土-结构动力相互作用下网架结构简化分析方法研究
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摘要
根据不同学者有关地基动力阻抗的计算公式,结合整体有限元法,从工程应用出发对S-R(Swing-Rocking)模型进行修正,提出适用于分析土-结构动力相互作用下大跨空间结构的简化计算方法。基于修正的S-R模型建立土-网架结构动力相互作用的计算模型,与已验证的三维整体有限元(3-D)模型进行对比分析。研究表明,根据修正S-R模型计算所得土-网架结构相互作用体系的自振特性和地震响应与已验证的3-D模型结果呈现出完全一致的规律性且吻合较好,从而验证了修正S-R模型的合理性;在不同地震波作用下,采用Gazetas提出的地基动力阻抗公式建立的土-网架结构相互作用体系中网架节点最大位移和峰值加速度与已验证的3-D模型结果最大误差不超过8.0%,结构杆件内力最大误差不超过10%,表明Gazetas提出的地基动力阻抗公式更适用于分析土-大跨空间结构动力相互作用问题,且具有较好的精度。
Based on the foundation dynamic impedance calculation formulas suggested by different scholars,the SR( swing-rocking) model was modified by combining with the integral finite element method and starting from the view point of engineering application. The practical simplified calculation method suitable for the soil-structure dynamic interaction analysis of long-span spatial structures was proposed. Then,the model of soil-grid structure interaction was established according to the modified S-R model,and the three-dimensional finite element model verified was also established for a comparative analysis. The study showed that the natural vibration properties and seismic response of the soil-grid structure interaction model based on the modified S-R model reveal same regularities and agree well with those of the 3-D FE model,the rationality of the modified S-R model is verified; the nodal maximum displacement error and peak acceleration error of the soil-grid structure interaction system established with the foundation dynamic impedance calculation formulas proposed by Gazetas are less than 8. 0%,and the maximum stress error of members is less than 10%compared with those obtained with the 3-D FE model under different seismic waves; thus the foundation dynamic impedance calculation formulas proposed by Gazetas are more suitable for the analysis of soil-large span spatial structure interaction and have a higher precision.
Based on the foundation dynamic impedance calculation formulas suggested by different scholars,the SR( swing-rocking) model was modified by combining with the integral finite element method and starting from the view point of engineering application. The practical simplified calculation method suitable for the soil-structure dynamic interaction analysis of long-span spatial structures was proposed. Then,the model of soil-grid structure interaction was established according to the modified S-R model,and the three-dimensional finite element model verified was also established for a comparative analysis. The study showed that the natural vibration properties and seismic response of the soil-grid structure interaction model based on the modified S-R model reveal same regularities and agree well with those of the 3-D FE model,the rationality of the modified S-R model is verified; the nodal maximum displacement error and peak acceleration error of the soil-grid structure interaction system established with the foundation dynamic impedance calculation formulas proposed by Gazetas are less than 8. 0%,and the maximum stress error of members is less than 10%compared with those obtained with the 3-D FE model under different seismic waves; thus the foundation dynamic impedance calculation formulas proposed by Gazetas are more suitable for the analysis of soil-large span spatial structure interaction and have a higher precision.
引文
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[15]王国华,薛素铎,李雄彦,等.考虑土-结构相互作用的单层球面网壳动力稳定性研究[J].工业建筑,2011(S2):499-506.WANG Guo-hua,XUE Su-duo,LI Xiong-yan,et al,Stability analysis of single-layer spherical reticulated considering soil-structure interaction[J].Industrial Construction,2011(S2):499-506.
[16]Luan X B,Xue S D.The effect of soil structure interaction on the seismic response of spatial structure subjected to the near fault excitation[J].Applied Mechanics and Materials,2011,94(96):877-882.
[17]楼梦麟,邸龙.考虑土-结构相互作用双层柱面网壳在多点输入下的地震反应[J].地震工程与工程振动,2006,26(3):228-231.LOU Meng-lin,DI Long.Seismic response analysis of double-layer cylindrical reticulated shell under multiple support excitations considering dynamic soil-structure interaction[J],Earthquake Engineering and Engineering Vibration,2006,26(3):228-231.
