Seismic Fragility Analysis of Self-centering Precast Segmental Concrete-filled Double Skin Steel Tubular Piers
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摘要: 为评估自复位预制节段拼装中空夹层钢管混凝土（Concrete-filled Double Skin Steel Tubular, CFDST）桥墩在地震动作用下的易损性，本研究基于现有的低周反复荷载试验数据，采用有限元分析方法，选用墩顶水平位移角和残余位移角2个指标作为评估标准进行定量分析。针对3种不同类型地震动（远场、近场无脉冲和近场有脉冲），分别建立了关于水平位移角和残余位移角2个指标的易损性曲线，并分析了不同损伤指标和地震动类型对其地震易损性的影响。研究结果表明，在自复位预制节段拼装CFDST桥墩地震易损性分析中，仅采用水平位移角作为损伤指标是安全可靠的；相比远场地震动和近场无脉冲型地震动而言，近场脉冲型地震动对自复位预制节段拼装CFDST桥墩的变形和自复位有显著影响。Abstract: This paper evaluates the seismic vulnerability of self-centering precast segmental concrete-filled double skin steel tubular (CFDST) piers by quantitatively assessing their seismic performance under three types of ground motions: far-field, near-field without pulse, and near-field pulse-like motions, based on existing quasi-static tests. Using finite element analysis, vulnerability curves for the self-centering precast segmental CFDST piers are established based on two damage indices: the horizontal displacement angle and the residual displacement angle. The study analyzes the effects of different damage indices and ground motion types on the vulnerability curves of the self-centering precast segmental CFDST piers. The results indicate that utilizing only the horizontal displacement angle as the damage index is both safe and reliable for the seismic vulnerability analysis of these piers. Additionally, it was found that near-field pulse-like ground motions significantly affect the deformation and self-centering behavior of the self-centering precast segmental CFDST piers compared to far-field and near-field non-pulse-like ground motions.
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引言
岩石圈磁场是地磁场的重要组成部分，来源于岩石圈居里等温面以上的岩石磁性，其变化受地质结构、构造环境、构造活动、温度与应力状态等多种因素影响。诸多学者已对岩石圈磁场进行相关研究工作，对于空间尺度而言，涵盖全球范围（徐文耀，2003；徐文耀等，2008）、中国大陆地区（杜劲松等，2017；冯丽丽等，2015；王粲等，2017；Ou等，2013）、局部地区（文丽敏等，2017；韶丹等，2015；徐晓雅等，2017；宋成科等，2017；Hemant等，2009）、特定构造带（张忠龙等，2017），数据来源主要为地磁场模型、卫星磁测、航空磁测、地面矢量磁测等。
