were ensured to be grounded at ends so that load could be distributed
Fig. 1. (a) Master BraceÒP3500/4500, and (b) CFRP sheet wrapped on concrete specimen.
uniformly on the concrete surface. Precision cut high strength 150 mm steel disc were placed at top and bottom of specimens to transfer load to the concrete core. Initially the load was increased at 3 KN per second and upon initial softening of samples, the displacement control was set at 0.003 mm per second. 3. Results and discussions 3.1. Stress strain curves The stress – strain curves of the samples are shown in Fig. 2. The specimen UC-UR achieved the compression strength 50.67 MPa at 28 days. The stress-strain curves shows that the peak stress was achieved on average strain value (eco) 0.235%. The samples underwent brittle failure, and the stress curve fell immediately after failure. The increase in compressive strength due to addition of steel fibers was not very much effected. However, an increase of 10–15% in strain values were recorded. The increase in steel fiber content resulted in increase of peak strain as compared to control samples. However, it can be seen that after peak stress, the loss of concrete strength was not as sudden as for the control samples. It was also observed that the inherent abrupt failure property of concrete was diminished to an extent (Fig. 2(a)). Strain increased even after peak strain, and the fibers bridged the cracks and delayed the failure. The single layer FRP confined specimens showed up to 20% increase in compressive strength and up to 60–70% in strain values. Significant difference in post peak response of confined samples in comparison to unconfined containing similar was observed. The branch after peak value shows that the strain increased substantially further and resulted in increase in compressive stress. The specimen C-R-F-2.5% experienced premature bond failure. The samples yielded at an average strain value of 0.25% and were able to achieve failure strain ecu value of 0.483%. However, Fig. 2(b) shows that after peak stress the loss of concrete strength was quite mild, as for the control samples and the specimens showed better ductile behavior due to confinement. It was observed that the inherent abrupt failure property of concrete was diminished to an extent. Strain value increased even after peak strain and steel fibers bridged the cracks and delayed the failure. The specimens confined with 3-layers of FRP demonstrated good behavior and significant increase in compressive strength up to 70–90% was recorded while corresponding strain values also increased up to 40%. The higher yielding compression strength of 84.66 MPa was recorded at higher strain value of 0.34%. The specimens exhibited better post peak behavior and ductility due to efficient confinement provided by 3 layers of CFRP as shown in Fig. 2 (d). The post peak behavior also shows strain increase and does not show sudden failure as seen in control samples. Specimens C-R-3F1.5% experienced bonding failure, which is attributed to the improperly wrapped confinement on the specimens surface due to entrapped air bubbles in between. The strain value increased with increase in fiber content. The post peak behavior shows that the samples were taking stress even after peak stress point. Steel tube confined specimens with different steel fiber contents yielded at the average stress of 60 MPa with strain value of 0.228%. The post peak response is seen to be different from all other types of specimens and the stress-strain curves flattened
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Table 3 Details of specimens. S/No
Specimen designation
Vf (%)
Confinement
f’c (MPa)
eo (%)
f0 cc/f
1 2 3 4 5 6 7 8 9 10 11 12 13
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-F-0.5% C-R-F-1.5% C-R-F-2.5% C-R-S-0.5% C-R- S 1.5% C-R- S- 2.5% C-R-3F-0.5% C-R-3F-1.5% C-R-3F-2.5%
– 0.5 1.5 2.5 0.5 1.5 2.5 0.5 1.5 2.5 0.5 1.5 2.5
– – – – CFRP (1 Layer) CFRP (1 Layer) CFRP (1 Layer) Steel Sheet Steel Sheet Steel Sheet CFRP (3 Layer) CFRP (3 Layer) CFRP (3 Layer)
50.67 51.45 49.91 49.95 59.91 58.33 58.93 61.94 62.94 62.11 91.23 91.14 95.75
0.235 0.259 0.263 0.268 0.463 0.394 0.431 0.426 0.444 0.419 0.495 0.476 0.477
1 1.015 0.985 0.986 1.181 1.151 1.163 1.223 1.243 1.226 1.801 1.800 1.890
100
100 UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5%
(a) 60 40 20
60 40 20 0
0 0.2
Strain (%)
0.4
100
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-S-0.5% C-R-S-1.5% C-R-S-2.5%
(c)
80 60
0
0.6
40 20 0
0.2
0.4 Strain (%)
(d)
80 60
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-3F-0.5%" C-R-3F-1.5% C-R-3F-2.5%
40 20 0
0
0.2
Strain (%)
0.4
0.6
0.6
100
Stress (MPa)
0
Stress (MPa)
UC-UR UC-R-0.5% UC-R-1.5% UC-R-2.5% C-R-F-0.5% C-R-F-1.5% C-R-F-2.5%
(b)
80 Stress (MPa)
Stress (MPa)
80
UC
0
0.2
0.4 Strain (%)
0.6
Fig. 2. Stress strain curves for (a) unconfined SFRC samples, (b) Comparison of unconfined reinforced and single layer CFRP confined samples, (c) Comparison of unconfined reinforced and steel sheet confined samples, and (d) Comparison of unconfined reinforced and CFRP three layer confined samples.
