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Correlations among mechanical properties of steel fiber reinforced concrete
Construction and Building Materials 23 (2009) 3468–3474
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Correlations among mechanical properties of steel fiber reinforced concrete B.W. Xu *, H.S. Shi Key Laboratory of Advance Civil Engineering Materials of the Ministry of Education, Tongji University, Shanghai 200092, PR China
a r t i c l e
i n f o
Article history: Received 23 April 2009 Received in revised form 3 July 2009 Accepted 5 August 2009 Available online 31 August 2009 Keywords: Steel fiber reinforced concrete (SFRC) Compressive strength Splitting tensile strength Flexural strength Correlation
a b s t r a c t In this paper, applicability of previously published empirical relations among compressive strength, splitting tensile strength and flexural strength of normal concrete, polypropylene fiber reinforced concrete (PFRC) and glass fiber reinforced concrete (GFRC) to steel fiber reinforced concrete (SFRC) was evaluated; moreover, correlations among these mechanical properties of SFRC were analyzed. For the investigation, a large number of experimental data were collected from published literature, where water/binder ratio (w/b), steel fiber aspect ratio and volume fraction were reported in the general range of 0.25–0.5, 55–80 and 0.5–2.0%, respectively, and specimens were cylinders with size of U 150 300 mm and prisms with size of 150 150 500 mm. Results of evaluation on these published empirical relations indicate the inapplicability to SFRC, also confirm the necessity of determination on correlations among mechanical properties of SFRC. Through the regression analysis on the experimental data collected, power relations with coefficients of determination of 0.94 and 0.90 are obtained for SFRC between compressive strength and splitting tensile strength, and between splitting tensile strength and flexural strength, respectively. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is known to be easily cracked under low level tensile stress, for its inherent weakness in resisting tensile forces. Incorporation of fibers into concrete is not only an effective way to enhance concrete tensile stress, but also fracture toughness, impact strength, durability, etc. [1–6]. Steel fiber is one of the most popular and widely used fibers in both research and practice. During the past four decades, numerous works [1,5,7–17] pertaining to experimental and analytical methods for evaluating strength characteristics of SFRC have been reported, with the consideration of concrete grades, concrete types, curing time, steel fiber geometry, aspect ratio and volume fraction, etc. Moreover, it now has been well accepted that incorporation of steel fiber can greatly benefit the mechanical behaviors of concrete, especially tensile strength and fracture toughness [7–17]. Compressive strength and tensile strength are two important indices used for characterizing concrete mechanical properties. Usually, compressive strength is necessarily required in structural design, and tensile strength is also required in structural design for some specific applications, such as structures near earthquake excitation, airfield runway, pavement slabs and so on. Generally, tensile strength can either be determined by direct tension test, splitting tensile test or flexural strength test. However, splitting tensile test and flexural strength test have been much more popularly carried out, probably due to their easier operation. Furthermore, it * Corresponding author. Tel.: +86 21 65987880. E-mail address: [email protected] (B.W. Xu). 0950-0618/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2009.08.017
has been widely reported that splitting tensile strength and flexural strength can be estimated from compressive strength of concrete through various empirical relations proposed by different concrete institutes and researchers [18–29]. Still, these empirical relations can be summarized by the following general equation:
fts ¼ Aðfcs ÞB
ð1Þ
where fts is splitting tensile strength/flexural strength, MPa; fcs is compressive strength, MPa; A and B are regression coefficients. It is observed that most of the published empirical relations were proposed for normal concrete; while, few were for fiber reinforced concrete, especially for SFRC. Through regression analysis on experimental results of both compressive strength and splitting tensile strength, Choi and Yuan [28] proposed two power relations for polypropylene fiber reinforced concrete (PFRC) and glass fiber reinforced concrete (GFRC). Ramadoss and Nagamani [7] reported that splitting tensile strength of SFRC is nonlinearly correlated to its flexural strength, which could also be expressed by a power relation. However, Nataraja et al. [30] suggested that correlation between splitting tensile strength and flexural strength of SFRC is linear. Since correlations among mechanical properties of SFRC are still few reported and unclear, investigation on correlations among compressive strength, splitting tensile strength and flexural strength of SFRC is carried out. 2. Database of mechanical properties of SFRC In order to investigate the correlations among mechanical properties of SFRC, a large number of experimental data have been
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collected from previously published literature. And, it should be noted that although there have been numerous publications concerning mechanical properties of SFRC, only those who reported compressive strength, splitting tensile strength and flexural strength at the same time or two of them at the same time were taken into consideration. Mechanical properties of SFRC could be affected by many factors, which mainly include specimen geometry, curing time, water/binder ratio (w/b), types of cement and supplementary cementitious material, steel fiber geometry, aspect ratio, volume fraction, etc. [7–17]. Since not all the information of these affecting factors was always presented in the literature, Table 1 summarizes the general information of those available ones. It can be seen from Table 1 that most of tests in the literature were taken at 28 days, only a few of them were taken at early age. And, w/b ratio of SFRC matrix was mainly ranged from 0.25 to 0.5, where w/b lower than 0.38 took the major percentage. Deformed steel fibers, especially hooked end steel fiber (HSF), were popularly used in the investigations, which may be due to their significantly more excellent reinforcement effects than that of straight steel fiber [31]. As it is known, incorporation of steel fiber has negative effects on workability of fresh concrete mixture, therefore, steel fiber aspect ratio and fiber volume fraction were carefully chosen in the range of 50–80 and 0.5–1.5%, respectively. It has been reported that experimental results of mechanical properties obtained from different specimen geometries can be converted between each other by some empirical relations [32,33]. However, most of the empirical conversion relations were proposed for normal concrete, which may be inapplicable to SFRC, for the totally different mechanical characteristics between normal concrete and fiber reinforced concrete. Therefore, in order to avoid introducing additional analysis errors, experimental data used in this investigation were further confined to those who obtained from cylindrical specimens with size of U 150 300 mm and prism specimens with size of 150 150 500 mm.
