• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.567-580
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• 2005

Numerous tests on concrete structure members under local pressure demonstrated that the compressive strength of concrete at the loaded surface is increased by the confinement effect provided by the enveloping concrete. Even though most design codes propose specific criteria for preventing bearing failure, they do not take into consideration size effect which is an important phenomenon in the fracture mechanics of concrete/reinforced concrete. In this paper, six series of square prism concrete blocks with three different depths (size range = 1:4) and two different height/depth ratios of 2 and 3 are tested under concentrated load. Ultimate loads obtained from the test results are analysed by means of the modified size effect law (MSEL). Then, a prediction formula, which considers effect of both depth and height on size effect, is proposed. The developed formula is compared with experimental data existing in the literature. It is concluded that the observed size effect is in good agreement with the MSEL.

• KCI Concrete Journal
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• v.12 no.1
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• pp.57-68
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• 2000

The effect of structure size on the nominal strength of unidirectional fiber-polymer composites, failing by propagation of a kink band with fiber microbuckling, is analyzed experimentally and theoretically. Tests of novel geometrically similar carbon-PEEK specimens, with notches slanted so as to lead to a pure kink band (without shear or splitting cracks), are conducted. The specimens are rectangular strips of widths 15.875, 31.75. and 63.5 mm (0.625, 1.25 and 2.5 in and gage lengths 39.7, 79.375 and 158.75 mm (1.563, 3.125 and 6.25 in.). They reveal the existence of a strong (deterministic. non-statistical) size effect. The doubly logarithmic plot of the nominal strength (load divided by size and thickness) versus the characteristic size agrees with the approximate size effect law proposed for quasibrittle failures in 1983 by Bazant This law represents a gradual transition from a horizontal asymptote, representing the case of no size effect (characteristic of plasticity or strength criteria), to an asymptote of slope -1/2 (characteristic of linear elastic fracture mechanics. LEFM) . The size effect law for notched specimens permits easy identification of the fracture energy of the kink bandand the length of the fracture process zone at the front of the band solely from the measurements of maximum loads. Optimum fits of the test results by the size effect law are obtained, and the size effect law parameters are then used to identify the material fracture characteristics, Particularly the fracture energy and the effective length of the fracture process zone. The results suggest that composite size effect must be considered in strengthening existing concrete structural members such as bridge columns and beams using a composite retrofitting technique.

• Proceedings of the Korea Concrete Institute Conference
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• 1999.04a
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• pp.135-140
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• 1999

The size effect of axial compressive strength of concrete in notched specimens was experimentally investigated. Based on the concept of the fracture mechanics and size effect law, theoretical studies for axial compressive failure of concrete were reviewed, and two failure modes of concrete specimen under compression were discussed. In this study, experiment of axial compressive failure, which is one of the two failure modes, was carried out by using double cantilever fracture specimens. By varying the slenderness of cantilevers and the eccentricity of applied loads with respect to the axis of each cantilever, the size effect of axial compressive strength of concrete was investigated, and predicted by Bazant's size effect law. The test results show that size effect appears conspicuously for all series of specimens. For the eccentricity of loads, the influence of tensile and compressive stress at the notch tip are significant and so that the size effect is varied. In other words, if the influence of tensile stress at the notch tip grows up, the size effect of concrete increases. And the fact that the fracture process zone must be sufficiently secured for more accurate experiment was affirmed.

• Journal of the Korea Concrete Institute
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• v.12 no.6
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• pp.99-108
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• 2000

The size effect on axial compressive strength in notched concrete specimens was experimentally investigated. Based on the concept of the fracture mechanics and size effect law, theoretical studies for axial compressive failure of concrete were reviewed, and two failure modes of concrete specimens under compression were discussed. In this study, experiments of axial compressive failure, which is one of the two failure modes, was carried out by using cylindrical specimens. Adequate notch length was taken from the experimental result of strength variation based on the notch length. And, by taking various sizes of specimens the size effect on axial compressive strength of concrete was investigated. Also, model equations were suggested by modified size effect law (MSEL). The test results show that size effect appears conspicuously for all series of specimens. Additionally, the effect of initial notch length on axial compressive strength was also apparent.

• Computers and Concrete
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• v.23 no.6
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• pp.409-419
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• 2019

In the present study, effect of size and placement of cubic specimens on compressive strength of self-compacting lightweight concrete (SCLC) were considered. To do so, 81 specimens of different sizes (50 mm, 75 mm, 100 mm, and 150 mm) were prepared by using three different mixes of SCLC. Results of the cured specimens were then used in regression analyses to find predictive equations with regard to both the placement direction and the size. Test results showed that the strength ratio in cases in which the direction of loading and placement were parallel, were higher than those specimens, whose configurations were normal between loading and placement. In addition, strength ratios in SCLC mixes were slightly higher than those are for self-compacting normal weight concrete. In order to analyze the effect of size on compressive strength the conventional size effect law as well as the modified size effect law (MSEL) were used. Besides, the convergence criterion of nonlinear regression process of size effect study has been discussed. Analyses of the results showed that the unconstraint nonlinear regression in size effect study of SCLC mixes could lead to erroneous results.

