深水桥墩地震响应研究现状与展望

赵秋红; 李晨曦; 董硕

doi:10.19818/j.cnki.1671-1637.2019.02.001

深水桥墩地震响应研究现状与展望

doi: 10.19818/j.cnki.1671-1637.2019.02.001

赵秋红^{1, 2,},
李晨曦¹,
董硕¹

1.
天津大学建筑工程学院, 天津 300350
2.
天津大学滨海土木工程结构与安全教育部重点实验室, 天津 300350

基金项目:

国家自然科学基金项目 51678406

详细信息

作者简介:
赵秋红(1975-), 女, 湖北宜昌人, 天津大学教授, 工学博士, 从事钢、组合结构高层建筑与桥梁抗震研究

中图分类号: U443.22
计量
- 文章访问数: 923
- HTML全文浏览量: 151
- PDF下载量: 437
- 被引次数: 0
出版历程
- 收稿日期: 2018-09-13
- 刊出日期: 2019-04-25

Research status and prospect of seismic response of deep-water bridge pier

1.
School of Civil Engineering, Tianjin University, Tianjin 300350, China
2.
Key Laboratory of Coast Civil Structure Safety of Ministry of Education, Tianjin University, Tianjin 300350, China

More Information

Author Bio:
ZHAO Qiu-hong (1975-), female, professor, PhD, qzhao@tju.edu.cn

摘要

摘要: 分析了地震激励下水-深水桥墩动力相互作用, 总结了动水压力作用机理、地震动水压力的计算方法和水-结构动力相互作用分析方法, 研究了深水桥墩地震响应特征和影响因素以及水下振动台试验进展, 并对比了各国规范中动水压力计算方法。研究结果表明: 动水压力降低桥墩自振频率, 增大桥墩地震响应, 其影响在桥梁的抗震设计中不可忽略; 现有研究采用的桥墩形式较为简化和单一, 建议开展更多以桥墩体系、桥梁体系为对象的深水桥梁地震响应研究; 对于地震作用下动水压力计算, 目前各国规范多基于Morison方程, 但对其适用范围尚不明确, 应深入研究Morison方程的适用范围、修正方法与准确便捷的地震动水压力计算方法; 目前水下振动台试验大多集中在动水压力对桥梁下部墩桩地震响应的影响上, 响应大多在弹性范围内, 应进一步研究在大震作用下深水桥墩的非线性响应与破坏模式; 目前针对深水桥墩在地震和波浪联合作用下的动力响应研究较少, 应深入研究在地震、波浪、海流联合作用下深水桥墩与水的相互作用机理; 目前缺乏对全桥结构的地震响应研究, 应开展深水桥梁全桥分析与多子台水下振动台试验。
- 桥梁工程 /
- 深水桥墩 /
- 水-结构相互作用 /
- 地震响应 /
- 动水压力计算方法 /
- 水下振动台试验
Abstract: The dynamic interaction between deep water bridge piers and surrounding water under seismic excitation was analyzed. The mechanisms and calculation methods of hydrodynamic pressure and the analysis methods of water-structure dynamic interaction were summarized. The seismic response characteristics and the influence factors of deep-water bridge piers and the research progress of underwater shaking table test were studied. The calculation methods of hydrodynamic pressure in national standards were also discussed. Research result indicates that the influence of hydrodynamic pressure on the seismic response of bridge pier cannot be neglected in the seismic design of bridges, because it reduces the natural frequency of bridge pier and increases the seismic response of bridge pier. The forms of the bridge piers adopted in current research are simplified and limited. The seismic response of deep-water bridge based on the bridge pier system and bridge system should be studied. In terms of calculation of hydrodynamic pressure under seismicity, most of the current national standards are based on the Morison equation, but the application range is still unclear. It is necessary to carry out the in-depth study on application range of Morison equation and revised methods and to propose an accurate and convenient method for calculating hydrodynamic pressure under seismicity. Currently, the underwater shaking table tests mostly focus on the influence of hydrodynamic pressure on the seismic responses of bridge piers and piles, and the responses are mostly within the elastic range. The nonlinear responses and failure modes of deep-water bridge piers under severe seismicity should be studied. There are few studies on the dynamic responses of deep-water bridge piers under combined seismicity and wave action, and the interaction mechanisms between bridge piers and water under combined action of seismicity, wave and current should be researched out in depth. There is a lack of research on the seismic response of whole bridge structure. It is necessary to carry out whole deep-water bridges analysis and multi table underwater shaking table test.
- bridge engineering /
- deep-water bridge pier /
- water-structure interaction /
- seismic response /
- calculation method of hydrodynamic pressure /
- underwater shaking table test

