Effect of Ground Motion Duration and Different Duration Indexes on the Seismic Response of Structures
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摘要: 选取70条具有不同持时的天然地震波，并采用5%～75%重要持时将谱匹配后的地震记录划分为长、短持时地震记录集，对10层RC框架结构进行IDA分析和弹塑性时程分析，研究地震动持时对结构地震响应的影响，进一步选取35条天然地震波，采用有效持续时间、5%～75%和5%～95%重要持时等不同强震持时指标分别截取相应的加速度时程段，构建不同的地震记录集，分析不同持时指标对RC框架结构峰值响应和滞回耗能的影响。研究结果表明：在相同的地震动强度下，长持时地震动会导致更大的结构层间变形和结构倒塌概率，且随着持时的增加，结构总滞回耗能大幅增加；在罕遇地震水准下，可选取有效持续时间和5%～95%重要持时指标用于结构层间变形和楼层峰值位移分析，而在极罕遇地震水准下，选用有效持续时间具有更高的可靠性；对于楼层峰值速度，不同地震集计算结果均值和变异系数未表现出明显差异；在相同地震动强度下，建议优先选用有效持续时间用于结构滞回耗能分析。Abstract: In this paper, 70 natural seismic waves with different durations are selected, and the seismic records after spectral matching are divided into long and short-duration seismic record sets with 5%~75% significant duration, IDA analysis and elasto-plastic time-history analysis are carried out for the 10-story RC frame structure to study the effects of seismic duration on the seismic response of the structure. Further, selected 35 natural seismic waves, different seismic record sets were constructed by intercepting the corresponding acceleration time segments with different strong motion duration indexes such as bracketed duration, 5%~75% and 5%~95% significant duration. The effects of different duration indexes on peak response and hysteretic energy dissipation of RC frame structures were analyzed. The results show that under the same ground motion intensity, the long duration ground motion will lead to greater inter story deformation and collapse probability of the structure, and the total hysteretic energy dissipation of the structure will increase significantly with the increase of the duration; Under the rare earthquake level, the bracketed duration and 5%~95% significant duration indexes can be selected for the analysis of structural inter story deformation and the peak displacement of the floors, while under the extremely rare earthquake level, the bracketed duration has higher reliability. For the peak velocity of the floor, the mean and variation coefficient of the calculation results of different earthquake sets did not show significant difference; In addition, under the same ground motion intensity, it is recommended to choose the bracketed duration for structural hysteretic energy dissipation analysis.
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图 2 经谱匹配后的地震波计算反应谱与目标谱对比
Figure 2. Comparison of 5% damped target spectrum and the spectra from selected records which have been matched to fit the target
图 3 所选地震记录的Da5-75频数分布直方图
Figure 3. Histogram frequency distribution diagram of Da5-75 of selected seismic records
图 4 长、短持时地震记录集的50%分位数IDA曲线
Figure 4. 50% quantile IDA curves of long and short duration seismic record sets
图 5 不同性能水平与结构破坏状态对应关系