and Lew [24] and Raphael [25] still can catch most of the experimental data points in this range. However, when compressive strength is in the range of 20–100 MPa, it can be clearly seen that most of the experimental data points are significantly above the prediction curves. Observation in Fig. 1 may be attributed to the different development trends of ratio between splitting tensile strength and compressive strength of normal concrete and SFRC. Steel fiber reinforcement mechanism is mainly composed of fiber debonding effect, fiber pullout effect, and additional mechanical anchorage effect for deformed steel fiber [34]. Efficiencies of these fiber effects greatly depend on property of the transition zone between steel fiber and concrete matrix [35,36]. Generally, the higher compressive strength of concrete matrix, the stronger transition zone is. Therefore, with the increase of compressive strength of concrete, steel fiber reinforcement in tensile strength will become more and more obvious, due to the increasingly strong transition zone. However, because of the different damage models between compressive strength and tensile strength, steel fiber has little effects on compressive strength of concrete. Therefore, considering the reinforcement effects of steel fiber on both compressive strength and tensile strength, it can be indicated that when compressive strength is low, ratio between splitting tensile strength and compressive strength of SFRC is more closed to normal concrete or concrete reinforced with low modulus fibers; while this ratio will grow significantly with the increase of compressive strength. However, as what was suggested by Zain et al. [22] for normal concrete, splitting tensile strength increases with the increase of compressive strength, but at a decreasing rate. In other words, ratio between splitting tensile strength and compressive strength might be decreased with the increase of compressive strength of normal concrete, showing a much more brittle characteristic. In order to further evaluate the deviation between experimental data points and prediction curves shown in Fig. 1, integral absolute error (IAE) is employed, which is written:
3. Applicability evaluation on published empirical relations to SFRC
IAE ¼
Previously published empirical relations between splitting tensile strength and compressive strength of normal concrete, PFRC and GFRC are presented in Table 2. From Table 2, it can be seen that for normal concrete, PFRC and GFRC, these empirical relations can be generally summarized by using Eq. (1). Fig. 1 presents the comparison between experimental data points and prediction curves of the empirical relations shown in Table 2. It can be observed from Fig. 1 that with the increase of compressive strength, experimental data points deviate more and more significantly above the prediction curves. It shows that when compressive strength is within 20 MPa, prediction curves by CEB-FIP [20], Zain et al. [22], Carino
X ½ðQ i Pi Þ2 1=2 P 100 Qi
ð2Þ
where Qi is experimental result; Pi is prediction result. IAE values of the empirical relations are also presented in Table 2. It can be seen that except the IAE values of empirical relations reported by Aríoglu et al. [21] and Carniero et al. [27] are within 20%, the others are all above 25%, which verifies the inapplicability of these empirical relations to SFRC. Similarly, empirical relations between compressive strength and flexural strength of normal concrete are presented in Table 3. Comparison between experimental data points and prediction curves of the empirical relations in Table 3 is shown in Fig. 2. It can be seen from Fig. 2 that although when compressive strength of SFRC is larger than 40 MPa, experimental data points show
Table 1 Database information of mechanical properties of SFRC. Sources
w/b
Ramadoss and Nagamani [7] Shaaban and Gesund [8] Thomas and Ramaswamy [9] Khaloo and Kim [10] Wafa and Ashour [11] Düzgün et al. [12] Song and Hwang [13] Köksal et al. [14] Dhonde et al. [15] Sahmaran and Yaman [16] Mohammadi et al. [17]
0.25; 0.5 0.28; – 0.25 – 0.28 0.38 0.29; 0.41; 0.35
0.3; 0.35; 0.4 0.35; 0.48
0.30 0.5
Testing day
Fiber type
Volume fraction Vf (%)
Aspect ratio
Specimen
28 7 28 3, 10, 32 28 7, 28 28 28 1, 3, 7, 28 28 28
CSF
0.5–1.5 0.5–1.0 0.5–1.5 0.5–1.5 0.25–1.5 0.5–1.5 0.5–2.0 0.5; 1.0 0.5–1.5 0.4–0.8 1.0–2.0
80 – 55 58 75 75 64 65; 80 55; 80 37.5; 55 20; 40
Compressive strength and splitting tensile strength: U 150 300 mm (Cylinder); flexural strength: 150 150 500 mm (Prism)
HSF
HSF/SF CSF
Note: CSF, HSF and SF are short for corrugated steel fiber, hooked end steel fiber and straight steel fiber.