HTML全文

图 1 矩形截面桥墩动水压力分布规律

Figure 1. Hydrodynamic pressure distribution rule of rectangular bridge pier

下载: 全尺寸图片幻灯片

图 2 不同水深动水压力对桥墩地震响应的影响

Figure 2. Influence of hydrodynamic pressures at different water depths on seismic responses of bridge pier

下载: 全尺寸图片幻灯片

表 1 动水压力作用机理的适用范围

Table 1. Application range of hydrodynamic pressure action mechanism

d/l	h/d	黏性效应	惯性力效应	绕射效应
≤0.2	≤1.0	很小	显著	很小
≤0.2	> 1.0	显著	显著	很小
> 0.2	≤1.0	很小	显著	显著
> 0.2	> 1.0	波浪破碎

下载: 导出CSV

表 2 水-结构相互作用的3类问题

Table 2. Three problems of water-structure interaction

问题类别	假定	作用机理	适用范围
横向小尺寸	结构的存在或运动不影响水的运动状态	主要考虑流体黏性效应引起的拖曳力与惯性力效应引起的惯性力	小尺寸墩柱地震动水压力与波浪力计算
辐射波浪	结构运动前水体保持静止	在某种激励下结构在水中运动, 在结构周围产生向外辐射的波。忽略流体的黏性效应	大尺寸墩柱的地震动水压力计算
绕射波浪	结构在入射波浪中保持静止	结构对入射波浪阻挡使其产生散射, 入射波与散射波叠加形成新的波浪场。主要考虑流体惯性力效应和绕射效应	大尺寸墩柱入射波浪力计算

下载: 导出CSV

表 3 流固耦合有限元法比较

Table 3. Comparison of fluid-structure interaction FEMs

方法	原理	特点
拉格朗日法	流体、固体均采用拉格朗日法描述。流体域为不能承受剪切作用的弹性体, 以有限单元节点位移描述流体域	单元矩阵对称且正定, 但模拟大变形问题易出现单元扭曲
欧拉法	流体、固体分别采用欧拉法、拉格朗日法描述。采用不同位势函数描述流体波动, 流体采用位移单元离散	描述大变形时没有网格扭曲, 但流固网格相对运动使处理对流效应困难
任意拉格朗日-欧拉法	流固界面处吸收了拉格朗日法长处, 能够有效跟踪物质结构边界运动; 流场网格划分吸收了欧拉法长处, 流场网格单元独立于物质实体存在, 在求解过程中可根据定义的参数适当调整	控制网格速度, 减少变形体内部网格扭曲, 有利于分析大变形问题。

下载: 导出CSV

表 4 深水桥墩地震响应试验研究

Table 4. Experimental research on seismic responses of deep-water bridge piers

学者	研究对象	模型材料	缩尺比例	研究内容与结果
赖伟等^{[1, 65]}	桩基础桥墩	有机玻璃	1/30	有水工况下的桥墩自振频率总体小于无水工况下, 即水体改变了结构水下部分受到的荷载
孙国帅等^[66-67]	墩身与基础	微粒混凝土与冷拉钢丝	1/32	对无水和有水工况下的试验结果对比发现2种工况下模型的传递函数与振型均不同, 构件的破坏集中在结点部位
Liu等^[53]	桥塔与基础	微粒混凝土与冷拉钢丝	1/100	对桥塔进行了地震、波浪、水流联合作用振动台试验, 发现桥塔与梁结点处易破坏, 地震作用导致的动水压力影响最大, 强震时波浪与水流导致动水压力可忽略
李悦等^[68]	高桩承台	微粒混凝土与钢管	1/50	有水工况下的模型加速度峰值均比无水工况下减小; 随着正弦波频率的增大, 水体对模型加速度峰值的影响不断增大
黄信^[36]	大直径桥墩	加重橡胶	1/50	动水压力减小桥墩结构自振频率, 而动力响应呈增大趋势; 水底柔性反射边界对地震动水压力的减幅并不明显
李乔等^[69]	圆形、矩形桥墩	仿真混凝土	1/50	圆形桥墩与矩形桥墩相比, 动水压力沿截面周边减小快, 其产生的阻力较小; 矩形桥墩产生的动水压力比圆形桥墩大, 随着水深的增大, 矩形桥墩动水压力增幅也较大
Ding等^[70]	矩形桥墩	加重橡胶	1/50	动水压力减小桥墩结构固有频率; 在单独地震作用下, 桥墩在水中的动力响应峰值大于无水工况; 波流作用对地震、波流联合作用下的桥墩动力响应的影响不可忽视
Li等^[71]	矩形桥墩	混凝土与加重橡胶	1/2	对原型模型以及分别基于协调相似律和传统附加质量法设计出的协调模型和常规模型进行水下振动台对比试验, 结果表明协调相似律能较好地再现原型的动力响应

