Approximate quantitative relationship between earthquake ground motion and structural responses
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摘要: 本文在对实际地震加速度记录统计分析的基础上，给出了能够合理描述地震动强度非平稳特性的参数及其取值范围；然后引入实验设计方法，建立了适合于地震动强度非平稳特性参数分析的实验设计算法，用来分析地震动强度非平稳特性参数的变化对结构响应的影响；最后通过与近似技术相结合，建立了地震动强度非平稳特性参数与结构响应之间的近似定量关系模型.结果表明，本文提出的实验设计方法适合于对地震动强度非平稳特性参数进行分析，该方法在有效地减小计算量的同时，获得了结构响应与参数变化之间的对应关系.基于实验设计方法进行的特性参数方差分析结果表明：地震动的稳态持时对结构地震响应的影响比较显著；对于周期较小的结构，特性参数之间的交互作用对结构地震响应的影响显著，但当周期大于1 s时，则不显著.本文建立的近似定量关系模型能够较好地反映不同特性参数、不同周期结构动力响应之间的联系，为工程实践中基于结构特性合理设置地震动特性参数、合成或挑选地震加速度时程提供理论依据.Abstract: On the basis of the statistical analysis of the actual seismic acceleration records, this paper gives the parameters describing the non-stationary of earthquake ground motion and their value ranges. And the design of experiments (DOE) method is introduced to establish suitable algorithm to analyze the influence of the change in the non-stationary characteristic parameter of ground motion on the structure responses. Furthermore, an approximate quantitative relationship between the non-stationary characteristic parameters of the earthquake ground motion and the structural responses is established by combining with approximate technology. The results show that: ① The DOE method presented in this paper is suitable for the analyses of non-stationary characteristic parameters of ground motion intensity, and satisfied results can be obtained based on the less amount of calculation. ② Variance analysis of characteristic parameters based on DOE method shows that the steady-state duration of ground motion has significant influence on the seismic response of the structure; for structures with shorter period, the interaction between characteristic parame-ters has a significant impact on seismic response of structures, but when the period is greater than 1 s, its influence gradually decreases. ③ The approximate quantitative relationship established in this paper can better reflect the relationship between different characteristic parameters and different structural dynamic response, providing the theory basis for engineering practice to setting up reasonable seismic characteristic parameters based on the structural characteristics and synthetize or select earthquake acceleration time history.
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图 1 阻尼比为0.05，周期T为0.05，0.2和1 s时特性参数(t1，ts，t3，c)对结构响应的影响
Figure 1. Effect of characteristic parameters (t1, ts, t3, c) on the structural responses when the damping ratio is 0.05 and the period T is 0.05, 0.2 and 1 s
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图 2 周期为0.05 s (a)，0.2 s (b)和1 s (c)时fRMS随平稳段持时ts，总持时t3和衰减系数c的变化趋势图
Figure 2. Variation of fRMS along with ts, t3 and c when period is 0.05 s (a), 0.2 s (b) and 1 s (c)
表 1 按照场地条件、震中距和震级划分的地震记录分组情况
Table 1 Data grouping according to site condition, epicentral distance and magnitude
MW 0≤R < 20 20≤R < 40 40≤R < 60 60≤R < 80 80≤R < 100 R≥100 Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ < 5.5 85 376 82 47 219 33 33 160 45 18 113 12 31 74 27 12 48 21 [5.5，6.0) 53 255 36 45 219 36 36 233 45 36 140 39 30 75 30 60 189 147 [6.0，6.5) 30 74 9 91 216 34 123 569 128 165 521 171 69 392 114 180 732 384 [6.5，7.0) 49 98 37 72 162 68 45 157 63 39 93 32 53 80 18 36 181 25 ≥7.0 30 18 36 95 18 48 87 51 63 235 27 42 168 30 132 782 225 注：Ⅰ，Ⅱ和Ⅲ为场地条件；R为震中距，单位为km; MW为矩震级. 