相对于卫星及航空磁测，地面测量更接近岩石圈磁场物理源，且具备更高的测量精度。在中国地震局经费支持下，流动地磁工作团队已在“冀晋蒙”“京津冀”局部地区开展了流动地磁总强度加密监测工作，布设了规模较大的高精度、高密度测点网络。监测区地处“首都圈”地震重点监视区，地质构造复杂，历史地震多发。观测作业以地磁场总强度F为单一测量要素，其测量精度高于卫星、航空磁测，测点密度优于地面矢量磁测，为相关研究工作提供了高质量数据来源。本文应用相关观测资料，计算观测区域高分辨率F要素岩石圈磁场数值模型（以ΔF表示），研究ΔF空间分布、地震地质特征，并重点针对历史地震震中在ΔF中的位置特征进行研究，以期为该地区震中预测工作提供新技术思路和资料依据。
1. 数据资料与数据处理
1.1 数据资料
观测区内共有180个地磁总强度测点，平均点间距约28km，由“晋冀蒙”及“京津冀”2个地磁总强度加密测网合并而成，观测作业执行《流动地磁测量基本技术要求》1及其规范性附录。为合理控制测区边界处模型产出结果，笔者在测区周边选取40个流动地磁矢量测点，作为模型边界约束点，并将其中4个测点用作补充测点，令研究区最终测点总数达184个（图 1）。
1 中国地震局监测预报司，中震测函[2015]39号：关于印发《流动地磁测量基本技术要求（试行）》的通知
图 1 研究区野外测点示意图Figure 1. Schematic diagram of field survey points in the study area（绿色圆点为地磁总强度加密区测点，红色圆点为地磁矢量约束点，黑色虚线框内部为研究区范围）1.2 数据处理
本文采用最新一期观测数据，通过日变通化改正、主磁场长期变改正、主磁场剥离等主要技术处理，获取研究区ΔF（陈斌等，2017），过程如下：
（1）日变通化改正
为消除流动地磁观测数据中包含的地磁场日变化等外源场成分，依托测区邻近地磁台站连续观测分钟值数据，采用单台参照法，对野外观测数据进行日变通化处理，获取监测区日变通化改正数据集。
（2）长期变改正
采用1995年1月1日以来的全国地磁台网观测数据，建立中国及周边地区地磁场长期变化3阶NOC非线性模型（顾左文等，2009），对日变通化改正数据集进行主磁场长期变改正，获取监测区长期变改正数据集。
（3）主磁场剥离
以IGRF12（2015.0年代）为研究区主磁场参考模型，并在监测区长期变改正数据结果中进行剔除，即获得各测点ΔF初始值。
（4）低通滤波
地面磁测结果必然包含杂乱的浅表岩层磁性影响成分（图 2）。为抑制和消除该数据成分，保证研究成果的合理性，笔者采用移动平均法对网格化后的ΔF初始值进行低通滤波处理，滤波器为5×5节点，对应的实际空间范围为0.5°×0.5°，滤波结果即为本研究最终采用的ΔF，本文研究模型描述了研究区2015.0年代ΔF空间分布形态（图 3）。本文ΔF等值线图中，红、蓝色实线分别代表正、负值区，黑色加粗实线为“0”值线，等值线间隔统一为25nT。
2. ΔF空间分布特征
2.1 总体特征
研究区ΔF呈正、负异常区零散相间的分布形态，负异常区面积略大于正异常区。ΔF空间结构复杂，局部异常特征表现强烈，强磁异常区形状多表现为条带状或团块状。研究区范围内共有184个测点，ΔF数值范围为-326.0—180.1nT，平均值为-40.0nT。其中负值测点128个，占69.6%，ΔF平均值为-83.1nT；正值测点56个，占30.4%，ΔF平均值为58.6nT。全部测点ΔF平均幅值（为表述方便，本文借用物理学名词“幅值”表示ΔF绝对值）为75.6nT，约占地磁场能量成分的0.14%（图 4）。
2.2 分区特征
根据ΔF形态特征，可在京南地区划出1条NE走向界线，将研究区分为以下2个分区（图 4）：
（1）中西部为ΔF能量集中区，其核心区由2个NE走向的高值负异常区及其间的高值正异常区组成，近似平行四边形。磁异常强度总体较高，且随空间展布快速变化，磁场高梯级带广泛分布。
（2）中东部为弱磁异常区，表现为幅值较低的背景性负异常区，在其边缘零散分布小片正磁异常区，最东端为局部强磁异常区。
ΔF分区与地形、地层分布形态具有明显相关性，表现为三者具备相似的分区特征，且分区界线位置基本吻合：
（1）分区界线与太行山脉东缘基本重合，其东侧为平原地区，磁异常强度总体较低；西侧为山区及高原地区，磁异常强度整体较高且形态复杂。山区强磁异常区呈条带状，走向基本与山脉吻合（图 5）。该现象的形成应与平原地区深厚冲积层对ΔF短波成分的屏蔽效应及山地浅表岩层磁性的影响直接相关。
（2）以分区界线为界，东部地区以第四系地层为主，面积较大、形状规整，与ΔF弱磁异常区基本重合；西部地区地层多样、分布杂乱，均为较古老的地层，火山岩、变质岩岩体及碎屑分布较广泛，与ΔF强磁异常区对应（图 6）。该特征显示了第四系地层地表磁性与其它地层明显不同。
3. 研究区ΔF地震地质特征
3.1 ΔF与二级地块构造
研究区位于燕山、华北平原及鄂尔多斯3个二级地块交汇部位，地块间的结合带贯穿其间。各地块在ΔF中显示出不同的特征：华北平原地块磁异常强度较弱，其西北边界线与ΔF中NE走向高梯级带及“0”值线具有较好的吻合度，东北边界线穿过ΔF弱磁异常区；鄂尔多斯地块东北局部为强磁异常区，边界线局部与ΔF高梯级带有一定程度的对应；燕山地块南缘贯穿ΔF正、负异常相间分布区（图 7）。地块结合带部位为强磁异常区，形态复杂。
3.2 ΔF与断裂构造
