Abstract
Three different effects control the influence of the loading rate on structural response: creep of bulk material, rate dependency of growing microcracks and structural inertia. The first effect is important only at extremely slow loading rates whereas the second and third effects dominate at higher loading rates. In the present paper, a rate sensitive model, which is based on the energy activation theory of bond rupture, and its implementation into the microplane model for concrete are discussed. It is first demonstrated that the model realistically predicts the influence of the loading rate on the uniaxial compressive behaviour of concrete. The rate sensitive microplane model is then applied in a 3D finite element analysis of the pull-out of headed stud anchors from a concrete block. In the study, the influence of the loading rate on the pull-out capacity and on the size effect is investigated. To investigate the importance of the rate of the growing microcracks and the influence of structural inertia, static and dynamic analyses were carried out. The results show that with an increase of the loading rate the pull-out resistance increases. For moderate loading rates, the rate of the microcrack growth controls the structural response and the results of static and dynamic analysis are similar. For very higher loading rates, however, the structural inertia dominates. The influence of structural inertia increases with the increase of the embedment depth. It is shown that for moderately high-loading rates the size effect becomes stronger when the loading rate increases. However, for very high-loading rate the size effect on the nominal pull-out strength vanishes and the nominal resistance increases with an increase of the embedment depth. This is due to the effect of structural inertia.
Highlights
It is well known that the loading rate influence significantly structural response
4 CONCLUSIONS In the present paper the rate sensitive model, which is based on the energy activation theory of bond rupture, and its implementation into the M2-O microplane model are discussed
The results show that with increase of the loading rate the nominal pull-out resistance increases
Summary
It is well known that the loading rate influence significantly structural response. The material response depends on the loading rate through influence two different effects: (1) through the rate dependency of the growing microcracks and (2) through the creep of the bulk material between the cracks. In the literature can be found a number of theoretical and experimental studies that deal with the problem of the rate effect for different materials (for literature review see Bažant et al [1]). In most of these studies various stress-displacement relations, similar to the spring-dashpot models of viscoelasticity, were used. Assuming average crack spacing of scr = 100 mm, from the calibration procedure follows: c0 = 0.0004 and c2 = 0.032 The microplane model prediction agrees well with the average trend observed in the experiments
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