Figure 5. Correspondence between different performance levels and structural failure states
图 6 长、短持时地震作用下结构地震易损性曲线
Figure 6. Seismic vulnerability curves of structures under long and short duration earthquakes
图 7 7度设防烈度不同设防水准对应的加速度设计反应谱
Figure 7. Acceleration design response spectrum corresponding to different fortification levels of 7 degrees fortification intensit
图 8 结构滞回耗能与5%～75%重要持时的相关性
Figure 8. Correlation between hysteretic energy dissipation of structures and 5%~75% significant duration
图 9 所选地震记录加速度计算反应谱与设计反应谱对比
Figure 9. Comparison diagram of the calculated response spectrum from selected earthquake ground motions and the design response spectrum
图 10 Denali-Alaska-2002强震持时计算结果
Figure 10. Calculation results of strong motion duration recorder
图 11 不同地震记录集作用下结构层间相对位移对比
Figure 11. Comparison diagram for maximum inter-story displacement of structure under different earthquake record sets
图 12 不同地震记录集作用下结构最大楼层位移均值对比
Figure 12. Comparison diagram of mean value for maximum layer displacement of structure under different earthquake record sets
图 13 不同地震集作用下结构最大层间相对位移变异系数对比
Figure 13. Comparison diagram of coefficient of variation for maximum inter-story displacement under different earthquake record sets
图 14 不同地震集作用下结构最大楼层位移变异系数对比
Figure 14. Comparison diagram of coefficient of variation for maximum layer displacement of structure under different earthquake record sets
图 15 不同地震集作用下结构最大楼层速度均值对比
Figure 15. Comparison diagram for maximum floor velocity of structure under different earthquake record sets
图 16 不同地震集作用下结构最大楼层速度变异系数对比
Figure 16. Comparison diagram of coefficient of variation for maximum floor velocity of structure under different earthquake record sets
图 17 不同地震记录集作用下结构层间滞回耗能均值对比
Figure 17. Comparison diagram of mean value for inter-story hysteric energy of structure under different earthquake record sets
图 18 不同地震记录集作用下结构层间滞回耗能变异系数对比
Figure 18. Comparison diagram of coefficient of variation for inter-story hysteric energy of structure under different earthquake record sets
表 1 框架梁截面尺寸及配筋
Table 1. Section and reinforcement information of frame beams
楼层 尺寸(高×宽)/mm 纵筋 边跨 中跨 边跨 中跨 1～3 600×300 600×300 3C25+1C22，2C22+1C20 3C25+1C22，3C20+1C22 4～6 600×300 600×300 3C25+1C20，3C20 3C25+1C20，2C22+1C20 7～8 600×300 600×300 3C25，3C20 3C25，3C20 9～10 600×300 600×300 3C20，3C20 3C20，3C20 
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表 2 框架柱截面尺寸及配筋
Table 2. Section and reinforcement information of frame columns
楼层 尺寸(高×宽)/mm 纵筋 边柱 中柱 边柱 中柱 1～2 650×650 650×650 17C20 17C20 3～4 600×600 600×600 17C20 17C20 5～6 550×550 550×550 12C22 12C22 7～8 500×500 500×500 12C20 12C22 9～10 450×450 450×450 12C20 12C20
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表 3 结构自振周期对比
Table 3. Comparison of structural natural vibration periods
振型号 振型方向 OpenSees(T1)/s ETABS(T2)/s T1/T2 1 X 1.276 1.286 99.2% 2 Y 1.251 1.280 97.7% 3 T 1.145 1.158 98.9%
