Nonlinear fracture mechanics parameters

Fracture energy, Gf, is the key parameter that is combined with elastic modulus, E, and tensile strength, at, to define the entire constitutive behaviour of concrete in the nonlinear fracture mechanics models. Usually, the tensile strength, at, beyond which a strain softening process is assumed to take place, is determined from uniaxial or split cylinder tests and the fracture energy, Gf, from wedge splitting tests (Briihwiler and Wittmann 1990). Values for at and E can be selected according to the guidelines used for strength-of-material failure criterion. Empirical relationships have been proposed to determine the fracture energy from standard material parameters (Bazant and Oh 1983; Oh and Kim 1989). Those relationships were derived from the results of laboratory experiments performed with small size aggregates specific of structural concrete behaviour. Extrapolation of the test results from structural concrete does not seem to be realistic to establish the behaviour of mass concrete that has distinct features of much larger and weaker aggregates.

Limited results have been reported from experimental investigations on concrete collected from dam construction sites (Briihwiler 1990; Briihwiler and Wittmann 1990). The Gf value under static loading condition was determined to be in the range of 0.175and 0.310 N/mm; meaning that the Gf of dam concrete is two to three times larger than that of structural concrete. Fracture energy values for the specimens subjected to compressive pre-loading were found considerably low. The Gf parameter determined under simulated seismic loading rates showed substantial strain rate sensitivity, and a maximum of 80% dynamic magnification over the pseudo-static value was observed. Briihwiler and Wittmann (1990) attributed the rate sensitivity of Gf mainly to the rate sensitivity of at. That means, the dynamic magnification criterion selected for tensile strength can be applied to the fracture energy of the nonlinear fracture mechanics model. More complex relationships can also be established, including the rate sensitivity of critical crack opening displacement, Sf (Briihwiler 1990).

Experiments performed by Saouma et al. (1990, 1991a) have shown that the fracture properties are not affected by the specimen or aggregate sizes used. In contrary to this finding, a study performed by H.N. Linsbauer (Dungar et al. 1991) reported larger Gf values for larger specimen sizes, and another study by H. Mihashi (Dungar et al. 1991) reported the increase of fracture energy with increasing aggregate size. The test results reported in the literature are thus sketchy at the present time, and they are often in contradiction to one another.

Laboratory tests performed at the University of Colorado (Briihwiler and Saouma 1991) showed significant reduction of the fracture properties of concrete with increased water pressure along the crack. The effect of multiple cracks on fracture energy dissipation phenomenon is not known precisely. Biaxial and triaxial stress-strain effects on fracture energy dissipation characteristic of concrete are also required to be investigated (Kreuzer et al. I 99 1).

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