[18]唐敢,陈少林,王法武,等.空间结构-地基动力相互作用的三维时域数值分析方法[J].工程力学,2009,26(8):143-149.TANG Gan,CHEN Shao-lin,WANG Fa-wu,et al.Threedimensional numerical analytical method in time domain for soil-spatial structure dynamic interaction[J].Engineering Mechanics,2009,26(8):143-149.
[19]刘毅,薛素铎,李雄彦.土-结构动力相互作用下网架结构动力性能研究[J].振动与冲击,2014,33(10):23-30.LIU Yi,XUE Su-duo,LI Xiong-yan.An analysis of grid structure dynamic performance considering soil-structure dynamic interaction[J].Journal of Vibration and Shock,2014,33(10):23-30.
[20]卢华喜,梁平英,尚守平.成层地基-桩基-结构动力相互作用体系的计算分析[J].岩土力学学报,2007,29(5):705-711.LU Hua-xi,LIANG Ping-ying,SHANG Shou-ping.Computational analysis of dynamic layered soil-pile-structure interaction[J].Chinese Journal of Geotechnical Engineering,2007,29(5):705-711.
[21]董石麟.中国空间结构的发展与展望[J].建筑结构学报,2010,31(6):38-51.DONG Shi-lin.Development and expectation of spatial structure in China[J].Journal of Building Structure,2010,31(6):38-51.
[22]张玉梅,宋玉普,张晓东.多向地震耦合作用下高耸结构土-结构动力相互研究[J].工程力学,2008,25(2):154-159.ZHANG Yu-mei,SONG Yu-pu,ZHANG Xiao-dong.Investigating the soil-structure dynamic interaction for tall buildings under coupled action of multi-directional earthquake[J].Engineering Mechanics,2008,25(2):154-159.
[23]徐鹏举,唐亮,凌贤长,等.液化场地桩-土-桥梁结构地震相互作用简化分析方法[J].吉林大学学报:地球科学版,2010,40(5):1121-1127.XU Peng-ju,TANG Liang,LING Xian-chang,et al.Simplified analysis method for seismic pile-soil-structure interaction in liquefying ground[J].Journal of Jilin University:Earth Science Edition,2010,40(5):1121-1127.
[24]贺广零,周勇,李杰.风力发电高塔系统地震动动力响应分析[J].工程力学,2009,26(7):72-77.HE Guang-ling,ZHOU Yong,LI Jie.Seismic analysis of wind turbine system[J].Engineering Mechanics,2009,26(7):72-77.
[25]Newmark N M,Rosenblueth E.Foundamentals of earthquake engineering[M].Prentice-Hall Inc Englewood Chiffs,1971.
[26]Pais A,Kausel E.Approximate formulas for dynamic stiffnesses of rigid foundations[J].Soil Dynamics and Earthquake Engineering,1988,7(4):213-227.
[27]Gazetas G.Formulas and charts for impedances of surface and embedded foundations[J].Journal of Geotechnical Engineering,1991,117(9):1363-1381.
[28]Dobry R,Gazetas G.Dynamic response of arbitrarily shaped foundation[J].Journal of Geotechnical Engineering,1986,112(2):109-135.
[29]曹资,薛素铎,王雪生,等.空间结构抗震分析中的地震波选取与阻尼比取值[J].空间结构,2008,14(3):3-8.CAO Zi,XUE Su-duo,WANG Xue-sheng,et al.Selection of earthquake waves and values of damping ratio for space structures in aseismic analysis[J].Spatial Structure,2008,14(3):3-8.
[2]石光磊,甘明,薛素铎.网架结构支座周边杆件抗震设计研究[C].第十四届空间结构学术会议,福州:2012-11-04.
