埋地管线-土横向动力相互作用等效弹簧系数解析解
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摘要
基于一维柱面弹性波动理论,推导了埋地管线-土横向动力相互作用等效弹簧系数解析表达式,并对该表达式的影响因素,诸如频率(ω)、管线埋深(d)、管线半径(b)、场地波速(VP)、泊松比(μ)的影响程度进行了分析。分析结果表明,无量纲频率bω/VP取较小值时(<0.1),弹簧系数取值随着管线埋深与管线半径之比γ的增加而增大,但总是限制在2.0G～4.0G(G为土体剪切模量)之间,且泊松比对其影响很小,对于工程实际情况,弹簧系数可在该范围内取值。
Based on one-dimensional wave motion theory in cylindrical coordinates,the analytical expression of soil spring constant for buried pipeline-soil lateral dynamic interaction is derived.The influence factors,such as frequency(ω),depth of pipeline(d),radius of pipeline(b),P-wave velocity(VP),Possion ratio(μ) are analyzed.The results show that when non-dimensional frequency bω/VP is smaller than 0.1,soil spring constant increases with the ratio γ of the depth of pipeline over the radius of pipeline,but is limited in 2.0G~4.0G(G= soil shear modulus),meanwhile,the influence of Possion ratio is negligible.For engineering application,the soil spring constant between 2.0G~4.0G is recommended.
Based on one-dimensional wave motion theory in cylindrical coordinates,the analytical expression of soil spring constant for buried pipeline-soil lateral dynamic interaction is derived.The influence factors,such as frequency(ω),depth of pipeline(d),radius of pipeline(b),P-wave velocity(VP),Possion ratio(μ) are analyzed.The results show that when non-dimensional frequency bω/VP is smaller than 0.1,soil spring constant increases with the ratio γ of the depth of pipeline over the radius of pipeline,but is limited in 2.0G~4.0G(G= soil shear modulus),meanwhile,the influence of Possion ratio is negligible.For engineering application,the soil spring constant between 2.0G~4.0G is recommended.
引文
[1]Matsubara K,Hoshiya M.Soil spring constants of buried pipelines for seismic design[J].Journal of Engineering Mechanic,2000,126(1):76-83.
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[2]Parmelee R,Ludtke C.Seismic soil-structure interaction of buried pipelines[C]//Proc.U.S.Nat.Conf.Earthq.Engng.Oakland:EarthquakeEng Res Inst,1975.406-415.
[3]Hindy A,Novak M.Earthquake response of underground pipelines[J].Earthquake Eng.Struct.Dyn,1979,7(5):451-476.
[4]王海波,林皋.半无限弹性介质中管线地震反应分析[J].土木工程学报,1988,20(3):80-91.WANG Haibo,LIN Gao.Seismic response of the pipeline buried in three dimensional semi-infinite elastic medium[J].China Civil EngineeringJournal,1988,20(3):80-91.(in Chinese)
[5]符圣聪.用于埋管抗震计算的地面位移和地基反力系数[J].特种结构,1992(4):4-9.FU Shengcong.Ground displacement and coefficient of subgrade reaction for buried pipeline seismic evaluation[J].Special Structure,1992,(4):4-9.(in Chinese)
[6]陆明万,罗学富.弹性理论基础[M].北京:清华大学出版社,1990:46.LU Mingwan,LUO Xuefu.Foundations of elasticity[M].Beijing:Tsinghua University Press,1990:46.(in Chinese)
[7]杜修力.工程场地波动理论与方法[M].北京:科学出版社,2008:282-285.DU Xiuli.Theories and Methods of Wave Motion for Engineering[M].Beijing:Science Press,2008:282-285.(in Chinese)
[8]梁昆淼.数学物理方法[M].北京:高等教育出版社,1998:328.LIANG Kunmiao.Method of Mathematical Physics[M].Higher Education Press,1998:328.(in Chinese)
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