饱和土半空间中地下圆形衬砌洞室对平面SV波的散射
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摘要
在Biot饱和多孔介质动力学理论的基础上,利用Fourier-Bessel级数展开法,通过对含有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。
On the basis of Biot's dynamic theory of porous media,the response of a cylindrical lined cavity to incident plane-SV-waves was investigated.An analytic solution has been derived for the scattering and diffraction of plane-SV-waves by the lined cavity embedded in a half-space of saturated porous media with the Fourier-Bessel series expansion technique for the first time in this paper.The solution identically applies to the condition when the half-space is degenerated into an elastic medium of single phase,which can be proven by direct comparison of the relevant solutions.Numerical as well as the analytical results have been presented to analyze the effect,of the dimensionless frequency of the incident plane-SV-waves and of the embedded depth of the lined cavity,on the dynamical stress concentration factor over the cavity surface.
On the basis of Biot's dynamic theory of porous media,the response of a cylindrical lined cavity to incident plane-SV-waves was investigated.An analytic solution has been derived for the scattering and diffraction of plane-SV-waves by the lined cavity embedded in a half-space of saturated porous media with the Fourier-Bessel series expansion technique for the first time in this paper.The solution identically applies to the condition when the half-space is degenerated into an elastic medium of single phase,which can be proven by direct comparison of the relevant solutions.Numerical as well as the analytical results have been presented to analyze the effect,of the dimensionless frequency of the incident plane-SV-waves and of the embedded depth of the lined cavity,on the dynamical stress concentration factor over the cavity surface.
引文
[1]齐辉,王艳,刘殿魁.半无限空间界面附近SH波对圆形衬砌的散射[J].地震工程与工程振动,2003,23 (3):41-46. Qi H,Wang Y,Liu D K.Dynamic analysis of shallow -embedded lining structure by incident SH-wave [J].Earthquake Engineering and Engineering Vibration, 2003,23(3):41-46.
[2]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 W P,Liu D K,Lin H,et al.Scattering of steady P-wave around a circular lining in half space[J]. Earthquake Engineering and Engineering Vibration, 2002,22(3):19-26.
[3]纪晓东,梁建文.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):512-517. Ji X D,Liang J W.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incident plane P and SV waves[J].Journal of Tianjin University,2006,39(5):512-517.
[4]Biot M A.Theory of propagation of elastic wave in fluid-saturated porous soil[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[5]吴世明.土介质中的波[M].北京:科学出版社,1997. Wu S M.Wave Propagation in Soils[M].Beijing:Science Press,1997.
[6]Greetsma J.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophys,1961, (26):169-181.
[7]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元数值模拟[D].北京:北京交通大学,2004. Li W H.Analytical solutions and numerical simulation of the scattering plane waves by local sites with saturated soil[D].Beijing:Beijing Jiaotong University, 2004.
[8]数学手册编写组.数学手册[M].北京:高等教育出版社,1979.
[2]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 W P,Liu D K,Lin H,et al.Scattering of steady P-wave around a circular lining in half space[J]. Earthquake Engineering and Engineering Vibration, 2002,22(3):19-26.
[3]纪晓东,梁建文.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):512-517. Ji X D,Liang J W.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incident plane P and SV waves[J].Journal of Tianjin University,2006,39(5):512-517.
[4]Biot M A.Theory of propagation of elastic wave in fluid-saturated porous soil[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[5]吴世明.土介质中的波[M].北京:科学出版社,1997. Wu S M.Wave Propagation in Soils[M].Beijing:Science Press,1997.
[6]Greetsma J.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophys,1961, (26):169-181.
[7]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元数值模拟[D].北京:北京交通大学,2004. Li W H.Analytical solutions and numerical simulation of the scattering plane waves by local sites with saturated soil[D].Beijing:Beijing Jiaotong University, 2004.
[8]数学手册编写组.数学手册[M].北京:高等教育出版社,1979.
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