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Table 2 Published empirical relations between compressive strength and splitting tensile strength of normal concrete, PFRC and GFRC, and the corresponding IAE (%). Sources
ACI 363R-92 [18]
ACI 318-99 [19]
Aríoglu et al. [21]
Oluokun [23]
fspt =
fspt = 0.21fcs0:7
37.05
fspt = 26.53
fsp = fcs/(0.1 fcu + 7.11)
30.94
16.16
31.64
35.10
Sources Empirical relation
Carino and Lew [24] fspt = 0.27fcs0:71 18.42
Raphael [25] fspt = 0.31fcs0:67 26.02
Ahmad and Shah [26] fspt = 0.46fcs0:55 34.08
Carniero et al. [27] fspt = 0.19fcs0:74 45.43
Choi and Yuan [28] fspt = 0.6fcs0:5 * 29.10
fspt = 0.55fcs0:5 # 39.28
2=3 0.3fcs
fspt =
0.39fcs0:63
Zain et al. [22]
Empirical relation
fspt =
0.56fcs0:5
CEB-FIP [20]
IAE
IAE
0.59fcs0:5
Note: is for PFRC, and # is for GFRC.
Fig. 1. Comparison between experimental data points and prediction curves of published empirical relations between splitting tensile strength (fspt) and compressive strength (fcs) of normal concrete, PFRC and GFRC.
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B.W. Xu, H.S. Shi / Construction and Building Materials 23 (2009) 3468–3474 Table 3 Published empirical relations between compressive strength and flexural strength of normal concrete, and the corresponding IAE (%). Sources Empirical relation IAE
ACI 318R-95 [29] 0.5
ffs = 0.62(fcs) 123.33
ACI 363R-92 [18] 0.5
ffs = 0.94(fcs) 49.21
Ahmad and Shah [26] ffs = 0.44(fcs)0.5 55.56
Fig. 2. Comparison between experimental data points and prediction curves of published empirical relations between flexural strength (ffs) and compressive strength (fcs) of normal concrete.
Fig. 3. Proposed relation between splitting tensile strength (fspt) and compressive strength (fcs) of SFRC.
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obviously scattered, a general trend that flexural strength increases with the increase of compressive strength can still be observed. Like the observation in Fig. 1, when compressive strength is low (620 MPa), experimental data points are closed to the empirical relations; however, with the increase of compressive strength, experimental data points deviate more and more above the prediction curves. IAE values of these empirical relations shown in Table 3 are significantly large, which are all above 49%. This may also be attributed to the obviously different development trends of ratio between tensile strength and compressive strength for normal concrete and SFRC.
fft ¼ 0:39fcs0:59
ð4Þ 2
The corresponding R of this proposed relation is 0.80. But, the IAE value calculated is as high as 35.62%, which indicates that the variability of this proposed relation is large and the reliability is bad. The scatter of data points may be due to the inconsideration of affecting factors, such as steel fiber aspect ratio, volume fraction, w/b, curing time etc. in the regression analysis. 4.3. Splitting tensile strength and flexural strength of SFRC Correlation between splitting tensile strength (fcs) and flexural strength (fft) of SFRC is also analyzed by regression analysis, which is shown in Fig. 5. By regression analysis, the following empirical relation can be written:
4. Regression analysis results and discussion 4.1. Compressive strength and splitting tensile strength of SFRC
0:89 fft ¼ 1:63fspt
As shown in Fig. 3, regression analysis was carried out on these experimental data points of splitting tensile strength (fspt) and compressive strength (fcs) of SFRC. Through regression analysis, the empirical relation obtained can be expressed:
fspt ¼ 0:21ðfcs Þ0:83
ð3Þ
Coefficient of determination (R2) of this proposed relation is 0.94, indicating a strong correlation. Compared with the large IAE values shown in Table 2, it is only 8.17% for Eq. (3), suggesting high reliability and accuracy of this proposed relation. 4.2. Compressive strength and flexural strength of SFRC In Fig. 4, as described previously, experimental data points of compressive strength (fcs) and flexural strength (fft) of SFRC are scattered; but a general trend could still be observed. By regression analysis, the following empirical relation could be obtained:
ð5Þ 2
The corresponding R of this proposed relation is 0.90, suggesting a strong correlation between these two mechanical properties. And, the corresponding IAE value calculated is 15.86%. This nonlinear regression result is in a good agreement with what was suggested by Ramadoss and Nagamani [7]; however, it disagrees with the linear relation reported by Nataraja et al. [30]. 4.4. Discussion As mention previously, mechanical properties of SFRC could be affected by factors, like specimen geometry, curing time, water/binder ratio (w/b), types of cement and supplementary cementitious material, steel fiber geometry, aspect ratio, volume fraction, etc. And, it should be pointed out that in this investigation regression analysis is directly carried out among compressive strength, splitting tensile strength and flexural strength of SFRC, without the consideration of these factors. However, from
Fig. 4. Proposed relation between flexural strength (ffs) and compressive strength (fcs) of SFRC.
