横观各向同性饱和地基竖向振动的衰减特性
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摘要
基于提出的横观各向同性饱和多孔介质Biot波动方程的一般解,研究了饱和半空间地基在竖向点源简谐激振荷载作用下地表振动的衰减特征,分析了激振频率以及横观各向同性饱和土介质的各向异性参数和孔隙渗透系数对地表振动特征的影响。计算结果表明,低频和高频激振时,地表位移衰减特性存在明显差异;在饱和土的各向异性参数中,纵向和水平方向动态渗透系数比值和刚度系数比值对地表位移衰减影响最大,这也说明采用各向同性饱和介质的动力学模型不能准确地描述具有明显各向异性特性的饱和土地基的动力特性。
Based on the general solutions of Biot's wave motions of transversely isotropic saturated poroelastic media established by the author,the vibration attenuation at ground surface under the point harmonic excitation is researched.And the combined effects of the soil permeability and the loading frequency on the results are analyzed.The calculation results indicate that the characteristics of vibration attenuation of vertical displacement under the low and the high exciting frequencies are different obviously.Of all the parameters of transversely isotropic saturated media,the rates both in osmotic coefficient and in elastic constants between vertical and horizontal direction influence the vertical vibration attenuation mostly.The results also indicate that adopting dynamic model of isotropic saturated medium could not describe exactly the dynamic characters of the saturated poroelastic medium that has obviously anisotropic properties.
Based on the general solutions of Biot's wave motions of transversely isotropic saturated poroelastic media established by the author,the vibration attenuation at ground surface under the point harmonic excitation is researched.And the combined effects of the soil permeability and the loading frequency on the results are analyzed.The calculation results indicate that the characteristics of vibration attenuation of vertical displacement under the low and the high exciting frequencies are different obviously.Of all the parameters of transversely isotropic saturated media,the rates both in osmotic coefficient and in elastic constants between vertical and horizontal direction influence the vertical vibration attenuation mostly.The results also indicate that adopting dynamic model of isotropic saturated medium could not describe exactly the dynamic characters of the saturated poroelastic medium that has obviously anisotropic properties.
引文
[1]PAUL S.On the disturbance produced in a semi-infinite poroelastic medium by a surface load[J].Pure Applied Geophysics,1976,114:615-625.
[2]PHILIPPACOPOULOUS A J.Lamb’s problem for fluid-Saturated porous media[J].Bulletin Seismic Society of America,1988,78:908-932.
[3]PHILIPPACOPOULOUS A J.Waves in partially saturated medium due to surface loads[J].Journal of Engineering Mechanics,ASCE,1988,114(10):1740-1759.
[4]王立忠,陈云敏,吴士明,等.饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,1996,(2):84-88.WANG Li-zhong,CHEN Yun-min,WU Shi-ming,et al.,The integral solution under the low-frequency harmonic concentrated force on the saturated elastic half-space[J].Journal of Hydraulic Engineering,1996,(2):84-88.
[5]刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播[J].地球物理学报,1994,37(4):499-514.LIU Yin-bin,LI You-ming,WU Ru-shan.Seismic wave propagation in transversely isotropic porous media[J].Geophysica Sinica,1994,37(4):499-514.
[6]汪越胜,章梓茂.横观各向同性液体饱和多孔介质中平面波的传播[J].力学学报,1997,29(30):257-268.WANG Yue-sheng,ZHANG Zi-mao.Propagation of plane waves in transversely isotropic fluid-saturatedporous media[J].Acta Mechanica Sinica,1997,29(30):257-268.
[7]胡亚元,王立忠,张忠苗,等.横观各向同性饱和土体的实用波动方程[J].振动工程学报,1998,12(2):170-176.HU Ya-yuan,WANG Li-zhong,ZHANG Zhong-miao,et al.The pragmatic wave equations of transversely isotropic saturated soil[J].Journal of Vibration Engin-eering,1998,12(2):170-176.
