| By the end of 2020,the total mileage of subway lines in mainland China has reached 6302 km.However,with the rapid growth of subway operating mileage,issues related to train-induced environmental vibration have become a matter of great concern.Train-induced vibration affects the everyday lives of nearby residents,the functioning of precision instruments,and the preservation of ancient buildings.In order to optimize subway line selection design and propose effective measures to mitigate the vibration,it is very important to predict the vibration caused by underground railway traffic efficiently and accurately.At present,as the main medium for elastic wave propagation,foundation soil is subjected to many simplifications in the prediction models of underground railway traffic induced vibration,which caused the coexistence of multiple types of media(dry soil,saturated soil and unsaturated soil),spatial variability of parameters,longitudinal variation of soil-structure and other complex characteristics of real foundation soil have not been considered.Therefore,considering the influence of the above complex characteristics of foundation soil on the dynamic response of the system,the calculation models of vehicle induced dynamic response of subway tunnel on multiphase layered foundation have been studied from the perspective of analytical and numerical methods in this paper.The main research contents and results summarized as follow:(1)Considering the three-phase characteristics of soil,the unsaturated soil was conceptualized as three-phase medium.The shield tunnel was simplified as an infinite Flügge cylindrical shell.The Helmholtz decomposition theorem and the separation-of-variable method were used to solve the governing equations of unsaturated soil and the motion equations of the Flügge shell respectively.Based on the continuity boundary conditions of displacement and stress,the coupling solution is carried out in the frequency-wavenumber domain,and the semi analytical solutions of the dynamic response of subway tunnel system in unsaturated full space and unsaturated half space are proposed.From the comparative analysis,it is found that the calculation results of full space model and half space model are different,but for the case of deep buried tunnel,the calculation results around the tunnel lining are almost the same.(2)Based on the semi analytical solution of dynamic response of unsaturated half space foundation-tunnel system,the influence of soil saturation on the dynamic response of the system is discussed.The results show that the change of saturation will change the dynamic shear modulus,effective stress coefficient and elastic wavelength of soil,which will has an obvious effect on the distribution law and amplitude of dynamic response.Among those the excess pore water pressure is particularly affected by saturation,the magnitude of which decreases rapidly with the decrease in saturation.When the saturation decreases from 1 to 99%,the pore water pressure decreases to 30%in the saturated state.In addition,the critical velocity of soil increases with decreasing soil saturation,which results in the increase of the critical velocity of the soil.(3)Considering realistic characteristics of soil layers(in which dry soil,saturated soil and unsaturated soil coexist),the unified total wave field expression of the different media has been achieved by parameter degradation.Based on the transformation method of plane wave functions and cylindrical wave functions.A dynamic matrix reflecting the wave vectors of the soil layers is established using the transfer matrix method.Based on the boundary conditions,semi analytical model of dynamic response of foundation-tunnel system with multiple media has been proposed using the transformation method of plane wave functions and cylindrical wave functions.The results show that new scattering surfaces appear at the interfaces between layers consisting of different media(dry soil,saturated soil or unsaturated soil),changing the propagation characteristics of elastic waves,such as reflection and refraction,and the seepage conditions of the foundation.The characteristics of the overlying unsaturated soil rarely affect the dynamic response of the soil at the tunnel bottom,which have a great effect on the magnitudes of the dynamic displacements of the soil at the ground surface.On the contrary,the critical velocity of the system is rarely affected by the saturation of the overlying soil layer,which is mainly affected by the saturation of the soil layer through the tunnel.(4)The finite element-perfectly matched layer method(FEM-PML)for calculating the dynamic response of unsaturated soil-structure system is proposed.Based on the differential equation of unsaturated soil motion and seepage equation,combined with stress and seepage boundary conditions,the finite element equation of u_b-p_l-p_g unsaturated foundation is derived by Galerkin method,which could reduce single node degrees of freedom.The finite element expression of PML is derived by introducing the coordinate stretch function,which could realize the rapid attenuation of incident wave without reflection in the finite boundary element.By reducing single node degrees of freedom and introducing PML method to deal with the boundary,the computational efficiency has been greatly improved.(5)Based on the FEM-PML method,the free wave propagation constant and free wave eigenvector are solved by introducing the free wave propagation theory,through which the stiffness matrix of the periodic element can be obtained.Combined with the Gaussian elimination method,a multi coupling periodic structure finite element method is proposed.The influence of longitudinal variation characteristics of foundation and tunnel structure on dynamic response is analyzed.The results show that the longitudinal variation characteristics of foundation and structure will affect the dynamic response of the system,especially the longitudinal variation characteristics of tunnel structure.(6)Based on the coupling periodic structure finite element method,the vibration reduction and isolation effect of isolation pile is discussed.The results show that the existence of isolation pile will change the amplitude distribution of surface dynamic response,and the surface dynamic response decreases significantly near the isolation piles.The vibration reduction effect of two rows of isolation piles is significantly better than that of single row of isolation piles.Compared with pile wall,the longitudinal pile spacing of isolation pile will affect the structural vibration reduction effect.The longitudinal variation characteristics of foundation soil will affect the prediction results of system dynamic response.Therefore,in order to accurately predict the vibration reduction effect of isolation pile,the longitudinal variation characteristics of isolation pile system should be considered.(7)The 2.5D FEM-PML method for calculating the dynamic response of unsaturated soil-tunnel system is derived.Coupling vehicle,track and rail surface irregularity,the 2.5D FEM-PML model for dynamic response analysis of vehicle-track-tunnel-soil system is established.Furthermore,the spatial variability of soil parameters was simulated by random fields using the Monte Carlo theory and the middle point method of Cholesky decomposition.By coupling the random fields of soil parameters to the 2.5D FEM-PML deterministic model,the stochastic finite element analysis of system dynamic response has been realized.The results show that the variability of soil parameters has little influence on the spatial distribution regularities of ground vibrations,but has a significant effect on the dynamic response amplitude.In addition,the random field construction parameters have little effect on the mean value of vibration response but mainly affected the variability coefficient of vibration. |
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