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表 2 地震动强度非平稳特性参数的取值范围
Table 2 The values range of intensity parameters of earthquake ground motion
上升段持时t1/s 平稳段持时ts/s 总持时t3/s 衰减系数c 1-25 2-20 30-90 0.08-0.56
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表 3 特性参数分组取值情况
Table 3 Parameter grouping
特性参数 上升段持时t1/s 平稳段持时ts/s 总持时t3/s 衰减系数c 第1组 1.0-6.3 2-6 30-45 0.354-0.562 第2组 6.3-12.5 6-10 45-60 0.185-0.354 第3组 12.5-18.7 10-15 60-75 0.134-0.185 第4组 18.7-25 15-20 75-90 0.080-0.134
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表 4 均匀设计表U8*(85)
Table 4 Uniform design table U8*(85)
实验号 1 2 3 4 5 1 1 2 4 7 8 2 2 4 8 5 7 3 3 6 3 3 6 4 4 8 7 1 5 5 5 1 2 8 4 6 6 3 6 6 3 7 7 5 1 4 2 8 8 7 5 2 1 U8*(85)使用表 s 列号 D 2 1 3 0.1445 3 1 3 4 0.2000 4 1 2 3 5 0.2709 注：s为因数的总数目，D为均匀度偏差.
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表 5 研究设计方案
Table 5 Research design plan
工况 DOE方法 参数组合 拟合地震动数量 单自由度体系周期及阻尼比 目标谱参数 目标参数 参数方差分析 正交设计L16(215) 16×4组 16×4×7×2 周期：0.05 s，0.2 s，1 s 地震影响系数最大值：0.9 结构加速度响应均方根值 参数变化对结构响应的影响分析 均匀设计U8*(85) 8×4组 8×4×7 阻尼比：0.02，0.05，0.07，0.10 特征周期值：0.35 s，0.90 s
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表 6 模型线性和二次项部分参数取值
Table 6 Model parameters of linear part and quadratic item
周期/s 线性 二次项 l l1 ls l3 lc q1 qs q3 qc 0.05 3.786 -0.121 0.096 -0.032 -11.866 0.003 0.010 0.001 13.812 0.2 5.309 -0.170 0.471 -0.096 14.080 -0.005 0.012 0.002 17.617 1 4.870 -0.155 0.233 -0.082 -13.560 0.006 0.010 0.001 14.212
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表 7 模型交互影响部分参数取值
Table 7 Model parameters of interaction item
周期/s λ1s λ13 λ1c λ3s λsc λ3c 0.05 -0.0027 0.0004 0.3077 -0.0047 0.1195 -0.0178 0.2 0.0068 0.0024 0.3914 -0.0126 -0.1603 -0.0047 1 -0.0121 0.0007 0.4072 -0.0038 -0.2321 0.0469
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曹晖, 林学鹏. 2006.地震动非平稳特性对结构非线性响应影响的分析[J].工程力学, 23 (12): 30-35. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200612005.htm Cao H, Lin X P. 2006. The effect of nonstationary characteristic of earthquake ground motion on the structural nonlinear responses[J]. Engineering Mechanics, 23 (12): 30-35 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200612005.htm
陈魁. 2005.试验设计与分析[M].北京:清华大学出版社: 15-36. Chen K. 2005. Experimental Design and Analysis[M]. Beijing: Tsinghua University Press: 15-36 (in Chinese).
堵丁柱, 葛可一, 胡晓东. 2011.近似算法的设计与分析[M].北京:高等教育出版社: 98-112. Du D Z, Ge K Y, Hu X D. 2011. Design and Analysis of Approximation Algorithms[M]. Beijing: Higher Education Press: 98-112 (in Chinese).
霍俊荣, 胡聿贤, 冯启民. 1991.地面运动时程强度包络函数的研究[J].地震工程与工程震动, 11 (1): 1-12. http://www.cnki.com.cn/Article/CJFDTOTAL-DGGC199101000.htm Huo J R, Hu Y X, Feng Q M. 1991. Study on envelope function of acceleration time history[J]. Earthquake Engineering and Engineering Vibration, 11 (1): 1-12 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-DGGC199101000.htm
李云雁. 2008.试验设计与数据处理[M].第2版.北京:化学工业出版社: 20-30. Li Y Y. 2008. Experiment Design and Data Processing[M]. 2nd edition. Beijing: Chemical Industry Press: 20-30 (in Chinese).
刘平, 李宁, 李忠献, 马华, 谢礼立. 2013.考虑天然地震特征的长周期人工地震动合成[J].土木工程学报, 46 (12): 43-49. http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201312010.htm Liu P, Li N, Li Z X, Ma H, Xie L L. 2013. The synthetic method of seismic waves for the long period ground motion considering the characteristics of real earthquake records[J]. China Civil Engineering Journal, 46 (12): 43-49 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201312010.htm
刘文卿. 2005.实验设计[M].北京:清华大学出版社: 36-54. Liu W Q. 2005. Design of Experiments[M]. Beijing: Tsinghua University Press: 36-54 (in Chinese).
