自复位预制节段拼装中空夹层钢管混凝土桥墩地震易损性分析

梁晓; 姜浩然; 李芳芳

doi:10.11899/zzfy20240319

自复位预制节段拼装中空夹层钢管混凝土桥墩地震易损性分析

doi: 10.11899/zzfy20240319

梁晓^1,,
姜浩然²,
李芳芳^{1, 3, ,}

1.
天津城建大学, 天津市土木建筑结构防护与加固重点实验室, 天津 300384
2.
中石化南京工程有限公司, 南京 210049
3.
天津大学, 建筑工程学院, 天津 300350

基金项目: 国家自然科学基金（52238012、52278515、52308519）；天津市科技计划项目（23JCYBJC00750、23JCQNJC00910）

详细信息

作者简介:
梁晓，女，生于1987年。博士，副教授。主要从事工程结构抗震研究。E-mail：xliang@tcu.edu.cn

通讯作者:
李芳芳，女，生于1988年。博士。主要从事工程结构抗震研究。E-mail：fangfangbjut@126.com

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出版历程
- 收稿日期: 2024-06-13
- 网络出版日期: 2024-10-15
- 刊出日期: 2024-09-01

Seismic Fragility Analysis of Self-centering Precast Segmental Concrete-filled Double Skin Steel Tubular Piers

Liang Xiao^1
,,
Jiang Haoran²,
Li Fangfang^{1, 3
, ,}

1.
Tianjin Key Laboratory of Civil Structure Protection and Reinforcement, Tianjin Chengjian University, Tianjin 300384, China
2.
Sinopec Nanjing Engineering Co., Ltd., Nanjing 210049, China
3.
School of Civil Engineering, Tianjin University, Tianjin 300350, China

摘要

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。
- 桥梁抗震 /
- 预制节段拼装桥墩 /
- 中空夹层钢管混凝土 /
- 地震动 /
- 地震易损性
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.
- Seismic resistance of bridges /
- Precast segmental bridge piers /
- Concrete-filled double skin steel tubes /
- Ground motions /
- Seismic vulnerability

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引言

地震前兆观测主要关注观测数据随时间的相对变化，装置系数误差不影响观测数据的相对变化，但不正确的装置系数可能导致地电阻率观测结果出现系统误差（王兰炜等，2014），因此，正确的装置系数有利于不同区域观测数据的对比和地震前兆数据的研究。自2009年起，河北大柏舍台，甘肃天水台、武都台、平凉台，陕西合阳台实施了井下地电阻率垂直观测试验，井孔深100—225m，供电极距60—120m，测量极距20—60m（刘君等，2015；王兰炜等，2015）。上述台站地电阻率垂向观测通常为1个钻孔，供电电极和测量电极均布设于1个钻孔中，部分垂向观测的供电电极A接近地表，如天水台、武都台、合阳台的供电电极A埋深仅4—5m；部分垂向观测的供电电极A埋深为40m左右，如大柏舍台。垂向地电阻率观测中的装置系数与电流的空间分布及电极位置有关，现有垂向观测装置系数计算方法依据地下点、地表点电流源产生的电场计算得出，忽略了供电电极A的埋深。江宁台深井垂向地电阻率观测装置为在2口深井进行垂向观测的试验装置，与传统垂向地电阻率观测装置不同。本文根据地下点电流源产生的电场讨论装置系数计算方法，并比较计算方法对江宁台垂向地电阻率观测的影响。

1. 台址概况

江宁台地处南京市江宁区禄口街道水荆墅村，地形开阔平坦，周围无大中型工矿企业，测区位于南京-湖熟断裂南西盘和方山-小丹阳断裂西盘的楔形地块上，东距茅山断裂带30km，西北距长江36km。测区内现有垂向地电阻率观测装置为在2口深井进行垂向观测的试验装置，井距5.17m，供电电极A、测量电极M分别布设在深275m的2号井内200m和275m处，供电电极B、测量电极N分别布设在深400m的1号井内400m和325m处（图 1）。该垂向观测系统采用ZD8BI型地电仪，根据《地震台站建设规范（地电台站第1部分）》（DB/T.18.1—2006）中关于地电阻率台站的技术要求，对新建垂向观测装置的场地进行高密度电法、电测深等测试。高密度电法探测和电测深报告中NW—SE和NS测线结果表明，观测区域电测深曲线具有K形特征，电性结构等效为3层（樊晓春等，2018），场地电性层参数见表 1。