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表 4 地震动信息
Table 4. Information about the seismic records
编号 地震事件-年份 震级 台站 分量 1 Kocaeli, Turkey-1999 7.51 Duzce KOCAELI_DZC180 2 Duzce, Turkey-1999 7.14 Duzce DUZCE_DZC180 3 Kocaeli, Turkey-1999 7.51 Goynuk KOCAELI_GYN090 4 Kocaeli, Turkey-1999 7.51 Yarimca KOCAELI_YPT060 5 Darfield, New Zealand-2010 7 HORC DARFIELD_HORCN18 E 6 Kocaeli, Turkey-1999 7.51 Arcelik KOCAELI_ARE000 7 Chi-Chi, Taiwan-1999 7.62 CHY028 CHICHI_CHY028-N 8 Kocaeli, Turkey-1999 7.51 Mecidiyekoy KOCAELI_MCD000 9 El Mayor-Cucapah-2010 7.2 El Centro Differential Array SIERRA.MEX_EDA090 10 Kocaeli, Turkey-1999 7.51 Iznik KOCAELI_IZN090 11 Hector Mine-1999 7.13 Amboy HECTOR_ABY090 12 Darfield, New Zealand-2010 7 Canterbury Aero Club DARFIELD_CACSN50 W 13 Taiwan SMART1（45）-1986 7.3 SMART1 O02 SMART1.45_45 O02 EW 14 Chi-Chi, Taiwan-1999 7.62 CHY101 CHICHI_CHY101-E 15 Denali, Alaska-2002 7.9 Carlo （temp） DENALI_CARLO-90 16 Taiwan SMART1（45）-1986 7.3 SMART1 I01 SMART1.45_45 I01 EW 17 Chi-Chi, Taiwan-1999 7.62 TCU034 CHICHI_TCU034-E 18 Taiwan SMART1（45）-1986 7.3 SMART1 M07 SMART1.45_45 M07 EW 19 Taiwan SMART1（45）-1986 7.3 SMART1 I11 SMART1.45_45 I11 EW 20 Landers-1992 7.28 Yermo Fire Station LANDERS_YER360 21 Taiwan SMART1（45）-1986 7.3 SMART1 O01 SMART1.45_45 O01 EW 22 Chi-Chi, Taiwan-1999 7.62 TCU074 CHICHI_TCU074-E 23 Taiwan SMART1（45）-1986 7.3 SMART1 C00 SMART1.45_45 C00 EW 24 Darfield, New Zealand-2010 7 SPFS DARFIELD_SPFSN73 W 25 Chi-Chi, Taiwan-1999 7.62 TCU122 CHICHI_TCU122-N 26 Chi-Chi, Taiwan-1999 7.62 TCU082 CHICHI_TCU082-E 27 Denali, Alaska-2002 7.9 TAPS Pump Station #10 DENALI_PS10-047 28 Taiwan SMART1（45）-1986 7.3 SMART1 I07 SMART1.45_45 I07 EW 29 Landers-1992 7.28 Amboy LANDERS_ABY000 30 Chi-Chi, Taiwan-1999 7.62 TCU050 CHICHI_TCU050-E 31 Chi-Chi, Taiwan-1999 7.62 TCU079 CHICHI_TCU079-E 32 Chi-Chi, Taiwan-1999 7.62 CHY088 CHICHI_CHY088-N 33 Landers-1992 7.28 Fun Valley LANDERS_FVR045 34 Chi-Chi, Taiwan-1999 7.62 TCU120 CHICHI_TCU120-E 35 Landers-1992 7.28 Joshua Tree LANDERS_JOS000 36 Chi-Chi, Taiwan-1999 7.62 ILA041 CHICHI_ILA041-N 37 Landers-1992 7.28 Indio - Coachella Canal LANDERS_IND000 38 Chi-Chi, Taiwan-1999 7.62 CHY082 CHICHI_CHY082-N 39 Chi-Chi, Taiwan-1999 7.62 TCU117 CHICHI_TCU117-N 40 Chi-Chi, Taiwan-1999 7.62 ILA048 CHICHI_ILA048-N 41 El Mayor-Cucapah-2010 7.2 Huntington Beach - Lake St SIERRA.MEX_HNT090 42 Chi-Chi, Taiwan-1999 7.62 TCU119 CHICHI_TCU119-N 43 Chi-Chi, Taiwan-1999 7.62 CHY027 CHICHI_CHY027-E 44 Chi-Chi, Taiwan-1999 7.62 CHY027 CHICHI_CHY027-N 45 El Mayor-Cucapah-2010 7.2 Anaheim - Kraemer & La Palma SIERRA.MEX_AKL090 46 Chi-Chi, Taiwan-1999 7.62 TCU119 CHICHI_TCU119-E 47 Chi-Chi, Taiwan-1999 7.62 TCU113 CHICHI_TCU113-E 48 Chi-Chi, Taiwan-1999 7.62 