Damping correction formula considering the period‐dependent characteristics of the design response spectra of long‐period ground motions for the hypothetical Nankai Trough earthquake: An investigation of the simplified spectra and waveform example provided by the Ministry of Land, Infrastructure, Transport and Tourism

Abstract

In June 2016, the Ministry of Land, Infrastructure, Transport and Tourism in Japan announced a countermeasure against the Nankai Trough's long-period ground motions. However, the response spectrum method provided in the Ministry of Construction notification Vol. 2009 was not included in the countermeasure because it could not reflect the influence of long-period ground motions. Therefore, this paper proposes a damping correction formula for long-period ground motions considering the period-dependent characteristics of the earthquake response spectra for the design. The applicability of the proposed damping correction formula to seismically isolated buildings is verified by comparing the result by the response spectrum method using this formula with those of a timehistory analysis using the single-degree-of-freedom models.

Earthquake response prediction of seismically isolated buildings based on the response spectrum method considering changes in characteristics of lead rubber bearings due to repeated deformations

“…If the damping factor is less than 5%, the same type of Equation as in MCN included in the Appendix of Ref. [12] and [13] should be used. $$$$ \left[\begin{array}{l}{F}_h=\frac{1+\alpha {h}_0}{1+\alpha h}\kern21em \left({T}_{eq}<{T}_1\right)\\ {}{F}_h=\frac{1+\alpha {h}_0}{1+\alpha h}+\beta \sqrt{h-{h}_0}\left(\frac{T_{eq}}{T_1}-1\right)\kern10.2em \left({T}_1\le {T}_{eq}<{T}_2\right)\\ {}{F}_h=\frac{1+\alpha {h}_0}{1+\alpha h}+\beta \sqrt{h-{h}_0}\left(\frac{T_2}{T_1}-1\right)+\gamma \sqrt{h-{h}_0}\left(\frac{T_{eq}}{T_2}-1\right)\kern1.6em \left({T}_2\le {T}_{eq}\right)\end{array}\right. $$$$ …”

“…The damping correction formula F h uses the proposed Equation (4), considering the periodic characteristics of the response spectra of the LPGMDs. 12,13 If the damping factor is less than 5%, the same type of Equation as in MCN included in the Appendix of Ref. [12] and [13] should be used.…”

“…12,13 If the damping factor is less than 5%, the same type of Equation as in MCN included in the Appendix of Ref. [12] and [13] should be used.…”

“…where h is the damping factor, h 0 is the initial damping factor (h 0 = 0.05), T eq is the equivalent period, T 1 and T 2 are boundary periods of periodic ranges 1, 2, and 3 based on the simplified spectra of the LPGMDs, 12,13 and α, β, and γ are the regression coefficients given for each area. 12,13 The equivalent damping factor h eq for a steady-state loop at peak response displacement of the LRB was evaluated from Equation ( 5).…”

“…where h is the damping factor, h 0 is the initial damping factor (h 0 = 0.05), T eq is the equivalent period, T 1 and T 2 are boundary periods of periodic ranges 1, 2, and 3 based on the simplified spectra of the LPGMDs, 12,13 and α, β, and γ are the regression coefficients given for each area. 12,13 The equivalent damping factor h eq for a steady-state loop at peak response displacement of the LRB was evaluated from Equation ( 5). 1 The reduction coefficient α R shown in Equation ( 6) is multiplied, and 0.8 is used in MCN to take into account the effect of irregularity of the response.…”