Journal of Advanced Concrete Technology Vol. 2, No. 3, 395-407, October 2004 / Copyright © 2004 Japan Concrete Institute 395 Experimental Study on Stress-Strain Curve of Concrete Considering Localized Failure in Compression Ken Watanabe1, Junichiro Niwa2, Hiroshi Yokota3 and Mitsuyasu Iwanami4 Received 1 December 2003, accepted 2 June 2004 Abstract One of the important factors for compressive stress-strain curves of concrete is the localization of failure. The stress-strain curve of concrete strongly depends on the aspect ratio of the concrete specimen; therefore, a unique stress-strain curve is not adequate to express the softening behavior of concrete. To overcome the problem related to the localization of failure, a series of uniaxial compressive tests of concrete specimens was conducted. From the measured energy distribution, the failed specimen was assumed to be composed of 2 or 3 zones. Then, an equation for an enve- lope curve involving a characteristic of compressive strength of concrete was formulated so as to match the experimen- tal curve of each zone. Combining 2 or 3 proposed equations considering the extent of each zone could express the ex- perimental stress-strain curve of the specimen regardless of the aspect ratio. 1. Introduction kulrat et al. (2001) quantified the localized compressive failure zone length (Lp) based on the consumed energy A compressive stress-strain curve is an important mate- distribution along the height of a concrete specimen. rial characteristic of concrete. Many studies (e.g., Kar- They concluded that localized failure in compression san and Jirsa 1969; Popovics 1973) experimentally occurs in concrete specimens having H/D (the ratio of clarified the influence of compressive strength and height to maximum width of cross-section) of 2 or kinds of coarse aggregate on the stress-strain curve of more. concrete. Because of various influencing factors and The objective of this study is to formulate a different conditions in experimental approaches, a gen- stress-strain curve in compression through matching of eral equation expressing the stress-strain curve has not the experimental results. During the formulation, the been proposed yet. localization and the compressive strength of concrete The localization of failure of concrete in compression were taken into account. By referring to the study of is one of the influential factors on the stress-strain curve. Lertsrisakulrat et al. (2001), a series of uniaxial Compressive failure is typically observed in reinforced one-directional repeated load tests was conducted for concrete (RC) deep beams having a shear span length to obtaining stress-strain curves at local portions of the effective depth ratio of less than 1, which show the specimen by the acrylic-rod method. To deal with prob- shear-compression failure mode. Lertsrisakulrat et al. lems related to the localization of failure, a specimen is (2002) confirmed that the localized failure was observed assumed to be composed of 3 different zones, a failure in RC deep beams. The localized failure governs the zone, a transition zone, and an unloading zone. Bazant load-deflection relationship in the post-peak region, and (1989) reported a series coupling model based on a also gives the size effect on the shear strength of deep concept similar to that of this study. The lengths of each beams, as reported by Walraven (1994). zone were quantified according to the consumed energy Localized failure in tension was examined according distribution proposed by Lertsrisakulrat et al. (2001). to the fracture mechanics and useful results were ob- Next, equations to express the stress-strain relationship tained (e.g., Hillerborg et al. 1976). Many researchers for each zone of the concrete specimen were formulated (Markeset and Hillerborg 1995; Bazant 1989; Nakamura so that the experimental results matched well the calcu- and Higai 1999) applied fracture mechanics to the study lated ones. Finally, it was confirmed that combining 3 of localization in compression. In particular, Lertsrisa- proposed equations considering the length of each zone satisfactorily describes the experimental stress-strain relationship of concrete, which is strongly affected by 1 Doctoral student, Dep. of Civil Engineering, Tokyo the aspect ratio and the compressive strength of the Institute of Technology, Tokyo, Japan. concrete specimen. E-mail: [email protected] 2 Professor, Dep. of Civil Engineering, Tokyo Institute of 2. Outline of experiment Technology, Tokyo, Japan. 