[8]张引科,黄义.横观各向同性饱和弹性多孔介质的非轴对称动力响应[J].应用数学和力学,2001,22(1):56-70.ZHANG Yin-ke,HUANG Yi.The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media[J].Applied Mathematic and Mechanics,2001,22(1):56-70.
[9]黄义,王小岗.横观各向同性饱和弹性多孔介质三维非轴对称Lamb问题[J].中国科学(E辑),2004,34(9):1037-1060.HUANG Yi,WANG Xiao-gang.The3D non-axisymmertrical Lamb’s problem in transversely isotropic saturated poroelestic media[J].Science in China(Ser.E),2004,47(5):526-549.
[10]王小岗,黄义.横观各向同性饱和地基的三维动力响应[J].应用数学和力学,2005,26(11):1078-1086.WANG Xiao-gang,HUANG Yi.3D Dynamic response of transversely isotropic saturated soils[J].Applied Mathematics and Mechanics,2005,26(11):1409-1419.
[11]王小岗.土与基础结构动力相互作用的饱和弹性半空间理论[博士学位论文D].西安:西安建筑科技大学,2004.
[2]PHILIPPACOPOULOUS A J.Lamb’s problem for fluid-Saturated porous media[J].Bulletin Seismic Society of America,1988,78:908-932.
[3]PHILIPPACOPOULOUS A J.Waves in partially saturated medium due to surface loads[J].Journal of Engineering Mechanics,ASCE,1988,114(10):1740-1759.
[4]王立忠,陈云敏,吴士明,等.饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,1996,(2):84-88.WANG Li-zhong,CHEN Yun-min,WU Shi-ming,et al.,The integral solution under the low-frequency harmonic concentrated force on the saturated elastic half-space[J].Journal of Hydraulic Engineering,1996,(2):84-88.
[5]刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播[J].地球物理学报,1994,37(4):499-514.LIU Yin-bin,LI You-ming,WU Ru-shan.Seismic wave propagation in transversely isotropic porous media[J].Geophysica Sinica,1994,37(4):499-514.
[6]汪越胜,章梓茂.横观各向同性液体饱和多孔介质中平面波的传播[J].力学学报,1997,29(30):257-268.WANG Yue-sheng,ZHANG Zi-mao.Propagation of plane waves in transversely isotropic fluid-saturatedporous media[J].Acta Mechanica Sinica,1997,29(30):257-268.
[7]胡亚元,王立忠,张忠苗,等.横观各向同性饱和土体的实用波动方程[J].振动工程学报,1998,12(2):170-176.HU Ya-yuan,WANG Li-zhong,ZHANG Zhong-miao,et al.The pragmatic wave equations of transversely isotropic saturated soil[J].Journal of Vibration Engin-eering,1998,12(2):170-176.
[8]张引科,黄义.横观各向同性饱和弹性多孔介质的非轴对称动力响应[J].应用数学和力学,2001,22(1):56-70.ZHANG Yin-ke,HUANG Yi.The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media[J].Applied Mathematic and Mechanics,2001,22(1):56-70.
[9]黄义,王小岗.横观各向同性饱和弹性多孔介质三维非轴对称Lamb问题[J].中国科学(E辑),2004,34(9):1037-1060.HUANG Yi,WANG Xiao-gang.The3D non-axisymmertrical Lamb’s problem in transversely isotropic saturated poroelestic media[J].Science in China(Ser.E),2004,47(5):526-549.
[10]王小岗,黄义.横观各向同性饱和地基的三维动力响应[J].应用数学和力学,2005,26(11):1078-1086.WANG Xiao-gang,HUANG Yi.3D Dynamic response of transversely isotropic saturated soils[J].Applied Mathematics and Mechanics,2005,26(11):1409-1419.
[11]王小岗.土与基础结构动力相互作用的饱和弹性半空间理论[博士学位论文D].西安:西安建筑科技大学,2004.
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