Influence of Response Acceleration-Dependent Damping on the Nonlinear Seismic Behavior of Reinforced Concrete Columns

Abstract

Accurately representing damping remains a major challenge in nonlinear seismic analysis of reinforced concrete (RC) elements, particularly under severe ground motions where stiffness degradation invalidates the assumptions of conventional models. Classical Rayleigh damping, despite its widespread use, often produces spurious energy dissipation and inaccurate response predictions in inelastic systems.

To address this limitation, this study proposes acceleration-dependent damping formulations in which damping evolves at each time step according to the instantaneous structural response. The proposed approach is implemented within a nonlinear time history analysis framework using direct integration. An RC column model based on distributed plasticity is developed by discretizing the member into multiple sub-elements to accurately capture inelastic behavior. Four damping models are investigated: Model A employs classical Rayleigh damping with constant coefficients based on initial stiffness and a fixed 5% damping ratio; Models B and C apply acceleration-updated Rayleigh damping, where Model B retains initial stiffness and Model C incorporates tangent stiffness; Model D introduces a fully response-driven diagonal damping matrix that varies directly with response acceleration over time.

The analytical results are validated against ETABS simulations and experimental data from shake table tests of an RC column subjected to scaled records of the 1994 Kushiro earthquake. Compared with conventional damping, the proposed acceleration-dependent models significantly reduce prediction errors and eliminate non-physical damping effects. Models B and C achieved deviations between −8.9% and +3.2%, while Model D further improved accuracy, limiting peak acceleration deviations to −8.11% and +2.3%.

The results demonstrate that coupling damping evolution with instantaneous response provides a physically consistent and numerically robust alternative to classical approaches. The novelty of this study lies in the formulation and validation of time-dependent, acceleration-driven damping models that dynamically adapt during analysis, enabling more accurate prediction of nonlinear seismic response in degrading RC systems without reliance on empirically fixed damping assumptions.