半空间饱和多孔介质中孔隙水压动力格林函数
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摘要
该文引入三维饱和场地轴对称情况时的势函数,通过傅里叶积分变换,给出了三维饱和半空间中作用一孔隙水压力时的动力格林函数。首先在作用孔隙水压力处引入一辅助面,然后通过自由表面的边界条件以及辅助面处的连续条件,得到势函数系数,利用位移应力与势函数关系即可得到三维饱和半空间任一点的响应,也即格林函数。对于地表透水情况,该文考虑了地表的完全透水和完全不透水两种透水条件,该文进行了大量计算,分析了激励频率和孔隙率对位移和孔隙水压力的影响。
Through introducing the axisymmetric potential function of a poroelastic half space, the dynamic Green’s function of concentrated pore fluid pressure is given. Firstly, an auxiliary surface is introduced along the location of the source, then through the condition of the free surface of the poroelastic half space and the continuous condition of the auxiliary surface. The coefficients of the potential function are obtained. Then the dynamic response of the three-dimensional poroelastic half space is obtained by using the relation between the potential function and the displacements and stresses. Two boundary drainages are considered: the drained surface and undrained surface and the effects to the displacements and pore pressure of the porosity are discussed, and some useful conclusions are given.
Through introducing the axisymmetric potential function of a poroelastic half space, the dynamic Green’s function of concentrated pore fluid pressure is given. Firstly, an auxiliary surface is introduced along the location of the source, then through the condition of the free surface of the poroelastic half space and the continuous condition of the auxiliary surface. The coefficients of the potential function are obtained. Then the dynamic response of the three-dimensional poroelastic half space is obtained by using the relation between the potential function and the displacements and stresses. Two boundary drainages are considered: the drained surface and undrained surface and the effects to the displacements and pore pressure of the porosity are discussed, and some useful conclusions are given.
引文
[1]Lamb H.On the propagation of tremors over the surface of an elastic solid[J].Phil Trans Roy Soc London,Ser A,1904,203:1―42.
[2]Poulos H G,Davis E H.Elastic solutions for soil and rock mechanics[M].New York:John Wiley&Sons,Inc.,1974.
[3]Mindlin R D.Force at a point in the interior of a semi-infinite solid[J].Physics,1936,7:195―202.
[4]Rajapakse R K N D,Wang Y.Green’s functions for transversely isotropic elastic half-space[J].J Eng Mech,ASCE,1993,119:1724―1746.
[5]Pak R Y S.Asymmetric wave propagation in an elastic half-space by a method of potentials[J].J Appl Mech,1987,54(1):121―126.
[6]Achenbach J D.Wave propagation in elastic solids[M].Amsterdam,The Netherlands:North-Holland Publishing Co.,1973.
[7]Philippacopoulos A J.Lamb’s problem for fluid-saturated porous media[J].Bull Seism Soc Am,1988,78(2):908―923.
[8]陆建飞,王建华,沈为平.半空间饱和土在内部简谐水平力作用下的动力Green函数[J].地震学报,2001,23(2):185―191.Lu Jianfei,Wang Jianhua,Shen Weiping.The Green’s function of the harmonic horizontal force applied to the interior of the saturated half-space[J].Acta Seismologica Sinica,2001,23(2):185―191.(in Chinese)
[9]Senjuntichai T,Rajapakse R K N D.Dynamic Green’s functions of homogeneous poroelastic half-plane[J].J Eng Mech Div,ASCE,1994,120:2381―2404.
[10]Biot M A.The theory of propagation of elastic waves in a fluid-saturated porous solid:ⅠLow-frequency range[J].J Acoust Soc Am,1956,28:168―178.
[11]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33:1482―1498.
[12]Lin C H,Lee V W,Trifunac M D.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dynamic and Earthquake Engineering,2005,25:205―223.
[2]Poulos H G,Davis E H.Elastic solutions for soil and rock mechanics[M].New York:John Wiley&Sons,Inc.,1974.
[3]Mindlin R D.Force at a point in the interior of a semi-infinite solid[J].Physics,1936,7:195―202.
[4]Rajapakse R K N D,Wang Y.Green’s functions for transversely isotropic elastic half-space[J].J Eng Mech,ASCE,1993,119:1724―1746.
[5]Pak R Y S.Asymmetric wave propagation in an elastic half-space by a method of potentials[J].J Appl Mech,1987,54(1):121―126.
[6]Achenbach J D.Wave propagation in elastic solids[M].Amsterdam,The Netherlands:North-Holland Publishing Co.,1973.
[7]Philippacopoulos A J.Lamb’s problem for fluid-saturated porous media[J].Bull Seism Soc Am,1988,78(2):908―923.
[8]陆建飞,王建华,沈为平.半空间饱和土在内部简谐水平力作用下的动力Green函数[J].地震学报,2001,23(2):185―191.Lu Jianfei,Wang Jianhua,Shen Weiping.The Green’s function of the harmonic horizontal force applied to the interior of the saturated half-space[J].Acta Seismologica Sinica,2001,23(2):185―191.(in Chinese)
[9]Senjuntichai T,Rajapakse R K N D.Dynamic Green’s functions of homogeneous poroelastic half-plane[J].J Eng Mech Div,ASCE,1994,120:2381―2404.
[10]Biot M A.The theory of propagation of elastic waves in a fluid-saturated porous solid:ⅠLow-frequency range[J].J Acoust Soc Am,1956,28:168―178.
[11]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33:1482―1498.
[12]Lin C H,Lee V W,Trifunac M D.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dynamic and Earthquake Engineering,2005,25:205―223.
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