[3]刘伟庆,李昌平,王曙光,等.不同土性地基上高层隔震结构振动台试验对比研究[J].振动与冲击,2013,32(16):128-133.LIU Wei-qing,LI Chang-ping,WANG Shu-guang,et al.Comparative study on high-rise isolated structure founded on various soil foundations by using shaking table tests[J].Journal of Vibration and Shock,2013,32(16):128-133.
[4]陈跃庆,吕西林,李培振,等.不同土性的地基-结构动力相互作用振动台模型实验对比研究[J].土木工程学报,2006,39(5):57-64.CHEN Yue-qing,LU Xi-lin,LI Pei-zhen,et al.Comparative study on the dynamic soil-structure interaction system with various soils by using shaking table model tests[J].China Civil Engineering Journal,2006,39(5):57-64.
[5]尚守平,陈婉若,鲁华伟,等.土-筏基钢框架结构动力相互作用试验研究[J].湖南大学学报:自然科学版,2013,40(3):1-6.SHANG Shou-ping,CHEN Wan-ruo,LU Hua-wei,et al.Experimental investigation of the dynamic soil-structure interaction about steel frame-raft foundation model[J].Journal of Hunan University:Natural Science,2013,40(3):1-6.
[6]冷伍明,杨奇,刘庆潭,等.软基高桥台桩-土相互作用计算新方法研究[J].岩土力学,2009,30(10):3079-3085.LENG Wu-ming,YANG Qi,LIU Qing-tan,et al.Study of new method for calculating response of piled bridged abutment in soft ground[J].Rock and Soil Mechanics,2009,30(10):3079-3085.
[7]刘洁平,张令心.高层建筑土-结构相互作用地震反应分析简化评估方法[J].土木工程学报,2010,43(12):28-34.LIU Jie-ping,ZHANG Ling-xin.A simplified assessment method for seismic response analysis of soil-structure interaction of hige-rise building[J].China Civil Engineering Journal,2010,43(12):28-34.
[8]陈令坤,蒋丽忠,陶磊,等.考虑桩-土作用的高速列车-桥梁地震响应分析[J].岩土力学,2012,33(10):3162-3169.CHEN Lin-kun,JIANG Li-zhong,TAO Lei,et al.Seismic response analysis of high-speed vehicle-bridge considering soil-structure interaction[J].Rock and Soil Mechanics,2012,33(10):3162-3169.
[9]Lysmer J,Westman R A.Dynamic response of footing to vertical loading[J].Journal of Soil Mechanics and Foundation Div,1966,92(1):65-91.
[10]Lysmer J,Seed M B.A computer program for approximate3-D analysis of soil structure interaction problem[J].UCB,1975:5-30.
[11]Penzien J.Seismic analysis of bridge on long piles[J].Journal of the Engineering Mechanics Division,ASCE,1964,90(3):223-254.
[12]Gutierrez J A,Chopra A K.A substructure method for earthquake analysis of structure including structure-soil interaction[J].Journal of Earthquake Engineering and Structure Dynamic,1978(6):51-69.
[13]Hassan A,Panos D.Non-linear dynamic earthquake damfoundation interaction using a BE-FE method[J].Earthquake Engineering and Structure Dynamic,1998,18(18):1065-1075.
[14]薛素铎,孙艳坤,栾小兵,等.考虑土-基础-结构相互作用的网架结构地震响应分析[J].建筑结构学报,2010(S2):34-38.XUESu-duo,SUN Yan-kun,LUAN Xiao-bing,et al.Seismic response analysis of space grid structure considering soil-foundation structure interaction[J].Journal of Building Structure,2010(S2):34-38.
[15]王国华,薛素铎,李雄彦,等.考虑土-结构相互作用的单层球面网壳动力稳定性研究[J].工业建筑,2011(S2):499-506.WANG Guo-hua,XUE Su-duo,LI Xiong-yan,et al,Stability analysis of single-layer spherical reticulated considering soil-structure interaction[J].Industrial Construction,2011(S2):499-506.
[16]Luan X B,Xue S D.The effect of soil structure interaction on the seismic response of spatial structure subjected to the near fault excitation[J].Applied Mechanics and Materials,2011,94(96):877-882.