CHY090 CHICHI_CHY090-N 49 Chi-Chi, Taiwan-1999 7.62 CHY057 CHICHI_CHY057-N 50 Chi-Chi, Taiwan-1999 7.62 CHY044 CHICHI_CHY044-N 51 Chi-Chi, Taiwan-1999 7.62 CHY033 CHICHI_CHY033-N 52 El Mayor-Cucapah-2010 7.2 Anaheim - Lakeview & Riverdale SIERRA.MEX_ALR090 53 Chi-Chi, Taiwan-1999 7.62 CHY107 CHICHI_CHY107-N 54 Chi-Chi, Taiwan-1999 7.62 CHY033 CHICHI_CHY033-E 55 Chi-Chi, Taiwan-1999 7.62 CHY054 CHICHI_CHY054-E 56 El Mayor-Cucapah-2010 7.2 EJIDO SALTILLO SIERRA.MEX_SAL000 57 El Mayor-Cucapah-2010 7.2 EJIDO SALTILLO SIERRA.MEX_SAL090 58 Chi-Chi, Taiwan-1999 7.62 CHY070 CHICHI_CHY070-N 59 El Mayor-Cucapah-2010 7.2 Santa Ana - Grand & Santa Clara SIERRA.MEX_ 13069 -9060 Chi-Chi, Taiwan-1999 7.62 CHY059 CHICHI_CHY059-N 61 Chi-Chi, Taiwan-1999 7.62 CHY002 CHICHI_CHY002-W 62 Denali, Alaska-2002 7.9 Valdez - Valdez Dock Company DENALI_VALDC090 63 Chi-Chi, Taiwan-1999 7.62 CHY004 CHICHI_CHY004-N 64 Chi-Chi, Taiwan-1999 7.62 CHY016 CHICHI_CHY016-N 65 Denali, Alaska-2002 7.9 Valdez - Valdez Dock Company DENALI_VALCC090 66 El Mayor-Cucapah-2010 7.2 Garden Grove - Hwy 22 & Harbor SIERRA.MEX_GGH360 67 El Mayor-Cucapah-2010 7.2 Garden Grove - Brookhurst & Westminster SIERRA.MEX_ 13885 -9068 El Mayor-Cucapah-2010 7.2 Garden Grove - Brookhurst & Westminster SIERRA.MEX_ 13885360 69 Denali, Alaska-2002 7.9 Valdez - Valdez Dock Company DENALI_VALDC360 70 Chi-Chi, Taiwan-1999 7.62 CHY017 CHICHI_CHY017-N
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表 5 RC框架结构不同性能点对应的最大层间位移角限值
Table 5. The limit of maximum inter-story displacement angle corresponding to different performance points of RC frame structure
正常使用（OP） 立即使用（IO） 生命安全（LS） 防止倒塌（CP） 损伤描述 层间位移角 损伤描述 层间位移角 损伤描述 层间位移角 损伤描述 层间位移角 结构完好 1/550 轻微破坏 1/250 中等破坏 1/120 严重破坏 1/50
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表 6 各设防水准条件下结构处于不同破坏状态的概率
Table 6. Failure probability of structures in different failure states under each fortification level
设防水准 地震动持时类别 破坏状态对应概率/% 基本完好 轻微破坏 中等破坏 严重破坏 发生倒塌 设防地震 长持时 100 0 0 0 0 短持时 100 0 0 0 0 罕遇地震 长持时 1 27 62 10 0 短持时 1 34 58 7 0 极罕遇地震 长持时 0 0 10 71 19 短持时 0 0 20 71 9
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表 7 所选地震记录信息及地震动持时计算结果
Table 7. Information and earthquake duration of Selected Seismic Record
编号 地震事件-年份 震级 台站 分量 PGA/g Rjb/km 场地类别 地震动持时/s 总时长 Db Da5-95 Da5-75 1 Denali Alaska-2002 7.9 TAPS_Pump_Station_#11 PS11066 0.071915 126.4 II 164.785 124.99 76.55 48.72 2 Loma Prieta-1989 6.9 Bear_Valley_#1-Fire_Station BVF220 0.072158 61.1 II 29.55 27.56 16.02 9.51 3 Chi Chi Taiwan 04-1999 6.2 TCU042 TCU042-N 0.024775 98.4 II 61.995 48.03 27.68 11.77 4 Borrego Mtn-1968 6.6 San_Onofre-So_Cal_Edison A-SON033 0.041315 129.1 II 39.995 37.66 28.45 20.31 5 Chi Chi Taiwan-05-1999 6.2 TCU068 TCU068-E 0.043411 49.9 II 59.99 37.50 20.74 8.21 6 Chi Chi-Taiwan-06-1999 6.3 TCU075 