下载: 导出CSV

参考文献(72)

[1]	赖伟. 地震和波浪作用下深水桥梁的动力响应研究[D]. 上海: 同济大学, 2004. LAI Wei. Study on dynamic response of deep-water bridges under earthquake and waves[D]. Shanghai: Tongji University, 2004. (in Chinese).
[2]	王东升, 孙治国, 郭迅, 等. 汶川地震桥梁震害经验及抗震研究若干新进展[J]. 公路交通科技, 2011, 28 (10): 44-53. https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201110011.htm WANG Dong-sheng, SUN Zhi-guo, GUO Xun, et al. Lessons learned from Wenchuan seismic damages and recent research on seismic design of highway bridges[J]. Journal of Highway and Transportation Research and Development, 2011, 28 (10): 44-53. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201110011.htm
[3]	FALTINSEN O M. Wave loads on offshore structures[J]. Annual Review of Fluid Mechanics, 1990, 22 (1): 35-56. doi: 10.1146/annurev.fl.22.010190.000343
[4]	HOGBEN N, OSBORNE J, STANDING R G. Wave loading on offshore structures-theory and experiment[J]. Fluid Dynamics, 1975, 12 (3): 41-50.
[5]	MORISON J R, JOHNSON J W, SCHAAF S A. The force exerted by surface waves on piles[J]. Journal of Petroleum Technology, 1950, 2 (5): 149-154. doi: 10.2118/950149-G
[6]	WEISS P H, JEANNEROD M, PAULIGNAN Y, et al. Vibration of vertical rectangular plate in contact with water on one side[J]. Earthquake Engineering and Structural Dynamics, 2015, 29 (5): 693-710.
[7]	SUN K, NOGAMI T. Earthquake induced hydrodynamic pressure on axisymmetric offshore structures[J]. Earthquake Engineering and Structural Dynamics, 1991, 20 (5): 429-440. doi: 10.1002/eqe.4290200504
[8]	WALKER D A G, TAYLOR R E. Wave diffraction from linear arrays of cylinders[J]. Ocean Engineering, 2005, 32 (17): 2053-2078.
[9]	WU Bi-jun, ZHENG Yong-hong, YOU Ya-ge, et al. On diffraction and radiation problem for two cylinders in water of finite depth[J]. Ocean Engineering, 2006, 33 (5): 679-704.
[10]	李悦. 强震作用下动水压力对深水桥梁动力性能的影响研究[D]. 北京: 北京科技大学, 2010. LI Yue. Study on the effects of hydrodynamic force on the dynamic performance of deep-water bridges subjected to strong earthquake[D]. Beijing: University of Science and Technology Beijing, 2010. (in Chinese).
[11]	KEULEGAN G H, CARPENTER L H. Force on cylinders and plates in an oscillating fluid[J]. Journal of Research of the National Bureau of Standards, 1958, 60 (5): 423-440. doi: 10.6028/jres.060.043
[12]	BERGE B, PENZIEN J. Three-dimensional stochastic response of offshore towers to wave forces[R]. Berkeley: California University, 1974.
[13]	TERRO M J, ABDEL-ROHMAN M, TERRO M J. Wave induced forces in offshore structures using linear and nonlinear forms of morison's equation[J]. Journal of Vibration and Control, 2007, 13 (2): 139-157. doi: 10.1177/1077546307067085
[14]	袁迎春, 赖伟, 王君杰, 等. Morison方程中动水阻力项对桥梁桩柱地震反应的影响[J]. 世界地震工程, 2005, 21 (4): 163-168. https://www.cnki.com.cn/Article/CJFDTOTAL-SJDC200504014.htm YUAN Ying-chun, LAI Wei, WANG Jun-jie, et al. The effects of hydrodynamic damping on seismic response of bridge piles[J]. World Earthquake Engineering, 2005, 21 (4): 163-168. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SJDC200504014.htm
[15]	YANG Wan-li, LI Qiao, YEH H. Calculation method of hydrodynamic forces on circular piers during earthquakes[J]. Journal of Bridge Engineering, 2017, 22 (11): 1-13.
[16]	李富荣, 陈国兴, 王志华. 考虑动水压力影响的单柱式桥墩地震反应分析[J]. 地震工程与工程振动, 2008, 28 (2): 114-121. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200802017.htm LI Fu-rong, CHEN Guo-xing, WANG Zhi-hua. Seismic responses of single-column pier considering the effects of hydrodynamic pressure[J]. Journal of Earthquake Engineering and Engineering Vibration, 2008, 28 (2): 114-121. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200802017.htm
