半空间饱和介质内圆形洞室对平面P1波的散射
|
摘要
考虑土颗粒和孔隙流体的压缩性以及孔隙流体与土骨架之间的粘性耦合作用,采用修正的B iot模型,假定半空间表面不透水,得到了平面P1波(快压缩波)在半空间表面的反射P1波、P2波(慢压缩波)和SV波(剪切波)的幅值。采用大圆弧假定将半空间内圆形洞室的散射问题转化为大圆弧和圆形洞室的多重散射问题,运用波函数展开法将入射波、反射波以及半空间表面和洞室的散射波的势函数展开成Fourier-Bessel函数的无穷级数形式,由Graf加法定理得到同一坐标系下的势函数的表达式,根据半空间表面和洞室完全自由的边界条件得到了待定复系数的理论解。通过数值计算,着重分析了平面P1波垂直向上入射时无量纲入射频率和洞室埋藏深度等对洞室的动应力集中因子和半空间表面的归一化水平和竖向位移的影响。
Considering the compression of soil grain and pore fluid,and viscid coupling of pore fluid with soil skeleton,adopting the amended Biot model,the amplitudes of P1 wave,P2 wave and SV wave which are reflected from the plane P1 wave are calculated when the semi-infinite space surface is impervious.The semi-infinite surface is taken as a large curved arc,the potential functions of incident waves,reflected waves from the semi-infinite surface,scattered waves from the circular cavity and the curved arc are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion method of wave functions,and then the single scattering problem of a cavity in semi-infinite space is turned to a multiple scattering problem of cavity and curved arc based on the Graf's addition theorem.According to the boundary conditions that the semi-infinite space surface and cavity are all free,the theoretical solutions the complex coefficients of the potential functions are obtained.The influence of the normalized incident frequency and the cavity depth on the normalized horizontal,vertical displacements of the semi-infinite space surface and the dynamic stress concentration factor of the cavity are studied by theoretical simulation when the P1 waves are vertically incident.
Considering the compression of soil grain and pore fluid,and viscid coupling of pore fluid with soil skeleton,adopting the amended Biot model,the amplitudes of P1 wave,P2 wave and SV wave which are reflected from the plane P1 wave are calculated when the semi-infinite space surface is impervious.The semi-infinite surface is taken as a large curved arc,the potential functions of incident waves,reflected waves from the semi-infinite surface,scattered waves from the circular cavity and the curved arc are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion method of wave functions,and then the single scattering problem of a cavity in semi-infinite space is turned to a multiple scattering problem of cavity and curved arc based on the Graf's addition theorem.According to the boundary conditions that the semi-infinite space surface and cavity are all free,the theoretical solutions the complex coefficients of the potential functions are obtained.The influence of the normalized incident frequency and the cavity depth on the normalized horizontal,vertical displacements of the semi-infinite space surface and the dynamic stress concentration factor of the cavity are studied by theoretical simulation when the P1 waves are vertically incident.
引文
[1]White R M.Elastic Wave scattering at a cylindrical discontinuityin a solid[J].Acoust.Soc.Am.,1958,30(8):405-418.
[2]Pao Y H,Mow,C C.Diffraction of elastic waves and dynamicstress concentrations[M].NewYork:Crane,Russak&CompanyInc,1973:208-305.
[3]Gaunaurd G C,berall H.Theory of resonant scattering fromspherical cavities in elastic and viscoelastic media[J].Acoust.Soc.Am.,1978,63(6):1699-1712.
[4]Veksler N,Izbicki J L,Conoir J M.Elastic wave scattering by acylindrical shell[J].Wave Motion,1999,29(3):195-209.
[5]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,10(4):643-659.
[6]Lee V W,Karl J.Diffraction of SV waves by underground,circu-lar,cylindrical cavities[J].Soil Dynamics and Earthquake Engi-neering,1991,11:445-456.
