弹性半空间含脱空区的衬砌隧道对平面P、SV波的散射  

Scattering of Plane P and SV Waves by Lined Tunnel with the Void Area in an Elastic Half Space

作　　者：刘中宪[1] 邵贤蕊 梁建文[2] 赵延喜[3] 杜建梅 LIU Zhongxian;SHAO Xianrui;LIANG Jianwen;ZHAO Yanxi;DU Jianmei(Tianjin Key Laboratory of Civil Structure Protection and Reinforcement,Tianjin Chengjian University,Tianjin 300384,China;Department of Civil Engineering,Tianjin University,Tianjin 300072,China;Nanjing Institute of Technology,Nanjing 211167,China;China Municipal Engineering North China design and Research Institute Co.,Ltd,Tianjin 300074,China)

机构地区：[1]天津城建大学,天津市土木建筑结构防护与加固重点实验室,天津300384 [2]天津大学土木工程系,天津300072 [3]南京工程学院,江苏南京211167 [4]中国市政工程华北设计研究总院有限公司,天津300074

出　　处：《应用基础与工程科学学报》2020年第5期1158-1171,共14页Journal of Basic Science and Engineering

基　　金：国家重点研发计划项目(2017YFC805000);天津市科技支撑计划重点项目(17YFZCSF01140);天津市自然基金重点项目(18JCZDJC39200)。

摘　　要：弹性半空间含脱空区衬砌隧道对平面P、SV波的散射规律尚不明确.采用一种高精度的间接边界积分方程法,将脱空区看作表面不相接触的界面裂纹,在衬砌内外表面附近引入虚拟波源面,衬砌内外的散射场由此面上的膨胀波源和剪切波源构造所得,进而据边界条件建立方程并求得虚拟波源密度,总波场由自由场和散射场叠加而得.数值分析结果表明:脱空区衬砌隧道附近波的散射同无脱空区情况相比差异显著,动力反应特征主要依赖于脱空范围、脱空位置、波入射角、无量纲频率等参数.总体上看,脱空对衬砌环向应力局部放大可达3倍以上,特别是对脱空区附近衬砌外壁放大更为显著.地表位移和衬砌应力均存在着“低频共振”现象,谱曲线峰值一般出现在低频段.实际隧道结构动力分析宜根据实际工况考虑脱空区的影响.The scattering of plane P and SV waves by a lined tunnel with the void zone in an elastic half space has not been revealed.A high-precision indirect boundary integral equation method(IBIEM)was used,the void zone can be regarded as an interface crack with no contact with the surface,using the Green's functions of compressional and shear wave source in half space,the scattered waves in the lining and half space was constructed using the fictitious wave sources close to the lining surfaces,and the density of the fictitious wave sources was obtained by boundary conditions,then the total wave field was obtained by the superposition of the free field and the scattering field.The numerical results show that the scattering of the waves near the void lining is largely different from that of the non-void lining.The dynamic response mainly depends on the void range,void position,the incident angle,incident frequency and other parameters.On the whole,the hoop stress of lining is enlarged locally more than 3 times by void,especially for the outer walls of the lining,the amplification effect is more obvious near the void zone.Both the surface displacement and the lining stress have the phenomenon of low frequency resonance,the spectral curve reaches the maximum at the lower frequency.The dynamic analysis of an actual tunnel structure should consider the void zone according to the actual working condition.

关 键 词：平面波散射 动应力集中 间接边界积分方程法 衬砌隧道 脱空区 半空间 

分 类 号：O0347.4[理学]