[17]	YANG Wan-li, LI Qiao. The expanded Morison equation considering inner and outer water hydrodynamic pressure of hollow piers[J]. Ocean Engineering, 2013, 69 (5): 79-87.
[18]	陈熙之, 解明雨, 孙焕纯. 桩-土-结构-水体系相互作用的弹塑性地震反应分析[J]. 计算力学学报, 2013, 69 (5): 79-87. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG198501005.htm CHEN Xi-zhi, XIE Ming-yu, SUN Huan-chun. Eiastopiastic seismic analysis of pile-soil-structure-water interaction[J]. Computational Structural Mechanics and Applications, 2013, 69 (5): 79-87. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG198501005.htm
[19]	白德贵, 王志华, 陈国兴. 深水桥梁桩基础考虑流固耦合效应的地震反应分析方法综述[J]. 防灾减灾工程学报, 2007, 27 (增): 88-94. https://cpfd.cnki.com.cn/Article/CPFDTOTAL-OGTY200703001020.htm BAI De-gui, WANG Zhi-hua, CHEN Guo-xing. Overview of seismic analysis method of deep-water-bridge pile foundation considering fluid-structure interaction[J]. Journal of Disaster Prevention and Mitigation Engineering, 2007, 27 (S): 88-94. (in Chinese). https://cpfd.cnki.com.cn/Article/CPFDTOTAL-OGTY200703001020.htm
[20]	刘浪, 杨万理, 李乔. 深水桥梁墩水耦合抗震分析方法[J]. 西南交通大学学报, 2015, 50 (3): 449-453. https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201503010.htm LIU Lang, YANG Wan-li, LI Qiao. Seismic analysis method of deep-water bridge pier and water coupling[J]. Journal of Southwest Jiaotong University, 2015, 50 (3): 449-453. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201503010.htm
[21]	赖伟, 王君杰. 沿水平向运动的水中截断圆柱体辐射波浪问题的解析解答[J]. 工程力学, 2007, 24 (4): 81-86. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200704014.htm LAI Wei, WANG Jun-jie. Radiation wave loadings on a truncated cylinder due to sway motion[J]. Engineering Mechanics, 2007, 24 (4): 81-86. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200704014.htm
[22]	刘振宇, 李乔, 赵灿晖, 等. 深水矩形空心桥墩在地震作用下附加动水压力分析[J]. 振动与冲击, 2008, 27 (2): 53-56. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200802010.htm LIU Zhen-yu, LI Qiao, ZHAO Can-hui, et al. Additional hydrodynamic pressure on rectangular hollow piers in deep water due to earthquake[J]. Journal of Vibration and Shock, 2008, 27 (2): 53-56. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200802010.htm
[23]	刘振宇, 李乔, 赵灿晖, 等. 圆形空心深水桥墩在地震作用下的附加动水压力[J]. 西南交通大学学报, 2008, 43 (2): 200-205. https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT200802011.htm LIU Zhen-yu, LI Qiao, ZHAO Can-hui, et al. Earthquake- induced added hydrodynamic pressure on circular hollow piers in deep water[J]. Journal of Southwest Jiaotong University, 2008, 43 (2): 200-205. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT200802011.htm
[24]	杨万理, 李乔. 基于辐射波浪理论的圆形桥墩动水压力表达式的简化研究[J]. 公路交通科技, 2012, 29 (7): 45-57. https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201207009.htm YANG Wan-li, LI Qiao. Simplified hydrodynamic pressure expressions of circular piers based on radiation wave theory[J]. Journal of Highway and Transportation Research and Development, 2012, 29 (7): 45-57. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK201207009.htm
[25]	EIDSMOEN H. Hydrodynamic parameters for a two-body axisymmetric system[J]. Applied Ocean Research, 1995, 17 (2): 103-115. doi: 10.1016/0141-1187(95)00003-J
[26]	ZHOU Ding, LIU Wei-qing. Bending-torsion vibration of a partially submerged cylinder with an arbitrary cross-section[J]. Applied Mathematical Modelling, 2007, 31 (10): 2249-2265. doi: 10.1016/j.apm.2006.08.011
