Dimension-reduction simulation of multi-dimensional ground motions based on strong motion records
LIU Zhangjun1,2, JIANG Yunmu1,2, LIU Zixin3, YUE Qingxia4
1. College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang 443002, China;
2. School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan 430074, China;
3. Key Laboratory of Building Collapse Mechanism and Disaster Prevention，Institute of Disaster Prevention, China Earthquake Administration, Sanhe 065201, China;
4. Key Laboratory of Building Structural Retrofitting and Underground Space Engineering, Ministry of Education, Shandong Jianzhu University, Jinan 250101, China
Abstract：Earthquake ground motion has multi-dimensional characteristic, of which the reasonable description is the basis for the refined seismic analysis of complex engineering structures. Firstly, based on 1766 groups of measured multi-dimensional strong motion records, a kind of lagged coherence function model of multi-dimensional ground motion is proposed. Secondly, the relationship among the amplitude, duration and spectrum of three-dimensional ground motion components is studied, and the evolutionary power spectrum model of multi-dimensional ground motion is established. Finally, by introducing the dimension-reduction method based on proper orthogonal decomposition for the random vector process, the simulation of multi-dimensional ground motion is realized using just two elementary random variables. Numerical examples show that the representative time-histories of multi-dimensional ground motion generated by the dimension-reduction method have good efficiency. The coherence, response spectrum and amplitude spectrum of three-dimensional components are consistent with the measured records, which verifies the accuracy and engineering applicability of the dimension-reduction model. Meanwhile, the representative time-histories have assigned probability and can consist a complete probability set. Thus, the dimension-reduction method can be combined with the probability density evolution theory, which provides an effective way for the refined seismic reliability evaluation of complex engineering structures.
Key words: multi-dimensional ground motion; strong motion records; coherence function; evolutionary power spectrum; dimension-reduction
刘章军1,2，姜云木1,2，刘子心3，岳庆霞4. 基于强震记录的多维地震动降维建模[J]. 振动与冲击, 2022, 41(18): 244-251.
LIU Zhangjun1,2, JIANG Yunmu1,2, LIU Zixin3, YUE Qingxia4. Dimension-reduction simulation of multi-dimensional ground motions based on strong motion records. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(18): 244-251.
[1] 李文婷, 陈清军. 地震次生火灾中城市地铁地下结构的灾变性能研究[J]. 振动与冲击, 2021, 40(14): 153-161+179.
LI Wen-ting, CHEN Qing-jun. Damage performance of underground structures in earthquake-induced fire [J]. Journal of Vibration and Shock, 2021, 40(14): 153-161+179.
[2] 李宏男. 结构多维抗震理论[M]. 北京: 科学出版社, 2006.
LI Hong-nan. Multidimensional Seismic Theory of Structures [M]. Beijing: Science Press, 2006
[3] 刘巴黎, 胡进军, 谢礼立. 双向地震激励下基于二维屈服面模型的残余位移谱研究[J]. 振动与冲击, 2021, 40(14): 40-46.
LIU Ba-li, HU Jin-jun, XIE Li-li. Residual displacement spectrum of a structural system based on a two-dimensional yield surface plasticity model subjected to bi-directional earthquake excitations [J]. Journal of Vibration and Shock, 2021, 40(14): 40-46.
[4] 欧进萍, 王光远. 结构随机振动[M]. 北京: 高等教育出版社, 1998.
OU Jin-ping, WANG Guang-yuan. Random Vibration of Structure [M]. Beijing: Higher Education Press, 1998.
[5] 李忠献, 李笑穹, 李宁. 空间相关多点多维地震动的模拟[J]. 地震工程与工程振动, 2014, 34(4): 64-72.
LI Zhong-xian, LI Xiao-qiong, LI Ning. Simulation of multi-point and multi-dimension spatially correlated earthquake ground motions[J]. Earthquake Engineering and Engineering Dynamics, 2014, 34(4): 64-72.
[6] 黄玉平, 刘季. 双向水平地震动的空间相关性[J]. 哈尔滨建筑工程学院学报, 1987(3):15-19.
HUANG Yu-ping, LIU Ji. The spatial correlation of two horizontal direction earthquake [J]. Journal of Harbin University of Civil Engineering and Architecture, 1987(3): 15-19.
[7] 薛素铎, 曹资, 王雪生, 等. 多维地震作用下网壳结构的随机分析方法 [J]. 空间结构, 2002(1): 44-51.
XUE Su-duo, CAO Zi, WANG Xue-sheng, et al. Random analysis method for lattice shells under multiple earthquake Excitations [J]. Spatial Structures, 2002(1): 44-51.
