饱和土中浅埋隧道耦合二维动力响应解答探讨

Solutions for Two-dimensional Dynamic Response of Shallow Tunnels in Saturated Soil under Coupling Interaction of P and S Waves

摘要:

针对平面波耦合作用下饱和半空间中浅埋隧道二维动力响应的典型问题的解答进行探讨。首先基于Biot饱和孔隙介质理论建立饱和土场方程,并通过中间势函数的代入推导得到饱和土体中的快纵波、慢纵波及横波的Helmholtz势函数方程,随后引入柱坐标系下饱和土体和弹性衬砌的势函数通解,并代入边界条件中,建立以第n组参数为变量的多元一次齐次线性方程组。采用本文的推导思路,可以解决饱和土体中的浅埋隧道在地震作用时P波和S波耦合作用下的响应问题。

Abstract:

This study briefly discusses solutions for a typical case concerning the two-dimensional dynamic response of shallow tunnels under the coupled influence of plane waves. The field equation of saturated soil is based on the Biot theory for a saturated porous medium.The Helmholtz equations for the potential functions of a fast P, slow P, and S waves are deduced by introducing additional potentials. By introducing the general solutions of the potential functions into the boundary conditions,the multivariate linear equations are built up in a cylindrical coordinate system. The deduction procedure of this paper can be utilized to solve problems concerning the seismic response of shallow tunnels in saturated soil under the coupled influence of P and S waves during an earthquake.