after peak compressive strength with higher increase in strain values as shown in Fig. 2(c). The welding failures at steel tubes joint were observed closer to peak stress because of lateral expansion of concrete. Ductile behavior for steel tube confined specimens was observed and up to 30% increase in compressive strength was recorded and the strain values of specimens also increased up to 37%. It was observed that the peak stress is dependable on the strength of welded joints and not on the percentage of steel fibers. The confinement level becomes variable because of the difference in welding strength of steel sheets. 3.2. Failure modes The control samples failed, showing cracks propagation at surface of concrete and having sudden collapse after peak loads. The samples with steel fibers showed cracks with lesser crack widths at surface. Presence of steel fibers in concrete matrix stopped complete crushing of the specimens. The increase in steel fiber percent-
age led to increase in the stability of concrete at failure. Fig. 3 shows some of the sample at failure containing steel fibers. The failure mode of confined concrete specimens was quite ductile. For single layer CFRP confined concrete, the samples failed with debonding and CFRP sheet failure. 1.5 in. overlap proved to be insufficient. Samples with three Layer CFRP confinements showed different failure mode than single Layer CFRP confined samples. Three Layers CFRP sheet provided sufficient confinement to HSC. The samples failed with crushing of concrete. Unlike single layer CFRP, three layers CFRP remained intact even after failure. Due to this, the concrete achieved high strength enhancement and the samples failed with the failure of concrete matrix. Only one sample was seen to have debonding failure. The debonding may be attributed to the entrapped air while coating and wrapping which may weaken the confinement effect. Steel Tube filled SFR HSC experienced altogether different failure mode than other types of confined specimens. The welded joints failed with increase in compressive loads. The bulging of concrete led
M. Usman et al. / Construction and Building Materials 230 (2020) 117043
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Fig. 3. Failure patterns observed in (a–c) Unconfined SFRC specimens, (d–f) Single layer CFRP confined specimens, (g–i) Three layers CFRP confined specimens, and (j–l) Steel sheet confined specimens.
to the development of tensile forces at welded joints of confining steel sheet. The joints failed at stress levels of 9000 psi, this led to the failure of HSC as the confinement effect diminished. The specimen failed at the very same instant with the failure of HSC.
3.3. Confinement effect on SFRC The comparison graphs of concrete specimens with different steel fibers are shown in Fig. 4. It can be seen that compressive
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100 80 Stress (MPa)
(a)
UC-U R UC-R-0.5% C-R-F-0.5% C-R-S-0.5% C-R-3F-0.5%
60 40 20 0 0 100
Strain (%)
0.4
UC-U R UC-R-1.5% C-R-F-1.5% C-R-3F-1.5% C-R-S-1.5%
80 Stress (MPa)
0.2
0.6
(b)
3.4. Comparison of strain values
60 40 20 0 0 100
Strain (%)
0.4
UC-U R UC-R-2.5% C-R-F-2.5% C-R-3F-2.5% C-R-S-2.5%
80 Stress (MPa)
0.2
0.6
(c)
60 40 20 0 0
ing strain and ultimate strain. The post peak behavior is of great interest for HSC as it is of brittle nature. It can be seen from graph that confinement makes concrete more ductile. The strain ductility values are greatest for steel tube filled SFRC with an increase of 57%. The increase in compression strength of CFRP confined specimens was quite significant but increase in strain ductility was not significant and an increase of 16% was recorded. Results of specimen with 2.5% Vf indicated that the compressive stress value increases with increasing level of confinement. For three layer CFRP confinement, the axial strength increases 91.6% to unconfined. With single layer of CFRP confinement, the strength increases to almost 25%. The steel tube confined specimen failed to achieve appreciable strength enhancement but achieved greatest strains. Steel tube filled SFRC is tougher than unconfined SFRC and 1 layer CFRP confined specimen. Confinement increased the ultimate strain to a great extent. The post peak behavior is improved with level of confinement.
