半空间饱和土中多孔洞对地震波作用的动力响应
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摘要
根据Biot波动理论并结合复变函数和多级坐标的方法,对半无限饱和土中地震波对地下多孔洞的动力响应问题进行了研究。给出了P波对2个圆形孔洞的动应力集中系数的数值结果,讨论了动应力集中系数在随孔间距、入射角以及无量纲波数的变化时在孔洞周边分布情况。研究结果表明:地下孔洞之间的间距对孔洞之间的相互作用影响明显,当孔洞之间间距达到6倍孔半径时动应力集中系数峰值明显减小且在周边分布偏移量减弱;随着入射角度的增加,孔洞周边应力集中系数呈现出先增大后减小的趋势,分布也发生一定角度的偏转;在低频入射波作用时,孔洞应力峰值相互影响较大,在高频波入射时,孔洞之间相互作用减弱。
According to the Biot's wave theory and the complex function combined with multi-coordinate method,the seismic wave dynamic response of underground holes in half saturated space is studied.Given P waves on two circular holes of the dynamic stress concentration factor of the numerical results,the distribution situations of the dynamic stress concentration factors are discussed with the variation of the hole spacing,incidence angle and dimensionless wave number.The results show that,the effect of the underground hole spacing on the interaction effects of the holes is obvious.When the hole spacing reaches up to 6 times the radius of the hole,the peak value of the dynamic stress concentration factor decreases obviously,and the peripheral distribution of offset is weakened.With the increase of the incident angle,the hole peripheral stress concentration coefficient shows the trend of first increasing then decreasing,and distribution also occurs at certain angle deflection.In low frequency waves,the hole stress peak value will influence mutually more,while in the high frequency input,the interaction between holes will reduce.
According to the Biot's wave theory and the complex function combined with multi-coordinate method,the seismic wave dynamic response of underground holes in half saturated space is studied.Given P waves on two circular holes of the dynamic stress concentration factor of the numerical results,the distribution situations of the dynamic stress concentration factors are discussed with the variation of the hole spacing,incidence angle and dimensionless wave number.The results show that,the effect of the underground hole spacing on the interaction effects of the holes is obvious.When the hole spacing reaches up to 6 times the radius of the hole,the peak value of the dynamic stress concentration factor decreases obviously,and the peripheral distribution of offset is weakened.With the increase of the incident angle,the hole peripheral stress concentration coefficient shows the trend of first increasing then decreasing,and distribution also occurs at certain angle deflection.In low frequency waves,the hole stress peak value will influence mutually more,while in the high frequency input,the interaction between holes will reduce.
引文
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[2]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):Numerical results[J].Rock and Soil Mechanics,2005,26(5):687-692.(in Chinese))
[3]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))
[4]岳庆霞,李杰.近似Rayleigh地震波作用下地下综合管廊响应分析[J].防灾减灾工程学报,2008,25(4):409-416.(YUE Qing-xia,LI Jie.Response analysis of utility tunnel inearthquake of approximate Rayleigh waves[J].Journal ofDisaster Prevention and Mitigation Engineering,2008,25(4):409-416.(in Chinese))
[5]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(I)—方法[J].自然灾害学报,2010,19(4):71-76.(LIU Zhong-xian,LIANG Jian-wen,ZHANG He.Scattering of plane P and SV waves by a lined tunnel inelastic half space(I):method[J].Journal of Natural Disasters,2010,19(4):71-76.(in Chinese))
[6]LEE V W,KARL J.Diffraction of SV waves by undergroundcircular cylindrical cavities[J].Soil Dynamics andEarthquake Engineering,1992(11):445-456.
[7]LEE V W,KARL J.On deformations of near a circularunderground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993(1):29-36.
[8]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))
[9]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.
[10]周香莲,周光明,王建华.饱和土中圆形衬砌结构对弹性波的散射[J].岩石力学与工程学报,2005,24(9):1572-1576.(ZHOU Xiang-lian,ZHOU Guang-ming,WANGJian-hua.Scattering of elastic wave by circular cavity withlining in saturated soil[J].Chinese Journal of RockMechanics and Engineering,2005,24(9):1572-1576.(inChinese))
[11]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solidⅠ:Low frequency range[J].Journal of the Acoustical Society of America,1956,28:168-178.
[12]鲍亦兴,毛昭宙.弹性波的衍射与动应力集中[M].北京:科学出版社,1993.(PAO Yi-xing,MAO Zhao-yu.Scatteringand dynamics stresses concentration of elastic wave[M].Beijing:Science Press,1993.(in Chinese))
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