基于黏着滑动耦合动力分析的Newmark滑块位移法
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摘要
基于摩擦滑移结构的抗震机制,在动力响应分析中考虑塑性滑动位移与加速度响应之间的关联性。当滑动体发生滑动时,将滑动加速度作为附加惯性荷载直接引入动力平衡方程的右端荷载项,联立滑动体底部的平衡方程,利用振型叠加法确定滑动时刻滑动体的响应加速度和滑动加速度,进而利用Newmark滑块位移法得到该时刻滑动位移增量和累计滑动位移,直至地震结束。利用上述方法对Wartman振动台试验中所采用的可变形土柱进行动力响应分析,加速度响应和滑动位移结果均与Wartman的试验结果较为一致。最后,借助重力墙挡土结构对处于共振状态下基于上述算法和传统解耦算法墙体的动力响应和滑动变形结果进行比较。计算结果表明,塑性滑动位移和动力响应之间的关联性对滑动体动力响应幅值和滑动变形均具有显著的影响,忽略两者关联性的解耦算法在滑动方向上的响应加速度幅值和累计滑移量与基于上述算法的计算结果存在较大差异,累计滑动位移和加速度的卓越周期为上述算法的2倍左右,计算结果较为保守。
Earthquake-induced sliding displacements of earth structures are generally evaluated using sliding block analyses that do not accurately model the seismic response of the sliding body or the exciting loads along the sliding plane.The traditional decoupled approximation introduced to capture each of these effects separately is generally unreasonable.A simple coupled analytical model based on the rules of resistant earthquake of sliding-isolated structures,which captures simultaneously the response of the sliding mass and the nonlinear stick-slip sliding response along the sliding plane,is presented.In this method,as the sliding is initiated,the sliding acceleration is substituted directly in motion equation as one loading item to get the increment of sliding displacement.The modified motion equation shows that high inertial forces can nevertheless develop in a sliding mass at the beginning of each sliding process because of the additional inertial forces resulted from the transient sliding acceleration,while the sliding surfaces might limit energy transmission.Moreovert,he fundamental period of sliding acceleration is about half of the mean period of the input motion in the processes of sliding.The proposed Newmark sliding model is validated with Wartman′s shaking table experiments of deformable soil columns sliding down an inclined plane.The correlation between plastic sliding displacement and the dynamic response of earth structures is evaluated,and comparisons are made between proposed and decoupled analytical methods with linear material properties based on results of sliding displacements and amplitudes of dynamic response in sliding direction through a deformable soil column and a practical retaining wall.It is shown that the differences between the two approaches are remarkable;the plastic sliding deformation can limit effectively the amplitude of dynamic response in sliding direction and the decoupled will lead to conservative results.
Earthquake-induced sliding displacements of earth structures are generally evaluated using sliding block analyses that do not accurately model the seismic response of the sliding body or the exciting loads along the sliding plane.The traditional decoupled approximation introduced to capture each of these effects separately is generally unreasonable.A simple coupled analytical model based on the rules of resistant earthquake of sliding-isolated structures,which captures simultaneously the response of the sliding mass and the nonlinear stick-slip sliding response along the sliding plane,is presented.In this method,as the sliding is initiated,the sliding acceleration is substituted directly in motion equation as one loading item to get the increment of sliding displacement.The modified motion equation shows that high inertial forces can nevertheless develop in a sliding mass at the beginning of each sliding process because of the additional inertial forces resulted from the transient sliding acceleration,while the sliding surfaces might limit energy transmission.Moreovert,he fundamental period of sliding acceleration is about half of the mean period of the input motion in the processes of sliding.The proposed Newmark sliding model is validated with Wartman′s shaking table experiments of deformable soil columns sliding down an inclined plane.The correlation between plastic sliding displacement and the dynamic response of earth structures is evaluated,and comparisons are made between proposed and decoupled analytical methods with linear material properties based on results of sliding displacements and amplitudes of dynamic response in sliding direction through a deformable soil column and a practical retaining wall.It is shown that the differences between the two approaches are remarkable;the plastic sliding deformation can limit effectively the amplitude of dynamic response in sliding direction and the decoupled will lead to conservative results.
引文
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[5]MAKDISI F I,SEED H B.Simplified procedure for estimation dam and embankment earthquake induced deformations[J].Journal of the Geotechnical Engineering Division,ASCE,1978,104(GT7):849–868.
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[9]姚谦峰,夏禾.基础滑移隔震结构振动特性分析[J].世界地震工程,2001,17(1):50–55.(YAO Qianfeng,XIA He.Analysis of vibration properties of structure with sliding base isolation[J].World Information on Earthquake Engineering,2001,17(1):50–55.(in Chinese))
[10]IDRISS I M,SEED H B.Seismic response of horizontal soil layers[J].Journal of the Soil Mechanics and Foundation Division,ASCE,1968,94(4):693–698.
