Abstract：Residual displacement is a vital index for performance-based seismic design.In order to study the computational method of structure’s residual displacement in near-fault region considering its velocity-pulse-like effect, a two-period-normalization (TTN) approach incorporating the site characteristic period Tg and pulse period Tp was adopted.To obtain the mean spectrum of TTN residual displacement coefficient, linear and nonlinear dynamic time history analyses on a single degree of freedom system excited by 226 groups of near-fault pulse-like earthquake records were conducted.The influence of the local site condition, natural vibration period T and structure strength reduction factor R on the residual displacement coefficient Cr was discussed, and the TTN design spectrum was obtained by fitting correspondent data.The results indicate that: ① The residual displacement coefficient spectrum generated by TTN method can directly reflect the amplification of pulse effect on the dynamic responses of long period structures; ②T and R are major parameters that affect Cr, while TTN residual displacement coefficient spectra have excellent consistency for different site conditions, which makes it possible to generate a site-unified spectrum; ③The proposed TTN residual displacement coefficient design spectrum can reflect the correlation among Cr and T as well as R in a concise mathematical expression and can be applied for anticipating the residual displacements of structures in near-fault region.
[1] 李建中，管仲国．桥梁抗震设计理论发展:从结构抗震减震到震后可恢复设计[J]．中国公路学报，2017（ 12）： 1-9+59．
LI Jian-zhong, GUAN Zhong-guo. Research progress on bridge seismic design: target from seismic alleviation to post-earthquake structural resilience[J]. China Journal of Highway and Transport, 2017( 12): 1-9+59.
[2] Kawashima K, Unjoh S. The damage of highway bridges in the 1995 Hyogo-ken Nanbu earthquake and its impact on Japanese seismic design[J]. Journal of Earthquake Engineering, 1997, 3(1): 505-541.
[3] Macrae G A, Kawashima K. Post-earthquake residual displacements of bilinear oscillators[J]. Earthquake Engineering and Structural Dynamics, 1997, 26(7): 701-716.
[4] Kawashima K, Macrae G A, Hoshikuma J,et al. Residual displacement response spectrum[J]. Journal of Structural Engineering New York, 1998, 124(5): 523-530.
[5] Japan Road Association, 5. Design specifications of highway bridges Part V: Seismic design[S], 1996.
[6] Garcia J R, Eduardo M. Residual displacement ratios for assessment of existing structures[J]. Earthquake Engineering and Structural Dynamics, 2006, 35(3): 315-336.
[7] 郝建兵，吴刚，吴智深．单自由度体系等强度残余位移谱研究[J]．土木工程学报，2013（10）： 82- 88．
HAO Jian-bing, WU Gang, WU Zhi-shen. A study on constant-relative-strength residual deformation ratio spectrum of SDOF system[J]. China Civil Engineering Journal, 2013( 10): 82- 88.
[8] 胡晓斌，贺慧高．等强残余位移系数谱研究[J]．工程力学，2015（01）： 163- 167．
HU Xiao-bin, HE Hui-gao. Study on equal-strength residual displacement ratio spectrum[J]. Engineering Mechanics, 2015( 01): 163- 167.
[9] Christopoulos C, Pampanin S, Priestley M. Performance-based seismic response of frame structures including residual deformations. Part I: Single-degree of freedom systems[J]. Journal of Earthquake Engineering, 2003, 7(1): 97-118.
[10] 余波，刘迪，杨绿峰．考虑P-△效应的桥梁结构震后概率残余位移分析[J]．振动与冲击，2014（01）： 154- 161．
YU Bo, LIU Di, YANG Lu-feng. Probabilistic residual displacement analysis of bridge structures considering P-Δ effect[J]. Journal of Vibration and Shock, 2014( 01): 154- 161.
[11] 张勤，贡金鑫，周继凯．基于概率的单自由度体系震后残余变形计算[J]．建筑结构学报，2017（08）： 74- 82．
ZHANG Qin, GONG Jin-xin, ZHOU Ji-kai. Seismic residual deformation analysis of single degree of freedom system based on probability[J]. Journal of Building Structures, 2017( 08): 74- 82.
[12] 徐龙军，谢礼立．近断层地区抗震设计谱研究[J]．东南大学学报(自然科学版)，2005（S1）：105- 108．
XU Long-jun, XIE Li-li. Study on seismic design spectra of near-fault region[J]. Journal of Southeast University (Natural Science Edition), 2005( S1): 105- 108.
[13] 徐龙军，谢礼立．近断层地震动双规准伪速度谱及其应用[J]．地震学报，2007（05）：512- 520．
XU Long-jun, XIE Li-li. Near-fault ground motion bi-normalized pseudo-velocity spectra and its applications[J]. ACTA Seismologica Sinica, 2007( 05): 512- 520.
