弹性半空间中含粘性滑移界面圆形衬砌洞室对平面SH波的散射
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摘要
为揭示粘性滑移界面对衬砌洞室地震响应规律的影响,采用一种高精度的间接边界积分方程法,基于粘性滑移界面模型,求解了弹性半空间中浅埋圆形衬砌洞室对入射平面SH波的散射。结果表明:中低频波入射时,随着界面滑移刚度系数的增加,衬砌洞室上方地表位移幅值减小,而界面粘性系数对地表位移反应不明显;衬砌内壁应力幅值随界面滑移刚度系数的增加而增大。高频波入射下,较小的界面粘性系数对地表位移放大效应更为显著;当界面滑移刚度系数较小时,部分频段由于体系共振效应会造成显著的应力集中;高频特别是共振频率段,粘性系数对应力幅值有明显的降幅效应。研究结论可为实际地下工程结构的抗震设计提供部分理论依据。
In order to reveal the effects of viscous-slip interface on the seismic response of lining cavity, this paper presents an indirect boundary integration equation method(IBIEM) of high precision for solving the scattering of plane SH waves by a shallow two-dimensional circular lining cavity with a viscous-slip interface model in elastic half-space. The results show that when the frequency of incident waves is low and medium, the surface displacement above the lining cavity decreases with increasing stiffness parameter of visco-elastic interface, on the contrast, the viscosity coefficient of visco-elastic interface has a light effects on the surfacedisplacement; the stress amplitude of internal surface of lining increases with increasing stiffness parameter of visco-elastic interface. When the frequency of incident waves is high, the small viscosity coefficient of visco-elastic interface has obvious effect on the surface displacement amplification; in the case of small stiffness parameter of visco-elastic interface, some frequency bands have significant stress concentration effects due to the system resonance effect; at high frequency, especially in resonant frequency band, the viscosity coefficient of visco-elastic interface has obvious decrease effect on the stress amplitude. The conclusions provide some theoretical basis for seismic design of underground engineering structures.
In order to reveal the effects of viscous-slip interface on the seismic response of lining cavity, this paper presents an indirect boundary integration equation method(IBIEM) of high precision for solving the scattering of plane SH waves by a shallow two-dimensional circular lining cavity with a viscous-slip interface model in elastic half-space. The results show that when the frequency of incident waves is low and medium, the surface displacement above the lining cavity decreases with increasing stiffness parameter of visco-elastic interface, on the contrast, the viscosity coefficient of visco-elastic interface has a light effects on the surfacedisplacement; the stress amplitude of internal surface of lining increases with increasing stiffness parameter of visco-elastic interface. When the frequency of incident waves is high, the small viscosity coefficient of visco-elastic interface has obvious effect on the surface displacement amplification; in the case of small stiffness parameter of visco-elastic interface, some frequency bands have significant stress concentration effects due to the system resonance effect; at high frequency, especially in resonant frequency band, the viscosity coefficient of visco-elastic interface has obvious decrease effect on the stress amplitude. The conclusions provide some theoretical basis for seismic design of underground engineering structures.
引文
[1]陈国兴,陈苏,杜修力,等.城市地下结构抗震研究进展[J].防灾减灾工程学报,2016,36(1):1-23.(CHEN Guoxing,CHEN Su,DU Xiuli,et al.Review of seismic damage,model test,available design and analysis methods of urban underground structures:retrospect and prospect[J].Journal of disaster prevention and mitigation engineering,2016,36(1):1-23(in Chinese)).
[2]LEE V W.Response of tunnels to incident SH waves[J].Journal of engineering mechanics,1979,105(4):643-659.
[3]梁建文,纪晓东,LEE V W.地下圆形衬砌隧道对沿线地震动的影响(II):数值结果[J].岩土力学,2005,26(5):687-692.(LIANGJianwen,JI Xiaodong,LEE V W.On the effects of an underground lined tunnel on ground motion(II):numerical results[J].Rock and soil mechanics,2005,26(5):687-692(in Chinese)).
