Multivariate Analysis Of Subway Vibration Propagation In Soil

The development of modern cities can not be separated from the perfect transportation system,and the underground rail transit is an important part of the urban transportation system.With the deepening of urbanization in China,the underground rail transit network of major cities gradually becomes dense,but the environmental vibration problems caused by this are also becoming more and more serious.Based on the background of subway vibration propagation in soil and its influence on the tunnel structure and surrounding environment,the influences of the layered property and multiphase porous property of soil and the dynamic characteristics of tunnel lining-soil interface on the spatial vibration propagation of subway were studied.The main research contents and results are as follows:1 In order to study the influence about the layered property of soil on the vibration propagation of subway,a 3D dynamic analysis model of layered medium under embedded moving loads was proposed.Based on the analysis model,the semi-analytical solution of vertical displacement of layered foundation under embedded moving harmonic line load was derived by using the moving harmonic point load basic solution,thin layer element method,moving coordinate system method,equivalent principle,Dirac function and triple Fourier transform,and the range of parameter n in the semi-analytical solution was given.The results showed that when the vibration frequency of moving load is constant,the influence of moving speed on the dynamic response in different frequency ranges is different.The influence of moving speed on the low frequency response is greater than that on the high frequency response;the critical speed of the dynamic response is different in different frequency bands.The elastic modulus of soil has the greatest influence on its critical velocity,followed by Poisson's ratio,and the damping ratio has no effect on the critical velocity.The closer the dynamic response frequency is to the load vibration frequency,the larger the amplitude is and the smaller the corresponding critical velocity is.2 In order to study the influence of multiphase porous property of soil on the spatial vibration propagation of subway,a dynamic analysis model of tunnel-lining-saturated soil under moving axial excitation was established.Based on the dynamic analysis model,the analytical solutions of the dynamic responses in frequency domain under moving axial excitation were derived by using the mirror principle,Dirac function,wave function expansion method and Fourier transform method,and the empirical formula of the critical velocity of saturated poroelastic medium under moving axial excitation force was fitted.The dynamic responses of saturated medium in time-space domain were obtained by inverse fast Fourier transform.The effects of the parameters such as the moving speed of axial excitation,the depth of tunnel,the shear modulus of lining and saturated medium and the porosity of saturated medium on the dynamic response and critical velocity were studied.The results showed that for the unlined tunnels,the critical speed of the saturated poroelastic medium is only related to the shear modulus and density of the medium when the vibration frequency of the excitation is not considered,and the critical speed is close to 1.1 times the shear wave velocity of the saturated medium.When the velocity of the exciting force is less than the critical velocity,the dynamic response values decrease with the increase of the shear modulus and porosity of the medium;when the velocity of the exciting force is greater than the critical velocity,the dynamic response values increase slightly with the increase of the shear modulus and porosity of the medium.For lining tunnels,the tunnel lining has a certain weakening effect on the propagation of subway space vibration.The greater the difference between the shear modulus of the lining and the shear modulus of the surrounding medium,the more obvious the weakening effect is.The density and shear modulus of the lining are important factors that influence the critical velocity value of the medium.The critical velocity decreases as the lining density increases and increases as the lining shear modulus increases.3 In order to study the influence of dynamic characteristics of tunnel lining-soil interface on the spatial vibration propagation of subway,a viscoelastic dynamic interface model was derived by using the propagation laws of cylindrical P,SV and SH waves.The analytical expressions of dimensionless spring and damping coefficients in the interface model and the low and high frequency limits of the spring and damping coefficients were given.The differences between the continuous interface model and the viscoelastic interface model in the spatial vibration propagation problem of subway were analyzed.The effects of shear modulus ratio and density ratio between lining and soil,and the Poisson's ratio of soil on dynamic response were analyzed based on the viscoelastic interface model deduced in this paper.The results show that the viscoelastic interface model can effectively simulate the loss of wave energy at the lining-soil interface compared with the continuous interface model;the radial dynamic response amplitudes under the continuous interface model are larger than those under the viscoelastic contact model;the amplitudes of the circumferential displacement and tangential stress calculated by the viscoelastic interface model are larger than those calculated by the continuous interface model when ?₁,<0.5;the amplitude of the axial displacement calculated by the viscoelastic interface model is less than that calculated by the continuous interface model when 0.25<?₁<1.0;the amplitude of shear stress?rzs calculated by the viscoelastic interface model is larger than that calculated by the continuous interface model when ?1<0.25,but when the dimensionless frequency?₁>0.25,the two cases are opposite.For the tunnel lining-soil dynamic interaction problem in saturated medium,an axial-viscoelastic contact model of lining-saturated medium was derived by using the wave equation of saturated medium.The effects of continuous interface model and viscoelastic interface model in saturated soil on the spatial vibration of metro were analyzed by combining the viscoelastic interface model with the content of Chapter 4.The results showed that there are two peaks in the dynamic response of saturated medium when the viscoelastic interface model is considered in a certain velocity range,and the dimensionless velocity corresponding to the first peak is obviously smaller than that corresponding to the continuous interface model.4 On the basis of Article 3,the soil was regarded as a viscoelastic medium with fractional derivative constitutive relation.The influence of viscoelasticity of soil on the dynamic interface model of tunnel lining-soil interface and the influence of the viscoelastic model on the vibration propagation of underground rail transit were studied.The results showed that the spring coefficient and damping coefficient in the interface model are complex when considering the viscoelastic property of soil,but the imaginary part values of spring coefficient and damping coefficient are obviously smaller than the real part values,and the imaginary part values tend to 0 when ?₁>0.5:the transmittance of the fractional derivative viscoelastic interface model to different frequency responses,especially to the low frequency responses,is higher than that of the viscoelastic interface model,but at the same time,the energy dissipation of the fractional derivative viscoelastic medium is greater than that of the elastic medium;with the increase of parameters ?₁ and T_?/T_?,the real part and imaginary part of the spring coefficient and damping coefficient of the model increase;when ?₁ tends to 0 and T_?/T_? tends to 1,the imaginary part of the spring coefficient and damping coefficient of the model is 0,and the model degenerates into the dynamic interface model in elastic medium.