0.2
0.4
0.6
Strain (%) Fig. 4. Stress – strain curves of specimens with (a) 0.5% steel fiber, (b) 1.5% steel fiber, & (c) 2.5% steel fiber.
strength of specimens increases with increasing level of confinement. The compression strength increased 16.5% for C-R-F specimen as compared to UC-R specimen and 77.36% increase was observed in case of C-R-3F specimen. It can be observed that the peak strain and ultimate failure strain values are greatest for CR-3F specimen. Energy absorption is also enhanced by confinement. Confinement increases the toughness of concrete and steel tube filled SFRC is seen to be the toughest amongst all groups tested. In case of C-R-S specimen, an increase of 72.2% in strain ductility was recorded this was the highest amongst all groups. For 1.5% Vf of steel fibers, it can be observed that the compressive stress value increased with increasing level of confinement. For three layer CFRP confinement, the axial strength increases 82.7% in contrast to unconfined. The steel tube confined specimen failed to achieve appreciable strength enhancement (only 26%) but achieved greatest strains. Response of C-R-S specimens was better than C-R-1F specimens. The graph also shows the strain comparison of curves. Confinement increases the peak stress correspond-
A comparison is made to analyze the change in average strain values with the increase of Steel Fiber Content (Vf) in each type of specimen tested in this research. The effect of steel fiber content is different for each type of concrete composite. The values of yield strain (ey), peak strain (e0) and ultimate strain (ecu) of unconfined SFRC are shown in Fig. 5(a). The yield strain Ey values increased with increase in steel fiber content (Vf) values. The increase in yield strain for different steel fiber content was within 3.7–7.4% as compared to 0.5% steel content. The ultimate strains are also seen to increase for unconfined SFRC with increase in steel fiber content (Vf) values. For Vf = 2.5% there is an increase of 8.4% as compared to ultimate strain (ecu) values of Vf = 0.5%. This is because the role of steel fibers becomes predominant after failure as they act as crack binders. With higher fiber content, the values ultimate strains (ecu) increase to an appreciable extent. The comparison of strain values of specimens confined with single layer CFRP is shown in Fig. 5(b). The yield strain ey values are seen to increase with increase in steel fiber content (Vf) values. For Vf = 1.5% and Vf = 2.5% there is an increase of 5.26%, as compared to yield strain (ey) values of Vf = 0.5%. The ultimate strains are also seen to increase for unconfined specimen with increase in steel fiber content (Vf) values. For Vf = 2.5% there is an increase of 36.8% as compared to ultimate strain (ecu) values of Vf = 0.5%. This is because the role of steel fibers becomes predominant after failure as they act as crack binders. With higher fiber content, the values ultimate strains (ecu) increase to an appreciable extent. The failure mode for these specimens was mainly due to delamination of CFRP sheet. Therefore, after the peak point, the specimen behaved as partially confined with role of steel fiber predominant in post peak region. For higher fiber content the hold and toughness was greater. Therefore there is a huge increase in ecu values. Fig. 5(c) shows the comparison of strain value of specimens confined by three layer of CFRP. The values for ey are seen to be greatest for Vf = 0.5%. No significant increase in strain values is observed for ey and eo peak strain values. This can be explained based on the failure mode of three layer CFRP confined specimens. The failure is due to the crushing of concrete. CFRP confinement remains intact so the level of confinement is sufficient. Therefore, the role of steel fibers is not very predominant up to failure. There is an increase in ecu values with increase in steel fiber content (Vf). This could be due to the tensile forces which develop in steel fibers. Even after failure, concrete remains confined and steel fibers help concrete to remain intact. The values of strain values of steel confined specimens are shown in Fig. 5(d). The yield strain ey values are seen to increase with increase in steel fiber content (Vf) values. For Vf = 2.5% there
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M. Usman et al. / Construction and Building Materials 230 (2020) 117043
0.5
Yield Strain
Peak Strain
0.5
Ultimate Strain
Strain %
Strain %
0.3 0.2
Ultimate strain
0.3 0.2 0.1
0.1
0
0 0%
0.50%
Yield Strain
(a)
1.50%
Peak Strain
0%
2.50% 0.5
Ultimate Strain
0.4
Yield Strain
0.50%
(b)
1.50%
Peak Strain
2.50%
Ultimate strain
0.4
Strain %
Strain %
Peak Strain
0.4
0.4
0.5
Yield Strain
0.3 0.2 0.1
0.3 0.2 0.1
0
0 0%
0.50%
(c)
1.50%
2.50%
0%
0.50%
(d)
1.50%
2.50%
Fig. 5. Strain values for (a) Unconfined SFRC, (b) One layer CFRP confined SFRC, (c) Three layer CFRP confined SFRC, and (d) Steel confined SFRC.
