| The continuous progress of urbanization makes the above-ground space far from meeting the needs of people's daily production and life.Therefore,it is urgent to speed up the development and utilization of underground space.As a kind of widely used underground space,the tunnel has many different sections and different depths of embedding.It is very difficult to study the dynamic response of the tunnel under earthquake.In addition,the complex natural environment of each tunnel makes the connection between different tunnels and surrounding media different,which results in different damage degree of the tunnel under earthquake.Therefore,studying the dynamic response law around the tunnel under different sections,different depths of embedding and different connections is of great significance for tunnel construction and optimization of tunnel design.In order to obtain the dynamic response law around the tunnel under different cross-sectional shapes,different buried depths and different boundary conditions under earthquake action,this paper introduces a new method of conformal change,which can establish between any shape tunnel and circular tunnel.The mapping relationship overcomes the difficulty of mapping the curved wall tunnel in the past.By using the wave function expansion method,the complex function method and the Graf formula,the displacement and stress in the surrounding medium and lining under different cross-section shapes and different boundary conditions are obtained respectively.The shape and boundary studied are typical and conform to the characteristics of practical engineering.Finally,the numerical results are compared with the existing ones to verify the correctness of the paper.The influence of different parameters on the dynamic stress around the tunnel is given by the specific parameter analysis.The main research contents of this paper are as follows:(1)Based on Laurent series and combined with triangular interpolation and odd-even iteration,the mapping relationships between curved horseshoe tunnel,rectangular tunnel and circular tunnel are established respectively.(2)The dynamic response of horseshoe tunnel with curved wall in full space under SH wave is studied.On the basis of conformal transformation,assuming that the connecting boundary is elastic and replaced by spring,the analytical solutions of stress and displacement in surrounding medium and lining are obtained by combining complex function method and wave function expansion method.The results are compared with the existing results to verify the correctness of this paper,and the influence of the number of incident wave,the type of lining and the interface stiffness coefficient on the external dynamic response of the lining is discussed in detail through specific numerical analysis.(3)The dynamic response of a rectangular tunnel in full space under SH wave is studied.On the basis of conformal transformation,assuming that the connecting boundary is viscoelastic and replaced by linear spring and damping,the analytical solutions of stress and displacement in surrounding medium and lining are obtained by combining complex variable function and wave function expansion method.The effects of incident wave number,stiffness coefficient and viscous coefficient of interface on the dynamic response of lining are discussed in detail through specific numerical analysis.(4)The dynamic response of horseshoe tunnel with curved wall in semi-infinite space under SH wave is studied.On the basis of conformal transformation,assuming that the connecting boundary is perfectly elastic,that is,the surrounding medium and lining are well connected,the scattering wave function satisfying the stress-free boundary conditions on the surface of half space is found,and the analytical solutions of stress and displacement are obtained by simplifying the two sides of the equation with Graf formula.Through the specific numerical analysis,the influence of the incident wave number,the thickness of the lining and the buried depth of the tunnel on the external dynamic response of the lining is discussed in detail. |
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