B.W. Xu, H.S. Shi / Construction and Building Materials 23 (2009) 3468–3474
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Fig. 5. Proposed relation between flexural strength (ffs) and splitting tensile strength (fspt) of SFRC.
the regression analysis results shown above, it can be seen that strong correlations are still existed among these mechanical properties. This may be attributed to the fact that testing day at 28d, type of HSF, fiber aspect ratio and volume fraction ranging in 55–80 and 0.5–1.5%, respectively, were mostly selected and concerned in the literature, which, to some extent, may minimizes the influence of these factors. However, the scatter of data points in Figs. 3–5 also suggest the influence of forementioned affecting factors is existed. Therefore, the further consideration of these affecting factors as multi-variables in nonlinear regression analysis on correlations among these mechanical properties can be taken. 5. Conclusions Based on the applicability evaluation on published empirical relations to SFRC and the regression analysis on experimental data of mechanical properties of SFRC, following conclusions can be made: [1] Previously published empirical relations proposed for normal concrete, PFRC and GFRC are inapplicable to SFRC; and, it is necessary to investigate the potential correlations among mechanical properties of SFRC. [2] For SFRC with w/b, steel fiber aspect ratio and volume fraction mainly ranging in 0.25–0.5, 55–80 and 0.5–2.0%, respectively, and with cylindrical specimen of U 150 300 mm and prism specimen of 150 150 500 mm, strong correlations are found between compressive strength and splitting tensile strength, and between splitting tensile strength and flexural strength, where R2 and IAE values are 0.94%, 0.90%, 8.17% and 15.86%, respectively. [3] Considering affecting factors, such as w/b, curing time, steel fiber geometry, aspect ratio, volume fraction, etc., as multivariables in nonlinear regression analysis can be further carried out.
Acknowledgement Support from China National Basic research Program (No. 2009CB623100) is greatly appreciated.
Reference [1] Bayramov F, Tasßdemir C, Tasßdemir MA. Optimization of steel fiber reinforced concretes by means of statistical response surface method. Cem Concr Compos 2004;26(6):665–75. [2] Banthaia N, Soleimani SM. Flexural response of hybrid fiber-reinforced cementitious composites. ACI Mater J 2005;102(6):382–9. [3] Li VC, Wang S, Wu C. Tensile strain-hardening behavior of polyvinyl alcohol engineered cementitious composites (PVA-ECC). ACI Mater J 2001;98(6):483–92. [4] Nelson PK, Li VC, Kamada T. Fracture toughness of microfiber reinforced cement composites. J Mater Civ Eng 2002;14(15):384–91. [5] Balendran RV, Zhou FP, Nadeem A, et al. Influence of steel fibers on strength and ductility of normal and lightweight high strength concrete. Build Environ 2002;37(2):1361–7. [6] Balaguru P, Najm H. High-performance fiber-reinforced concrete mixture proportions with high fiber volume fractions. ACI Mater J 2004;101(4):281–6. [7] Ramadoss P, Nagamani K. Investigation on the tensile strength of highperformance fiber reinforced concrete using statistical methods. Comput Concr 2006;3(6):389–400. [8] Shaaban AM, Gesund H. Splitting tensile strength of steel fiber reinforced concrete cylinders consolidated by rodding or vibrating. ACI Mater J 1993;90(4):366–9. [9] Thomas J, Ramaswamy A. Mechanical properties of steel fiber-reinforced concrete. J Mater Civ Eng 2007;19(5):385–92. [10] Khaloo AR, Kim N. Mechanical properties of normal to high-strength steel fiber-reinforced concrete. Cem Concr Aggr 1996;18(2):92–7. [11] Wafa FF, Ashour SA. Mechanical properties of high-strength fiber reinforced concrete. ACI Mater J 1992;89(5):449–54. [12] Düzgün OA, Gül R, Aydin AC. Effect of steel fibers on the mechanical properties of natural lightweight aggregate concrete. Mater Lett 2005;59(27):3357–63. [13] Song PS, Hwang S. Mechanical properties of high-strength steel fiberreinforced concrete. Constr Build Mater 2004;18(9):669–73. [14] Köksal F, Altun F, Yig˘it Ì. Combined effect of silica fume and steel fiber on mechanical properties of high strength concretes. Constr Build Mater 2008;22(8):1874–80. [15] Dhonde HB, Mo YL, Hsu TTC, et al. Fresh and hardened properties of selfconsolidating fiber reinforced concrete. ACI Mater J 2007;104(5):491–500. [16] Sahmaran M, Yaman IO. Hybrid fiber reinforced self-compacting concrete with a high-volume coarse fly ash. Constr Build Mater 2007;27:150–6.
