۱- Introduction

۲- Stochastic modelling of seismic motion

۳- Definition of modulation function considering the earthquake duration

۴- Evaluation of damping reduction factor by the peak theory

۵- Analysis results

۶- Proposed DRF formulation

۷- Conclusion and further developments

References

Abstract

Damping Reduction Factor plays a key role in scientific literature and Technical Codes, but till now existing formulations present differences and inconsistences probably because obtained by integration of real recorded events, thus sensible to specific used data. This paper investigates the relation between damping reduction factor and earthquake duration by means of random vibration theory. A stochastic process, that is non-stationary and filtered, is used to model a seismic event. The modulation function is suitably chosen to describe earthquakes characterized by different durations. The stochastic process peak theory allows to calculate damping reduction factor after the definition of the probabilistic response of a simple linear visco-elastic oscillator. The variability with seismic duration for different soil conditions and damping ratios is investigated. The study points out that damping reduction factor is more sensitive to seismic duration in the range of high period and on rigid soil with respect to other conditions. The results show that, if damping ratio or effective duration values are increased, the damping reduction factor value diminishes.

Introduction

Serious seismic damage observed on structures and infrastructures systems up to today [1] can be prevented by means of retrofitting interventions if the capacity of these systems and the seismic demand are properly evaluated [2–۶] In structural seismic design, Damping Reduction Factor (DRF) represents an effective tool for design purposes to estimate the demand by response spectra characterized also by damping ratios different from 5% as in the case of structures equipped with passive energy dissipation or isolation systems. DRF modifies the values of the conventional elastic spectral response with damping ratio equal to 5% to the values corresponding to a different 7 damping level. It is defined as the ratio between the spectral ordinate at 5% conventional damping and the spectral ordinate at a different level of damping. DRF finds many applications to study the behavior of structures [7], especially for the ones equipped with passive energy dissipation or isolation systems [8–۱۲]. In these situations, the DRF permits to estimate the variation of the structural response (displacements and forces) due to the high supplemental damping values [5,13–۱۵] In addition, for inelastic structures, DRF allows to calculate the maximum displacement demand from the one of an equivalent linear system [8]. For these and other reasons the DRF is particularly suitable for the seismic design of a structure since it provides a practical evaluation of the reduction of earthquake loads for effects of structural, non-structural and supplementary energy dissipation systems. For that reason, it is selected as a key parameter in the present study.