2.50
Ductility
2.00 1.50
0 0.50% 1.50% 2.50%
1.00 0.50 0.00 UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 6. Strain Ductility values Comparison for specimens.
is an increase of 5.03%, as compared to yield strain (ey) values of Vf = 0.5%. No visible trend is seen in peak strain (eo) values. This is because the failure mode depicts that the specimen failed with the welded joints rupture. The role of steel fibers is not predominant in this type. The values of ultimate strains are seen to increase with increase in steel fiber content (Vf). However, there is no clear trend as the failure mode depicted that the failure was due to the rupture of welds. The behavior was dependent on steel tube confinement and steel content had very less influence. 3.5. Strain ductility of concrete (m) A very important characteristic of any material is its strain ductility (m), which refers to the ability to deform after yield point. As concrete is a brittle material, special interest is paid to the ductility of composites. Ductility of different types of concretes tested in
this research was calculated, by dividing strain at 80% of peak load by Strain at yield. Fig. 6 shows the ductility values and comparison. The ductility (m) of control specimen was calculated to be 1.10 and ductility values for steel fiber reinforced specimen was about 1.3. The value of ductility (m) increased with increase in fiber content. This result is as expected because greater the fiber content, greater the energy absorption after peak hence greater the ductility. The C-R-3F specimens showed greater strain ductility (m) values ranged from 1.4 to 1.53. The trend line shows that the strain ductility increases as the fiber content increases in the concrete. It also shows that greater the level of confinement, the higher the values of strain ductility (m). For steel confined specimens, the strain ductility values (m) touched 1.9. This increase in ductility is caused by the ductility of steel sheets. The welds tend to elongate at joints, which increase the axial strains to a great extent. It can be seen that the inherent brittle nature of HSC can be made ductile through the use of composites. The use of CFRP not only increases the axial compressive strength to a double but also enhances the post peak behavior of HSC. It increases ductility to an appreciable extent. 3.6. Energy absorption and toughness index Toughness of a material can be defined as the ability to absorb energy before rupturing. It requires a balance of strength and ductility. In mathematics terms, it can be obtained by integrating the stress-strain curve. Energy absorbed for deformation per unit volume is known as the modulus of resilience of that material. ‘‘Precrack energy absorbed in compression (PEC) can be determined by calculating the area under the stress-strain curve up to the yield stress. Yield stress is taken as the stress at which first visual crack is observed during compressive strength test. The area under the stress-strain curve from yield stress to the peak stress is taken as
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M. Usman et al. / Construction and Building Materials 230 (2020) 117043
0.10
PEC
0.08
6%
0 0.50% 1.50% 2.50%
(a)
5% 4% CEC
0.12
0.06
2%
0.02
1% 0%
0.00 UC-UR
0.10
UC-R
C-R-F
C-R-3F
UC-UR
C-R-S 0.25
0 0.50% 1.50% 2.50%
(c) 0.20 0.15
0.06
TEC
PCEC
0.08
(b)
3%
0.04
0.12
0% 0.50% 1.50% 2.50%
0.04
UC-R
C-R-F
C-R-3F
0 0.50% 1.50% 2.50%
C-R-S
(d)
0.10 0.05
0.02 0.00
0.00 UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
UC-UR
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 7. (a) PEC values Comparison for specimens, (b) CEC values Comparison for specimens, (c) PCEC values Comparison for specimens, and (d) TEC values Comparison for specimens 21.