研究区内断裂构造广泛发育，分布密集。中、西部断裂为晚更新世—全新世（距今10—12万年）以来的活动断裂，其走向以NE向为主，与该地区强磁异常条带的空间位置大体对应，走向基本一致；研究区中、东部断裂属平原区隐伏断裂，对应ΔF弱磁异常区；研究区东端局部强磁异常区与对应断裂带的走向基本一致，同为NEE向（图 8）。
3.3 历史地震在ΔF中的位置特征
研究区涵盖张渤地震带大部分及华北平原地震带北端，为华北地区重要的地震活动区，历史上共发生Ms5.0以上地震85次，其中包括Ms6.0以上地震20次、Ms7.0以上地震4次（图 9）。为全面研究历史地震震中在ΔF中的分布规律与位置特征，笔者按震级分类，对震中位置处ΔF值、ΔF特殊位置处的震中数量进行分类统计，结果见表 1。
表 1 研究区历史地震震中部位ΔF数值统计结果Table 1. Basic statistical results of ΔF value at the epicenter of historical earthquakes in the study area项目 震级 5级以上 6级以上 7级以上 地震总数/个 85 20 4 震中位置处ΔF均值/nT -70.6 -75.6 -60.2 震中位置处ΔF平均幅值/nT 82.9 91.0 60.2 位于ΔF负值区的震中个数与占比/（个，%） 70，82.4% 17，85.0% 4，100.0% ΔF低幅值（小于平均幅值）区震中个数与占比/（个，%） 51，60.0% 11，55.0% 4，100.0% ΔF高幅值（大于2倍平均幅值）区震中个数与占比/（个，%） 10，11.8% 2，10.0% 0，0.0% ΔF“0”值线附近（两侧各15km范围内）震中个数与占比/（个，%） 50，58.8% 8，40.0% 2，50.0% ΔF高梯级带处震中个数与占比/（个，%） 70，82.4% 16，80.0% 3，75.0% 根据统计结果，对历史地震震中在ΔF中的位置特征进行以下分析：
（1）震中位置处ΔF平均值明显低于研究区总体平均值（-40nT）；
（2）ΔF负值区内地震个数远多于正值区，且随着震级的增大，其比例增加；
（3）低幅值区内震中个数明显多于高幅值区。ΔF超高幅值区（大于2倍平均幅值）内震中数量占比较低，且随着震级的增大，其占比进一步减小；
（4）在ΔF“0”值线附近的狭长地带中，密集发生了大量历史地震；
（5）绝大多数地震发生于ΔF高梯级带部位；
（6）强磁异常区内，地震震中表现出的位置特征明显区别于弱磁异常区。前者以ΔF负值区、“0”值线、高梯级带为主；后者主要表现为ΔF负值区、低幅值区。相对而言，前者的震中位置特殊性显著程度远大于后者。
4. 总结与讨论
通过本文研究主要得到以下结论：
（1）研究区ΔF空间结构复杂，局部异常特征表现强烈。总体具有分区特征，且与地形、地层的关系密切。
（2）磁场高梯级带走向与断裂构造体系总体一致；各二级地块ΔF特征明显不同，地块边界线局部与ΔF高梯级带吻合；地块间结合带部位为强磁异常区，形态复杂。
（3）5级以上历史地震与ΔF负值区、低幅值区、“0”值线、高梯级带等特殊位置关系密切。强磁异常区内的震中位置统计规律性明显强于弱磁异常区。该特征可为本地区未来震中位置预测工作提供新的参考依据。
在已有研究的基础上，计算研究区岩石圈磁场数值模型时，应用了较大规模的高精度、高密度地面磁测资料，因此模型计算与研究结论具备更好的数据基础。进而对该模型进行了较细致的量化研究，并从“为地震预测服务”角度出发，分层次、多角度对历史地震在ΔF中的分布规律进行统计分析，并进行有针对性的研究工作。
在数据处理过程中，笔者发现地面磁测结果中包含地表浅层岩层磁性影响成分，并对ΔF初始值进行低通滤波处理。为抑制和消除其影响，相关学者在进行类似研究工作时，也应采用适当的数据处理方法对其进行剔除处理，以保证研究结果的合理性。
受研究区域范围及笔者研究水平的限制，研究结论可能具有一定片面性，更深入、全面的研究工作有待进一步开展。
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图 1 自复位预制节段拼装CFDST桥墩构造示意图
Figure 1. Diagram of self-centering precast segmental assembled CFDST pier
图 3 自复位预制节段拼装CFDST桥墩数值模型
Figure 3. Numerical model of self-centering precast segmental assembled CFDST pier
图 4 滞回曲线（Li等，2023b）
Figure 4. Hysteretic curve of self-centering precast segmental assembled CFDST piers （Li et al., 2023b）
图 5 基于最大水平位移角的地震概率需求模型
Figure 5. Earthquake probability demand model base on maximum horizontal displacement angle
