平面P_(1)波入射下双层衬砌对海底隧道地震响应的影响

Effects of double-layer lingings on seismic responses of undersea tunnels under incidence of plane P1 waves

将海水和海床土分别视为理想流体和饱和多孔介质,基于理想流体波动理论和Biot流体饱和多孔介质理论,考虑海水-海床土-隧道结构动力相互作用,利用波函数展开法和Hankel函数积分变换法,给出平面P1波入射下海底双层衬砌隧道地震响应的解析解。与以往的“大圆弧假定”方法相比,Hankel函数积分变换法可以将海底双层衬砌隧道场地中的散射波场势函数从柱坐标系下直接转换到直角坐标系下,可以更好地处理海水层表面和水土交界面处边界条件。在解析解的基础上,分析内外衬砌刚度比和内外衬砌厚度比对海底双层衬砌隧道位移响应和应力响应的影响,对海底双层衬砌隧道的抗减震设计提出合理建议。研究结果表明:①海底双层衬砌隧道的应力响应明显小于同参数条件下的单层衬砌隧道;②内外衬砌刚度比和厚度比对隧道位移响应的影响与隧道衬砌位置有关;③随着内外衬砌刚度比和厚度比的增加,隧道外衬砌应力响应均有减小趋势;④综合内外衬砌刚度比和厚度比对隧道位移响应和应力响应影响,海底双层衬砌隧道抗减震设计时,隧道内外衬砌刚度比和厚度比的选取范围分别建议为E_(2)/E_(1)≤3和δ_(2)/δ_(1)≤2。

Seawater and seabed soil are regarded as the ideal fluid and saturated porous media respectively.Based on the ideal fluid wave theory and Biot’s theory,considering the dynamic interaction of seawater-seabed-tunnel,using the wave function expansion method and Hankel function integral transformation method,the analytical solutions for the seismic response of a double-layer lining undersea tunnel under the incidence of plane P1 waves are obtained.Compared with the previous"large arc hypothesis"method,the Hankel function integral transformation method can directly convert the scattered waves by the double-layer lining undersea tunnel from the cylindrical coordinate system to the rectangular coordinate system,which can better deal with the boundary conditions(surface for the seawater and seawater-seabed interface).On the basis of the analytical solutions,the influences of the stiffness ratio of the inner to outer linings as well as their thickness ratio on the displacement and stress responses of the double-layer lining undersea tunnel are analyzed,and some suggestions are put forward for its anti-shock design.The research results show that:(1)The seismic dynamic stress responses of the undersea double-layer lining tunnel is significantly smaller than those of the single-layer one under the same parameters.(2)The effects of the stiffness ratio and thickness ratio of the inner to outer linings on the displacement responses of tunnel are related to the different locations of the linings.(3)With the increase of the stiffness ratio and thickness ratio of the inner to outer linings,the stress responses of the outer linings of the tunnel all decrease.(4)Considering the influences of the stiffness ratio and thickness ratio of the inner to outer linings on the displacement and stress responses of the tunnel,it is suggested that the selection ranges of the stiffness ratio and thickness ratio of the inner to outer linings of the undersea double-layer lining tunnel should be no more than 3 and 2,respectively.