[4]GAO Y,DAI D,ZHANG N,et al.Scattering of plane and cylindrical SH waves by a horseshoe shaped cavity[J].Journal of earthquake&tsunami,2016,10(2):1650011.
[5]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P波的散射[J].岩土力学,2004,25(12):1867-1872.(LI Weihua,ZHAOChenggang.An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space[J].Rock and soil mechanics,2004,25(12):1867-1872(in Chinese)).
[6]李伟华,申齐豪,赵成刚.饱和土半空间中地下圆形衬砌隧道对平面SV波的散射[J].防灾减灾工程学报,2009,29(2):172-178.(LIWeihua,SHEN Qihao,ZHAO Chenggang.Scattering of plane SVwaves by a underground circular lined tunnel in half space saturated soil[J].Journal of disaster prevention and mitigation engineering,2009,29(2):172-178(in Chinese)).
[7]LIU Q J,WANG R Y.Dynamic response of twin closely-spaced circular tunnels to harmonic plane waves in a full space[J].Tunnelling and underground space technology,2012,32(6):212-220.
[8]庄海洋,陈国兴.双洞单轨地铁区间隧道非线性地震反应分析[J].地震工程与工程振动,2006,26(2):131-137.(ZHUANG Haiyang,CHEN Guoxing.Analysis of nonlinear earthquake response of metro double-tunnels[J].Earthquake engineering and engineering vibration,2006,26(2):131-137(in Chinese)).
[9]刘中宪,梁建文,张贺.弹性半空间中衬砌洞室对平面P波和SV波的散射(II):数值结果[J].自然灾害学报,2010,19(4):77-88.(LIUZhongxian,LIANG Jianwen,ZHANG He.Scattering of P and SVwaves by a lined tunnel in elastic half space(II):numerical results[J].Journal of natural disasters,2010,19(4):77-88(in Chinese)).
[10]刘中宪,王楚楚,蒋坪临,等.球面压缩波入射下深埋三维衬砌洞室的动应力集中效应[J].应用力学学报,2017,34(5):904-911.(LIU Zhongxian,WANG Chuchu,JIANG Pinglin,et al.The dynamic stress concentration effect of deeply buried three-dimensional lining cavity under the spherical compression wave[J].Chinese journal of applied mechanics,2017,34(5):904-911(in Chinese)).
[11]张海,杨国岗,刘中宪,等.弹性半空间中含直边界半圆形衬砌隧道对SH波的散射解析解[J].应用力学学报,2017,34(2):243-249.(ZHANG Hai,YANG Guogang,LIU Zhongxian,et al.An analytical solution to scattering of plane SH waves by a semi-circle lined tunnel in elastic half-space boundary[J].Chinese journal of applied mechanics,2017,34(2):243-249(in Chinese)).
[12]孙铁军,王伟,罗明睿,等.不同衬砌结构缺陷对隧道结构整体安全性的影响[J].建筑科学与工程学报,2017,34(3):82-90.(SUNTiejun,WANG Wei,LUO Mingrui,et al.Influences of different lining structure defects on overall safety of tunnel structure[J].Journal of architecture and civil engineering,2017,34(3):82-90(in Chinese)).
[13]YI C,JOHANSSON D,NYBERG U,et al.Scattering of SH-waves by a shallow circular lined tunnel with an imperfect interface[C]//Proceedings of the 8th International Symposium on Ground Support in Mining and Underground Construction.Nordlund:[s.n.],2016.
[14]YI C,ZHANG P,JOHANSSON D,et al.Dynamic response of a circular lined tunnel with an imperfect interface subjected to cylindrical P-waves[J].Computers&geotechnics,2014,55(1):165-171.
[15]FANG Xueqian,JIN H X.Visco-elastic imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to P and SVwaves[J].Soil dynamics and earthquake engineering,2016,88:1-7.
[2]LEE V W.Response of tunnels to incident SH waves[J].Journal of engineering mechanics,1979,105(4):643-659.