[14] 杜永峰，徐天妮，王亚楠，等．近断层地震动作用下设计速度反应谱研究[J]．地震工程学报，2014（04）： 997-1002+．
DU Yong-feng, XU Tian-ni, WANG Ya-nan,et al. Analysis of designed velocity response spectra subjected to near-fault ground motion[J]. China Earthquake Engineering Journal, 2014(04): 997-1002+.
[15] 张洪智，刘秀明，徐龙军．近断层方向性效应地震动双规准组合反应谱[J]．哈尔滨工业大学学报，2014（ 10）： 17- 22．
ZHANG Hong-zhi, LIU Xiu-ming, XU Long-jun. Bi-normalized combined response spectra of directivity effect ground motions in near-fault region[J]. Journal of Harbin Institute of Technology, 2014(10): 17- 22.
[16] 谢俊举，李小军，温增平．近断层速度大脉冲对反应谱的放大作用[J]．工程力学，2017（08）：194- 211．
XIE Jun-ju, LI Xiao-jun, WEN Zeng-ping. The amplification effects of near-fault distinct velocity pulses on response spectra[J]. Engineering Mechanics, 2017(08): 194- 211.
[17] 卢明奇，田玉基．近断层地震作用下基于位移的震设计方法[J]．哈尔滨工程大学学报，2008（01）：16-21．
LU Ming-ji, TIAN Yu-ji. Safety of displacement-based seismic designs in near -fault ground motions[J]. Journal of Harbin Engineering University, 2008(01): 16-21.
[18] 李明，谢礼立，杨永强，等．基于反应谱的近断层地震动潜在破坏作用分析[J]．西南交通大学学报，2010（03）： 331- 335．
LI Ming, XIE Li-li, YANG Yong-jiang,et al. Potential damage analysis of Near-Fault ground motion based on response spectra[J]. Journal of Southwest Jiaotong University, 2010(03): 331- 335.
[19] 陈令坤，张楠，胡超，等．近断层地震方向脉冲效应对高速铁路桥梁弹塑性反应的影响[J]．振动与冲击，2013（15）：149-155+1．
CHEN Ling-kun, ZHANG Nan, HU Chao,et al. Effects of near- fault directivity pulse- like ground motion on elastic- elastic seismic response of high-speed railway bridge[J]. Journal of Vibration and Shock, 2013(15): 149-155+1.
[20] 李芳宝，朱晞．近场具有脉冲地层运动的单自由度双线性结构残余位移比谱[J]．中国铁道科学，2007（03）： 49- 55．
LI Fang-bao, ZHU Xi. Residual displacement ratio spectrum of Single-Degree-of-Freedom bilinear structure under ground motions with pulse in Near-Fault zones[J]. China Railway Science, 2007(03): 49- 55.
[21] Ruiz G J. Inelastic displacement ratios for seismic assessment of structures subjected to forward-directivity near-fault ground motions[J]. Journal of Earthquake Engineering, 2011, 15(3): 449-468.
[22] Iervolino I, Chioccarelli E. Baltzopoulos g. inelastic displacement ratio of near-source pulse-like ground motions[J]. Earthquake Engineering & Structural Dynamics, 2012, 41(15): 2351-2357.
[23] 杨华平，钱永久，黎璟，等．近断层脉冲型地震设计谱研究[J]．中国公路学报，2017（12）： 159-168+1．
YANG Hua-ping, QIAN Yong-jiu, LI Jing,et al. Design response spectra for near-fault pulse-like ground motions[J]. China Journal of Highway and Transport, 2017(12): 159-168+1.
[24] Shahi S K, Baker J W. An empirically calibrated framework for including the effects of near-fault directivity in probabilistic seismic hazard analysis[J]. Bulletin of the Seismological Society of America, 2011, 101(2): 742-755.
[25] Baker J W. Quantitative classification of near-fault ground motions using wavelet analysis[J]. Bulletin of the Seismological Society of America, 2007, 97(5): 1486-1501.
[26] 吕红山，赵凤新．适用于中国场地分类的地震动反应谱放大系数[J]．地震学报，2007, 29（01）：67-76+114．
LV Hong-shan, ZHAO Feng-xin. Site coefficients suitable to China site category[J]. ACTA Seismologica Sinica, 2007, 29( 01): 67-76+114.
[27] Baber T T, Noori M N. Random vibration of degrading pinching systems[J]. Journal of Engineering Mechanics. ASCE, 1985, 111(8): 1010-1026.
[28] Bouc R. Forced vibration of mechanical systems with hysteresis[C]//In Proceedings of the Fourth Conference on Nonlinear Oscillation．Prague, Czechoslovakia, 1967: 315-318.
[29] Goda K, HONG H-p, Lee C S. Probabilistic characteristics of seismic ductility demand of SDOF systems with Bouc-Wen hysteretic behavior[J]. Journal of Earthquake Engineering, 2009, 13(5): 600-622.