[27]	王君杰, 赖伟, 胡世德. 深水高桩基础桥梁地震水动力效应分析[J]. 同济大学学报(自然科学版), 2011, 39 (5): 650-655. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201105006.htm WANG Jun-jie, LAI Wei, HU Shi-de. Seismic hydrodynamic effects on group-pile foundations with caps merged in water[J]. Journal of Tongji University (Natural Sciences), 2011, 39 (5): 650-655. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201105006.htm
[28]	HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39 (1): 201-225. doi: 10.1016/0021-9991(81)90145-5
[29]	FAN S C, LI S M, YU G Y. Dynamic fluid-structure interaction analysis using boundary finite element method-finite element method[J]. Journal of Applied Mechanics, 2005, 72 (4): 591-598. doi: 10.1115/1.1940664
[30]	PAIK K J, CARRICA P M. Fluid-structure interaction for an elastic structure interacting with free surface in a rolling tank[J]. Ocean Engineering, 2014, 84 (7): 201-212.
[31]	陈国兴, 席仁强, 王志华. 考虑流固耦合的桥墩地震反应方法[J]. 防灾减灾工程学报, 2010, 30 (1): 1-9. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201001003.htm CHEN Guo-xing, XI Ren-qiang, WANG Zhi-hua. Dynamic response method of bridge piers under earthquake excitation considering fluid-structure interaction[J]. Journal of Disaster Prevention and Mitigation Engineering, 2010, 30 (1): 1-9. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201001003.htm
[32]	SPYRAKOS C C, XU Chao-jin. Soil-structure-water interaction of intake-outlet towers allowed to uplift[J]. Soil Dynamics and Earthquake Engineering, 1997, 16 (2): 151-159. doi: 10.1016/S0267-7261(96)00034-6
[33]	CHOPRA A K, GOYAL A. Simplified earthquake analysis of intake-outlet towers[J]. Journal of Structural Engineering, 1991, 117 (3): 767-788. doi: 10.1061/(ASCE)0733-9445(1991)117:3(767)
[34]	SUN K, NOGAMI T. Earthquake induced hydrodynamic pressure on axisymmetric offshore structures[J]. Earthquake Engineering and Structural Dynamics, 1991, 20 (5): 429-440. doi: 10.1002/eqe.4290200504
[35]	柳春光, 齐念. 考虑流固耦合作用的深水桥墩地震响应分析[J]. 防灾减灾工程学报, 2009, 29 (4): 433-437. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK200904014.htm LIU Chun-guang, QI Nian. Seismic response analysis of piers in deep water considering fluid-structure interaction[J]. Journal of Disaster Prevention and Mitigation Engineering, 2009, 29 (4): 433-437. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK200904014.htm
[36]	黄信. 水-桥墩动力相互作用机理及深水桥梁非线性地震响应研究[D]. 天津: 天津大学, 2011. HUANG Xin. Study on water-bridge pier dynamic interaction and nonlinear seismic response analysis of deep-water bridge[D]. Tianjin: Tianjin University, 2011. (in Chinese).
[37]	GOYAL A, CHOPRA A K. Earthquake analysis of intake-outlet towers including tower-water-foundation-soil interaction[J]. Earthquake Engineering and Structural Dynamics, 2006, 18 (3): 325-344.
[38]	李悦, 宋波. 动水对斜拉桥结构动力响应影响研究[J]. 土木工程学报, 2010, 43 (12): 94-99. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201012013.htm LI Yue, SONG Bo. Study of the effect of hydrodynamic force on cable-stayed bridges under earthquake[J]. China Civil Engineering Journal, 2010, 43 (12): 94-99. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201012013.htm
[39]	刘振宇, 李乔, 赵灿晖, 等. 深水连续刚构桥地震响应分析[J]. 地震工程与工程振动, 2009, 29 (4): 119-124. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200904017.htm LIU Zhen-yu, LI Qiao, ZHAO Can-hui, et al. Analysis of seismic responses of continuous rigid-frame bridge in deep water[J]. Journal of Earthquake Engineering and Engineering Vibration, 2009, 29 (4): 119-124. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200904017.htm
[40]	李玉龙. 地震与波浪联合作用下深水桥墩动力响应分析[D]. 天津: 天津大学, 2012. LI Yu-long. Dynamic response analysis of deep-water piers subjected to earthquake and wave loadings[D]. Tianjin: Tianjin University, 2012. (in Chinese).
