地下衬砌洞室群在平面P波多角度入射下的动应力
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摘要
采用波函数展开法,给出了半空间中衬砌洞室群在平面P波多角度入射下动应力集中问题的一个级数解析解,在满足一定的精度要求下,对无穷级数进行了截断数值计算。衬砌分为刚性衬砌、无衬砌、柔性衬砌3种。计算结果表明:不同的入射角度对动应力集中系数具有重要的影响;洞室间距对动应力集中系数也有重要影响,当洞室之间距离较近时,洞室之间的相互作用对地下洞室群的动应力集中具有显著的放大作用,动应力集中系数可能达到单个洞室的2倍以上;衬砌刚度对动应力集中问题也具有显著的影响,其中,刚性衬砌的动应力集中系数最大,无衬砌次之,柔性衬砌最小。
An analytical series solution for dynamic stress concentration of underground lined cavities under incident plane P waves is given by wave function expansion method.The infinite series is cut and calculated under the required precision.The lining includes rigid lining,unlined cavities and flexible lining.The numerical results show that angle of the incident waves plays an important role in the dynamic stress concentration factor;The interaction between two cavities greatly amplifies the dynamic stress concentration,and the dynamic stress concentration may reach to 2 times that in single cavity case;The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining,second for unlined cavities and is lowest for the flexible lining.
An analytical series solution for dynamic stress concentration of underground lined cavities under incident plane P waves is given by wave function expansion method.The infinite series is cut and calculated under the required precision.The lining includes rigid lining,unlined cavities and flexible lining.The numerical results show that angle of the incident waves plays an important role in the dynamic stress concentration factor;The interaction between two cavities greatly amplifies the dynamic stress concentration,and the dynamic stress concentration may reach to 2 times that in single cavity case;The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining,second for unlined cavities and is lowest for the flexible lining.
引文
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[6]Lee VW,Karl J.On deformation near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake En-gineering,1993,(1):29-36.
[7]梁建文,张浩,Vincent W LEE.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.
[2]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane,Russak&Company Inc,1973.
[3]Lee V W.On deformation near circular underground cavity subjected to incident plane SHwaves[C]//Proceedings of the Application of ComputerMethods in Engineering Conference.Los Angeles,1977.951-962.
[4]Lee V W,Trifunac MD.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[5]Lee V W,Karl J.Diffraction of SVwaves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11:445-456.
[6]Lee VW,Karl J.On deformation near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake En-gineering,1993,(1):29-36.
[7]梁建文,张浩,Vincent W LEE.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.
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