Physics-based and locally updated nonlinear damping model for cracked reinforced concrete beams

Abstract

The structural design increasingly requires considering earthquake excitations even in low-seismic risk areas, particularly for critical infrastructures, such as nuclear ones. Sophisticated models are required to characterise the structural behaviour under low seismic excitations. In the case of reinforced concrete structures, nonlinear material models are considered to characterise some energy dissipative phenomena such as (i) damage due to cracking or (ii) friction of cracked surfaces. However, more than the amount of energy dissipated by these nonlinear models are required to accurately represent the physical structural dynamic responses. That is why viscous damping is generally added to dissipate the excess energy. Numerous damping models are proposed in the literature. However, their principal drawback is their need for the representativeness of physical dissipative phenomena. So, this paper proposes a viscous damping model based on such phenomena to dissipate the energy not represented through the nonlinear material model. The proposed strategy is to update the damping matrix at the element level using the intensity of nonlinearities in each element. Three local variables are compared in the paper: one variable associated to damage, another associated with friction and a damage index computed from the secant elemental rigidity. Dynamic nonlinear computations are performed with the proposed locally updated damping matrices. The results are compared with experimental data, when available, and with Rayleigh-type damping formulations classically used in engineering. As a result, it is observed that all damping formulations properly characterise the global response of the studied reinforced concrete beam. However, the use of the proposed formulations allows better representativeness of local dissipative phenomena and adds a physical meaning to the damping model.