王佳毅. 2011.高层结构在长周期地震动作用下的弹塑性响应[J].山西建筑, 37 (16): 39-41. http://www.cnki.com.cn/Article/CJFDTOTAL-JZSX201116022.htm Wang J Y. 2011. On elastic-plastic response of high-rise structure under long-period ground motion[J].Shanxi Architecture, 37 (16): 39-41 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JZSX201116022.htm
王志强. 2011. SAS软件及其在数理统计上的应用[J].技术研发, 18 (6): 128-140. http://www.cnki.com.cn/Article/CJFDTOTAL-JSYS201106081.htm Wang Z Q. 2011. SAS software and its application in mathematical statistics[J]. Technology and Market, 18 (6): 128-140 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JSYS201106081.htm
徐国栋, 史培军, 周锡元. 2010.基于目标反应谱和包线的地震动合成[J].地震工程与工程振动, 30 (1): 1-7. http://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201001000.htm Xu G D, Shi P J, Zhou X Y. 2010. Artificial ground motion based on target response spectra and envelope[J]. Earthquake Engineering and Engineering Vibration, 30 (1): 1-7 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201001000.htm
杨红, 曹晖, 白绍良. 2001.地震波局部时频特性对结构非线性响应的影响[J].土木工程学报, 34 (4): 78-82. http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC200104011.htm Yang H, Cao H, Bai S L. 2001. Effects of local time-frequency characteristics of earthquake waves on structural non-linear responses[J]. China Civil Engineering Journal, 34 (4): 78-82 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC200104011.htm
俞瑞芳, 樊珂, 彭凌云, 袁美巧. 2010.地震动非平稳特性对结构反应影响的试验研究[J].土木工程学报, 43 (12): 13-20. http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201012002.htm Yu R F, Fan K, Peng L Y, Yuan M Q. 2010. Effect of non-stationary characteristics of ground motion on structural response[J]. China Civil Engineering Journal, 43 (12): 13-20 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201012002.htm
袁美巧, 俞瑞芳, 俞言祥. 2010.满足时-频统计特性的地震动时程调整[J].应用基础与工程科学学报, 18 (S): 162-172. http://www.cnki.com.cn/Article/CJFDTOTAL-YJGX2010S1023.htm Yuan M Q, Yu R F, Yu Y X. 2010. A time history adjusting method meeting the statistical ground motion time-frequency characteristics[J]. Journa of Basic Science and Engineering, 18 (S): 162-172 (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YJGX2010S1023.htm
Assimaki D, Jeong S. 2013. Ground-motion observations at Hotel Montana during the M7. 0 2010 Haiti earthquake: Topography or soil amplification? [J]. Bull Seismol Soc Am, 103 (5): 2577-2590. doi: 10.1785/0120120242
Basu B, Gupta V K. 1997. Non-stationary seismic response of MDOF systems by wavelet transform[J]. Earthquake Eng & Struct Dyn, 26 (12): 1243-1258. https://www.researchgate.net/publication/229539967_Non-stationary_seismic_response_of_MDOF_systems_by_wavelet_transform
Clough R W, Penzien J. 1993. Dynamics of Structures[M]. 2nd editon. New York: McGraw-Hill: 112-120.
Meeker W Q, Escobar L A. 1998. Statistical Methods for Reliability Data [M]. New York: John Wiley & Sons: 105-121.
Yang D X, Wang W. 2012. Nonlocal period parameters of frequency content characterization of near-fault ground motions[J]. Earthquake Eng & Struct Dyn, 41 (13): 1793-1811. https://www.researchgate.net/publication/263461788_Nonlocal_period_parameters_of_frequency_content_characterization_for_near-fault_ground_motions
Yang Q S, Saiidi M S, Wang H, Itani A. 2002. Influence of earthquake ground motion incoherency on multi-support structures[J]. Earthquake Eng & Eng Vibrat, 1 (2): 167-180. https://www.researchgate.net/publication/225663451_Influence_of_earthquake_ground_motion_incoherency_on_multi-support_structures
Yeh C H, Wen Y K. 1990. Modeling of nonstationary ground motion and analysis of inelastic structural response[J]. Struct Safety, 8 (1/2/3/4): 281-298.
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