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[17] Mohammadi Y, Singh SP, Kaushik SK. Properties of steel fibrous concrete containing mixed fibres in fresh and hardened state. Constr Build Mater 2008;22(5):956–65. [18] ACI Committee 363. State-of-the art report on high strength concrete (ACI 363R-92). Farmington Hills, MI: American Concrete Institute; 1992. [19] ACI Committee 318. Building code requirements for structural concrete (ACI 318-99) and commentary (318R-99). Farmington Hills, MI: American Concrete Institute; 1999. [20] CEB-FIP model code for concrete structures. Evaluation of the time dependent behavior of concrete. Bulletin d’ information No. 199. Lausanne: Comite Europe du Béton/Fédération Internationale de Precontrainte; 1991. [21] Aríoglu N, Girgin ZC, Aríoglu E. Evaluation of ratio between splitting tensile strength and compressive strength for concrete up to 120 MPa and its application in strength criterion. ACI Mater J 2006;103(1):18–24. [22] Zain MFM, Mahmud HB, Ilham A, et al. Prediction of splitting tensile strength of high-performance concrete. Cem Concr Res 2002;32(8):1251–8. [23] Oluokun FA. Prediction concrete tensile strength from its compressive strength: evaluation of existing relations for normal weight concrete. ACI Mater J 1991;88(3):302–9. [24] Carino NJ, Lew HS. Re-examination of the relation between splitting tensile strength and compressive strength of normal weight concrete. ACI J Proc 1972;79(3):136–47. [25] Raphael JM. Tensile strength of concrete. ACI J Proc 1984;81(2):158–65. [26] Ahmad SH, Shah SP. Structural properties of high strength concrete and its applications for precast prestressed concrete. PCI J 1985;30(6):97–123.
[27] Carniero, Fernando Luiz Lobo B, Barcello, et al. Tensile strength of concretes. RILEM Bull (Paris) 1953(13):97–123. [28] Choi Y, Yuan RL. Experimental relationship between splitting tensile strength and compressive strength of GFRC and PFRC. Cem Concr Res 2006;35(8): 1587–91. [29] ACI Committee 318. Building code requirements for structural concrete (ACI 318-1995) and Commentary. Farmington Hills, MI: American Concrete Institute; 1995. [30] Nataraja MC, Dhang N, Gupta AP. Splitting tensile strength of SFRC. Indian Concr J 2001;75(4):287–90. [31] Banthia N. A study of some factors affecting the fiber–matrix bond in steel fiber reinforced concrete. Can J Civ Eng 1990;17(4):610–20. [32] Yazici Sß, Sezer GÌ. The effect of cylindrical specimen size on compressive strength of concrete. Build Environ 2007;42(6):2417–20. [33] Rashid MA, Mansur MA, SCE MA, et al. Correlations between mechanical properties of high-strength concrete. J Mater Civ Eng 2002;14(3):230–9. [34] Alwan JM, Naaman AE, Gurrero P. Effect of mechanical clamping on the pullout response of hooked steel fibers embedded in cementitious matrices. Concr Sci Eng 1999;1(3):15–25. [35] Chan YW, Li VC. Effects of transition zone densification on fiber/cement paste bond strength improvement. Adv Cem Based Compos 1997;5(1): 8–17. [36] Chen YW, Chu SH. Effect of silica fume on steel fiber bond characteristics in reactive power concrete. Cem Concr Res 2004;34(7):1167–72.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Correlations among mechanical properties of steel fiber reinforced concrete B.W. Xu *, H.S. Shi Key Laboratory of Advance Civil Engineering Materials of the Ministry of Education, Tongji University, Shanghai 200092, PR China
a r t i c l e
i n f o
Article history: Received 23 April 2009 Received in revised form 3 July 2009 Accepted 5 August 2009 Available online 31 August 2009 Keywords: Steel fiber reinforced concrete (SFRC) Compressive strength Splitting tensile strength Flexural strength Correlation
a b s t r a c t In this paper, applicability of previously published empirical relations among compressive strength, splitting tensile strength and flexural strength of normal concrete, polypropylene fiber reinforced concrete (PFRC) and glass fiber reinforced concrete (GFRC) to steel fiber reinforced concrete (SFRC) was evaluated; moreover, correlations among these mechanical properties of SFRC were analyzed. For the investigation, a large number of experimental data were collected from published literature, where water/binder ratio (w/b), steel fiber aspect ratio and volume fraction were reported in the general range of 0.25–0.5, 55–80 and 0.5–2.0%, respectively, and specimens were cylinders with size of U 150 300 mm and prisms with size of 150 150 500 mm. Results of evaluation on these published empirical relations indicate the inapplicability to SFRC, also confirm the necessity of determination on correlations among mechanical properties of SFRC. Through the regression analysis on the experimental data collected, power relations with coefficients of determination of 0.94 and 0.90 are obtained for SFRC between compressive strength and splitting tensile strength, and between splitting tensile strength and flexural strength, respectively. