P波作用下深埋隧道动应力集中问题参数敏感性分析
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摘要
采用波函数展开法,推导了无限介质中双层衬砌圆形洞室在P波作用下衍射问题的解析解,并结合南水北调西线1期工程3#引水隧道开展了动应力集中系数参数敏感性分析。计算结果表明,围岩和内层衬砌的弹性模量对结构的动应力集中系数影响较大,而围岩泊松比对计算结果的影响几乎可以忽略不计;围岩和衬砌之间的介质层在一定程度上具有减震作用,前提条件是其弹性模量低于围岩弹性模量的1/20,否则减震效果不明显。
Based on wave function expansion method,an analytical solution for dynamic stress concentration of circular tunnel with double-layer-liner in infinite media under incident plane P waves is deduced.According to the solution,parameters sensitivity analysis of dynamic stress concentration is carried out in combination with the tunnel #3of the first phase project along the Western Route Project of South-to-North Water Transfer Project.The calculation results show that the elasticity modulus of surrounding rock and inner concrete liner have a greater effect on dynamic stress concentration factor;and the effect of rock Poisson's ratio on the factor almost can be neglected.The layer between surrounding rock and inner concrete liner exhibited role in seismic isolation under the prerequisite conditions of its elasticity modulus is less than 1/20 of one of the surrounding rock;otherwise,the effect on seismic isolation is not obvious.
Based on wave function expansion method,an analytical solution for dynamic stress concentration of circular tunnel with double-layer-liner in infinite media under incident plane P waves is deduced.According to the solution,parameters sensitivity analysis of dynamic stress concentration is carried out in combination with the tunnel #3of the first phase project along the Western Route Project of South-to-North Water Transfer Project.The calculation results show that the elasticity modulus of surrounding rock and inner concrete liner have a greater effect on dynamic stress concentration factor;and the effect of rock Poisson's ratio on the factor almost can be neglected.The layer between surrounding rock and inner concrete liner exhibited role in seismic isolation under the prerequisite conditions of its elasticity modulus is less than 1/20 of one of the surrounding rock;otherwise,the effect on seismic isolation is not obvious.
引文
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[15]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.LIANG Jian-wen,LIU Zhong-xian.Scattering of cylindrical waves around a cavity in a half-space[J].Earthquake Engineering and Engineering Vibration,2008,28(5):27-37.
[16]梁建文,张浩,LEE V W.地下洞室群对地面运动影响问题的级数解答—P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,LEE V W.A series solution for surface motion amplifi-cation due to underground group cavities—incident P waves[J].Acta Seismologica Sinica,2004,26(3):269-280.
[17]梁建文,张浩,LEE V W.地下双洞室在SV波入射下动力响应问题解析解[J].振动工程学报,2004,17(2):16-24.LIANG Jian-wen,ZHANG Hao,LEE V W.An analytical solution for dynamic stress concentration of underground twin cavities due to incident SV waves[J].Journal of Vibration Engineering,2004,17(02):16-24.
[18]梁建文,张浩,LEE V W.地下洞室群对地面运动的影响[J].土木工程学报,2005,38(02):106-113.LIANG Jian-wen,ZHANG Hao,LEE V.W.Effect of underground group cavities on ground surface motion[J].China Civil Engineering Journal,2005,38(02):106-113.
[19]纪晓东,梁建文,杨建江.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):511-517.JI Xiao-dong,LIANG Jian-wen,YANG Jian-jiang.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incident plane P and SV waves[J].Journal of Tianjin University,2006,39(5):511-517.
[20]尤红兵,梁建文.层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bin,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
[2]PAO Y H,MAO C C.The diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane,Russak&Company Inc.,1972.
[3]LEE V,CAO H.Diffraction of SV waves by circular canyons of various depths[J].Journal of Engineering Mechanics,1989,115(9):2035-2056.
[4]LEE V,KARL J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11(8):445-456.
[5]LEE V,TRIFUNAC M.Response of tunnels to incident SH-waves[J].Journal of the Engineering Mechanics Division,1979,105(4):643-659.