图 1 江宁台垂向观测电极布极图

Figure 1. The diagram of electrodes deployment

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表 1 江宁台场地电性层参数

Table 1. The underground electrical structure of Jiangning geoelectric station

NW—SE测线		NS测线
层厚/m	电阻率/Ω·m	层厚/m	电阻率/Ω·m
29.40	39.29	24.56	18.71
220.94	143.06	203.42	274.52
∞	60.39	∞	54.79

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2. 点电流源在非全空间产生的电场

点电流处于不完全全空间时，对点电流源位于地下和地表 2种情况进行讨论。地下点电流源产生的电场指点电流源的电流I在地下一定深度时流入地下介质中产生的电场，为不完全全空间。假设地下介质电性均匀，介质电阻率为ρ，电流I从地下A点流入（图 2），采用镜像法计算（刘昌谋等，1994；刘国兴，2005），见式（1）。地表点电流源产生的电场指地表点电流源电流I流入地下介质，从无限远处流出时在介质中产生的电场，为半无限空间。假设地下介质电性均匀，介质电阻率为ρ，电流I从地表A点流入地下，电流线的分布以A为中心向周围呈辐射状，该情况为图 2的特例（王兰炜等，2014），见式（2）。

图 2 地下点电源产生的电场示意图

Figure 2. The schematic diagram of the electric field generated by underground point power supply

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（1）地下点电流源产生的电场（不完全全空间）

$$ {V_{{\rm{MN}}}} = \frac{{\rho I}}{{4{\rm{ \mathsf{ π} }}}}\left({\frac{1}{{\overline {AM} }} + \frac{1}{{\overline {{A_1}M} }} - \frac{1}{{\overline {{A_1}N} }} - \frac{1}{{\overline {AN} }}} \right) $$

(1)

（2）地表点电流源产生的电场（半无限空间）

$$ {V_{{\rm{MN}}}} = \frac{{\rho I}}{{2{\rm{ \mathsf{ π} }}}}\left({\frac{1}{{\overline {AM} }} - \frac{1}{{\overline {AN} }}} \right) $$

(2)

3. 装置系数计算方法

装置系数是地电阻率观测中特有的参数，通常用K表示，与观测装置中电极分布情况有关，表征地电阻率是视电阻率（王兰炜等，2014）。当测区区域介质电阻率均匀分布时，地电阻率ρ_s与介质真实的电阻率ρ数值相同。

根据奥斯定理和镜像原理（钱家栋等，1985），假设测区为均匀介质，垂向观测中的装置系数计算方法如下：

（1）方法Ⅰ：传统垂向观测装置系数计算方法（王兰炜等，2014）

传统方法井下垂向观测装置忽略电极A的埋深，在点电源B与地面对称的位置设镜像点B₁，见图 3（a）。根据式（1）和式（2），则K为：

图 3 江宁台垂向观测示意

Figure 3. The schematic diagram of vertical geo-resistivity observation

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$$ K = \frac{{4{\rm{ \mathsf{ π} }}}}{{\left({\frac{2}{{\overline {AM} }} - \frac{2}{{\overline {AN} }}} \right) - \left({\frac{1}{{\overline {BM} }} + \frac{1}{{\overline {{B_1}M} }} - \frac{1}{{\overline {{B_1}N} }} - \frac{1}{{\overline {BN} }}} \right)}} $$

(3)

不考虑江宁台垂向观测电极A埋深时，因江宁台垂向观测AM=BN，AN=BM，则：

$$ K = \frac{{4{\rm{ \mathsf{ π} }}}}{{\frac{3}{{\overline {AM} }} - \frac{3}{{\overline {AN} }} - \frac{1}{{\overline {{B_1}M} }} + \frac{1}{{\overline {{B_1}N} }}}} $$