[3]梁建文,纪晓东,LEE V W.地下圆形衬砌隧道对沿线地震动的影响(II):数值结果[J].岩土力学,2005,26(5):687-692.(LIANGJianwen,JI Xiaodong,LEE V W.On the effects of an underground lined tunnel on ground motion(II):numerical results[J].Rock and soil mechanics,2005,26(5):687-692(in Chinese)).
[4]GAO Y,DAI D,ZHANG N,et al.Scattering of plane and cylindrical SH waves by a horseshoe shaped cavity[J].Journal of earthquake&tsunami,2016,10(2):1650011.
[5]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P波的散射[J].岩土力学,2004,25(12):1867-1872.(LI Weihua,ZHAOChenggang.An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space[J].Rock and soil mechanics,2004,25(12):1867-1872(in Chinese)).
[6]李伟华,申齐豪,赵成刚.饱和土半空间中地下圆形衬砌隧道对平面SV波的散射[J].防灾减灾工程学报,2009,29(2):172-178.(LIWeihua,SHEN Qihao,ZHAO Chenggang.Scattering of plane SVwaves by a underground circular lined tunnel in half space saturated soil[J].Journal of disaster prevention and mitigation engineering,2009,29(2):172-178(in Chinese)).
[7]LIU Q J,WANG R Y.Dynamic response of twin closely-spaced circular tunnels to harmonic plane waves in a full space[J].Tunnelling and underground space technology,2012,32(6):212-220.
[8]庄海洋,陈国兴.双洞单轨地铁区间隧道非线性地震反应分析[J].地震工程与工程振动,2006,26(2):131-137.(ZHUANG Haiyang,CHEN Guoxing.Analysis of nonlinear earthquake response of metro double-tunnels[J].Earthquake engineering and engineering vibration,2006,26(2):131-137(in Chinese)).
[9]刘中宪,梁建文,张贺.弹性半空间中衬砌洞室对平面P波和SV波的散射(II):数值结果[J].自然灾害学报,2010,19(4):77-88.(LIUZhongxian,LIANG Jianwen,ZHANG He.Scattering of P and SVwaves by a lined tunnel in elastic half space(II):numerical results[J].Journal of natural disasters,2010,19(4):77-88(in Chinese)).
[10]刘中宪,王楚楚,蒋坪临,等.球面压缩波入射下深埋三维衬砌洞室的动应力集中效应[J].应用力学学报,2017,34(5):904-911.(LIU Zhongxian,WANG Chuchu,JIANG Pinglin,et al.The dynamic stress concentration effect of deeply buried three-dimensional lining cavity under the spherical compression wave[J].Chinese journal of applied mechanics,2017,34(5):904-911(in Chinese)).
[11]张海,杨国岗,刘中宪,等.弹性半空间中含直边界半圆形衬砌隧道对SH波的散射解析解[J].应用力学学报,2017,34(2):243-249.(ZHANG Hai,YANG Guogang,LIU Zhongxian,et al.An analytical solution to scattering of plane SH waves by a semi-circle lined tunnel in elastic half-space boundary[J].Chinese journal of applied mechanics,2017,34(2):243-249(in Chinese)).
[12]孙铁军,王伟,罗明睿,等.不同衬砌结构缺陷对隧道结构整体安全性的影响[J].建筑科学与工程学报,2017,34(3):82-90.(SUNTiejun,WANG Wei,LUO Mingrui,et al.Influences of different lining structure defects on overall safety of tunnel structure[J].Journal of architecture and civil engineering,2017,34(3):82-90(in Chinese)).
[13]YI C,JOHANSSON D,NYBERG U,et al.Scattering of SH-waves by a shallow circular lined tunnel with an imperfect interface[C]//Proceedings of the 8th International Symposium on Ground Support in Mining and Underground Construction.Nordlund:[s.n.],2016.
[14]YI C,ZHANG P,JOHANSSON D,et al.Dynamic response of a circular lined tunnel with an imperfect interface subjected to cylindrical P-waves[J].Computers&geotechnics,2014,55(1):165-171.
[15]FANG Xueqian,JIN H X.Visco-elastic imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to P and SVwaves[J].Soil dynamics and earthquake engineering,2016,88:1-7.
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