3 Head, Structural Mechanics Division, Port and Airport (1) Specimen Research Institute, Yokosuka, Japan. The characteristics of the test specimens (cylinders 100 4 Center researcher, Structural Mechanics Division, Port mm in diameter (D)) are listed in Table 1. Two speci- and Airport Research Institute, Yokosuka, Japan. 396 K. Watanabe, J. Niwa, H. Yokota and M. Iwanami / Journal of Advanced Concrete Technology Vol. 2, No. 3, 395-407, 2004 Table 1 Test specimens. Water-to- Compressive Diameter of the Height-to- Maximum Height cement strength of cylindrical speci- diameter G stress (H) max ratio Designation*1 concrete*2 men (D) ratio (H/D) ' (σmax) (W/C) (fc ) (mm) (mm) (mm) (MPa) (MPa) 0.4 T20-0.4-2 47.3 54.1 200 2 20 0.6 A20-0.6-2 31.1 29.4 0.4 A20-0.4-3 46.1 48.1 300 3 20 0.6 A20-0.6-3 30.0 28.4 0.4 A13-0.4-4 47.3 48.4 0.5 A13-0.5-4 42.0 39.3 13 0.6 A13-0.6-4 32.2 29.4 0.7 A13-0.7-4 26.2 21.9 400 4 100 0.4 A20-0.4-4 48.4 47.5 0.5 A20-0.5-4 39.0 28.2 20 0.6 A20-0.6-4 36.7 30.3 0.7 A20-0.7-4 28.4 22.5 0.4 T20-0.4-6 46.6 48.4 600 6 20 0.6 T20-0.6-6 31.2 29.3 0.4 T20-0.4-8 46.6 44.7 800 8 20 A20-0.6-8 28.5 16.6 0.6 T20-0.6-8 31.2 29.9 *1 A: With AC-rod, T: Without AC-rod *2 Average cylindrical compressive strength at the age of 7 days mens were used for each test case. Table 2 Mixture proportion. Mixture proportions of concrete are presented in Ta- 3 ble 2 and material properties used for the concrete are Weight per unit volume (kg/m ) G s/a*1 presented in Table 3 (a). Before casting of concrete, an max W/C Gravel (mm) (%) acrylic rod, on which strain gauges (3 mm length) were Water Cement Sand 5-13 13-20 attached at intervals of 40 mm, was installed vertically (mm) (mm) in the mold of a specimen named “Type A”. In speci- 0.4 43 182 455 736 493 493 0.5 45 185 370 799 494 494 mens named “Type T”, no acrylic rod was embedded. 20 The properties of the acrylic rod are listed in Table 3 0.6 47 188 313 853 487 487 (b). 0.7 49 191 273 903 475 475 To investigate the effect of the strength of concrete on 0.4 47 187 468 787 897 − 0.5 49 190 380 853 897 − the stress-strain curve, the water-to-cement ratio (W/C) 13 of concrete was changed to 0.4, 0.5, 0.6 and 0.7. Coarse 0.6 51 193 322 909 883 − 0.7 53 193 280 959 860 − aggregate with the maximum size (Gmax) of 13 mm or *1 20 mm was used. The height of the specimen was 400 : Volume ratio of sand to aggregate mm, which indicated that a very clear localized failure Table 3 Material properties of concrete and acrylic rod. would occur (Lertsrisakulrat et al. 2001). The compres- ’ (a) Concrete sive strength of concrete (fc ) ranged from 26.2 to 48.4 Water Fineness MPa at the time of the loading test, which was averaged Density using three standard cylindrical specimens of 200 mm in Designation absorption modulus height and 100 mm in diameter. Specimens with H/D=2, (kg/m3) (%) 3, 6 and 8 were additionally prepared to discuss the ef- Fine aggregate 2.59 1.94 2.51 fect of H/D on the stress-strain curve. These specimens (from Obitsu, Chiba) were made of concrete having W/C=0.4 and 0.6 and Coarse aggregate 2.64 0.93 7.00 Gmax=20 mm. (from Oume, Tokyo) All the specimens were cast concrete vertically and Blaine High-early strength cement 3.16 remolded at one day after casting. Immediately after 3550 (cm2/g) remolding, they were cured in water for 6 or 7 days until (b) Acrylic rod the loading tests. The top end of the specimen was pol- Specific gravity 1.19 ished to ensure a smooth horizontal surface. Tensile strength (MPa) 76 (2) Loading test and instrumentation Elastic modulus (MPa) 3200 Figure 1 shows the test setup. To reduce friction, fric- Compressive strength (MPa) 120 tion reducing pads, i.e., two Teflon sheets (0.05 mm Thermal expansion coefficient (1/°C) 7×10-6 K. Watanabe, J. Niwa, H. Yokota and M. Iwanami / Journal of Advanced Concrete Technology Vol. 2, No. 3, 395-407, 2004 397 Loading platen Peak point (σmax, εpeak) Stress (MPa) 40 Friction-reducing Envelope curve pad Specimen 30 Displacement gauge Unloading curve 20 Reloading curve 10 Loading platen Friction-reducing 0 pad 0 2000 4000 6000 Average strain (×10-6) (a) Test setup (b) Traced and envelope curves (A13-0.5-4) Fig. 1 Outline of experiment. thick) sandwiching silicon grease, were inserted be- leased until 0 kN (one-directional repeated loading).