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
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摘要
利用Fourier-Bessel级数展开法,研究了平面P波和SV波入射情况下,圆形衬砌洞室的动应力集中问题, 并给出了其级数解．数值结果表明,衬砌刚度对动应力集中系数具有重要影响,刚性衬砌、无衬砌和柔性衬砌三种情况的动应力集中系数在空间上的分布相同,但刚性衬砌情况的动应力集中系数最大,无衬砌情况次之,柔性衬砌情况最小;随着入射频率的增大,动应力集中系数的空间变化由简单逐渐变得复杂,动应力集中系数在多数情况下逐渐减小;波入射角度对动应力集中系数也有很大影响．
By using Fourier-Bessel series expansion method, dynamic stress concentration of a cylindrical lined cavity in an elastic half-space subjected to incident plane P and SV waves is studied, and the series solution is presented. The numerical results show that, the rigidity of lining has great effect on the dynamic stress concentration factor, and the dynamic stress concentration factor distributions of cavities with rigid lining, without lining , and with flexible lining are the same, but the dynamic stress concentration factor is the highest for a cavity with rigid lining, and takes the second place for an unlined cavity, and is the lowest for a cavity with flexible lining; as the incident frequency increases, the dynamic stress concentration factor becomes complicated and gradually decreases in most cases; the angle of the incident waves also plays an important role in the dynamic stress concentration factor.
By using Fourier-Bessel series expansion method, dynamic stress concentration of a cylindrical lined cavity in an elastic half-space subjected to incident plane P and SV waves is studied, and the series solution is presented. The numerical results show that, the rigidity of lining has great effect on the dynamic stress concentration factor, and the dynamic stress concentration factor distributions of cavities with rigid lining, without lining , and with flexible lining are the same, but the dynamic stress concentration factor is the highest for a cavity with rigid lining, and takes the second place for an unlined cavity, and is the lowest for a cavity with flexible lining; as the incident frequency increases, the dynamic stress concentration factor becomes complicated and gradually decreases in most cases; the angle of the incident waves also plays an important role in the dynamic stress concentration factor.
引文
[1]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dy- namic Stress Concentrations [M].New York:Crane Russak and Company,Inc,1973.
[2]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE, 1979,105:643-659.
[3]Lee V W,Karl J.Diffraction of SV waves by underground, circular,cylindrical cavities [J].Soil Dynamics and Earth- quake Engineering,1992,11:445-456.
[4]Lee V W,Karl J.On deformations of near a circular under- ground cavity subjected to incident plane P waves[J].Euro- pean Journal of Earthquake Engineering,1993(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves [J]. Earthquake Engineering and Structural Dynamics,2001, 30:383-410.
[6]梁建文,张浩,Lee V W．平面P波入射下地下洞室群 动应力集中问题解析解[J]．岩土工程学报,2004,26 (6):815-819． Liang Jianwen,Zhang Hao,Lee V W.An analytical solu- tion for dynamic stress concentration of underground cavities under incident plane P waves [J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819(in Chi- nese ).
[7]梁建文,张浩,Lee V W．地下双洞室在SV波入射下 动力响应问题解析解[J]．振动工程学报,2004,17(2): 132-140． Liang Jianwen,Zhang Hao,Lee V W.An analytical solu- tion for dynamic stress concentration of underground twin cavities due to incident SV waves [J].Journal of Vibration Engineering,2004,17(2):132-140(in Chinese).
[8]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 Hui,Wang Yan,Liu Diankui.Dynamic analysis of sha- llow-embedded lining structure by incident SH-waves [J]. Earthquake Engineering and Engineering Vibration,2003,23 (3):41-46(in Chinese).
[9]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 Wenpu,Liu Diankui,Lin Hong,et al.Scattering of steady P-waves around a circular lining in half space [J]. Earthquake Engineering and Engineering Vibration,2002,22 (3):19-26(in Chinese).
[10]Abramowitz M,Stegun I A.Handbook of Mathematical Functions,with Formulae,Graphs,and Mathematical Ta- bles[M].New York:Dover Publisher,1972.
[2]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE, 1979,105:643-659.
[3]Lee V W,Karl J.Diffraction of SV waves by underground, circular,cylindrical cavities [J].Soil Dynamics and Earth- quake Engineering,1992,11:445-456.
[4]Lee V W,Karl J.On deformations of near a circular under- ground cavity subjected to incident plane P waves[J].Euro- pean Journal of Earthquake Engineering,1993(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves [J]. Earthquake Engineering and Structural Dynamics,2001, 30:383-410.
[6]梁建文,张浩,Lee V W．平面P波入射下地下洞室群 动应力集中问题解析解[J]．岩土工程学报,2004,26 (6):815-819． Liang Jianwen,Zhang Hao,Lee V W.An analytical solu- tion for dynamic stress concentration of underground cavities under incident plane P waves [J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819(in Chi- nese ).
[7]梁建文,张浩,Lee V W．地下双洞室在SV波入射下 动力响应问题解析解[J]．振动工程学报,2004,17(2): 132-140． Liang Jianwen,Zhang Hao,Lee V W.An analytical solu- tion for dynamic stress concentration of underground twin cavities due to incident SV waves [J].Journal of Vibration Engineering,2004,17(2):132-140(in Chinese).
[8]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 Hui,Wang Yan,Liu Diankui.Dynamic analysis of sha- llow-embedded lining structure by incident SH-waves [J]. Earthquake Engineering and Engineering Vibration,2003,23 (3):41-46(in Chinese).
[9]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 Wenpu,Liu Diankui,Lin Hong,et al.Scattering of steady P-waves around a circular lining in half space [J]. Earthquake Engineering and Engineering Vibration,2002,22 (3):19-26(in Chinese).
[10]Abramowitz M,Stegun I A.Handbook of Mathematical Functions,with Formulae,Graphs,and Mathematical Ta- bles[M].New York:Dover Publisher,1972.
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