TCU075-N 0.108042 24.3 II 60.98 38.47 24.75 10.96 7 Coalinga-01-1983 6.4 Parkfield-Vineyard_Cany_6 W H-VC6090 0.075836 39.9 II 39.99 34.67 20.48 9.71 8 Northridge-01-1994 6.7 LA-Century_City_CC_North CCN090 0.255667 15.5 II 39.98 24.84 13.16 7.02 9 Chi Chi Taiwan-04-1999 6.2 CHY057 CHY057-N 0.02421 61.9 II 49.995 42.57 22.14 11.42 10 Chi Chi Taiwan-02-1999 5.9 TAP052 TAP052-N 0.013018 121.7 II 46.995 41.37 23.33 14.18 11 Whittier Narrows-01-1987 6 Fountain_Valley-Euclid A-EUC292 0.056122 36.7 II 29.18 25.88 17.54 9.36 12 Loma Prieta-1989 6.9 Coyote_Lake_Dam_（Downst） CLD195 0.160425 20.4 II 39.945 24.12 13.38 4.66 13 Chalfant Valley-01-1986 5.8 Bishop-LADWP_South_St B-LAD270 0.098332 23.4 II 39.915 31.66 21.69 12.21 14 Landers-1992 7.3 LA-N_Westmoreland WST000 0.037335 159.1 II 39.66 35.40 22.46 14.90 15 Coalinga-03-1983 5.4 Coalinga-14 th&Elm（Old_CHP） B-CHP090 0.058725 11.9 II 39.99 20.06 16.22 8.21 16 Chalfant Valley-02-1986 6.2 Bishop-LADWP_South_St A-LAD180 0.24861 14.4 II 39.975 20.39 12.57 3.60 17 Imperial Valley-06-1979 6.5 Agrarias H-AGR003 0.287257 0 II 28.35 23.92 13.12 6.23 18 Northridge-01-1994 6.7 N_Hollywood-Coldwater_Can CWC270 0.253543 7.9 II 21.91 20.26 16.39 6.99 19 Manjil, Iran-1990 7.4 Qazvin 185336 0.130738 50 II 60.41 49.08 25.70 11.05 20 Mammoth Lakes-03-1980 5.9 Convict_Creek A-CVK090 0.233491 1.0 II 39.995 14.24 6.31 2.76 21 Northridge-01-1994 6.7 Inglewood-Union_Oil ING000 0.090724 37.2 II 35.98 30.78 21.66 11.78 22 Big Bear-01-1992 6.5 Hesperia-4 th_&_Palm H4 P090 0.057397 44.3 II 60 48.22 26.95 10.71 23 San Fernando-1971 6.6 Maricopa_Array_#3 MA3220 0.010369 109 II 26.235 25.37 21.67 14.43 24 Kocaeli Turkey-1999 7.5 Arcelik ARC090 0.134198 10.6 II 29.995 19.99 10.27 5.11 25 Northridge-01-1994 6.7 Newport_Bch-Irvine_Ave._F.S NBI090 0.060722 83 II 39.98 31.80 21.26 12.54 26 Kocaeli Turkey-1999 7.5 Istanbul IST090 0.042683 49.7 II 138.78 61.82 37.30 18.01 27 Manjil, Iran-1990 7.4 Tehran-SarifUniversity 186008 0.011335 171.8 II 17.55 17.18 14.46 8.74 28 Hector Mine-1999 7.1 Mill_Creek_Ranger_Station MCR270 0.047473 84.9 II 54.995 42.07 21.21 15.12 29 Landers-1992 7.3 Mission_Creek_Fault MCF090 0.131554 27 II 69.995 54.09 40.23 30.48 30 San Fernando-1971 6.6 Buena_Vista-Taft BVP180 0.011976 111.4 II 26.63 25.83 21.55 13.61 31 North Palm Springs-1986 6.1 Desert_Hot_Springs DSP000 0.321239 1 II 23.995 16.13 6.55 2.90 32 San Fernando-1971 6.6 2516 _Via_Tejon_PVPVE155 0.041521 55.2 II 70.17 62.70 52.37 26.19 33 Loma Prieta-1989 6.9 Saratoga-Aloha_Ave STG090 0.326228 7.6 II 39.95 15.63 8.29 4.18 34 Borrego Mtn-1968 6.6 San_Onofre-So_Cal_Edison A-SON303 0.047202 129.1 II 39.995 36.59 28.22 20.11 35 Northridge-01-1994 6.7 Santa_Monica_City_Hall STM360 0.369888 17.3 II 39.98 16.00 10.70 6.86
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