[7]Lee VW,Karl J.On deformation near a circular underground cav-ity subjected to incident plane P waves[J].European Journal ofEarthquake Engineering,1993,7(1):29-36.
[8]Luco J E,Debarros F C P.Dynamic displacements and stresses inthe vicinity of a cylindrical cavity embedded in a half-space[J].Earthquake Engineering and Structural Dynamics,1994,23:321-340.
[9]Davis C A,Bardet J P.Seismic analysis of large diameter exibleunderground pipes[J].Journal of Geotechnical and Geoenviron-mental Engineering ASCE,1998,124(10):1005-1015.
[10]Davis C A,Lee VW,Bardet J P.Transverse response of under-ground cavities and pipes to incident SV waves[J].EarthquakeEngineering and Structural Dynamics,2001,30:383-410.
[11]Biot MA.Mechanics of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust.Soc.Am.,1956,28(2):168-191.
[12]王建华,姜领发,周香莲.稳态P波对半无限饱和土中的圆形孔洞的散射[J].南昌工程学院学报,2005,24(1):8-19.
[13]张丽琴,於文辉,王家映.离散介质中地震波传播的数值模拟[J].西北地震学报,2004,26(1):8-19.
[14]吴世明.土介质中的波[M].北京:科学出版社,1997.
[15]徐平,夏唐代.P1波入射角对建筑基础振动的影响[J].振动与冲击,2006,25(5):58-61.
[16]徐平,夏唐代,闫东明.P1波入射下饱和度对深埋圆形衬砌动应力集中因子的影响[J].振动与冲击,2007,26(4):46-49.
[2]Pao Y H,Mow,C C.Diffraction of elastic waves and dynamicstress concentrations[M].NewYork:Crane,Russak&CompanyInc,1973:208-305.
[3]Gaunaurd G C,berall H.Theory of resonant scattering fromspherical cavities in elastic and viscoelastic media[J].Acoust.Soc.Am.,1978,63(6):1699-1712.
[4]Veksler N,Izbicki J L,Conoir J M.Elastic wave scattering by acylindrical shell[J].Wave Motion,1999,29(3):195-209.
[5]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,10(4):643-659.
[6]Lee V W,Karl J.Diffraction of SV waves by underground,circu-lar,cylindrical cavities[J].Soil Dynamics and Earthquake Engi-neering,1991,11:445-456.
[7]Lee VW,Karl J.On deformation near a circular underground cav-ity subjected to incident plane P waves[J].European Journal ofEarthquake Engineering,1993,7(1):29-36.
[8]Luco J E,Debarros F C P.Dynamic displacements and stresses inthe vicinity of a cylindrical cavity embedded in a half-space[J].Earthquake Engineering and Structural Dynamics,1994,23:321-340.
[9]Davis C A,Bardet J P.Seismic analysis of large diameter exibleunderground pipes[J].Journal of Geotechnical and Geoenviron-mental Engineering ASCE,1998,124(10):1005-1015.
[10]Davis C A,Lee VW,Bardet J P.Transverse response of under-ground cavities and pipes to incident SV waves[J].EarthquakeEngineering and Structural Dynamics,2001,30:383-410.
[11]Biot MA.Mechanics of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust.Soc.Am.,1956,28(2):168-191.
[12]王建华,姜领发,周香莲.稳态P波对半无限饱和土中的圆形孔洞的散射[J].南昌工程学院学报,2005,24(1):8-19.
[13]张丽琴,於文辉,王家映.离散介质中地震波传播的数值模拟[J].西北地震学报,2004,26(1):8-19.
[14]吴世明.土介质中的波[M].北京:科学出版社,1997.
[15]徐平,夏唐代.P1波入射角对建筑基础振动的影响[J].振动与冲击,2006,25(5):58-61.
[16]徐平,夏唐代,闫东明.P1波入射下饱和度对深埋圆形衬砌动应力集中因子的影响[J].振动与冲击,2007,26(4):46-49.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心