[41]	柏晓东, 郭安薪, 李惠. 深水悬臂桥墩动力特性及地震响应分析[J]. 防灾减灾工程学报, 2011, 31 (5): 506-511. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201105008.htm BAI Xiao-dong, GUO An-xin, LI Hui. Dynamic characteristics and seismic responses of cantilever pier immersed in water[J]. Journal of Disaster Prevention and Mitigation Engineering, 2011, 31 (5): 506-511. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201105008.htm
[42]	张洁, 朱东生, 张永水, 等. 考虑动水压力作用的深水桥墩地震响应分析[J]. 重庆交通大学学报(自然科学版), 2012, 31 (3): 357-361. https://www.cnki.com.cn/Article/CJFDTOTAL-CQJT201203002.htm ZHANG Jie, ZHU Dong-sheng, ZHANG Yong-shui, et al. Seismic response of piers in deep water considering hydrodynamic pressure[J]. Journal of Chongqing Jiaotong University (Natural Science), 2012, 31 (3): 357-361. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CQJT201203002.htm
[43]	黄信, 李忠献. 动水压力作用对深水桥墩地震响应的影响[J]. 土木工程学报, 2011, 44 (1): 65-73. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201101013.htm HUANG Xin, LI Zhong-xian. Influence of hydrodynamic pressure on seismic response of bridge piers in deep water[J]. China Civil Engineering Journal, 2011, 44 (1): 65-73. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201101013.htm
[44]	刘保东, 李鹏飞, 高超. 不同水深情况下水中桥墩地震响应研究[J]. 土木工程学报, 2010, 43 (增): 199-203. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC2010S2032.htm LIU Bao-dong, LI Peng-fei, GAO Chao. Seismic response analysis of bridge pier in water by different water depth[J]. China Civil Engineering Journal, 2010, 43 (S): 199-203. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC2010S2032.htm
[45]	杨万理, 李乔. 墩-水耦合计算模式及深水桥墩动力响应研究[J]. 地震工程与工程振动, 2012, 32 (3): 130-137. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201203021.htm YANG Wan-li, LI Qiao. Study on pier-water interaction calculation method and dynamic response of submerged piers[J]. Earthouake Engineering and Engineering Vibration, 2012, 32 (3): 130-137. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201203021.htm
[46]	CHEN B F. Hybrid three-dimensional finite-difference and finite-element analysis of seismic wave induced fluid-structure interaction of a vertical cylinder[J]. Ocean Engineering, 1998, 25 (8): 639-656.
[47]	高学奎, 朱晞, 李辉. 近场地震作用下深水桥墩的地震响应分析[J]. 工程抗震与加固改造, 2006, 28 (3): 83-87. https://www.cnki.com.cn/Article/CJFDTOTAL-GCKZ200603016.htm GAO Xue-kui, ZHU Xi, LI Hui. Seismic response analysis of bridge pier in deep water excited by near-fault earthquakes[J]. Earthquake Resistant Engineering and Retrofitting, 2006, 28 (3): 83-87. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCKZ200603016.htm
[48]	宋波, 黄帅. 长周期地震对矩形桥墩动水压力及墩身动力响应的影响[J]. 徐州工程学院学报(自然科学版), 2012, 27 (1): 19-25. https://www.cnki.com.cn/Article/CJFDTOTAL-OXZG201201005.htm SONG Bo, HUANG Shuai. The effect of long period ground motions on the hydrodynamic pressure and dynamic response of rectangular pier[J]. Journal of Xuzhou Institute of Technology (Natural Sciences Edition), 2012, 27 (1): 19-25. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-OXZG201201005.htm
[49]	SHARIATMADAR H, MIRHAJ A. Dam-reservoir-foundation interaction effects on the modal characteristic of concrete gravity dams[J]. Structural Engineering and Mechanics, 2011, 38 (1): 65-79.
[50]	林曾, 袁万城. 考虑波浪作用下的深水桥墩地震响应分析[J]. 土木工程与管理学报, 2015, 32 (2): 37-41. https://www.cnki.com.cn/Article/CJFDTOTAL-WHCJ201502009.htm LIN Zeng, YUAN Wan-cheng. Seismic response of bridge pier in deep water considering wave action[J]. Journal of Civil Engineering and Management, 2015, 32 (2): 37-41. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WHCJ201502009.htm
