Ranking the seismic input motion based on seismic response of soft soil tunnels
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摘要: 为探讨“最不利地震动”概念在地下结构抗震设计中的适用性，以软土地铁区间隧道为对象建立相应的地层-结构动力分析模型。以直径变形率为分析指标，基于动力时程方法研究18条不同输入地震动作用下隧道结构动力响应的分布及差异性，得出基于隧道地震响应的输入地震动排序，并通过调幅手段对比分析了地面峰值加速度（PGA）和隧道埋深变化对隧道结构地震动响应排序的影响规律。最后，评价了不同输入地震动参数，包括峰值加速度、峰值速度、峰值位移、绝对累积速度（CAV）和阿里亚斯（Arias）强度（IA）与隧道地震响应之间的相关性。分析结果表明：① 随着PGA从0.5 m/s2增加到2 m/s2，地震动排序发生明显变化，并且不同输入地震动引起的隧道地震响应差异显著提高，最不利地震动引起的直径变形率与平均值的比值从1.1增加到1.9；② 隧道从浅埋到深埋的过程中，地震动排序结果基本保持不变；③ PGA为2 m/s2时，隧道地震响应与基岩面峰值速度（PBV）的相关性最好，相关系数达到0.94，其次是与基岩面峰值位移（PBD）和IA，相关系数分别为0.62和0.48，相关性最差的是基岩面峰值加速度（PBA）和CAV，相关系数仅为0.37和0.22。研究结论可为今后软土隧道的输入地震动选择提供科学依据。Abstract: The selection of input motion is of most importance in seismic design and analysis of underground structures. In recent years, the concept of “the most unfavorable ground motion” has been widely studied and applied in the field of seismic design for surface structures. However, there is no research on ranking the seismic input motion based on the seismic response of underground structures. To explore the applicability of the concept of “the most unfavorable ground motion” for the seismic design of underground structures, a circular tunnel in soft soil is taken as the research object, and the corresponding soil-structure dynamic analysis modelis established. Taking the ovaling deformation rate of the circular liner as the critical index of tunnel responses, the distribution as well as the difference of dynamic responses of the tunnel structure under excitations of 18 different input motions are studied with the dynamic time-history method, and thus the ranking of seismic input motions based on the tunnel response is obtained. By means of amplitude modulation, the effects of peak ground acceleration （PGA）and tunnel depth on the input motion ranking are further investigated. Finally , the correlation between different input motion parameters, including peak acceleration, peak velocity, peak displacement, absolute cumulative velocity （CAV） and Arias intensity （IA）, and the tunnel seismic response is evaluated. Results show that, ① When PGA increases from 0.5 m/s2 to 2 m/s2, the ranking of ground motion changes apparently, and the diversity of tunnel responses caused by different input motions is significantly amplified, such that the ratio of the maximum diametrical deformation rate caused by the most unfavorable input motion to the mean value is increasing from 1.1 to 1.9; ② The input motion ranking results remain unchanged for different depths of the tunnel; ③ For the PGA of 2 m/s2, the correlation between the tunnel response and the peak bedrock velocity （PBV） matches well, i.e. the correlation coefficient is 0.94, then followed by the peak bedrock displacement （PBD） and the IA, i.e. the correlation coefficient is 0.62 and 0.48, respectively, and the worse is, the peak bedrock acceleration （PBA） and the CAV have a correlation coefficient of only 0.37 and 0.22, respectively. The conclusions provide a scientific basis for the selection of seismic input motions of soft soil tunnels.
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图 3 埋深为1D时模型1在不同地震动强度下的直径变形率累积分布函数F
Figure 3. Cumulative distribution function of diameter deformation rate for model one under different ground motion intensities with buried depth of 1D
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图 4 埋深为1D时不同地震动强度条件下输入地震动的颜色映射序列（从左至右地震动的破坏能力依次下降）
Figure 4. Color mapping sequence of input ground motions of different ground motion intensities with buried depth of 1D （The destructiveness of ground motions decrease from left to right）
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图 5 峰值加速度PGA为2 m/s2时不同埋深条件下直径变形率累积分布函数
Figure 5. Cumulative distribution function of diameter deformation rate under different buried depths with peak ground acceleration is 2 m/s2
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图 6 峰值加速度PGA为2 m/s2时不同埋深同埋深条件下输入地震动的颜色映射序列（从左至右地震动的破坏能力依次下降）
Figure 6. Color mapping sequence of input ground motions of different buried depth with peak ground acceleration of 2 m/s2 （The destructiveness of ground motions decrease from left to right）
表 1 衬砌结构材料参数
Table 1 Material parameters of lining structure
密度/（kg·m−3） 弹性模量/（1010 N·m−2） 泊松比 混凝土C30 2 600 3 0.2 
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表 2 地震动记录
Table 2 Ground motion recordings
地点 日期 台站 方向 Chi-Chi，Taiwan，China 1999-09-20 ILA004 N Chi-Chi，Taiwan，China 1999-09-20 ILA004 W Chi-Chi，Taiwan，China 1999-09-20 ILA044 W Niigata，Japan 2004-10-23 NIG014 EW Chuetsu-oki，Japan 2007-07-16 NIG014 NS Iwate，Japan 2008-06-13 MYG006 EW Tottori，Japan 2000-10-06 TTR008 EW El Mayor-Cucapah，Mexico 2010-04-04 El Centro Array #3 270° Christchurch，New Zealand 2011-02-21 Christchurch Resthaven S88°E Tottori，Japan 2000-10-06 SMN002 NS Iwate，Japan 2008-06-13 AKT015 EW El Mayor-Cucapah，Mexico 2010-04-04 El Centro Array #3 360° Chuetsu-oki，Japan 2007-07-16 NIG025 NS Iwate，Japan 2008-06-13 AKT016 EW Iwate，Japan 2008-06-13 AKT016 NS Imperial Valley-07 1979-10-15 El Centro Array #3 140° Iwate，Japan 2008-06-13 IWT020 EW Iwate，Japan 2008-06-13 IWT020 NS 注：表中方向数字代表地震动记录的方位角。
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表 3 计算工况
Table 3 Computational cases
编号 PGA/(m·s−2) 隧道埋深/m 隧道埋深直径比 工况1 0.5 6.0 1.0 工况2 1 6.0 1.0 工况3 2 6.0 1.0 工况4 2 9.0 1.5 工况5 2 12.0 2.0 工况6 2 18.0 3.0 工况7 2 30.0 5.0
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表 4 直径变形率与地震动参数相关性
Table 4 Correlation coefficients between diameter deformation rate and input motion parameters
工况编号 PBA PBV PBD CAV IA 动剪切模量 工况1 −0.59 0.72 0.35 −0.27 −0.18 −0.99 工况2 −0.20 0.93 0.43 −0.01 0.22 −0.98 工况3 0.37 0.94 0.62 0.22 0.48 −0.94 工况6 0.39 0.94 0.61 0.23 0.50 −0.96 工况7 0.38 0.94 0.61 0.23 0.49 −0.96
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