[11]DAKOULAS P,GAZETAS G.A class of inhomogeneous shear models for seismic response of dams and embankments[J].Soil Dynamics and Earthquake Engineering,1985,4(4):166–182.
[12]WARTMAN J,BRAY J D,SEED R B.Shaking table experimental of a model slope subjected to a pair of repeated ground motions[C]//Proceedings of the Fourth International Conference on Recent Advance in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium.San Diego,California:[s.n.],2001.
[13]WARTMAN J,BRAY J D,SEED R B.Inclined plane studies of the Newmark sliding block procedure[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,2003,129(8):673–684.
[14]WARTMAN J.Physical model studies of seismically induced deformations in slopes[Ph.D.Thesis][D].Berkeley,California:Department of Civil Engineering,University of California,1999.
[15]中华人民共和国行业标准编写组.DL5073–2000水工建筑物抗震设计规范[S].北京:中国建筑工业出版社,2000.(The Professional Standards Compilation Group of People′s Republic of China.DL5073–2000 Specifications for seismic design of hydraulic structures[S].Beijing:China Architecture and Building Press,2000.(in Chinese))
[2]李湛,栾茂田.土工建筑物地震永久滑移变形计算方法研究进展评述[J].防灾减灾工程学报,2005,25(2):227–234.(LI Zhan,LUAN Maotian.State-of-the-art review on simplified procedures for evaluation of seismically-induced sliding deformation of earth structures[J].Journal of Disaster Prevention and Mitigation Engineering,2005,25(2):227–234.(in Chinese))
[3]JINMAN K,NICHOLAS S.Direct estimation of yield acceleration in slope stability analyses[J].Journal of Geotechnical and Geoenvironmental Engineering,2004,130(1):111–115.
[4]栾茂田,李湛.堤坝非线性地震响应的离散型剪切条模型等价线性化方法[J].岩石力学与工程学报,2006,25(1):40–46.(LUAN Maotian,LI Zhan.Equivalent linearization technical based on discrete shear-slice model for nonlinear seismic response of embankments[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(1):40–46.(in Chinese))
[5]MAKDISI F I,SEED H B.Simplified procedure for estimation dam and embankment earthquake induced deformations[J].Journal of the Geotechnical Engineering Division,ASCE,1978,104(GT7):849–868.
[6]GAZETAS G,UDDIN N.Permanent deformation on preexisting sliding surfaces in dams[J].Journal of Geotechnical Engineering,ASCE,1994,120(11):2 041–2 061.
[7]李俊杰,邵龙潭,邵宇.面板堆石坝地震永久变形计算方法研究[J].大连理工大学学报,1998,38(5):580–585.(LI Junjie,SHAO Longtan,SHAO Yu.Study on calculation method of permanent deformation due to earthquake for concrete faced rockfill dam[J].Journal of Dalian University of Technology,1998,38(5):580–585.(in Chinese))
[8]YEONG B Y,LEE T Y.Response of multi-degree of freedom structures with sliding supports[J].Earthquake Engineering and Structural Dynamics,1990,19(5):739–752.
[9]姚谦峰,夏禾.基础滑移隔震结构振动特性分析[J].世界地震工程,2001,17(1):50–55.(YAO Qianfeng,XIA He.Analysis of vibration properties of structure with sliding base isolation[J].World Information on Earthquake Engineering,2001,17(1):50–55.(in Chinese))
[10]IDRISS I M,SEED H B.Seismic response of horizontal soil layers[J].Journal of the Soil Mechanics and Foundation Division,ASCE,1968,94(4):693–698.
[11]DAKOULAS P,GAZETAS G.A class of inhomogeneous shear models for seismic response of dams and embankments[J].Soil Dynamics and Earthquake Engineering,1985,4(4):166–182.
[12]WARTMAN J,BRAY J D,SEED R B.Shaking table experimental of a model slope subjected to a pair of repeated ground motions[C]//Proceedings of the Fourth International Conference on Recent Advance in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium.San Diego,California:[s.n.],2001.
[13]WARTMAN J,BRAY J D,SEED R B.Inclined plane studies of the Newmark sliding block procedure[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,2003,129(8):673–684.
[14]WARTMAN J.Physical model studies of seismically induced deformations in slopes[Ph.D.Thesis][D].Berkeley,California:Department of Civil Engineering,University of California,1999.
[15]中华人民共和国行业标准编写组.DL5073–2000水工建筑物抗震设计规范[S].北京:中国建筑工业出版社,2000.(The Professional Standards Compilation Group of People′s Republic of China.DL5073–2000 Specifications for seismic design of hydraulic structures[S].Beijing:China Architecture and Building Press,2000.(in Chinese))
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