[6]CAO H,LEE V W.Scattering and diffraction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio[J].European Journal of Obstetrics&Gynecology and Reproductive Biology,1979,9(3):141-150.
[7]DAVIS C A,LEE V W,BARDET J.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering and Structural Dynamics,2001,30(3):383-410.
[8]MANOOGIAN M,LEE V.Diffraction of SH-waves by subsurface inclusions of arbitrary shape[J].Journal of Engineering Mechanics,1996,122(2):123-129.
[9]梁建文,巴振宁,LEE V W.平面P波在饱和半空间中洞室周围的散射(II):数值结果[J].地震工程与工程振动,2007,27(2):1-11.LIANG Jian-wen,BA Zhen-ling,LEE V W.Scattering of plane P waves around a cavity in poroelastic half-space(II):numerical results[J].Earthquake Engineering and Engineering Vibration,2007,27(2):1-11.
[10]梁建文,巴振宁,LEE V W.平面P波在饱和半空间中洞室周围的散射(I):解析解[J].地震工程与工程振动,2007,27(01):1-6.LIANG Jian-wen,BA Zhen-ling,LEE V W.Scattering of plane P waves around a cavity in poroelastic half-space(I):analytical solution[J].Earthquake Engineering and Engineering Vibration,2007,27(01):1-6.
[11]梁建文,尤红兵.层状半空间中洞室对入射平面P波的放大作用[J].地震工程与工程振动,2005,25(2):16-24.LIANG Jian-wen,YOU Hong-bing.Amplification of plane P waves by a cavity in a layered half-space[J].Earthquake Engineering and Engineering Vibration,2005,25(2):16-24.
[12]梁建文,张浩,LEE V W.平面P波入射下地下洞室群动应力集中问题解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jian-wen,ZHANG Hao,LEE V W.An analytical solution for dynamic stress concentration of underground cavities under incident plane P waves[J].Chinese Jounal of Geotechnical Engineering,2004,26(6):815-819.
[13]LIANG J,BA Z,LEE V.Diffraction of plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space[J].Soil Dynamics and Earthquake Engineering,2006,26(6-7):582-610.
[14]梁建文,纪晓东.地下衬砌洞室对Rayleigh波的放大作用[J].地震工程与工程振动,2006,26(4):24-31.LIANG Jian-wen,JI Xiao-dong.Amplification of Rayleigh waves due to underground lined cavitie[J].Earthquake Engineering and Engineering Vibration,2006,26(4):24-31.
[15]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.LIANG Jian-wen,LIU Zhong-xian.Scattering of cylindrical waves around a cavity in a half-space[J].Earthquake Engineering and Engineering Vibration,2008,28(5):27-37.
[16]梁建文,张浩,LEE V W.地下洞室群对地面运动影响问题的级数解答—P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,LEE V W.A series solution for surface motion amplifi-cation due to underground group cavities—incident P waves[J].Acta Seismologica Sinica,2004,26(3):269-280.
[17]梁建文,张浩,LEE V W.地下双洞室在SV波入射下动力响应问题解析解[J].振动工程学报,2004,17(2):16-24.LIANG Jian-wen,ZHANG Hao,LEE V W.An analytical solution for dynamic stress concentration of underground twin cavities due to incident SV waves[J].Journal of Vibration Engineering,2004,17(02):16-24.
[18]梁建文,张浩,LEE V W.地下洞室群对地面运动的影响[J].土木工程学报,2005,38(02):106-113.LIANG Jian-wen,ZHANG Hao,LEE V.W.Effect of underground group cavities on ground surface motion[J].China Civil Engineering Journal,2005,38(02):106-113.
[19]纪晓东,梁建文,杨建江.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):511-517.JI Xiao-dong,LIANG Jian-wen,YANG Jian-jiang.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incident plane P and SV waves[J].Journal of Tianjin University,2006,39(5):511-517.
[20]尤红兵,梁建文.层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bin,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
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