Scattering Of SH-wave By Shallow Underground Orthotropic Lining

As an important underground structure,tunnels are widely used in transportation and urban underground drainage.The destroy and damage of tunnel in the earthquake will cause huge economic losses to the society.In the study of the response of the lining tunnel to seismic waves,the lining tunnel are often assumed to be a homogeneous isotropic medium for easy solution.With the great improvement of modern engineering technology,high-strength and special functional materials are often used in processing engineering problems.These materials are generally not classified as homogeneous isotropic media.At the same time,considering the application of reinforced concrete and fiber reinforced composites in tunnels,they are orthotropic properties in the cylindrical coordinate system.Therefore,based on the elastic wave theory,the wave equations in two different orthotropic media are given and the analytical expressions of the SH wave are also obtained by the conformal mapping and the separation variable method.Considering the actual engineering background,the scattering problem of SH waves with orthotropic lining in the cylindrical coordinate system is studied.First,three different shallow-buried orthotropic lining tunnel models are established: shallow-buried orthotropic lining in half-space,shallow-buried orthotropic lining in quarter space and a shallow-buried multi-orthogonal anisotropic lining model in half space.Then,based on the theory of elastic wave,the expression of SH wave incident displacement field and scattering displacement field in half space and quarter space is given by mirror method and multi-pole coordinate method,and the standing wave displacement field in orthotropic lining Expression;By using the orthogonal series integral method and the boundary conditions under different models,the undetermined coefficients in the displacement field of the scattered wave and the standing wave are solved,also the dynamic stress concentration factor on the lining boundary of the three models and the expression of the free surface displacement amplitude of the lining are given.Finally,the results of three different parameters of the model are obtained by computer programming.According to the numerical results,the wavenumber and incident angle of SH-wave,the different thick and buried depth of the lining,and elastic parameters are applied to the inner boundary dynamic stress concentration coefficient of the half-space medium.The dynamic stress concentration factor of the lining boundary and the influence law on the amplitude of the free interface displacement in the half space are studied.