| With the acceleration of global urbanization and the rapid concentration of population,urban traffic jams have become a major public problem,while city underground rail traffic has gradually become the public transport mode relied on by large cities in recent years due to its advantages of fast transportation speed,large transportation volume,small pollution,small land area,safe and comfortable riding,and its construction has also been promoted rapidly in recent decades.However,city underground rail traffic not only brings convenience,convenience,comfort and safety to people,but also interferes with people's normal production and life.The environmental problems caused by its operation have increasingly become a topic of concern to people,especially the environmental vibration problems,which seriously affect the normal life of residents along the subway,buildings and the normal use of various precision instruments.In this paper,based on the previous research,three-dimensional elastic medium wave theory is used to carry out the research work related to the environmental vibration caused by subway train operation,the main contents are as follows:(1)In order to analyze the effectiveness of in-filled trench on the ground vibration isolation caused by subway operation,a coupling model which is divided into five parts including the moving train,the track structure,the liner,the ground and the in-filled trench is established.The train load is simulated by a set of constant loads consistent with the spatial distribution of train axles.Rails and floating plates are simplified as infinite Euler beams.Liner and ground were simulated as homogeneous elastic media.The theoretical model is coupled with the continuous stress and displacement conditions at the inverted arch of lining and rail and the stress and displacement continuity between the lining and ground.The concrete in-filled trench was modelled as a heterogeneous medium in the ground.The interface between in-filled trench and ground is treated by common node method and solved in wavenumber domain.Finally,the three-dimensional dynamic response in the time-space domain is obtained from the fast inverse Fourier transform(IFFT).The vibration isolation effect of in-filled trench under different train speed,in-filled trench depth,trench width and tunnel depth is calculated and analyzed.(2)Based on the three-dimensional elastic dynamic equation,the coordinate attenuation function is introduced,and the 2.5D PML control equation is established by Galerkin method,and the 2.5D PML formula is obtained by discretization.Then through the comparison between the analytical solution and the one-dimensional finite element calculation results,the attenuation effect of the wave in PML is analyzed,and the selection of the relevant attenuation function is discussed.Finally,the displacement of the model in the frequency domain and time domain under different loading conditions is calculated and compared with the existing research results,which verifies the correctness of the selection of attenuation function and the 2.5D FEM-PML coupling model.(3)Based on the above-mentioned 2.5D FEM-PML coupling model,a 2.5D dynamic load model of underground tunnel is established.In the premise of keeping the equivalent radius equal,considering different cross-section shape of underground tunnel the same dynamic load,the displacement response in the wavenumber domain is obtained.After that,the displacement response of the soil around the tunnel is obtained by using the fast Fourier inverse transform(IFFT),and the displacement response of the soil around the tunnel is analyzed.The similarities and differences of dynamic response between elliptical,horseshoe and rectangular tunnels and their equivalent circular tunnels is analyzed. |
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