水下双层衬砌隧道对平面SV波散射问题的解
朱赛男1,陈凯江1,李伟华2

(1.华北理工大学 建筑工程学院,河北 唐山 063210; 2.北京交通大学 土木建筑工程学院,北京 100044)

水下双层衬砌隧道; 水-饱和土-隧道动力相互作用; 散射问题; 地震响应; SV波

Analytical solution to the scattering of plane SV waves in an underwater double-lined tunnel
ZHU Sainan1, CHEN Kaijiang1, LI Weihua2

(1.College of Civil and Architecture Engineering, North China University of Technology, Tangshan 063210, China; 2.School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China)

underwater double-lined tunnel; water-saturated soil-tunnel dynamic interaction; scattering; seismic response; SV waves

DOI: 10.15986/j.1006-7930.2023.02.009

备注

将水层和水下土体分别视为无黏性流体和饱和多孔介质,基于无黏性流体波动理论和Biot饱和多孔介质波动理论,考虑水-饱和土-隧道动力相互作用,借助Hankel函数积分变换法,给出水下双层衬砌隧道对平面SV波散射问题的解.与以往研究中的“大圆弧假定”方法相比,Hankel函数积分变换法可以有效地将饱和土中散射波势函数的表达式从柱坐标系直接转换到直角坐标系下,更有利于水下双层衬砌隧道场地边界条件的处理.在解析解的基础上,重点分析内外衬砌刚度比和内外衬砌厚度比对水下双层衬砌隧道地震响应的影响.研究结果表明:(1)内外衬砌刚度比和厚度比的变化对隧道位移和孔压集中系数影响不明显;(2)随着内外衬砌刚度比的增加,内衬砌动应力集中系数明显增加;(3)随着内外衬砌厚度比的增加,内衬砌动应力集中系数减小.
The water layer and underwater soil are regarded as inviscid fluid and saturated porous medium respectively, and then, based on the inviscid fluid wave theory and the Biot's theory, considering the dynamic interaction of water-saturated soil-tunnel, the solution to the problem of plane SV wave scattering by an underwater double-lined tunnel is givenby means of Hankel function integral transformation method.Compared with the "great circle assumption" method in previous studies, the Hankel function integral transformation method can effectively convert the expression of potential function for scattered waves in saturated soil from the cylindrical coordinate system to the rectangular coordinate system, which is more beneficial to the processing of the boundary conditions of the underwater double-lined tunnel site.On the basis of the analytical solution, the effect of the inner and outer lining stiffness ratio and the inner and outer lining thickness ratio on the seismic response of an underwater double-lined tunnel is mainly analyzed.The research results show that:(1)the change of the inner and outer lining stiffness ratio and thickness ratio has no obvious effect on the tunnel displacement and pore pressure concentration coefficient;(2)with the increase of the inner and outer lining stiffness ratio, the inner lining dynamic stress concentration coefficient increases significantly;(3)with the increase of the thickness ratio of inner and outer lining, the dynamic stress concentration factor of inner lining decreases.