(4)

（2）方法Ⅱ：采用全空间方式的装置系数计算方法（钱家栋等，1985；王兰炜等，2014）

当电极埋深h远大于供电极长度AB时，为全空间，则K为地表观测装置系数的2倍，即：

$$ K = \frac{{4{\rm{ \mathsf{ π} }}}}{{\frac{1}{{\overline {AM} }} - \frac{1}{{\overline {AN} }} - \frac{1}{{\overline {BM} }} + \frac{1}{{\overline {BN} }}}} $$

(5)

（3）方法Ⅲ：采用不完全全空间方式的装置系数计算方法

江宁台垂向观测的电极A、M、N、B分别位于埋深200m、275m、325m、400m处，应按地下点电源产生的电场模型计算（不完全全空间），如图 3（b）所示。在点电源A、B与地面对称的位置设镜像点A₁、B₁，忽略1号井和2号井的水平距离l，根据式（1），则供电电流I（+I和-I）在M、N间产生的电位差为：

$$ {V_{MN}} = \frac{{\rho I}}{{4{\rm{ \mathsf{ π} }}}}\left[ {\left({\frac{1}{{\overline {AM} }} + \frac{1}{{\overline {{A_1}M} }} - \frac{1}{{\overline {{A_1}N} }} - \frac{1}{{\overline {AN} }}} \right) - \left({\frac{1}{{\overline {BM} }} + \frac{1}{{\overline {{B_1}M} }} - \frac{1}{{\overline {{B_1}N} }} - \frac{1}{{\overline {BN} }}} \right)} \right] $$

(6)

则K为：

$$ K = \frac{{4{\rm{ \mathsf{ π} }}}}{{\left({\frac{1}{{\overline {AM} }} + \frac{1}{{\overline {{A_1}M} }} - \frac{1}{{\overline {AN} }} - \frac{1}{{\overline {{A_1}N} }}} \right) - \left({\frac{1}{{\overline {BM} }} + \frac{1}{{\overline {{B_1}M} }} - \frac{1}{{\overline {BN} }} - \frac{1}{{\overline {{B_1}N} }}} \right)}} $$

(7)

因江宁台垂向观测AM=BN，AN=BM，则：

$$ K = \frac{{4{\rm{ \mathsf{ π} }}}}{{\frac{2}{{\overline {AM} }} - \frac{2}{{\overline {AN} }} + \frac{1}{{\overline {{A_1}M} }} - \frac{1}{{\overline {{A_1}N} }} - \frac{1}{{\overline {{B_1}M} }} + \frac{1}{{\overline {{B_1}N} }}}} $$

(8)

（4）方法Ⅳ：采用不完全全空间方式（考虑井距l）的装置系数计算方法

按照地下点电源产生电场的模型计算（不完全全空间），在点电源A、B与地面对称的位置设镜像点A₁、B₁，h₁、h₂、h₃表示供电电极A、B、M的电极埋深，井距l表示2口井孔水平距离（图 3（c）），则：

$$ \overline {AM} = {h_3} - {h_1} $$

(9)

$$ \overline {AN} = \sqrt {{l^2} + {{({h_2} - {h_3})}^2}} $$

(10)

$$ \overline {{A_1}M} = {h_1} + {h_3} $$

(11)

$$ \overline {{A_1}N} = \sqrt {{l^2} + {{({h_2} + 2{h_1} - {h_3})}^2}} $$

(12)

$$ \overline {{B_1}M} = \sqrt {{l^2} + {{({h_2} + {h_3})}^2}} $$

(13)

$$ \overline {{B_1}N} = 2{h_2} - {h_3} + {h_1} $$

(14)

将式（9）至式（14）代入式（8），则K变为：

$$ K = \frac{{4\pi }}{{\frac{2}{{{h_3} - {h_1}}} - \frac{2}{{\sqrt {{l^2} + {{({h_2} - {h_3})}^2}} }} + \frac{1}{{{h_1} + {h_3}}} - \frac{1}{{\sqrt {{l^2} + {{({h_2} + 2{h_1} - {h_3})}^2}} }} - \frac{1}{{\sqrt {{l^2} + {{({h_2} + {h_3})}^2}} }} + \frac{1}{{2{h_2} - {h_3} + {h_1}}}}} $$

