Vibration Analysis Of Metro Tunnel In Viscoelastic Medium

With the continuous development of domestic urban construction,more and more cities have their own subway systems.At present,China has become the country with the longest subway operation mileage and the fastest development in the world.The environmental vibration caused by subway train operation is becoming increasingly prominent,and the public pays more and more attention to the environmental pollution caused by rail traffic load.In this paper,based on the actual data of shield construction of subway tunnel in China,according to the thickness diameter-ratio of subway tunnel structures,the theory of moderately thick cylindrical shell is used to simulate subway tunnel.Then the coupling system model of moderately thickness cylindrical shell and soil medium is established,the tunnel-soil system is studied by analytical method,and the vibration characteristics of the tunnel itself and the dynamic response of soil around the tunnel under load are analyzed.1.Based on the theory of elastic wave propagation in soil medium and Helmholtz potential function theory and Bessel function,the vibration control equation and dispersion equation of tunnel structure under the interaction between saturated soil and tunnel structure are established by using pipe-in-Pip e model under the continuous condition of tunnel and soil interface.Then According to the dispersion equation,the vibration characteristics of subway tunnel coupled with saturated soil are calculated and analyzed by taking soil porosity,tunnel wall thickness,tunnel radius and tunnel length as variables.These conclusions can provide theoretical basis for subway tunnel design,vibration reduction and damage prevention.2.The soil medium around the tunnel is simplified as isotropic viscoelastic medium,and the vibration control equation and dispersion characteristic equation of tunnel coupled with viscous soil are derived analytically by using the moderately thickness cylindrical shell theory.Then,the minimum modulus approximation method is used to solve the problem in complex domain.The influence of soil viscosity coefficient on the natural vibration frequency of tunnel structure and its attenuation are studied.Furthermore,the variation trend and attenuation of tunnel natural vibration frequency in viscoelastic soil under the influence of various factors are discussed.3.In this paper,subway trains are regarded as moving loads,and the dynamic response of subway tunnels under moving point loads in the whole space is studied by analytical method.In the model,a moderately thickness cylinder of infinite length is used to simulate the tunnel lining,and a viscoelastic model is used to simulate the soil around the tunnel.Based on the potential function theory of viscoelastic soil and Fourier transform,the boundary conditions of the interface between tunnel and soil are coupled by matrix extension,and the dynamic response of tunnel and viscoelastic soil is transformed into the superposition of dynamic response under various modes.Then the displacement solution in frequency-wave-number domain is obtained by dimensionality reduction.Finally,the dynamic response in time-space domain is obtained by inverse Fourier transform.Therefore,the dynamic response of soil viscosity to the displacement field under the tunnel invert is studied,and the threshold value of soil field around the tunnel affected by the viscosity under moving load is discussed.4.On the basis of the above work,the subway train is simplified as harmonic load,and the three-dimensional dynamic response model of moderately thick cylindrical shell tunnel-clay medium under harmonic point load is established.Then,the influence of soil viscosity and load velocity on the tunnel-soil displacement field under harmonic loading is calculated and discussed.The theoretical model is established to calculate the displacement vibration of each particle in the soil field under different load frequencies.The study shows that the energy diffusion in the soil is non-uniform,and the main energy propagation is in the direction of the maximum particle amplitude in the soil medium,and the specific angle is mainly related to the load frequency.These results explain the reason why the buildings around subway are mainly subjected to low frequency vibration,and provide a theoretical basis for the existence of vibration amplification region around subway tunnel.In this thesis,a series of theoretical models for the coupling of moderately thick cylindrical shells and soil medium are established,which enrich the selectivity of tunnel-soil system model.These models can provide reference for the design of subway vehicles,anti-vibration design of subway tunnel structure,anti-vibration and vibration reduction of underground buildings around the tunnel,as well as for the prediction and monitoring of environmental impact around the tunnel and other related research,which has practical significance.