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is known to be easily cracked under low level tensile stress, for its inherent weakness in resisting tensile forces. Incorporation of fibers into concrete is not only an effective way to enhance concrete tensile stress, but also fracture toughness, impact strength, durability, etc. [1–6]. Steel fiber is one of the most popular and widely used fibers in both research and practice. During the past four decades, numerous works [1,5,7–17] pertaining to experimental and analytical methods for evaluating strength characteristics of SFRC have been reported, with the consideration of concrete grades, concrete types, curing time, steel fiber geometry, aspect ratio and volume fraction, etc. Moreover, it now has been well accepted that incorporation of steel fiber can greatly benefit the mechanical behaviors of concrete, especially tensile strength and fracture toughness [7–17]. Compressive strength and tensile strength are two important indices used for characterizing concrete mechanical properties. Usually, compressive strength is necessarily required in structural design, and tensile strength is also required in structural design for some specific applications, such as structures near earthquake excitation, airfield runway, pavement slabs and so on. Generally, tensile strength can either be determined by direct tension test, splitting tensile test or flexural strength test. However, splitting tensile test and flexural strength test have been much more popularly carried out, probably due to their easier operation. Furthermore, it * Corresponding author. Tel.: +86 21 65987880. E-mail address: [email protected] (B.W. Xu). 0950-0618/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2009.08.017
has been widely reported that splitting tensile strength and flexural strength can be estimated from compressive strength of concrete through various empirical relations proposed by different concrete institutes and researchers [18–29]. Still, these empirical relations can be summarized by the following general equation:
fts ¼ Aðfcs ÞB
ð1Þ
where fts is splitting tensile strength/flexural strength, MPa; fcs is compressive strength, MPa; A and B are regression coefficients. It is observed that most of the published empirical relations were proposed for normal concrete; while, few were for fiber reinforced concrete, especially for SFRC. Through regression analysis on experimental results of both compressive strength and splitting tensile strength, Choi and Yuan [28] proposed two power relations for polypropylene fiber reinforced concrete (PFRC) and glass fiber reinforced concrete (GFRC). Ramadoss and Nagamani [7] reported that splitting tensile strength of SFRC is nonlinearly correlated to its flexural strength, which could also be expressed by a power relation. However, Nataraja et al. [30] suggested that correlation between splitting tensile strength and flexural strength of SFRC is linear. Since correlations among mechanical properties of SFRC are still few reported and unclear, investigation on correlations among compressive strength, splitting tensile strength and flexural strength of SFRC is carried out. 2. Database of mechanical properties of SFRC In order to investigate the correlations among mechanical properties of SFRC, a large number of experimental data have been
3469
B.W. Xu, H.S. Shi / Construction and Building Materials 23 (2009) 3468–3474
collected from previously published literature. And, it should be noted that although there have been numerous publications concerning mechanical properties of SFRC, only those who reported compressive strength, splitting tensile strength and flexural strength at the same time or two of them at the same time were taken into consideration. Mechanical properties of SFRC could be affected by many factors, which mainly include specimen geometry, curing time, water/binder ratio (w/b), types of cement and supplementary cementitious material, steel fiber geometry, aspect ratio, volume fraction, etc. [7–17]. Since not all the information of these affecting factors was always presented in the literature, Table 1 summarizes the general information of those available ones. It can be seen from Table 1 that most of tests in the literature were taken at 28 days, only a few of them were taken at early age. And, w/b ratio of SFRC matrix was mainly ranged from 0.25 to 0.5, where w/b lower than 0.38 took the major percentage. Deformed steel fibers, especially hooked end steel fiber (HSF), were popularly used in the investigations, which may be due to their significantly more excellent reinforcement effects than that of straight steel fiber [31]. As it is known, incorporation of steel fiber has negative effects on workability of fresh concrete mixture, therefore, steel fiber aspect ratio and fiber volume fraction were carefully chosen in the range of 50–80 and 0.5–1.5%, respectively. It has been reported that experimental results of mechanical properties obtained from different specimen geometries can be converted between each other by some empirical relations [32,33]. However, most of the empirical conversion relations were proposed for normal concrete, which may be inapplicable to SFRC, for the totally different mechanical characteristics between normal concrete and fiber reinforced concrete. Therefore, in order to avoid introducing additional analysis errors, experimental data used in this investigation were further confined to those who obtained from cylindrical specimens with size of U 150 300 mm and prism specimens with size of 150 150 500 mm.