图 6 基于残余位移角的地震概率需求模型
Figure 6. Earthquake probability demand model base on residual displacement angle
图 7 基于最大墩顶水平位移角指标的易损性曲线
Figure 7. Vulnerability curve based on the maximum horizontal displacement angle of pier top
图 8 基于墩顶残余位移角指标的易损性曲线
Figure 8. Vulnerability curve based on the residual displacement angle of pier top
图 9 近场无脉冲地震动作用下基于不同损伤指标的易损性曲线
Figure 9. Vulnerability curves based on different damage indexes under near-field non-pulse-like ground motion
图 10 近场脉冲地震动作用下基于不同损伤指标的易损性曲线
Figure 10. Vulnerability curves based on different damage indexes under near-field pulse-like ground motion
图 11 远场地震动作用下基于不同损伤指标的易损性曲线
Figure 11. Vulnerability curves based on different damage indexes under far-field ground motion
图 12 基于最大水平位移角的自复位预制节段拼装CFDST桥墩地震易损性曲线
Figure 12. Self-centering precast segmental CFDST pier vulnerability curves based on the maximum horizontal displacement angle under earthquake ground motions
图 13 基于残余位移角的自复位预制节段拼装CFDST桥墩地震易损性曲线
Figure 13. Self-centering precast segmental CFDST pier vulnerability curves based on the residual displacement angle under earthquake ground motions
表 1 关键性能指标
Table 1. Critical performance indexes
屈服位移/mm 屈服荷载/kN 峰值荷载/kN 弹性刚度/(kN·mm−1) 峰值残余位移/mm 试验 17.8 208 319 11.7 30.0 模拟 18.0 216 308 12.0 31.8 相对误差 1.1% 3.8% 3.4% 2.6% 6.0% 
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表 2 远场地震动记录
Table 2. Far-field ground motion records
编号 地震名称 年份 站台名称 震级/级 Rrup/km T90%/s 1 "Northwest Calif-01" 1938 "Ferndale City Hall" 5.5 53.58 11.6 2 "Northwest Calif-02" 1941 "Ferndale City Hall" 6.6 91.22 22.2 3 "Northern Calif-01" 1941 "Ferndale City Hall" 6.4 44.68 15.5 4 "Borrego" 1942 "El Centro Array #9" 6.5 56.88 37.2 5 "Northwest Calif-03" 1951 "Ferndale City Hall" 5.8 53.77 15.4 6 "Kern County" 1952 "LA - Hollywood Stor FF" 7.36 117.75 33.5 7 "Kern County" 1952 "Pasadena - CIT Athenaeum" 7.36 125.59 29.5 8 "Kern County" 1952 "Santa Barbara Courthouse" 7.36 82.19 33.6 9 "Kern County" 1952 "Taft Lincoln School" 7.36 38.89 30.3 10 "Northern Calif-02" 1952 "Ferndale City Hall" 5.2 43.28 18.4 11 "Northern Calif-03" 1954 "Ferndale City Hall" 6.5 27.02 19.4 12 "El Alamo" 1956 "El