地下圆形衬砌洞室对SV及Rayleigh波的动应力集中(Ⅰ):3-D级数解
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摘要
为了研究地下圆形衬砌洞室在入射平面SV波和Rayleigh波作用下的动应力集中问题,利用波函数展开法,求解出三维条件下的级数解。当衬砌与半空间介质相同时,级数解将退化为无衬砌时的结果。级数解为进一步定量分析衬砌洞室对入射平面SV波和Rayleigh波的动力集中提供了理论基础。
Using wave function expansion method,a dynamic stress concentration of an underground cylindrical lined cavern subjected to incident plane SV waves and Rayleigh waves was studied and a three-dimensional series solution is presented in this study.When the lined medium and half-space medium are identical,the series solution can be reduced to that of an unlined cavern.The series solution can be used to quantitatively analyze the dynamic stress concentration of the lined cavern subjected to incident plane SV waves and Rayleigh waves.
Using wave function expansion method,a dynamic stress concentration of an underground cylindrical lined cavern subjected to incident plane SV waves and Rayleigh waves was studied and a three-dimensional series solution is presented in this study.When the lined medium and half-space medium are identical,the series solution can be reduced to that of an unlined cavern.The series solution can be used to quantitatively analyze the dynamic stress concentration of the lined cavern subjected to incident plane SV waves and Rayleigh waves.
引文
[1]Lee V W,Karl J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992(11):445-456.
[2]Lee V W,Karl J.On deformations of near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993(1):29-36.
[3]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.
[4]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.
[5]纪晓东,梁建文,Lee V W.地下圆形衬砌洞室在平面P波入射下的动应力集中:三维级数解[J].世界地震工程,2010,26(3):115-122.
[6]梁建文,严林隽,Lee V W.圆弧形层状沉积谷地对入射平面SV波的散射解析解[J].固体力学学报,2003,24(2):235-243.
[7]Abramowitz M,Stegun I A.Handbook of mathematical functions,with formulas,graphs,and mathematical tables[M].New York:Dover Publisher,1972.
[8]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane Russak and Company,Inc.,1973.
[2]Lee V W,Karl J.On deformations of near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993(1):29-36.
[3]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.
[4]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.
[5]纪晓东,梁建文,Lee V W.地下圆形衬砌洞室在平面P波入射下的动应力集中:三维级数解[J].世界地震工程,2010,26(3):115-122.
[6]梁建文,严林隽,Lee V W.圆弧形层状沉积谷地对入射平面SV波的散射解析解[J].固体力学学报,2003,24(2):235-243.
[7]Abramowitz M,Stegun I A.Handbook of mathematical functions,with formulas,graphs,and mathematical tables[M].New York:Dover Publisher,1972.
[8]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane Russak and Company,Inc.,1973.
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