剪切波对饱和土体中圆形衬砌的动力集中
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摘要
采用修正的Biot波动方程,运用波函数展开法研究了剪切波入射时,饱和土体内深埋圆形衬砌的散射问题,通过数值计算分析了衬砌内侧的动应力集中因子Sd与界面处饱和土体的孔压集中因子p*f的变化规律.结果表明:当剪切波为低频和中频入射时,Sd和p*f沿周向的分布曲线比较光滑,而且Sd和p*f受衬砌厚度影响较小,而高频时Sd和p*f沿周向的分布曲线出现大量的凹进和凸出部分,而且在大部分区域Sd和p*f随着衬砌厚度的增大而减小.
The amended Biot's model of wave motion and the expansion method of wave functions are adopted,and the scattering problem of circular lining deeply buried in saturated soil by incident shear waves is studied.Dynamic stress concentration factor(Sd) at inner side of the lining and pore pressure concentration factor(pf*) at the boundary between the lining and saturated soil are analyzed.The results show that the curves of Sd and pf* are smooth and nearly not influenced by the lining's thickness when the incident frequencies of shear waves are lower,while the curves of Sd and pf* have concave and convex parts and Sd and pf* decrease with the increasing of lining's thickness when the incident frequencies of shear waves are higher.
The amended Biot's model of wave motion and the expansion method of wave functions are adopted,and the scattering problem of circular lining deeply buried in saturated soil by incident shear waves is studied.Dynamic stress concentration factor(Sd) at inner side of the lining and pore pressure concentration factor(pf*) at the boundary between the lining and saturated soil are analyzed.The results show that the curves of Sd and pf* are smooth and nearly not influenced by the lining's thickness when the incident frequencies of shear waves are lower,while the curves of Sd and pf* have concave and convex parts and Sd and pf* decrease with the increasing of lining's thickness when the incident frequencies of shear waves are higher.
引文
[1]黄雨,叶为民,唐益群,等.上海软土场地的地震反应特征分析[J].地下空间与工程学报,2005,1(5):773-778.
[2]马行东,李海波,冯海鹏.动参数对三维洞室动态特性的影响分析[J].地下空间与工程学报,2006,2(1):83-86.
[3]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane,Russak&Company Inc,1973:291-305.
[4]Biot MA.Mechanics of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust Soc Am,1956,28(2):168-191.
[5]周香莲,周光明,王建华.饱和土中圆形衬砌结构对弹性波的散射[J].岩石力学与工程学报,2005,24(9):1572-1576.
[6]徐平,夏唐代,韩同春.饱和弹性土体中圆柱壳体对弹性波的散射[J].地震学报,2006,28(2):183-189.
[7]徐平,夏唐代,闫东明.平面P1波入射下饱和度对深埋圆形衬砌动应力集中因子的影响[J].振动与冲击,2007,26(4):46-50.
[8]徐平,夏唐代.准饱和土体中圆形衬砌对弹性波的散射[J].力学季刊,2007,28(2):274-280.
[9]吴世明.土介质中的波[M].北京:科学出版社,1997.
[10]Bardet J P.Aviscoelastic model for the dynamic behavior of saturated poroelastic soils[J].Appl Mech,1992,59:128-159.
[2]马行东,李海波,冯海鹏.动参数对三维洞室动态特性的影响分析[J].地下空间与工程学报,2006,2(1):83-86.
[3]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane,Russak&Company Inc,1973:291-305.
[4]Biot MA.Mechanics of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust Soc Am,1956,28(2):168-191.
[5]周香莲,周光明,王建华.饱和土中圆形衬砌结构对弹性波的散射[J].岩石力学与工程学报,2005,24(9):1572-1576.
[6]徐平,夏唐代,韩同春.饱和弹性土体中圆柱壳体对弹性波的散射[J].地震学报,2006,28(2):183-189.
[7]徐平,夏唐代,闫东明.平面P1波入射下饱和度对深埋圆形衬砌动应力集中因子的影响[J].振动与冲击,2007,26(4):46-50.
[8]徐平,夏唐代.准饱和土体中圆形衬砌对弹性波的散射[J].力学季刊,2007,28(2):274-280.
[9]吴世明.土介质中的波[M].北京:科学出版社,1997.
[10]Bardet J P.Aviscoelastic model for the dynamic behavior of saturated poroelastic soils[J].Appl Mech,1992,59:128-159.
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