cracked energy absorbed in compression (CEC). Post-crack energy absorbed in compression (PCEC) is taken as the area under the stress strain curve from peak stress to the ultimate stress. Ultimate stress is taken as the stress after the peak stress drops by 20%. Total energy absorbed in compression (TEC) is calculated as the area under the stress–strain curve from zero to ultimate stress” [34–37]. 3.6.1. Pre-Crack energy (PEC) The Energy absorbed by concrete specimens from start point up to yield point can be calculated from stress-strain graphs. The Fig. 7 (a) shows the values and comparison for different types of composites with different steel fiber content (Vf). The graph shows that PEC value increase slightly for UC-R specimens as steel fibers reinforce the concrete and bridge cracks. They absorb energy therefore PEC values are greater than control samples. For single layer CFRP, the values increase significantly because of the composite behavior. The confinement imparts toughness to concrete. PEC value is the highest for 3 layer CFRP due to its high confinement sustainability. It shows that as the confinement increases the toughness of concrete increases. Similar trend was observed for C-R-S specimens. 3.6.2. Cracked energy absorbed in compression (CEC) CEC is the energy absorbed from yield to the peak stress point. It shows the behavior of concrete after the cracks appear at yield point till peak stress is achieved. The Fig. 7(b) shows the comparison of CEC for all types of specimens. It can be observed that there is an appreciable difference in CEC values between control sample and unconfined specimens. The specimens with steel fibers have almost double values in comparison to unreinforced samples. This
is because of the presence of steel fibers and their ability to dissipate energy, which imparts toughness to concrete during this critical period. Samples with single layer CFRP showed greater values of CEC than control samples but were lower than unconfined specimens. Samples with three layers CFRP sheet gave the highest values of toughness in this period. Samples containing 2.5% steel fibers and 3 layer CFRP confinement showed the best results. This shows that best toughness in this region is achieved with 3 Layer CFRP confinement and 2.5% steel fibers by volume.
3.6.3. Post-Crack energy absorbed in compression (PCEC) PCEC is the energy absorbed after peak stress till failure and comparison is shown in Fig. 7(c). It can be observed that the control samples show very less energy absorption values. This was expected as High Strength Concrete shows brittle behavior as expected. HSC is inherently of brittle nature and is shown by the PCEC values obtained from test data. The specimens with steel fibers showed much greater values than control samples. This elaborates the effect of steel fibers in concrete matrix. It imparts toughness to concrete even after peak stress is achieved. For unconfined specimens with steel fibers, the greatest values are obtained for 2.5% fiber content because as the fiber content increases, the resistance to crack increases. Single Layer CFRP confined specimens showed much greater values than unconfined specimens. The use of confinement holds the concrete even after peak stress. Therefore, PCEC values show significant increase. The values for three layers CFRP confined specimens are slightly greater than single layer CFRP specimens of similar type. It could be because the presence of three layers CFRP increase the compressive strength but do not impart greater toughness after peak stress. Steel Tube filled specimens shows the greatest values of PCEC. This is because the
M. Usman et al. / Construction and Building Materials 230 (2020) 117043
3.75
Toughness Index
concrete (HSC) to investigate its properties under axial compression (strength, modulus, and post peak behavior), for civil engineering applications. Specimens reinforced with steel fibers were then confined with three variable confinements (1 layer CFRP, 3 Layer CFRP and Steel tube). The stress strain curves for all the specimens were analyzed and following conclusions are made:
0 0.50%
3.00
1.50% 2.50%
2.25 1.50 0.75 0.00 0
9
UC-R
C-R-F
C-R-3F
C-R-S
Fig. 8. Toughness index of the specimens.