(15)

4. 江宁台垂向地电阻率观测装置系数计算

采用方法Ⅰ—Ⅳ分别计算江宁台垂向地电阻率观测的装置系数K，结果见表 2。考虑江宁台垂向地电阻率观测的电极布设不同于传统垂向观测装置，所有电极埋深均在200m以上，本文认为应以方法Ⅳ为参考值，采用式（16）计算不同装置系数计算方法的相对误差。方法Ⅰ、Ⅱ、Ⅲ相对误差分别为-32.01%、1.37%、0.43%，可知方法Ⅰ不适用于江宁台垂向地电阻率观测，该计算方法通常仅适用于供电电极A埋深小于5m的垂向观测，如天水台、合阳台。方法Ⅱ相对误差较小，江宁台垂向观测于2018年4月25日至2018年11月22日曾采用该方法。考虑仅当电极埋深远大于供电极距时称为全空间，而江宁台垂向装置最小电极埋深仅与供电极距相当，因此，方法Ⅱ同样不适用于江宁台垂向观测。除江宁台外，大部分台站观测装置电极埋深明显小于供电极距，均不宜采用方法Ⅱ。方法Ⅲ相对误差最小，江宁台垂向地电阻率观测于2018年11月23日至2019年10月30日曾采用该方法，2018年11月出现的台阶是由调整装置系数导致的（图 4）。由于江宁台垂向地电阻率观测为多孔观测，须考虑井距才能准确计算其装置系数，因而最终采用方法Ⅳ进行计算。

$$ \sigma = \frac{{k_{方法}} - {k_{方法Ⅳ}}}{{{k_{方法Ⅳ}}}} $$

(16)

表 2 江宁台垂向观测的装置系数

Table 2. The configuration coefficient of vertical geo-resistivity observation in Jiangning earthquake station

计算方法	AM/m	AN/m	B₁M/m	B₁N/m	A₁M/m	A₁N/m	装置系数K
Ⅰ	75.000	125.000	675.000	725.000	—	—	790.000
Ⅱ	75.000	125.000	—	—	—	—	1178.000
Ⅲ	75.000	125.000	675.000	725.000	475.000	525.000	1167.000
Ⅳ	75.000	125.374	675.020	725.000	475.000	525.292	1162.000

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图 4 江宁台垂向观测整点值曲线

Figure 4. The hourly observational value curves of vertical geo-resistivity observation at Jiangning Seismic Station

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5. 结论

本文以江宁台垂向地电阻率观测为例，提出2种以不完全全空间方式计算的新方法，并与现有垂向观测装置计算方法进行比较。研究结果表明，方法Ⅳ最符合江宁台垂向地电阻率观测装置。考虑方法Ⅳ中部分参数存在小数部分，认为保留小数点后三位能满足装置系数精度要求。方法Ⅳ除适用于2口井垂向观测装置外，同样适用于忽略井距时供电电极A埋深超过5m的单口井垂向观测装置。

致谢: 衷心感谢中国地震局地壳应力研究所王兰炜研究员对本文提出的建议和意见。

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

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图 2 试件截面尺寸（单位：毫米）

Figure 2. Cross-sectional dimension of specimen （Unit: mm）

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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

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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）

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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	R_rup/km	T_90%/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	R_rup /km	T_90%/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	R_rup/km	T_90%/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ε_p	θ_dr	θ_R
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(θ_dr) = 1.1468 ln(PGA)−3.8139	ln(θ_dr) = 1.21112 ln(PGA) −2.3137	ln(θ_dr) = 0.8328 ln(PGA) −2.8025
墩顶残余位移角	ln(θ_R) = 1.7973 ln(PGA) −4.8048	ln(θ_R) = 1.8553 ln(PGA) −4.9436	ln(θ_R) = 1.4748 ln(PGA) −5.9554

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