[51]	李忠献, 黄信. 地震和波浪联合作用下深水桥梁的动力响应[J]. 土木工程学报, 2012, 45 (11): 134-140. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201211016.htm LI Zhong-xian, HUANG Xin. Dynamic responses of bridges in deep water under combined earthquake and wave actions[J]. China Civil Engineering Journal, 2012, 45 (11): 134-140. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201211016.htm
[52]	吴安杰, 杨万理, 赵雷. 波流与地震共同作用下深水桥墩动力响应分析[J]. 西南交通大学学报, 2018, 53 (1): 79-87. https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201801010.htm WU An-jie, YANG Wan-li, ZHAO Lei. Dynamic response analysis of bridge pier in deep water under combined loads of wave, current and earthquake[J]. Journal of Southwest Jiaotong University, 2018, 53 (1): 79-87. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201801010.htm
[53]	LIU Chun-guang, ZHANG Shi-bo, HAO Er-tong. Joint earthquake, wave and current action on the pile group cable-stayed bridge tower foundation: an experimental study[J]. Applied Ocean Research, 2017, 63: 157-169.
[54]	宋波, 马翠娟, 齐福强. 冰体边界范围对桥墩地震反应的影响研究[J]. 海洋工程, 2013, 31 (2): 53-60. https://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201302009.htm SONG Bo, MA Cui-juan, QI Fu-qiang. Study on the effect of ice mass boundary range on seismic responses of a bridge pier[J]. The Ocean Engineering, 2013, 31 (2): 53-60. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201302009.htm
[55]	齐福强, 宋波. 海冰对冰水域大跨拱桥地震动力反应的影响研究[J]. 土木工程学报, 2013, 46 (增1): 256-261. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC2013S1044.htm QI Fu-qiang, SONG Bo. Study on the effect of sea ice on seismic response of a long-span arch bridge in icy water[J]. China Civil Engineering Journal, 2013, 46 (S1): 256-261. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC2013S1044.htm
[56]	SONG Bo, LI Chao-niu, QI Fu-qiang. Study on a simplified calculation method for seismic response analysis of bridge pier in icy water[J]. Journal of Earthquake Engineering, 2015, 19 (7): 1-18.
[57]	兰雅梅, 薛雷平, 刘桦, 等. 东海大桥桥梁桩柱承台水动力模型试验研究——第一部分: 作用于单个小尺度桩柱上的波流力[J]. 水动力学研究与进展, 2004, 19 (6): 753-758. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ200406009.htm LAN Ya-mei, XUE Lei-ping, LIU Hua, et al. Experimental studies on hydrodynamic loads on piles and slab of Donghai Bridge—Part I: hydrodynamic forces on a single pile in wave-current combinations[J]. Journal of Hydrodynamics, 2004, 19 (6): 753-758. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ200406009.htm
[58]	兰雅梅, 郭文华, 刘桦, 等. 规则波中承台和桩柱水动力的实验研究[J]. 水动力学研究与进展, 2010, 25 (4): 551-558. https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201004018.htm LAN Ya-mei, GUO Wen-hua, LIU Hua, et al. Experimental study on hydrodynamic loads on a horizontal slab and pile in regular wave[J]. Journal of Hydrodynamics, 2010, 25 (4): 551-558. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SDLJ201004018.htm
[59]	皇甫熹, 刘红燕, 颜爱华. 东海大桥70 m跨低墩基础波浪力研究[J]. 世界桥梁, 2004 (增1): 13-16. https://www.cnki.com.cn/Article/CJFDTOTAL-GWQL2004S1004.htm HUANGFU Xi, LIU Hong-yan, YAN Ai-hua. Study of wave forces on low-lying pier foundations of 70-m spans of Donghai Bridge[J]. World Bridge, 2004 (S1): 13-16. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GWQL2004S1004.htm
[60]	袁卫国, 刘沐宇. 波浪和地震作用下的跨海大桥桥墩荷载效应分析[J]. 武汉理工大学学报, 2013, 35 (12): 120-124. https://www.cnki.com.cn/Article/CJFDTOTAL-WHGY201312024.htm YUAN Wei-guo, LIU Mu-yu. Load effect analysis of cross-sea bridges pier on the wave and earthquake effect[J]. Journal of Wuhan University of Technology, 2013, 35 (12): 120-124. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WHGY201312024.htm
