凸起地形中半圆形衬砌隧道对SH波的散射解析解  

An Analytical Solution to Scattering of Plane SH Waves by a Semi-circular Lining Tunnel in a Semi-circular Shape Hill

作　　者：张海 苏振飞 刘中宪 王雪杰 Zhang Hai;Su Zhenfei;Liu Zhongxian;Wang Xuejie(Tianjin Key Laboratory of Civil Structure Protection and Reinforcement,Tianjin 300384,P.R.China;College of Civil Engineering,Tianjin Chengjian University,Tianjin 300384,P.R.China)

机构地区：[1]天津市土木建筑结构防护与加固重点实验室,天津300384 [2]天津城建大学土木工程学院,天津300384

出　　处：《地下空间与工程学报》2019年第3期769-777,共9页Chinese Journal of Underground Space and Engineering

基　　金：天津市自然科学基金(17JCYBJC21700);天津市应用基础与前沿技术研究计划(13JCQNJC07400);天津市高校学科领军人才培养计划;天津市“131”创新型人才培养工程人选计划

摘　　要：根据弹性波动理论,结合分区和契合思想,利用傅里叶级数展开法,由连续性条件和自由地表边界条件,求得了凸起地形中衬砌隧道对SH波散射的解析解。通过研究半圆形山岭衬砌隧道对SH波散射的影响,得到的计算结果表明:对于软性和硬性衬砌隧道而言,凸起地形对地震波有明显的放大作用,当入射频率增大时,地表位移幅值也增大,这种现象在凸起地形范围内尤为明显;当入射频率较低时,位移幅值在凸起地形附近变化明显。与此同时,刚性衬砌表面的动应力集中现象尤为显著。除此以外,结果还表明动力反应特征主要影响因素包括入射波角度、入射波频率及衬砌材料属性等。According to the elastic wave function expansion method, continuity conditions, and free surface boundary conditions, by using Fourier-series expansion method combined with the ideas of area-partition and regionmatching technique, the analytical solutions for the scattering of SH wave by the hill lined tunnel in convex topography is obtained in this paper. By studying the effect of semi-circular mountain lining tunnel on SH wave scattering, the calculation results show that:for the different hardness of lining tunnels, the raised topography has a significant amplification effect on seismic waves. When the incident frequency increases, the amplitude of the surface displacement will enhance, which is especially noticeable in the convex topography. When the incident frequency is low, the displacement amplitude changes significantly near the scope of the convex topography. At the same time, the dynamic stress concentration on the surface of the rigid lining is particularly significant. In addition, the results show that the main influencing factors of dynamic response characteristics include incident wave angle, incident wave frequency and lining material properties.

关 键 词：山岭隧道 衬砌 SH波 散射 解析解 波函数展开法 动应力集中 

分 类 号：P315.3[天文地球—地震学]