Centro Array #9" 6.8 121.7 40.9 13 "Northern Calif-04" 1960 "Ferndale City Hall" 5.7 57.21 28.4 14 "Northern Calif-05" 1967 "Ferndale City Hall" 5.6 28.73 22.1 15 "Borrego Mtn" 1968 "El Centro Array #9" 6.63 45.66 49.3 16 "Borrego Mtn" 1968 "San Onofre - So Cal Edison" 6.63 129.11 28 17 "San Fernando" 1971 " 2516 Via Tejon PV"6.61 55.2 54.2 18 "San Fernando" 1971 "Carbon Canyon Dam" 6.61 61.79 18.9 19 "San Fernando" 1971 "Castaic-Old Ridge Route" 6.61 22.63 16.8 20 "San Fernando" 1971 "Fairmont Dam" 6.61 30.19 14.4
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表 3 近场无脉冲型地震动
Table 3. Near-field non-pulse-like ground motion
编号 地震名称 年份 站台名称 震级/级 Rrup /km T90%/s 1 "Imperial Valley-02" 1935 "El Centro Array #9" 6.95 6.09 24.2 2 "Hollister-02" 1961 "Hollister City Hall" 5.5 18.08 16.5 3 "Parkfield" 1966 "Cholame - Shandon Array #12" 6.19 17.64 29 4 "Parkfield" 1966 "Cholame - Shandon Array #5" 6.19 9.58 7.5 5 "Parkfield" 1966 "Cholame - Shandon Array #8" 6.19 12.9 13.1 6 "Managua_Nicaragua-01" 1972 "Managua_ ESSO" 5.24 4.06 10.6 7 "Hollister-03" 1974 "Hollister City Hall" 5.17 9.39 10.9 8 "Coyote Lake" 1979 "Coyote Lake Dam - Southwest Abutment" 5.74 6.13 8.5 9 "Imperial Valley-06" 1979 "Calexico Fire Station" 6.53 10.45 14.8 10 "Imperial Valley-06" 1979 "Cerro Prieto" 6.53 15.19 36.4 11 "Imperial Valley-06" 1979 "Chihuahua" 6.53 7.29 24 12 "Imperial Valley-06" 1979 "Parachute Test Site" 6.53 12.69 18.6 13 "Imperial Valley-07" 1979 "El Centro Array #5" 5.01 11.23 7 14 "Imperial Valley-07" 1979 "El Centro Array #6" 5.01 10.37 6.5 15 "Mammoth Lakes-02" 1980 "Mammoth Lakes H. S." 5.69 9.12 3.9 16 "Mammoth Lakes-03" 1980 "Convict Creek" 5.91 12.43 6.3 17 "Mammoth Lakes-03" 1980 "Long Valley Dam （Downst）" 5.91 18.13 12.4 18 "Mammoth Lakes-03" 1980 "Long Valley Dam （Upr L Abut）" 5.91 18.13 8.4 19 "Mammoth Lakes-06 1980 "Fish & Game （FIS）" 5.94 12.93 5.1 20 "Westmorland" 1981 "Salton Sea Wildlife Refuge" 5.9 7.83 9.1
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表 4 近场脉冲型地震动
Table 4. Near-field pulse-like ground motion records
