球面压缩波入射下深埋三维衬砌洞室的动应力集中效应
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摘要
采用一种间接边界元方法求解了球面压缩波入射下深埋球形衬砌洞室的三维动力反应,并与弹性全空间球形空洞精确解及平面波入射结果对比,验证了本文方法具有较好的计算精度;进而分析了入射球面波的频率、波源与洞室距离、衬砌厚度等参数对衬砌洞室动应力集中因子(DSCF)的放大效应。结果表明:近源和较低频率波入射情况下,入射波频率对动应力集中因子和空间分布特征有显著影响。整体上看,球面波入射下衬砌内动应力集中现象更为明显,DSCF值可达到相应平面波入射情况的2倍左右;当波源距离在5倍波长之外,可近似采用平面波模拟球面波入射;衬砌内不同位置频谱幅值差别明显,且峰值频率也有较大差异,迎波面一侧应力集中更为显著;在正常参数范围内,随衬砌厚度增大,衬砌内DSCF值有所降低。
When the spherical compressive wave being incident into the full space, the dynamic responses of three-dimensional spherical lining cavity are solved by using an indirect boundary element method. The case of spherical cavity with incident plane wave, which has exact solution, is taken as an example. The calculation accuracy of the presented approach is verified. Influences of the frequency of the incident spherical wave, wave source and cavity distance change and the thickness of the lining on the dynamic stress concentration factor(DSCF) cavity lining amplification effect are analyzed. Results show that in the cases of near the source and low frequency incident wave, the incident wave frequency on the dynamic stress concentration factor and spatial distribution characteristics has a significant influence. Overall, for spherical wave incidence, the dynamic stress concentration phenomenon is more obvious in the lining, DSCF value can reach the 2 times more than the corresponding plane wave incidence. When outside of the source five times the wavelength, the wave can be approximated as the plane wave; in different position of lining, the difference of spectral amplitude is obvious, there are also bigger differences in peak frequencies. For waves of attack on one side ranging from 110-140 degrees, the stress concentration is more significant. In normal parameter range, with the increase of lining thickness, the DSCF value inside lining reduces.
When the spherical compressive wave being incident into the full space, the dynamic responses of three-dimensional spherical lining cavity are solved by using an indirect boundary element method. The case of spherical cavity with incident plane wave, which has exact solution, is taken as an example. The calculation accuracy of the presented approach is verified. Influences of the frequency of the incident spherical wave, wave source and cavity distance change and the thickness of the lining on the dynamic stress concentration factor(DSCF) cavity lining amplification effect are analyzed. Results show that in the cases of near the source and low frequency incident wave, the incident wave frequency on the dynamic stress concentration factor and spatial distribution characteristics has a significant influence. Overall, for spherical wave incidence, the dynamic stress concentration phenomenon is more obvious in the lining, DSCF value can reach the 2 times more than the corresponding plane wave incidence. When outside of the source five times the wavelength, the wave can be approximated as the plane wave; in different position of lining, the difference of spectral amplitude is obvious, there are also bigger differences in peak frequencies. For waves of attack on one side ranging from 110-140 degrees, the stress concentration is more significant. In normal parameter range, with the increase of lining thickness, the DSCF value inside lining reduces.
引文
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[11]梁宏斌,苏军,赵社戌.平面波在双孔隙介质中球形夹杂上的散射[J].应用力学学报,2013,30(1):25-30.(Liang Hongbin,Su Jun,Zhao Shexu.Scattering of plane wave by a spherical ideal fluid inclusion in a double-porosity medium[J].Chinese journal of applied mechanics,2013,30(1):25-30(in Chinese)).
[12]刘中宪,王冬.大规模弹性波三维散射快速多极子间接边界元法模拟[J].工程力学,2017,34(1):33-44.(Liu Zhongxian,Wang dong.The FMM-IBEM simulation of large-scale three dimensional scattering of elastic waves[J].Engineering mechanics,2017,34(1):33-44(in Chinese)).
[2]LEE V W.Three-dimensional diffraction of plane P,SV&SH waves by a hemispherical alluvial valley[J].International journal of soil dynamics&earthquake engineering,1984,3(3):133-144.
[3]GONSALVES I R,SHIPPY D J,RIZZO F J.Direct boundary integral equations for elasto dynamics in 3-D halfspaces[J].Computational mechanics,1990,6(4):279-292.
[4]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.(LIANG Jianwen,LIU Zhongxian.Scattering of cylindrical waves around a cavity in a half-space[J].Earthquake engineering and engineering vibration,2008,28(5):27-37(in Chinese)).
[5]梁建文,胡淞淋,刘中宪,等.平面SH波在弹性半空间中三维洞室周围的散射[J].地震工程与工程振动,2015,35(4):40-50.(LIANG Jianwen,HU Songlin,LIU Zhongxian,et al.Scattering of plane SH waves by a 3-D cavity in elastic half-space[J].Earthquake engineering and engineering vibration,2015,35(4):40-50(in Chinese)).
[6]梁建文,巴振宁,Lee Vincent W.平面P波在饱和半空间中洞室周围的散射(I):解析解[J].地震工程与工程振动,2007,27(1):1-6.(Liang Jianwen,Ba Zhenning,LEE Vincent W.Scattering of plane P waves around a cavity in poroelastic half-space(I):analytical solution[J].Earthquake engineering and engineering vibration,2007,27(1):1-6(in Chinese)).
[7]梁建文,巴振宁,Lee Vincent W.平面P波在饱和半空间中洞室周围的散射(II):数值结果[J].地震工程与工程振动,2007,27(2):1-11.(Liang Jianwen,Ba Zhenning,Lee Vincent W.Scattering of plane P waves around a cavity in poroelastic half-space(II):numerical results[J].Earthquake engineering and engineering vibration,2007,27(2):1-11(in Chinese)).
[8]刘殿魁,林宏.浅埋的圆柱形孔洞对SH波的散射与地震动[J].爆炸与冲击,2003,23(1):6-12(Liu Diankui,Lin Hong.Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion[J].Explosion and shock waves,2003,23(1):6-12(in Chinese)).
[9]徐平,刘干斌.黏弹性饱和介质中半封闭圆形衬砌对弹性波的散射[J].铁道学报,2010,32(2):86-92.(Xu Ping,Liu Ganbin.Scattering of elastic waves by a partially sealed circular lining in viscoelastic saturated media[J].Journal of the China railway society,2010,32(2):86-92(in Chinese)).
[10]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392-397.(SHE Yong,QI Hui,YANG Zailin.Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J].Chinese journal of applied mechanics,2008,25(3):392-397(in Chinese)).
[11]梁宏斌,苏军,赵社戌.平面波在双孔隙介质中球形夹杂上的散射[J].应用力学学报,2013,30(1):25-30.(Liang Hongbin,Su Jun,Zhao Shexu.Scattering of plane wave by a spherical ideal fluid inclusion in a double-porosity medium[J].Chinese journal of applied mechanics,2013,30(1):25-30(in Chinese)).
[12]刘中宪,王冬.大规模弹性波三维散射快速多极子间接边界元法模拟[J].工程力学,2017,34(1):33-44.(Liu Zhongxian,Wang dong.The FMM-IBEM simulation of large-scale three dimensional scattering of elastic waves[J].Engineering mechanics,2017,34(1):33-44(in Chinese)).