Anti-plane Dynamics Analysis Of Shallow Buried Elliptical Tunnel In Elliptical Coordinate System

As China’s reform and opening-up continues and the economy develops rapidly,infrastructure construction,including lifeline projects,has been improved.Typical objects of lifeline projects include water supply and drainage projects,power,oil and gas pipelines and other energy projects,communication projects,roads and railroads,and other transportation projects.Underground tunnels and pipeline projects are an important component of lifeline projects.According to available studies,tunnels and pipeline works are very sensitive to seismic effects and are highly susceptible to damage under the influence of earthquakes.Therefore,ensuring the seismic performance of underground tunnels and pipeline works is the key to ensure that the lifeline works have sufficient seismic resistance.Due to the practical engineering needs in recent years,the scattering and dynamic stress concentration phenomena around underground structures and the site response problems caused by the presence of tunnels have received increasing attention from researchers.The problem of seismic wave scattering in underground tunnels is both a site response problem and a soil-structure interaction problem.Essentially,there are analytical and numerical methods to solve such problems.Numerical methods are more suitable for solving complex and realistic structures,while analytical methods are not only intrinsically meaningful in revealing the physical processes of wave scattering,but also serve as a benchmark for calibrating numerical results.Therefore,from the perspective of seismic design concept and its disaster prevention and mitigation,it is necessary to make reliable analysis and research on the inverse plane dynamics of shallow buried elliptical tunnels under the action of seismic waves.The main research contents of this paper are as follows:Under the incident of steady SH wave,the inverse plane dynamics of shallow buried elliptical tunnel in elliptical coordinate system is analyzed in detail,and the expression form of dynamic stress concentration coefficient around circular tunnel is given.Firstly,based on the great circle hypothesis,a great elliptic arc hypothesis based on the ellipse coordinate system,the Mathieu function and the outer domain Mathieu function addition theorem is proposed.Under this assumption,the angular Mathieu function and the radial Mathieu function are used to expand the wave function in the elliptical coordinate system,and the wave function conversion between multiple elliptical coordinate systems is realized by the addition theorem of the outer domain Mathieu function.Analytical solution of SH-wave scattering in a shallow circular tunnel.Comparing the results of the model obtained by predecessors using the great circle hypothesis method,the correctness of the method and the model is judged,the accuracy of the solution is discussed,and the applicability and limitations of the method are given.On this basis,by changing the axial ratio of the tunnel,the circular tunnel is transformed into an elliptical tunnel,and the SH wave scattering problem of the half-space shallowly buried circular tunnel is extended to the scattering problem of the half-space shallowly buried elliptical tunnel.According to the established model,the proposed large elliptical arc hypothesis method and the results of formula derivation,by changing the axial ratio and placement angle of the elliptical tunnel,the scattering of SH waves by typical elliptical tunnels in half space is further studied.Numerical calculations are carried out for a typical case where the long axis of an elliptical tunnel is placed horizontally.And based on the numerical calculation results,the research on the influence of the incident angle,the dimensionless frequency of the incident wave(or the dimensionless wave number),the ratio of the minor to major axis of the elliptical tunnel,and the buried depth of the elliptical tunnel on the dynamic stress concentration at the boundary of the elliptical tunnel is carried out.These conclusions have certain reference value for studying how to reduce the dynamic stress concentration phenomenon in tunnel engineering design.