steel confinement provided sufficient ductility. The welds elongate to an appreciable extent, absorbing the energy before failure. 3.6.4. Total energy absorbed in compression (TEC) TEC value refers to the total energy absorbed by the specimens before ultimate failure as shown in Fig. 7(d). The control specimen achieved TEC value of 0.061. When HSC specimens were reinforced with steel fibers, TEC values increased to 0.078 for 0.5% steel fiber content and increased with increase in fiber content. This is in line with previous research results that as the percentage increase, the energy absorption also increases. For single layer CFRP wrapping on SFRC, TEC values increased substantially. This is the combined effect of fibers and confinement that the energy absorption increases to an appreciable extent. Specimens with 3 layer CFRP wrapping, showed the highest TEC values. The specimens with 2.5% steel fibers were the toughest amongst all the specimens. The specimens confined with steel also dissipated energy much greater than control specimens. It absorbed energy greater than single Layer CFRP samples. This is as expected due to the high tensile strength of steel confining sheet. The value would had been greater if the weld would not had failed at slightly lower loads than expected. 3.6.5. Toughness index (TI) Toughness of a material can be defined as the ability to absorb energy before rupturing. It requires a balance of strength and ductility. In mathematics terms, it can be obtained by integrating the stress-strain curve. Toughness index in compression (TIC) is ‘‘the ratio of total energy absorbed in compression to the pre-crack energy absorbed in compression” [34] (i.e. TEC/PEC). Fig. 8 shows the comparison of TI values of all concrete specimens. The values for control samples are 1.21, which are the lowest of all specimen groups. For specimens reinforced with steel fibers, the values are 24% greater than the control specimen. This is due to the fact that steel fibers make the concrete tougher by bridging the cracks. For 1 Layer confined specimens, TI values increase by 66.6% as compared to control samples due to presence of steel fibers and CFRP confinement. This type of composite imparts toughness to concrete to an appreciable level. TI values for three layer CFRP confined specimens are same as single layer CFRP confined specimens indicating that the additional layers of CFRP do not have considerable effect on the toughness. Steel confined specimens shows the highest TI values and an increase of 247% was recorded as compared to control specimen. 4. Conclusions In this study, steel fibers were added at variable contents ((Vf = 0.5%, 1.5% and 2.5% by volume of sample) to high strength
i. Three layer CFRP wrapping provides efficient confinement at which the concrete crushes but confinement does not fail. It enhances axial compressive strength by 70–80% of unconfined strength. 1 layer CFRP confinement also shows strain enhancement but with much less increase in compressive strength (20–25%). ii. The addition of Steel Fiber has little effect on the axial compressive strength but make HSC tougher and ductile. With increase in steel fiber content (Vf) the Post Peak behavior is affected predominantly and causes increase in the ultimate strains Eu. iii. Steel Filled SFRC exhibit highest toughness and ductility, but endure failure at lower loads due to failure of welded joints. In can be concluded that the strength and behavior of this type of composite depends on the strength of welded joints as steel sheet poses much greater tensile strength for confinement. iv. The use of steel fiber and confinement simultaneously in compression members leads to increased compressive strength, energy absorption, increased strain values, enhanced post peak response; thus can reduce the brittleness and defects of HSC.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Funding support from China National Key R&D Program – Intergovernmental International Scientific and Technological Innovation Cooperation Key Project, ‘‘Research on the application and demonstration of the green construction materials for the postdisaster reconstruction in Pakistan and Nepal”, Grant No. 2018YFE0106300, 2019.07-2022.06, is gratefully acknowledged. References [1] S.Y.N. Chan, N.Q. Feng, M.K.C. Tsang, Durability of high-strength concrete incorporating carrier fluidifying agent, Mag. Concr. Res. 52 (2009) 235–242, https://doi.org/10.1680/macr.2000.52.4.235. [2] H.P. Behbahani, B. Nematollahi, M. Farasatpour, Steel Fiber Reinforced Concrete : A Review, in: ICSECM 2011 – Kandy – Sri Lanka – 15th to 17th December 2011, 2011. [3] A. Gholampour, T. Ozbakkaloglu, Fiber-reinforced concrete containing ultra high-strength micro steel fibers under active confinement, Constr. Build. Mater. 187 (2018) 299–306, https://doi.org/10.1016/ j.conbuildmat.2018.07.042. [4] H. Farooq, M. Usman, K. Mehmood, M.S. Malik, A. Hanif, Effect of steel confinement on axially loaded short concrete columns, IOP Conf. Ser. Mater. Sci. Eng. 414 (2018), https://doi.org/10.1088/1757-899X/414/1/012026 012026. [5] S.P.S. and B.V. Rangan, Fiber Reinforced Concrete Properties, J. Proc. 68 (n.d.). doi: 10.14359/11299. [6] P.R. Tadepalli, Y.L. Mo, T.T.C. Hsu, Mechanical properties of steel fibre concrete, Mag. Concr. Res. 65 (2013) 462–474, https://doi.org/10.1680/macr.12.00077. [7] M. Grzybowski, S.P. Shah, Shrinkage cracking of fiber reinforced concrete, ACI Mater. J. 87 (1990), https://doi.org/10.14359/1951. [8] J.C. Lim, T. Ozbakkaloglu, Confinement model for FRP-confined high-strength concrete, J. Compos. Constr. 18 (2013) 04013058, https://doi.org/10.1061/ (asce)cc.1943-5614.0000376.
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