[17]楼梦麟,邸龙.考虑土-结构相互作用双层柱面网壳在多点输入下的地震反应[J].地震工程与工程振动,2006,26(3):228-231.LOU Meng-lin,DI Long.Seismic response analysis of double-layer cylindrical reticulated shell under multiple support excitations considering dynamic soil-structure interaction[J],Earthquake Engineering and Engineering Vibration,2006,26(3):228-231.
[18]唐敢,陈少林,王法武,等.空间结构-地基动力相互作用的三维时域数值分析方法[J].工程力学,2009,26(8):143-149.TANG Gan,CHEN Shao-lin,WANG Fa-wu,et al.Threedimensional numerical analytical method in time domain for soil-spatial structure dynamic interaction[J].Engineering Mechanics,2009,26(8):143-149.
[19]刘毅,薛素铎,李雄彦.土-结构动力相互作用下网架结构动力性能研究[J].振动与冲击,2014,33(10):23-30.LIU Yi,XUE Su-duo,LI Xiong-yan.An analysis of grid structure dynamic performance considering soil-structure dynamic interaction[J].Journal of Vibration and Shock,2014,33(10):23-30.
[20]卢华喜,梁平英,尚守平.成层地基-桩基-结构动力相互作用体系的计算分析[J].岩土力学学报,2007,29(5):705-711.LU Hua-xi,LIANG Ping-ying,SHANG Shou-ping.Computational analysis of dynamic layered soil-pile-structure interaction[J].Chinese Journal of Geotechnical Engineering,2007,29(5):705-711.
[21]董石麟.中国空间结构的发展与展望[J].建筑结构学报,2010,31(6):38-51.DONG Shi-lin.Development and expectation of spatial structure in China[J].Journal of Building Structure,2010,31(6):38-51.
[22]张玉梅,宋玉普,张晓东.多向地震耦合作用下高耸结构土-结构动力相互研究[J].工程力学,2008,25(2):154-159.ZHANG Yu-mei,SONG Yu-pu,ZHANG Xiao-dong.Investigating the soil-structure dynamic interaction for tall buildings under coupled action of multi-directional earthquake[J].Engineering Mechanics,2008,25(2):154-159.
[23]徐鹏举,唐亮,凌贤长,等.液化场地桩-土-桥梁结构地震相互作用简化分析方法[J].吉林大学学报:地球科学版,2010,40(5):1121-1127.XU Peng-ju,TANG Liang,LING Xian-chang,et al.Simplified analysis method for seismic pile-soil-structure interaction in liquefying ground[J].Journal of Jilin University:Earth Science Edition,2010,40(5):1121-1127.
[24]贺广零,周勇,李杰.风力发电高塔系统地震动动力响应分析[J].工程力学,2009,26(7):72-77.HE Guang-ling,ZHOU Yong,LI Jie.Seismic analysis of wind turbine system[J].Engineering Mechanics,2009,26(7):72-77.
[25]Newmark N M,Rosenblueth E.Foundamentals of earthquake engineering[M].Prentice-Hall Inc Englewood Chiffs,1971.
[26]Pais A,Kausel E.Approximate formulas for dynamic stiffnesses of rigid foundations[J].Soil Dynamics and Earthquake Engineering,1988,7(4):213-227.
[27]Gazetas G.Formulas and charts for impedances of surface and embedded foundations[J].Journal of Geotechnical Engineering,1991,117(9):1363-1381.
[28]Dobry R,Gazetas G.Dynamic response of arbitrarily shaped foundation[J].Journal of Geotechnical Engineering,1986,112(2):109-135.
[29]曹资,薛素铎,王雪生,等.空间结构抗震分析中的地震波选取与阻尼比取值[J].空间结构,2008,14(3):3-8.CAO Zi,XUE Su-duo,WANG Xue-sheng,et al.Selection of earthquake waves and values of damping ratio for space structures in aseismic analysis[J].Spatial Structure,2008,14(3):3-8.
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