Influence of permanent displacement of ground motion on seismic response of structures
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摘要: 本文推导了基于位移激励计算单自由度体系拟速度谱公式，通过构造的脉冲位移时程对公式精度进行了验证；之后利用小波变换去除强震记录噪声而保留地震动永久位移，再基于去趋势项方法和滤波方法去除永久位移后，计算拟速度谱。算例结果表明：短周期段内，不保留永久位移的位移激励拟速度谱值与保留永久位移的位移激励拟速度谱值相差很小；中长周期段内，不保留永久位移的位移激励拟速度谱值总体上小于保留永久位移的位移激励拟速度谱值，且不保留永久位移时，滤波方法引起的拟速度谱降幅大于去趋势项方法所引起的拟速度谱降幅。因此，基于位移激励计算中长周期结构的地震反应时，应保留地震动永久位移，或基于去趋势项方法去除永久位移。Abstract: When calculating the seismic response of a structure based on the displacement excitation, the displacement excitation is obtained by integration of the velocity, which is obtained by integration of the acceleration records. At the same time, the acceleration noise must be removed. However, limited by the method for eliminating noise from acceleration records, the permanent displacement of the ground motion in the near-fault earthquake acceleration records is often weakened or even eliminated. This makes it impossible for researchers to judge the effect of permanent displacement of ground motion on the seismic response of structures excited by displacement. In this paper, the authors deduce the pseudo-velocity spectra formula of single degree of freedom system based on displacement excitation, verify the accuracy of the formula with the constructed pulse displacement time history, and then analyze the effect of the permanent displacement of the ground motion on the pseudo-velocity spectra. Firstly, the noise is executed on the acceleration records via wavelet transform, and gound motion with permanent displacement is remained. And then the permanent displacement is wiped out using reducing trend item method or filtering method from those records. Those excitations are used to calculate pseudo-velocity spectra. The results show that in short period, the pseudo-velocity spectra are similar whether ground motions contain the permanent displacement or not; in medium-long period, the pseudo-velocity spectra excited by non-permanent displacement excitation are lower than those by displacement excitation with permanent displacement, and this kind of difference are enlarged when the filtering method is used. Therefore, for seismic design of long-period structures, the ground motion with permanent ground displacement excitation should be used, or reducing trend item method is used to wipe out permanent displacement.
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图 4 加速度激励、无永久位移的位移激励及包含永久位移的位移激励
（a） 欧姆林公寓邦德角记录到的2010年4月4日美国卡莱克西科市地震；（b） 卡莱克西科市消防站记录到的2010年4月4日美国卡莱克西科市地震：（c） 林肯作物与食物研究中心记录到的2010年9月3日新西兰地震；（d） 里奇克莱斯特395号公路/布朗路桥记录到的2019年7月5日美国里奇克莱斯特地震
Figure 4. Acceleration excitations，displacement excitations containing permanent ground displacement and displacement excitations without permanent ground displacement
（a） Calexico earthquake in USA on 4 April 2010 recorded by the Bond’s Corner of Omlin Residence；（b） Calexico earthquake in USA on 4 April 2010 recorded by the Calexico Fire Station；（c） New Zealand earthquake on 3 September 2010 recorded by the Lincoln Crop and Food Research；（d） Ridgecrest earthquake in USA on 5 July 2019 recorded by the Ridgecrest-Highway 395/Brown Road Bridge
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图 5 不同点位的拟速度谱对比图（单自由度体系阻尼比ζ＝0.02）
（a） 欧姆林公寓邦德角；（b） 卡莱克西科市消防站；（c） 林肯作物与食物研究中心；（d） 里奇克莱斯特395号公路/布朗路桥
Figure 5. Comparing of pseudo-velocity spectra （damping ratio ζ＝0.02）for different sites
（a） The Bond’s Corner，Omlin Residence；（b） The Calexico Fire Station；（c） The Lincoln Crop and Food Research； （d） The Ridgecrest-Highway 395/Brown Road Bridge
表 1 地震动信息
Table 1 Ground motion information
序号 地震 发震时间
年−月−日ML 观测位置 断层距/km 峰值加速度
/（cm·s−2）1 美国加州卡莱克西科市
（Calexico）地震2010−04−04 7.2 卡莱克西科市欧姆林（Omlin）
公寓邦德角（Bond’s Corner）35.7 120.32 2 美国加州卡莱克西科市
（Calexico）地震2010−04−04 7.2 卡莱克西科市消防站 23.1 266.45 3 新西兰地震 2010−09−03 7.0 新西兰林肯作物与食物研究中心 6.3 426.80 4 美国加州里奇克莱斯特
（Ridgecrest）地震2019−07−05 7.1 加州里奇克莱斯特395号
公路/布朗路桥22.3 237.74 
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