and Lew [24] and Raphael [25] still can catch most of the experimental data points in this range. However, when compressive strength is in the range of 20–100 MPa, it can be clearly seen that most of the experimental data points are significantly above the prediction curves. Observation in Fig. 1 may be attributed to the different development trends of ratio between splitting tensile strength and compressive strength of normal concrete and SFRC. Steel fiber reinforcement mechanism is mainly composed of fiber debonding effect, fiber pullout effect, and additional mechanical anchorage effect for deformed steel fiber [34]. Efficiencies of these fiber effects greatly depend on property of the transition zone between steel fiber and concrete matrix [35,36]. Generally, the higher compressive strength of concrete matrix, the stronger transition zone is. Therefore, with the increase of compressive strength of concrete, steel fiber reinforcement in tensile strength will become more and more obvious, due to the increasingly strong transition zone. However, because of the different damage models between compressive strength and tensile strength, steel fiber has little effects on compressive strength of concrete. Therefore, considering the reinforcement effects of steel fiber on both compressive strength and tensile strength, it can be indicated that when compressive strength is low, ratio between splitting tensile strength and compressive strength of SFRC is more closed to normal concrete or concrete reinforced with low modulus fibers; while this ratio will grow significantly with the increase of compressive strength. However, as what was suggested by Zain et al. [22] for normal concrete, splitting tensile strength increases with the increase of compressive strength, but at a decreasing rate. In other words, ratio between splitting tensile strength and compressive strength might be decreased with the increase of compressive strength of normal concrete, showing a much more brittle characteristic. In order to further evaluate the deviation between experimental data points and prediction curves shown in Fig. 1, integral absolute error (IAE) is employed, which is written:
3. Applicability evaluation on published empirical relations to SFRC
IAE ¼
Previously published empirical relations between splitting tensile strength and compressive strength of normal concrete, PFRC and GFRC are presented in Table 2. From Table 2, it can be seen that for normal concrete, PFRC and GFRC, these empirical relations can be generally summarized by using Eq. (1). Fig. 1 presents the comparison between experimental data points and prediction curves of the empirical relations shown in Table 2. It can be observed from Fig. 1 that with the increase of compressive strength, experimental data points deviate more and more significantly above the prediction curves. It shows that when compressive strength is within 20 MPa, prediction curves by CEB-FIP [20], Zain et al. [22], Carino
X ½ðQ i Pi Þ2 1=2 P 100 Qi
ð2Þ
where Qi is experimental result; Pi is prediction result. IAE values of the empirical relations are also presented in Table 2. It can be seen that except the IAE values of empirical relations reported by Aríoglu et al. [21] and Carniero et al. [27] are within 20%, the others are all above 25%, which verifies the inapplicability of these empirical relations to SFRC. Similarly, empirical relations between compressive strength and flexural strength of normal concrete are presented in Table 3. Comparison between experimental data points and prediction curves of the empirical relations in Table 3 is shown in Fig. 2. It can be seen from Fig. 2 that although when compressive strength of SFRC is larger than 40 MPa, experimental data points show
Table 1 Database information of mechanical properties of SFRC. Sources
w/b
Ramadoss and Nagamani [7] Shaaban and Gesund [8] Thomas and Ramaswamy [9] Khaloo and Kim [10] Wafa and Ashour [11] Düzgün et al. [12] Song and Hwang [13] Köksal et al. [14] Dhonde et al. [15] Sahmaran and Yaman [16] Mohammadi et al. [17]
0.25; 0.5 0.28; – 0.25 – 0.28 0.38 0.29; 0.41; 0.35
0.3; 0.35; 0.4 0.35; 0.48
0.30 0.5
Testing day
Fiber type
Volume fraction Vf (%)
Aspect ratio
Specimen
28 7 28 3, 10, 32 28 7, 28 28 28 1, 3, 7, 28 28 28
CSF
0.5–1.5 0.5–1.0 0.5–1.5 0.5–1.5 0.25–1.5 0.5–1.5 0.5–2.0 0.5; 1.0 0.5–1.5 0.4–0.8 1.0–2.0
80 – 55 58 75 75 64 65; 80 55; 80 37.5; 55 20; 40
Compressive strength and splitting tensile strength: U 150 300 mm (Cylinder); flexural strength: 150 150 500 mm (Prism)
HSF
HSF/SF CSF
Note: CSF, HSF and SF are short for corrugated steel fiber, hooked end steel fiber and straight steel fiber.
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Table 2 Published empirical relations between compressive strength and splitting tensile strength of normal concrete, PFRC and GFRC, and the corresponding IAE (%). Sources
ACI 363R-92 [18]
ACI 318-99 [19]
Aríoglu et al. [21]
Oluokun [23]
fspt =
fspt = 0.21fcs0:7
37.05
fspt = 26.53
fsp = fcs/(0.1 fcu + 7.11)
30.94
16.16
31.64
35.10
Sources Empirical relation
Carino and Lew [24] fspt = 0.27fcs0:71 18.42
Raphael [25] fspt = 0.31fcs0:67 26.02
Ahmad and Shah [26] fspt = 0.46fcs0:55 34.08
Carniero et al. [27] fspt = 0.19fcs0:74 45.43
Choi and Yuan [28] fspt = 0.6fcs0:5 * 29.10
fspt = 0.55fcs0:5 # 39.28
2=3 0.3fcs
fspt =
0.39fcs0:63
Zain et al. [22]
Empirical relation
fspt =
0.56fcs0:5
CEB-FIP [20]
IAE
IAE
0.59fcs0:5
Note: is for PFRC, and # is for GFRC.
Fig. 1. Comparison between experimental data points and prediction curves of published empirical relations between splitting tensile strength (fspt) and compressive strength (fcs) of normal concrete, PFRC and GFRC.
