Non-linear Analysis of Reinforced Concrete Structures with a Fibres Two-Parameters Damage Model

The modern structural design approach makes provision for the possibility to completely exploit the materials performance. It is allowed that the structures can loose their initial properties of strength and stiffness under ultimate design loading and the achievement of residual strength is characterised by the damage and the yielding of the materials in non-linear conditions. In the last decades many formulations have been proposed in order to analyse and evaluate with sufficient accuracy the mechanical behaviour of concrete in the non-linear field. They are mainly based on the theory of plasticity, the theory of fracture and the continuum damage mechanic. Among these, the latter have demonstrated to provide both the adequate computer efficiency and the accuracy necessary to allow the analysis of complex RC structures also in dynamic conditions. Even if the improvement of the concrete constitutive law is always possible through more complex mathematics formulations, these generally require the definition of a number of parameters which often loose their physical meaning and are of difficult calibration with standard experimental tests. Furthermore the more refined constitutive laws, even if they can theoretically better describe the concrete behaviour, due to their complexity result to be unsuitable for computer calculation of real structures. These drawbacks, far from to be efficiently overcome, have caused a limited spreading of non-linear models and analyses among the practical engineers, although the world-wide building codes take them into consideration as possible methods of design. The present work intends to perform a step toward the diffusion of the use of non-linear analysis in the practical design activities. A new two-parameters plastic damage law is proposed, starting from the model first forwarded by Faria and Oliver [1] and subsequently developed by Scotta [2]. The parameters used in the new model have clear physical meaning and are of easy experimental determination. Moreover, because of its implicit analytical genesis the constitutive law has demonstrated to be also efficient from the computer calculation point of view. The new damage-based constitutive law has been implemented into a fibres model which needs neither the preliminary positioning of non-linear hinges nor the definition of their characteristic curves. With the developed numerical code some analyses of reinforced concrete frames have been performed, both in static and dynamic conditions. The obtained results have confirmed the efficiency and reliability of the proposed method, showing a good agreement with the experimental test results.