Seismic Response of Seismic Isolated Beam Bridge with HDR Bearing under Bilateral Near-field Ground Motions
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摘要: 以HDR隔震梁桥多自由度（MDOF）模型和等效双线性单自由度（SDOF）模型为研究对象，以典型近场地震动作为输入，研究HDR支座双向耦合效应对HDR隔震梁桥地震响应的影响。研究结果表明：不考虑双向耦合效应的HDR支座滞回曲线呈典型双线性；考虑双向耦合效应的HDR支座滞回曲线面积小于不考虑双向耦合效应的HDR支座滞回曲线面积。不考虑双向耦合效应的顺桥向HDR支座位移峰值db大于考虑双向耦合效应时，但横桥向的结果相反。近场地震作用下，对梁桥进行HDR支座隔震设计时，忽略双向耦合效应计算得到的墩底剪力峰值和弯矩峰值均偏于保守。可忽略HDR支座双向耦合效应对HDR隔震梁桥近场地震能量的影响。Abstract: The effect of the bidirectional coupling effect of the HDR bearing on the seismic response of the seismic isolated beam bridge (SIBB) is studied by inputting the typical near-field ground motions into the multi-degree-of-freedom model and equivalent bilinear single-degree-of-freedom system of the SIBB with the HDR bearing. The main conclusions are as follows: the hysteretic curve of the HDR bearing is typical bilinear without considering the bidirectional coupling effect; the area of the hysteretic curve of the HDR bearing considering bidirectional coupling effect is smaller than that of the HDR bearing without considering bidirectional coupling effect; in the longitudinal direction, the peak displacement of the HDR bearing without considering the bidirectional coupling effect is larger than that of the HDR bearing with considering the bidirectional coupling effect, but the results are opposite in the transverse direction; when the seismic isolated design with the HDR bearing is done for beam bridges under near-field ground motions, the peak shear and moment on the bottom of piers are conservative without considering the bidirectional coupling effect; the effect of the bidirectional coupling effect of HDR bearing on the near-field seismic energy response of the SIBB with the HDR bearing can be neglected.
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图 6 HDR支座恢复力-位移关系曲线（顺桥向）
Figure 6. Relation curves of force and displacement of HDR bearing(in longitudinal directions)
图 7 HDR支座恢复力-位移关系曲线（横桥向）
Figure 7. Relation curves of force and displacement of HDR bearing (in lateral directions)
图 8 考虑双向耦合效应前后的HDR支座滞回耗能时程曲线
Figure 8. Hysteretic energy dissipation time-history curves of HDR bearing before and after considering bilateral coupled effect
表 1 近场地震动特征
Table 1. Characteristics of near-field ground motions
地震波 PGA/g 持时/s 顺桥向 横桥向 顺桥向 横桥向 Irpinia 0.126 0.136 35.21 35.21 Chalfant 0.175 0.401 40.00 40.00 Loma 0.285 0.323 40.00 39.99 Northridge 0.411 0.617 28.61 28.60 Chi-Chi 0.156 0.143 90.00 90.00 Chuetsu-oki 0.360 0.475 60.00 60.00 Darfield 0.237 0.234 137.70 136.9 
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表 2 HDR支座参数
Table 2. Parameters of HDR bearing
支座编号 K1/106N·m-1 K2/106N·m-1 $\eta$ Fy/kN HDR-1 23.86 3.67 0.1538 509 HDR-2 14.32 2.20 0.1536 183
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表 3 考虑双向耦合效应前后1号墩峰值近场地震响应
Table 3. Peak near-field response of no.1 pier before and after considering bilateral coupled effect
地震波 不考虑双向耦合效应 考虑双向耦合效应 db-X
/cmdb-Y
/cmQX
/106NQY
/106NMX
/108N·mMY
/108N·mdbXY-X
/cmdbXY-Y
/cmQXY-X
/106NQXY-Y
/106NMXY-X
/108N·mMXY-Y
/108N·mIrpinia 6.9 8.5 3.5 4.3 0.6 0.7 5.7 8.9 3.1 4.1 0.6 0.7 Chalfant 5.6 8.5 3.9 5.7 0.6 0.9 5.0 8.5 3.4 5.7 0.5 0.9 Loma 14.7 17.8 5.2 6.0 0.8 1.1 12.5 17.5 4.6 6.3 0.7 1.2 Northridge 71.4 33.1 13.4 9.0 2.2 1.3 74.3 37.1 13.3 8.6 2.2 1.3 Chi-Chi 9.3 11.8 4.0 4.3 0.7 0.9 9.6 11.1 4.1 4.2 0.7 0.8 Chuetsu-oki 113.8 214.8 18.0 30.0 3.2 7.8 115.7 220.7 17.1 30.7 3.1 8.0 Darfield 11.7 22.7 5.9 6.7 0.9 1.4 17.3 27.3 5.5 6.8 0.9 1.4 平均值 35.1 45.3 7.7 9.4 1.3 2.0 34.3 47.3 7.3 9.5 1.2 2.0
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表 4 考虑双向耦合效应前后的1号墩峰值响应之比
Table 4. Peak response ratio of no.1 pier before and after considering bilateral coupled effect
地震波 ${R_{{d_{\rm{b}}}X, i}}$ ${R_{{d_{\rm{b}}}Y, i}}$ RQX,i RQY,i RMX,i RMY,i Irpinia 1.223 0.956 1.118 1.033 1.046 1.017 Chalfant 1.112 1.002 1.164 1.000 1.238 1.000 Loma 1.173 1.015 1.149 0.949 1.242 0.947 Northridge 0.962 0.892 1.013 1.046 1.008 0.944 Chi-Chi 0.971 1.060 0.977 1.014 0.987 1.053 Chuetsu-oki 0.984 0.973 1.055 0.978 1.054 0.977 Darfield 0.676 0.834 1.065 0.982 1.033 0.957
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表 5 1、2号墩响应峰值比的平均值
Table 5. Average of peak response ratio of no.1 pier and no.2 pier
墩号 平均值 ${\bar R_{{d_{\rm{b}}}X}}$ ${\bar R_{{d_{\rm{b}}}Y}}$ ${\bar R_{QX}}$ ${\bar R_{QY}}$ ${\bar R_{MX}}$ ${\bar R_{MY}}$ 1 1.014 0.962 1.077 1.000 1.087 0.985 2 1.011 0.962 1.063 1.014 1.095 0.999
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表 6 考虑HDR支座双向耦合效应的SDOF模型近场地震能量响应（105N·m）
Table 6. Energy response of SDOF model by considering the bilateral coupled effect of HDR bearing under near-field ground motions(105N·m)
地震波 EIx+EIy EIxy ${\lambda _{{E_\text{I}}}}$ EHx+EHy EHxy ${\lambda _{{E_\text{H}}}}$ EDx+EDy EDxy ${\lambda _{{E_{\rm{D}}}}}$ Irpinia 7.849 7.160 1.096 4.514 4.517 0.999 3.317 2.631 1.261 Chalfant 5.289 5.170 1.023 2.709 2.819 0.961 2.576 2.348 1.097 Loma 9.331 8.280 1.127 5.509 4.832 1.140 3.821 3.448 1.108 Northridge 50.942 48.780 1.044 25.564 22.689 1.127 25.367 26.084 0.973 Chi-Chi 8.088 7.994 1.012 4.984 5.373 0.928 3.103 2.621 1.184 Chuetsu-oki 298.158 297.071 1.004 104.162 90.424 1.152 193.991 206.639 0.939 Darfield 7.215 8.003 0.901 4.827 5.519 0.875 2.388 2.485 0.961
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