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ACI 318R-95 [29] 0.5
ffs = 0.62(fcs) 123.33
ACI 363R-92 [18] 0.5
ffs = 0.94(fcs) 49.21
Ahmad and Shah [26] ffs = 0.44(fcs)0.5 55.56
Fig. 2. Comparison between experimental data points and prediction curves of published empirical relations between flexural strength (ffs) and compressive strength (fcs) of normal concrete.
Fig. 3. Proposed relation between splitting tensile strength (fspt) and compressive strength (fcs) of SFRC.
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obviously scattered, a general trend that flexural strength increases with the increase of compressive strength can still be observed. Like the observation in Fig. 1, when compressive strength is low (620 MPa), experimental data points are closed to the empirical relations; however, with the increase of compressive strength, experimental data points deviate more and more above the prediction curves. IAE values of these empirical relations shown in Table 3 are significantly large, which are all above 49%. This may also be attributed to the obviously different development trends of ratio between tensile strength and compressive strength for normal concrete and SFRC.
fft ¼ 0:39fcs0:59
ð4Þ 2
The corresponding R of this proposed relation is 0.80. But, the IAE value calculated is as high as 35.62%, which indicates that the variability of this proposed relation is large and the reliability is bad. The scatter of data points may be due to the inconsideration of affecting factors, such as steel fiber aspect ratio, volume fraction, w/b, curing time etc. in the regression analysis. 4.3. Splitting tensile strength and flexural strength of SFRC Correlation between splitting tensile strength (fcs) and flexural strength (fft) of SFRC is also analyzed by regression analysis, which is shown in Fig. 5. By regression analysis, the following empirical relation can be written:
4. Regression analysis results and discussion 4.1. Compressive strength and splitting tensile strength of SFRC
0:89 fft ¼ 1:63fspt
As shown in Fig. 3, regression analysis was carried out on these experimental data points of splitting tensile strength (fspt) and compressive strength (fcs) of SFRC. Through regression analysis, the empirical relation obtained can be expressed:
fspt ¼ 0:21ðfcs Þ0:83
ð3Þ
Coefficient of determination (R2) of this proposed relation is 0.94, indicating a strong correlation. Compared with the large IAE values shown in Table 2, it is only 8.17% for Eq. (3), suggesting high reliability and accuracy of this proposed relation. 4.2. Compressive strength and flexural strength of SFRC In Fig. 4, as described previously, experimental data points of compressive strength (fcs) and flexural strength (fft) of SFRC are scattered; but a general trend could still be observed. By regression analysis, the following empirical relation could be obtained:
ð5Þ 2
The corresponding R of this proposed relation is 0.90, suggesting a strong correlation between these two mechanical properties. And, the corresponding IAE value calculated is 15.86%. This nonlinear regression result is in a good agreement with what was suggested by Ramadoss and Nagamani [7]; however, it disagrees with the linear relation reported by Nataraja et al. [30]. 4.4. Discussion As mention previously, mechanical properties of SFRC could be affected by factors, like specimen geometry, curing time, water/binder ratio (w/b), types of cement and supplementary cementitious material, steel fiber geometry, aspect ratio, volume fraction, etc. And, it should be pointed out that in this investigation regression analysis is directly carried out among compressive strength, splitting tensile strength and flexural strength of SFRC, without the consideration of these factors. However, from
Fig. 4. Proposed relation between flexural strength (ffs) and compressive strength (fcs) of SFRC.
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Fig. 5. Proposed relation between flexural strength (ffs) and splitting tensile strength (fspt) of SFRC.
the regression analysis results shown above, it can be seen that strong correlations are still existed among these mechanical properties. This may be attributed to the fact that testing day at 28d, type of HSF, fiber aspect ratio and volume fraction ranging in 55–80 and 0.5–1.5%, respectively, were mostly selected and concerned in the literature, which, to some extent, may minimizes the influence of these factors. However, the scatter of data points in Figs. 3–5 also suggest the influence of forementioned affecting factors is existed. Therefore, the further consideration of these affecting factors as multi-variables in nonlinear regression analysis on correlations among these mechanical properties can be taken. 5. Conclusions Based on the applicability evaluation on published empirical relations to SFRC and the regression analysis on experimental data of mechanical properties of SFRC, following conclusions can be made: [1] Previously published empirical relations proposed for normal concrete, PFRC and GFRC are inapplicable to SFRC; and, it is necessary to investigate the potential correlations among mechanical properties of SFRC. [2] For SFRC with w/b, steel fiber aspect ratio and volume fraction mainly ranging in 0.25–0.5, 55–80 and 0.5–2.0%, respectively, and with cylindrical specimen of U 150 300 mm and prism specimen of 150 150 500 mm, strong correlations are found between compressive strength and splitting tensile strength, and between splitting tensile strength and flexural strength, where R2 and IAE values are 0.94%, 0.90%, 8.17% and 15.86%, respectively. [3] Considering affecting factors, such as w/b, curing time, steel fiber geometry, aspect ratio, volume fraction, etc., as multivariables in nonlinear regression analysis can be further carried out.
Acknowledgement Support from China National Basic research Program (No. 2009CB623100) is greatly appreciated.
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