平面SH波入射下深埋圆形组合衬砌洞室的动力反应分析
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摘要
利用波函数展开法,研究平面SH波入射下,深埋圆形组合衬砌洞室的动力反应问题.利用得到的级数解和数学应用软件MathCAD编写计算机程序,讨论了入射波频率、组合衬砌结构的厚度比、弹性模量、泊松比、密度等因素对围岩和衬砌结构动应力集中系数的影响.结果表明组合衬砌确实能有效地发挥围岩的自承能力,降低衬砌结构的动应力集中,且在低频入射时效果显著.
By using wave function expansion method,the dynamic response analysis of a deep buried cylindrical composite-lining cavity in an elastic space subjected to incident plane SH waves was studied.By compiling programs with the obtained series solution and mathematical application software MathCAD,the main factors affecting the dynamic stress concentration of the surrounding rock and composite-lining structure,such as the frequency of incident waves,the ratio of the size of composite-lining structure and the elastic modulus,the poisson's ratio and the density of composite-lining structure,were discussed.The result has indicated that the composite-lining structure brings the surrounding rock's self-supporting into full play and reduces the dynamic stress concentration factor of lining structure.Furthermore,the effect is remarkable when the frequency of the incident waves is low.
By using wave function expansion method,the dynamic response analysis of a deep buried cylindrical composite-lining cavity in an elastic space subjected to incident plane SH waves was studied.By compiling programs with the obtained series solution and mathematical application software MathCAD,the main factors affecting the dynamic stress concentration of the surrounding rock and composite-lining structure,such as the frequency of incident waves,the ratio of the size of composite-lining structure and the elastic modulus,the poisson's ratio and the density of composite-lining structure,were discussed.The result has indicated that the composite-lining structure brings the surrounding rock's self-supporting into full play and reduces the dynamic stress concentration factor of lining structure.Furthermore,the effect is remarkable when the frequency of the incident waves is low.
引文
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[10]纪晓东,梁建文,杨建江.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):511-517.JI Xiao-dong,LIANG Jian-wen,YANG Jian-jiang.On dy-namic stress concentration of an underground cylindrical linedcavity subjected to incident plane P and SV waves[J].Journalof Tianjin University,2006,39(5):511-517.(In Chinese)
[2]LEE V W,TRIFUNAC M D.Response of tunnels to incidentSH waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[3]LEE V W,KARL J.Diffraction of SV waves by under-ground,circular,cylindrical cavities[J].Soil Dynamics andEarthquake 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].Europe-an Journal of Earthquake Engineering,1993(1):29-36.
[5]DAVIS C A,LEE V W,BARDET J P.Transverse responseof underground cavities and piles to incident SV waves[J].Earthquake Engineering and Structural Dynamics,2001,30:383-410.
[6]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,2003,22(3):41-46.QI Hui,WANG Yan,LIU Dian-kui.Dynamic analysis ofshallow embedded lining structure by incident SH waves[J].Earthquake Engineering and Engineering Vibration,2003,22(3):41-46.(In Chinese)
[7]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 Wen-pu,LIU Dian-kui,LIN Hong,et al.Scatting ofsteady P waves around a circular lining in half space[J].Earthquake Engineering and Engineering Vibration,2002,22(3):19-26.(In Chinese)
[8]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的解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jian-wen,ZHANG Hao,LEE V W.An analytical so-lution for dynamic stress concentration of underground cavitiesunder incident plane P waves[J].Chinese Journal of Geotech-nical Engineering,2004,26(6):815-819.(In Chinese)
[9]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 Jian-wen,ZHANG Hao,LEE V W.Analytical solu-tion for dynamic stress concentration of underground twin cavi-ties due to incident SV waves[J].Journal of Vibration Engi-neering,2004,17(2):132-140.(In Chinese)
[10]纪晓东,梁建文,杨建江.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):511-517.JI Xiao-dong,LIANG Jian-wen,YANG Jian-jiang.On dy-namic stress concentration of an underground cylindrical linedcavity subjected to incident plane P and SV waves[J].Journalof Tianjin University,2006,39(5):511-517.(In Chinese)
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