平面P波在饱和半空间中洞室周围的散射(I):解析解
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摘要
利用波函数展开法给出了入射平面P波在饱和半空间中圆形洞室周围散射问题的一个解析解。半空间假定为无粘性流体饱和介质,满足Biot理论。采用一种基于实验数据的孔隙率和模量之间的线性关系来确定Biot模型中的介质参数。解答考虑了透水边界和非透水边界两种情况。对边界条件进行了数值检验,结果表明,随着级数截断项数的增大,边界残量衰减很快。解答为进一步研究入射波频率和角度、边界渗透条件、孔隙率、泊松比等参数对散射的影响奠定了基础。
An analytical solution to scattering of plane P waves around a circular cavity in poroelastic half-space is derived using the wave function expansion method.The half-space is modeled by Biot's theory,and is assumed to be saturated with inviscid fluid.A linear porosity-modulus relation based on experimental data is used to determine the material parameters for Biot's model.Two cases of drained boundary and undrained boundary are considered in the solution.The boundary conditions are verified numerically, and it is shown that the residuals at boundaries diminish quickly as the truncation order of series increases.The solution may be utilized to study the effects of incident frequency and angle,drainage condition,porosity,Poisson's ratio,etc.on the wave scattering.
An analytical solution to scattering of plane P waves around a circular cavity in poroelastic half-space is derived using the wave function expansion method.The half-space is modeled by Biot's theory,and is assumed to be saturated with inviscid fluid.A linear porosity-modulus relation based on experimental data is used to determine the material parameters for Biot's model.Two cases of drained boundary and undrained boundary are considered in the solution.The boundary conditions are verified numerically, and it is shown that the residuals at boundaries diminish quickly as the truncation order of series increases.The solution may be utilized to study the effects of incident frequency and angle,drainage condition,porosity,Poisson's ratio,etc.on the wave scattering.
引文
[1]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].NewYork:Crane Russak and Company,Inc.,1973.
[2]Lee V W,Trifunac MD.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[3]Lee VW,Karl J.Diffraction of SVwaves by underground,circular cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11(8):445-456.
[4]Lee V W,Karl J.Diffraction of elastic placne P waves by circular,underground unlined tunnels[J].European Journal of Earthquake Engineer-ing,1993,VI(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SVwaves[J].Earthquake Engineering andStructural Dynamics,2001,30:383-410.
[6]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.
[7]Biot MA.The theory of propagation of elastic waves in a fluid-saturated porous solid:I.low-frequency range[J].Journal of Acoustic Societyof America,1956,28:168-178.
[8]Deresiewicz H.The effect of boundaries on wave propagation in a liquid-fill porous solid:I.Reflection of plane waves at a free plane boundary(non-dissipative case)[J].Bulletin of Seismological Society of America,1960,50(4):599-607.
[9]Lin C H,Lee VW,Trifunac MD.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dynamicand Earthquake Engineering,2005,25:205-223.
[10]梁建文,巴振宁,Lee V W.Diffraction of plane SV waves by a shallowcircular-arc canyon in a saturated poroelastic half-space[J].Soil Dy-namics and Earthquake Engineering,2006,26:582-610.
[11]梁建文,巴振宁,Lee V W.Diffraction of plane SV waves by an underground circular cavity in a saturated poroelastic half-space[J].ISETJournal of Earthquake Technology,2007,44(1):(to be published).
[12]Berrman J G.Confirmation of Biot’s theory[J].Applied Physics Letters,1980,34(4):382-384.
[13]Biot MA,Willis D G.The elastic coefficients of the theory of consolidation[J].Journal of Applied Mechanics,1957,24:594-601.
[2]Lee V W,Trifunac MD.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[3]Lee VW,Karl J.Diffraction of SVwaves by underground,circular cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11(8):445-456.
[4]Lee V W,Karl J.Diffraction of elastic placne P waves by circular,underground unlined tunnels[J].European Journal of Earthquake Engineer-ing,1993,VI(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SVwaves[J].Earthquake Engineering andStructural Dynamics,2001,30:383-410.
[6]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.
[7]Biot MA.The theory of propagation of elastic waves in a fluid-saturated porous solid:I.low-frequency range[J].Journal of Acoustic Societyof America,1956,28:168-178.
[8]Deresiewicz H.The effect of boundaries on wave propagation in a liquid-fill porous solid:I.Reflection of plane waves at a free plane boundary(non-dissipative case)[J].Bulletin of Seismological Society of America,1960,50(4):599-607.
[9]Lin C H,Lee VW,Trifunac MD.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dynamicand Earthquake Engineering,2005,25:205-223.
[10]梁建文,巴振宁,Lee V W.Diffraction of plane SV waves by a shallowcircular-arc canyon in a saturated poroelastic half-space[J].Soil Dy-namics and Earthquake Engineering,2006,26:582-610.
[11]梁建文,巴振宁,Lee V W.Diffraction of plane SV waves by an underground circular cavity in a saturated poroelastic half-space[J].ISETJournal of Earthquake Technology,2007,44(1):(to be published).
[12]Berrman J G.Confirmation of Biot’s theory[J].Applied Physics Letters,1980,34(4):382-384.
[13]Biot MA,Willis D G.The elastic coefficients of the theory of consolidation[J].Journal of Applied Mechanics,1957,24:594-601.