• Magazine of the Korea Concrete Institute
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• v.2 no.1
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• pp.91-100
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• 1990

In most of the structural members with initial cracks(or initial notches), the strength tends to decmase as the member size increases. This phenomenon is known as size effect. Among the structural materials of glass, metal or concrete, etc., concrete represents the size effect even without initial crack. According to the previous size effect law, the concrete mem¬ber of very large size can resist little stress. Actually, however, even the large size member can resist some stress if there is no initial crack made artificially, consequently showing a rather milder strength reduction compared to the severe strength reduction by tbe previously derived size effect law. In this study, the theoretical size effect law previously derived by Z.P. Bazant was discussed based on nonlinear fracture mechanics of concrete structures With dissimilar initial cracks, and the prediction models are proposed by regression analysis with the existing test data of more large size speciments for splitting tensile strength, shear strength and uniaxial compressive strength tests.

• Computers and Concrete
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• v.23 no.5
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• pp.321-327
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• 2019

Experimental isotherm compressive tests show that concrete behaviour is dependent on temperature. The aim of such tests is to reproduce how concrete will behave under environmental changes within a moderate range of temperature. In this paper, a novel constitutive elastic damage behaviour law is proposed based on a free energy with an apparent damage depending on temperature. The proposed constitutive behaviour leads to classical theory of thermo-elasticity at small strains. Fixed elastic mechanical characteristics and fixed evolution law of damage independent of temperature and the material volume element size are considered. This approach is applied to compressive tests. The model predicts compressive strength and secant modulus of elasticity decrease as temperature increases. A power scaling law is assumed for specific entropy as function of the specimen size which leads to a volume size effect on the stress-strain compressive behaviour. The proposed model reproduces theoretical and experimental results from literature for tempertaures ranging between $20^{\circ}C$ and $70^{\circ}C$. The effect of the difference in the coefficient of thermal expansion between the mortar and coarse aggregates is also considered which gives a better agreement with FIB recommendations. It is shown that this effect is of a second order in the considered moderate range of temperature.

• Computers and Concrete
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• v.15 no.4
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• pp.673-686
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• 2015

R-curve based on the size effect law previously developed for geometrically similar specimens (geometry type III) is extended to geometries with variable depth (geometry type I) as well as with variable notch (geometry type II), where the R-curve is defined as the envelope of the family of critical strain energy release rates from specimens of different sizes. The results show that the extended R-curve for type I tends to be the same for different specimen configurations, while it is greatly dependent on specimen geometry in terms of the initial crack length. Furthermore, the predicted load-deflection responses from the suggested R-curve are found to agree well with the testing results on concrete and rock materials. Besides, maximum loads for type II specimen are predicted well from the extended R-curve.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.2
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• pp.299-306
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• 2015

The quality for the domestic pavement is evaluated based on flexural strength at the age of 28 days in accordance with KS regulation. Most specimens of the flexural tensile strength used currently are relatively large ones with a dimension of $150{\times}150{\times}550mm$. Accordingly, it is difficult to treat the specimens, and the utilization of a curing tank is low. In this paper, the study tried to resolve the problem by specimen size specified in the code. For this purpose, a flexural strength test was conducted according to the log scale within the specimen size specified by the KS. And, based on the results of this experiment, a comparative analysis was conducted using the prediction formula of Size Effect Law (SEL) proposed by Bazant to examine the correlation between specimen sizes, so as to use the result as basic data for the reduction of the specimen size in the quality evaluation of concrete pavement.

• Structural Engineering and Mechanics
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• v.32 no.3
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• pp.459-475
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• 2009

This paper presents analytical methodologies for remaining life prediction of plain concrete structural components considering tension softening and size effects. Non-linear fracture mechanics principles (NLFM) have been used for crack growth analysis and remaining life prediction. Various tension softening models such as linear, bi-linear, tri-linear, exponential and power curve have been presented with appropriate expressions. Size effect has been accounted for by modifying the Paris law, leading to a size adjusted Paris law, which gives crack length increment per cycle as a power function of the amplitude of a size adjusted stress intensity factor (SIF). Details of tension softening effects and size effect in the computation of SIF and remaining life prediction have been presented. Numerical studies have been conducted on three point bending concrete beams under constant amplitude loading. The predicted remaining life values with the combination of tension softening & size effects are in close agreement with the corresponding experimental values available in the literature for all the tension softening models.