[8] 李英民, 刘立平. 工程结构的设计地震动[M]. 北京: 科学出版社, 2011.
LI Ying-min, LIU Li-ping. Design Ground Motion of Engineering Structure [M]. Beijing: Science Press, 2011.
[9] PENZIEN J, WATABE M. Characteristics of 3‐dimensional earthquake ground motions [J]. Earthquake Engineering and Structural Dynamics, 2010, 3(4):365-373.
[10] BOZORGNIA Y，Campbell K W．The vertical-to-horizontal response spectral ratio and tentative procedures for developing simplified V/H and vertical design spectra [J]．Journal of Earthquake Engineering, 2004,8(2): 175-207
[11] BOMMER J J, Akkar S, Kale Z. A model for vertical-to-horizontal response spectral ratios for Europe and the middle East [J]. Bulletin of the Seismological Society of America, 2011, 101(4):1783-1806.
[12] 姜云木, 阮鑫鑫, 刘章军. 主余震型地震动过程的降维模拟[J].振动与冲击, 2021, 40(24): 282-292.
JIANG Yun-mu, RUAN Xin-xin, LIU Zhang-jun. Dimension-reduction simulation of main aftershock type ground motion process [J]. Journal of Vibration and Shock, 2021, 40(24): 282-292.
[13] 刘章军, 刘子心, 阮鑫鑫, 等. 地震动随机场的POD降维表达[J]. 中国科学: 技术科学, 2019, 49(5), 589-601.
LIU Zhang-jun, LIU Zi-xin, Ruan Xin-xin, et al. POD-based dimension reduction representation of stochastic ground motion fields [J]. Scientia Sinica (Technologica), 2018, 49(05): 103-111.
[14] LIU Z J, Liu W, PENG Y B. Random function based spectral representation of stationary and non-stationary stochastic processes [J]. Probabilistic Engineering Mechanics, 2016, 45: 115-126.
[15] LI J, CHEN J B. Stochastic Dynamics of Structures [M]. Singapore: John Wiley & Sons, 2009.
[16] LI J, CHEN J B. The principle of preservation of probability and the generalized density evolution equation [J]. Structural Safety, 2008, 30(1): 65-77.
[17] GB 18306-2015, 中国地震动参数区划图[S]. 北京: 中国标准出版社, 2015
GB 18306-2015, Seismic ground motion parameter zonation map of China [S]. Beijing: China Standards Publishing House, 2015.
[18] 郭锋, 吴东明, 许国富, 等. 中外抗震设计规范场地分类对应关系[J]. 土木工程与管理学报, 2011, 28(2): 63-66.
GUO Feng, WU Dong-ming, XU Guo-fu, et al. The corresponding relationship of site classification in Chinese and foreign seismic design codes[J]. Journal of Civil Engineering and Management, 2011, 28(2): 63-66.
[19] 陈亮, 陈昌斌, 王庶懋. 中欧抗震设计规范的对比[J]. 武汉大学学报：工学版, 2013(S1): 129-134.
CHEN Liang, CHEN Chang-bin, Wang Shu-mao. Comparative study of seismic design codes of China and Europe [J]. Journal of Wuhan University, 2013(S1): 129-134.
[20] PRIESTLEY M B. Evolutionary spectra and non-stationary processes [J]. Journal of the Royal Statistical Society: Series B, 1965, 27(2): 204-237.
[21] KANAI K, YOSHIZAWA S, SUZUKI T. An empirical formula for the spectrum of strong earthquake motions. II.[J]. 東京大学地震研究所彙報, 1961, 41:261-270.
[22] CLOUGH R W, PENZIEN J. Dynamic of Structures [M]. New York: McGraw-HILL Inc, 1993.
[23] VANMARCKE E H, LAI S S P. Strong-motion duration and RMS amplitude of earthquake records [J]. Bulletin of the Seismological Society of America, 1980, 70(4): 1293-1307.
[24] 刘子心, 刘章军. 多点多维全非平稳地震动场的降维模拟[J]. 振动工程学报, 2020, 33(5): 146-156.
LIU Zi-xin, LIU Zhang-jun. Dimension-reduction simulation for multi-support and multi-component spatially correlated fully non-stationary ground motion fields [J]. Journal of Vibration Engineering, 2020, 33(5): 146-156.
[25] LI J, CHEN J B. The principle of preservation of probability and the generalized density evolution equation [J]. Structural Safety, 2008, 30(1): 65-77.
