地基弹性参数对于长型大截面地下结构横向自由振动的影响
摘要
自由振动分析是地下结构地震动力响应分析的基础。本文利用笔者先前得到的长型地下结构的自由振动方程,研究了地基弹性参数对地下结构自由振动的影响。由分析可以看出,随着地基弹性参数值的增加,结构中波速值总的趋势是增加,但是温克尔地基参数对结构中波速的影响远大于第二地基参数的影响;地下结构振动频率总的趋势是随着温克尔地基参数k和第二地基参数gP值的增加而增加;与地基参数对地下结构中波的传播速度的影响不同,k和gP对地下结构振动频率的影响是同阶的,因此不能忽略gP对地下结构自由振动的影响。
Free vibration analysis is the foundation of dynamic seismic analysis for underground structures. The effect of soil elastic parameters on the free vibration of long large cross section underground structure is studied on the basis of the vibration equation of linear underground structures derived by the authors previously.Parameter study shows that in general wave propagation velocities in the structure increase with soil elastic parameters.But the influence of Winkler's parameter k is significant,while the effect of the second soil elastic parameter gP is insignificant.Free vibration frequency of underground structure increases with relative wave number and soil elastic parameters.Differing from the influence of soil elastic parameters on wave propagation velocities,the influences of soil elastic parameters k and gP on vibration frequency of underground structure have the same order,therefore the influence of the second soil parameter gP on free vibration of underground structure should not be neglected.
Free vibration analysis is the foundation of dynamic seismic analysis for underground structures. The effect of soil elastic parameters on the free vibration of long large cross section underground structure is studied on the basis of the vibration equation of linear underground structures derived by the authors previously.Parameter study shows that in general wave propagation velocities in the structure increase with soil elastic parameters.But the influence of Winkler's parameter k is significant,while the effect of the second soil elastic parameter gP is insignificant.Free vibration frequency of underground structure increases with relative wave number and soil elastic parameters.Differing from the influence of soil elastic parameters on wave propagation velocities,the influences of soil elastic parameters k and gP on vibration frequency of underground structure have the same order,therefore the influence of the second soil parameter gP on free vibration of underground structure should not be neglected.
引文
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[2]Newmark N M.Problems in wave propagation in soil and rock[C]//Proceeding of the international sympo- ??sium on wave propagation and dynamic properties of earth materials,New Mexico,USA:University of New Mexico Press,1968.7-26.
[3]Kuesel T R.Earthquake design criteria for subway [J].Journal of Structural Division - ASCE,1969,95 (6):1213-1231.
[4]St John C M,Zahrah T F.Aseismic design of under-ground structures[J].Tunneling Underground Space Technology,1987,2(2):165-197.
[5]Power M S,Rosidi D,Kaneshiro J.Strawman: screening,evaluation,and retrofit design of tunnels [R].Buffalo:National Center for Earthquake Engineering Research,1996.
[6]Constantopolous I V,Motherwel J T,Hall J R.Dynamic analysis of tunnels[C]//Proceedings of Third International Conference in Geomechanics,Aachen, Germary:A.A.Balkema Press,1979.262-265.
[7]Navarro C,Samartin A.Simplified longitudinal seismic analysis of buried tunnels[J].Software Engineering Workstation,1988,4(1):3-10.
[8]Shukla D K,Rizzo P C,Stephenson D E.Earthquake load analysis of tunnels and shafts[C]//Proceeding of the Seventh World Conference on Earthquake Engineering, Istanbul,Turkey:Turkish National Commitee on Earthquake Engineering Press,1980.201-208.
[9]小泉淳.盾构隧道的抗震研究及算例[M].北京:中国建筑工业出版社,2009.小泉淳.Earthquake Resistant Research on Shield Tunnels and Examples[M].Beijing:China Construction Industry Press,2009.
[10]郑永来,杨林德,李文艺,等.地下结构抗震[M].上海:同济大学出版社,2005. Zheng Y L,Yang L D,Li W Y,et al.Earthquake Resistant Underground Structures[M].Shanghai: Tongji University Press,2005.
[11]Sanchez-Merino A L,Fernandez-Saez J,Navarro C. Simplified longitudinal seismic response of tunnel linings subjected to surface waves[J].Soil Dynamics and Earthquake Engineering,2009,29(3):579-582.
[12]匡志平,刘竹钊,曹国安.地下结构纵向随机地震响应和极值分析[J].同济大学学报,2002,30(8):922-926. Kuang Z P,Liu Z Z,Cao G A.Axial random seismic response and external value analysis of underground structures[J].Journal of Tongji University,2002,30 (8):922-926.
[13]严松宏,梁波,高波.地下结构纵向抗震动力可靠度分析[J].岩石力学与工程学报,2005,24(1):71-76. Yan S H,Liang B,Gao B.Dynamic analysis of longitudinal seismic reliability of underground structures [J].Chinese Journal of Rock Mechanics and Engineering, 2005,24(1):71-76.
[14]Luco J E,Barros F C P.Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space [J].Foundation Earthquake Engineering and Structural Dynamics,1994,(23):553-567.
[15]Karadeniz H.Earthquake analysis of buried structures and pipelines based on Rayleigh wave propagation ??[J].International Journal of Offshore Polar Engineering, 2001,11(2):133-140.
[16]Matsubara K.Hirasawa K,Urano K.On the wave-length for seismic design of underground pipeline structures[C]//Proceedings of the First International Conference on Earthquake Geotechnical Engineering. Tokyo,Japan:Press of Tokyo University,1995.587- 590.
[17]陈灿寿,戚承志,陈剑杰,等.长形大截面地下结构的横向自由振动[J].世界地震工程,2010,27(1):90-95. Chen C S,Qi C Z,Chen J J,et al.Dynamic response of the roof slab of shallowly buried underground structure under vertical seismic excitation[J].World Earthquake Engineering,2010,27(1):90-95.
[18]Pasternak P L.On a new method of analysis of rigid and flexible foundations on an elastic subsoil(in Russian) [C]//Collection of Papers of Moscow Civil Engineering Institute.Moscow,Russia:Press of MISI, 1956.116-144.
[19]Hutchinson J R.Shear coefficients for Timoshenko beam theory[J].Journal of Applied Mechanics, 2001,68(1):87-92.
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