Seismic energy dissipation in reinforced concrete beam: investigating damping formulations

Abstract

Earthquake events in recent years and their consideration in performance-based design have led to the development of increasingly sophisticated physical models in structural computations. The aim of such models has been to predict the structural behaviour when excited by an earthquake. In particular, in the context of nuclear power plants (high-risk structures), operators must justify the airtightness of ageing structures to study the nonlinear behaviours of these structures, requiring the study and modelling of the phenomena associated with seismic energy dissipation in concrete. Energy dissipation has been described at two levels: global and local scales. At the local scale, material behaviour laws express some phenomena, such as concrete damage, friction, unilateral effects or plasticity. At the global scale, for dynamic analyses, energy dissipation has been practically modelled with equivalent viscous damping. Rayleigh-type damping formulations are still the most commonly used in engineering. Numerous formulations have been proposed in the literature, and some papers have compared some of these formulations. However, comparisons have rarely been based on experimental data, and the structures studied have varied considerably among studies. Therefore, the first objective of this paper is to assess the accuracy of a wide range of damping formulations by comparing them to the experimental data. Reinforced concrete beams were tested in quasistatic mode on a strong floor and in dynamic mode on a shaking table. The aim was to study the energy dissipation involving nonlinear mechanisms in concrete while steel rebar remained in their elastic range. The study developed in this paper concerns the dynamic behaviour of reinforced concrete critical structures, which are over-sized in engineering, under moderate earthquake levels. Thus, a beam multifibre model is proposed with two different concrete constitutive models. The second objective is to compare the energy dissipation at structural and material scales to evaluate the most efficient damping formulations to represent dynamic nonlinear responses.

Keywords:

• Reinforced concrete
• beam
• energy dissipation
• viscous damping
• energy balance
• fibre element model

Acknowledgements

A part of this work has been performed at École Polytechnique de Montréal thanks to funding from Institute SEISM.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was performed using HPC resources from the ‘Mésocentre’ computing centre of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France (http://mesocentre.centralesupelec.fr/).