地震加速度作用下饱和土中深埋隧道的动力响应
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摘要
通过建立和求解饱和土中圆形隧道在地震加速度作用下的动力控制方程,得出了该问题的通解;再根据弹性力学问题的几何方程和物理方程,推导出了饱和土及隧道结构中的应变及应力分量表达式;结合饱和土中圆形隧道在地震加速度作用下动力响应的边界条件,对其进行了数值计算,较为全面的分析了地震频率、隧道结构参数以及地震加速度大小对饱和土中圆形隧道对地震响应的影响。研究结果表明:随着地震频率的增加,孔隙水压力和土体应力分量最大值减小;隧道衬砌结构剪切模量的增加,孔隙水压力和土体应力分量最大值均有所增加;地震加速度的大小对孔隙水压力和土体应力分量影响最为明显,地震加速度增加的倍数与各应力分量增加的倍数基本一致,随着离开隧道距离的增加,饱和土中孔隙水压力、径向应力分量和切向应力分量迅速衰减,而剪应力分量值最大且呈正负交替较慢衰减;这些研究结果对正确理解饱和土中圆形衬砌隧道的抗震性能、破坏机理以及指导隧道抗震设计都有参考意义。
By establishing and solving the dynamic control equations for circular tunnels in saturated soil to the effect of the seismic acceleration,the general solution is obtained.According to the geometrical equation and physical equation for the elastic mechanics problem,the stress and strain expressions in the saturated soil and tunnel structure are deduced.Based on a circular tunnel in saturated soil under the action of earthquake acceleration boundary conditions,the numerical calculation is carried out,and the influences of seismic frequency,tunnel structure parameters and seismic acceleration on the seismic response of the circular tunnel in saturated soil are comprehensively analyzed.The results show that,with the increase of the earthquake frequency,the pore water pressure and the maximum values of stress components decrease.The pore water pressure and the maximum values of stress components increase when the tunnel lining structure shear modulus increases.The effect of the seismic acceleration on the pore water pressure and stress component is the most obvious,and the increase ratio of earthquake acceleration and the increase multiples of stress components are basically the same.With the increase of the distance away from the tunnel,the pore water pressure,radial stress component and tangential stress component decrease obviously,and the shear stress component is large and has slow attenuation.These results are very helpful for correctly understanding the seismic performance,damage mechanisms and seismic design of tunnels.
By establishing and solving the dynamic control equations for circular tunnels in saturated soil to the effect of the seismic acceleration,the general solution is obtained.According to the geometrical equation and physical equation for the elastic mechanics problem,the stress and strain expressions in the saturated soil and tunnel structure are deduced.Based on a circular tunnel in saturated soil under the action of earthquake acceleration boundary conditions,the numerical calculation is carried out,and the influences of seismic frequency,tunnel structure parameters and seismic acceleration on the seismic response of the circular tunnel in saturated soil are comprehensively analyzed.The results show that,with the increase of the earthquake frequency,the pore water pressure and the maximum values of stress components decrease.The pore water pressure and the maximum values of stress components increase when the tunnel lining structure shear modulus increases.The effect of the seismic acceleration on the pore water pressure and stress component is the most obvious,and the increase ratio of earthquake acceleration and the increase multiples of stress components are basically the same.With the increase of the distance away from the tunnel,the pore water pressure,radial stress component and tangential stress component decrease obviously,and the shear stress component is large and has slow attenuation.These results are very helpful for correctly understanding the seismic performance,damage mechanisms and seismic design of tunnels.
引文
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[9]梁昆淼.数学物理方法[M].北京:高等教育出版社,2010.(LIANG Kun-miao.Methods of mathematical physics[M].Beijing:Higher Education Press,2010.(in Chinese))
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[12]纪晓东.半空间中圆形洞室对弹性波的散射[D].天津:天津大学,2005.(JI Xiao-dong.Scattering and diffraction ofa cylindrical cavity in half-space subjected to elasticwaves[D].Tianjin:Tianjin University,2005.(in Chinese))
[2]张引科,黄义.弹性饱和多孔介质在非轴对称荷载下的稳态动力响应[J].土木工程学报,2002,35(3):41-45.(ZHANG Yin-ke,HUANG Yi.Steady dynamic response ofelastic saturated porous medium under non-axisymmetricalload[J].China Civil Engineering Journal,2002,35(3):41-45.(in Chinese))
[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.(LIANG Jian-wen,JI Xiao-dong,LEE V W.Effects ofan underground lined tunnel on ground motion(II):numericalresults[J].Rock and Soil Mechanics,2005,26(5):687-692.(in Chinese))
[4]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.(LIANGJian-wen,JI Xiao-dong.Amplification of Rayleigh waves dueto underground lined cavities[J].Earthquake Engineering andEngineering Vibration,2006,26(4):24-31.(in Chinese))
[5]史文谱,刘殿魁,林宏,等.半无限空间中稳态P波在衬砌周围的散射[J].地震工程与工程振动,2002,22(3)19-26.(SHI Wen-pu,LIU Dian-kui,LIN Hong,et al.Scattering of steady P-wave around a circular lining in halfspace[J].Earthquake Engineering and Engineering Vibration,2002,22(3):19-26.(in Chinese))
[6]姜领发,王建华,周香莲.半空间饱和土中圆形衬砌对弹性压缩波的散射[J].岩土力学,2008,29(2):315-317.(JIANG Ling-fa,WANG Jian-hua,ZHOU Xiang-lian.Scattering around a circular lining in saturated poroelastichalf-space under dilatational waves[J].Rock and SoilMechanics,2008,29(2):315-317.(in Chinese))
[7]WANG J H,ZHOU X L,LU J F.Dynamic stress concentrationaround elliptic cavities in saturated poroelastic soil underharmonic plane waves[J].International Journal of Solids andStructures,2005,42:4295-4310.
[8]张引科.饱和土中圆形衬砌隧道地震响应的研究[D].上海:同济大学,2004.(ZHANG Yin-ke.Seismic response ofcircular lined tunnels in saturated soils[D].Shanghai:TongjiUniversity,2004.(in Chinese))
[9]梁昆淼.数学物理方法[M].北京:高等教育出版社,2010.(LIANG Kun-miao.Methods of mathematical physics[M].Beijing:Higher Education Press,2010.(in Chinese))
[10]徐芝纶.弹性力学[M].北京:高等教育出版社,2006.(XUZhi-guan.Elastic mechanics[M].Beijing:Higher EducationPress,2006.(in Chinese))
[11]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.(LIU Zhong-xian,LIANG Jian-wen,ZHANGHe.Scattering of plane P and SV waves by a lined tunnel inelastic half space(II):numerical results[J].Journal of NaturalDisasters,2010,19(4):77-88.(in Chinese))
[12]纪晓东.半空间中圆形洞室对弹性波的散射[D].天津:天津大学,2005.(JI Xiao-dong.Scattering and diffraction ofa cylindrical cavity in half-space subjected to elasticwaves[D].Tianjin:Tianjin University,2005.(in Chinese))
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