[61]	吴安杰, 杨万理, 赵雷. 开孔圆形截面空心桥墩水动力研究[J]. 防灾减灾工程学报, 2017, 37 (5): 725-731. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201705005.htm WU An-jie, YANG Wan-li, ZHAO Lei. Study on hydrodynamic characteristics of circular hollow pier with holes[J]. Journal of Disaster Prevention and Mitigation Engineering, 2017, 37 (5): 725-731. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK201705005.htm
[62]	SAVAGE J L. Earthquake studies for pit river bridge[J]. Civil Engineering, 1939, 9 (8): 470-472.
[63]	MITRI F G. Theoretical and experimental determination of the acoustic radiation force acting on an elastic cylinder in a plane progressive wave-far-field derivation approach[J]. New Journal of Physics, 2006, 8 (8): 138.
[64]	TANAKA Y, HUDSPETH RT. Restoring forces on vertical circular cylinders forced by earthquake[J]. Earthquake Engineering and Structural Dynamics, 1988, 16: 99-119.
[65]	赖伟, 王君杰, 韦晓, 等. 桥墩地震动水效应的水下振动台试验研究[J]. 地震工程与工程振动, 2006, 26 (6): 164-171. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200606026.htm LAI Wei, WANG Jun-jie, WEI Xiao, et al. The shaking table test for submerged bridge pier[J]. Earthquake Engineering and Engineering Vibration, 2006, 26 (6): 164-171. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200606026.htm
[66]	孙国帅. 深水桥梁下部结构体系振动台模型试验研究及理论分析[D]. 大连: 大连理工大学, 2013. SUN Guo-shuai. Theoretical and experimental study on substructure system of bridge in deep water[D]. Dalian: Dalian University of Technology, 2013. (in Chinese).
[67]	柳春光, 孙国帅, 张士博, 等. 深水桩墩结构振动台试验及地震响应预测分析[J]. 大连理工大学学报, 2013, 53 (1): 114-120. https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG201301021.htm LIU Chun-guang, SUN Guo-shuai, ZHANG Shi-bo, et al. Experimental investigation of shaking table on pile-pier structure in deep water and prediction analysis of seismic response[J]. Journal of Dalian University of Technology, 2013, 53 (1): 114-120. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG201301021.htm
[68]	李悦, 宋波, 黄帅. 地震时作用于深水桥墩上的动水力及对桥墩动力响应的影响[J]. 北京科技大学学报, 2011, 33 (3): 388-394. https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201103022.htm LI Yue, SONG Bo, HUANG Shuai. Hydrodynamic force and its effect on the dynamic response of deep-water bridge piers in earthquake[J]. Journal of University of Science and Technology Beijing, 2011, 33 (3): 388-394. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201103022.htm
[69]	李乔, 刘浪, 杨万理. 深水桥梁墩水耦合振动试验研究与数值计算[J]. 工程力学, 2016, 33 (7): 197-203. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201607027.htm LI Qiao, LIU Lang, YANG Wan-li. Experimental and numerical investigation on pier-water coupling vibration of bridges in deep water[J]. Engineering Mechanics, 2016, 33 (7): 197-203. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201607027.htm
[70]	DING Yang, MA Rui, SHI Yan-chao, et al. Underwater shaking table tests on bridge pier under combined earthquake and wave-current action[J]. Marine Structure, 2018, 58: 301-320.
[71]	LI Zhong-xian, WU Kong, SHI Yan-chao, et al. Coordinative similitude law considering fluid-structure interaction for underwater shaking table tests[J]. Earthquake Engineering and Structural Dynamics, 2018, 47 (11): 2315-2332.
[72]	朱晞, 高学奎. 桥梁抗震分析中动水压力的计算[J]. 中国铁道科学, 2007, 28 (3): 44-48. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK200703009.htm ZHU Xi, GAO Xue-kui. Calculation of hydrodynamic pressure in seismic analysis of bridges[J]. China Railway Science, 2007, 28 (3): 44-48. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK200703009.htm