编号 地震名称 年份 站台名称 震级/级 Rrup/km T90%/s 1 "Coyote Lake" 1979 "Gilroy Array #2" 5.74 9.02 7.5 2 "Coyote Lake" 1979 "Gilroy Array #3" 5.74 7.42 8.7 3 "Coyote Lake" 1979 "Gilroy Array #4" 5.74 5.7 11 4 "Imperial Valley-06" 1979 "Agrarias" 6.53 0.65 13.3 5 "Imperial Valley-06" 1979 "Brawley Airport" 6.53 10.42 14.9 6 "Imperial Valley-06" 1979 "EC County Center FF" 6.53 7.31 13.2 7 "Imperial Valley-06" 1979 "El Centro Array #10" 6.53 8.6 12.8 8 "Imperial Valley-06" 1979 "El Centro Array #3" 6.53 12.85 14.1 9 "Imperial Valley-06" 1979 "Holtville Post Office" 6.53 7.5 12.8 10 "Irpinia_ Italy-01" 1980 "Bagnoli Irpinio" 6.9 8.18 19.6 11 "Irpinia_ Italy-01" 1980 "Sturno （STN）" 6.9 10.84 15.2 12 "Westmorland" 1981 "Parachute Test Site" 5.9 16.66 18.7 13 "Morgan Hill" 1984 "Gilroy Array #6" 6.19 9.87 7.3 14 "Kalamata_ Greece-02" 1986 "Kalamata （bsmt） （2 nd trigger）" 5.4 5.6 2.9 15 "Superstition Hills-02" 1987 "Kornbloom Road （temp）" 6.54 18.48 13.9 16 "Loma Prieta" 1989 "Gilroy - Historic Bldg." 6.93 10.97 13.1 17 "Loma Prieta" 1989 "Saratoga - W Valley Coll." 6.93 9.31 11.1 18 "Kocaeli_ Turkey" 1999 "Arcelik" 7.51 13.49 11.1 19 "Kocaeli_ Turkey" 1999 "Gebze" 7.51 10.92 8.2 20 "Coyote Lake" 1979 "Gilroy Array #2" 5.74 9.02 7.5
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表 5 自复位预制节段拼装CFDST桥墩抗震性能水准指标取值范围
Table 5. Range of performance level indexes of self-centering precast segmental CFDST pier
性能等级 性能水准 耗能钢筋拉应变ε 钢绞线拉应变εp θdr θR Ⅰ 基本完好 $ < {\varepsilon _{\text{y}}}$ / <1.00 % / Ⅱ 轻微损伤 $ < {\varepsilon _{{\text{sh}}}} = 0.015$ / <2.25% <0.50% Ⅲ 可恢复损伤/生命安全 $ < 0.6{\varepsilon _{{\text{su}}}} = 0.06$ / <5.50% <1.00% Ⅳ 严重损伤/防止倒塌 $ < {\varepsilon _{{\text{su}}}} = 0.10$ $ < {\varepsilon _{{\text{py}}}} = 0.0086$ <8.50% <1.75% Ⅴ 局部失效/倒塌 $ > {\varepsilon _{{\text{su}}}} = 0.10$ $ > {\varepsilon _{{\text{py}}}} = 0.0086$ >8.50% >1.75%
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表 6 桥墩概率地震需求模型
Table 6. Probabilistic earthquake demand model of pier
性能指标 近场无脉冲地震 近场脉冲地震动 远场地震动 墩顶最大水平位移角 ln(θdr) = 1.1468 ln(PGA)−3.8139 ln(θdr) = 1.21112 ln(PGA) −2.3137 ln(θdr) = 0.8328 ln(PGA) −2.8025 墩顶残余位移角 ln(θR) = 1.7973 ln(PGA) −4.8048 ln(θR) = 1.8553 ln(PGA) −4.9436 ln(θR) = 1.4748 ln(PGA) −5.9554
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