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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工程地震与抗震防灾的研究最早始于十九世纪末，集中于强地震震害现场调查中对房屋震害程度、震害原因、预防方法、设计标准等的研究和探讨。工程地震学的主要目的是基于工程抗震设计的需要，研究地震引起的强地面运动的规律与特性。目前的研究热点包括：强地震动场模拟、近断层强地震动特征、地震预警与报警等。我国的抗震防灾事业历经六十多年，取得了世人瞩目的成就。其中，地震学、地质学及工程结构的密切结合与深度融合更是研究的重点，而这也是胡聿贤先生在其学术生涯中长期关注并躬身实践的。胡聿贤先生是世界著名的地震工程学家，也是我国工程地震研究的创始人，在国内外学术界和工程界都享有很高的威望，具有广泛的影响力。胡聿贤先生的研究领域涉及地震现场震害考察、地震动工程特性、地震区划、结构地震反应、城市震害预测和地震灾害风险分析与防震减灾对策、抗震设计规范、核电站抗震设计等多方面。他学术造诣精深，治学严谨，学术思想开阔，勇于探索未知领域，对地震工程和工程地震理论及其应用研究作出了重要贡献。
为庆祝胡聿贤先生从事抗震防灾研究七十周年暨百岁寿辰， 《 地震学报 》 特组织出版 《 工程地震与抗震防灾研究 》 专辑。该专辑文章是从促进我国防震减灾事业发展的角度，对工程地震学及地震工程学已有研究进行的思考和综述，还有部分相关领域的最新研究成果，共15篇。专辑内容主要包括：地震区划新理论与方法、活动断层危险性评估、地震动衰减规律、近断层强地震动特征、地震动的场地效应、强地震动的数值模拟、强地震动多点输入及结构反应、城市地震灾害风险分析以及地震灾情信息获取技术等。这些论文传承了胡聿贤先生将地质学、地震学和工程学有机结合的学术思想，从中可领略胡聿贤先生半个多世纪的科学活动所涉及的广阔研究领域。
欣逢胡聿贤先生百岁寿辰之际，谨将此专辑献给在地震工程和工程地震领域辛勤工作的科技工作者和对该领域研究感兴趣的各界朋友们，期待更多同仁加入。
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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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