Dynamic Responses Of A Layered Transversely Isotropic Ground And Overlying Subgrade Structure Subjected To Moving Loads

The construction of railway infrastructure promotes economic growth and brings convenience to people.However,vibration problems arising from train operations have become increasingly significant with the speed-up of trains and expansion of the railway network.Hence,the problem of the dynamic response of the ground coupled with the subgrade structure due to moving loads has drawn extensive concern.In practical engineering,natural soils and rocks possess different physical and mechanical properties in horizontal and vertical directions and show transverse isotropy.Moreover,the moisture conditions of different ground layers vary.Nevertheless,most of the existing works took the ground as isotropic and solely one type of medium,which neglected the aforementioned characteristics of the ground.The transverse isotropy of geomaterials and the difference in moisture conditions between different ground layers change the properties of waves,thus affecting the intensity and propagation of vibrations.A ground model consisting of different types of transversely isotropic（TI）media is developed in this study.Based on the ground model,models of a layered TI ground coupled with different superstructures including beam,track-subgrade,and vibration mitigation measures are further developed.The propagation characteristics and mitigation measures of vibrations of the coupling models are investigated by adopting an analytical method and a hybrid method.The main works and results are as follows:（1）A ground model comprising TI elastic layer group,TI poroelastic layer group,and a layered TI elastic half-space from top to bottom is developed.The model considers the transverse isotropy and difference in moisture conditions of different ground layers.A potential function method aiming to solve governing equations of TI elastic medium in the Cartesian coordinate system is extended to the solution of governing equations of TI poroelastic medium.To solve the layered ground comprising alternately distributing TI elastic and poroelastic media,an extended form of the exact stiffness matrix method is developed.After obtaining the solutions to the layered ground,the model in this study is compared with an equivalent layered TI elastic model and a model composed of a TI elastic layer,a TI poroelastic layer,and a rigid base.The influence of groundwater table variation is also analyzed.（2）Considering the axial load in the beam structure due to temperature variation,an analytical model of a beam coupled with the ground comprising alternately distributing TI elastic and poroelastic media is developed.The differential equations of the Euler and Timoshenko beam including an axial force term are solved utilizing Fourier transform.Based on solutions to the layered TI ground,the moving load response of the coupling model is obtained via the concept of equivalent flexibility.Analyses show that neglecting the existence of underground water in the TI poroelastic layer results in an error of above 20%when predicting the beam deflection.The second-order critical speed of the ground significantly increases due to the coupling of the beam.The transverse isotropies of elastic and shear moduli change the critical speed and magnitude of the beam deflection by altering the dispersion characteristics of the coupling system.The influence of the horizontal permeability on excess pore pressure is reduced when it is lower than 10^-11 m²,while the vertical permeability can still affect the distribution of excess pore pressure when it is lower than 10^-13 m².The rise of temperature results in a compressive axial force that decreases the critical speed and increases the magnitude of beam deflection,thus posing threat to the superstructure.（3）An analytical model of a ballasted track coupled with the ground comprising alternately distributing TI elastic and poroelastic media is developed.The differential equations of the track system are solved with Fourier transform.Based on solutions to the layered TI ground,the ballasted track is coupled with the ground according to continuity conditions at the interface of ballast and ground.Dynamic responses of the track-ground system due to constant and harmonic trainloads are then obtained.Analyses show that the critical speeds of the displacement and excess pore pressure increase with the ratio of the horizontal elastic modulus to the vertical one.Multiple-order critical speeds of displacement and excess pore pressure occur in the TI poroelastic layer due to the reflection and superposition effect of waves.Peak values of the displacement exist within the load excitation frequency of 5 Hz,and the peak frequency increases with the ratio of the horizontal elastic modulus to the vertical one.The mechanism of the effect of load speed and frequency on vibrations can be studied with the spectral analysis method.（4）A refined model of a ballastless double-line track-subgrade system coupled with the ground comprising alternately distributing TI elastic and poroelastic media is developed.A 2.5-D hybrid method of analytical and numerical methods is applied to solve the model,among which the ballastless track-subgrade and the layered TI ground are solved by the 2.5-D finite element method（FEM）and 2.5-D Green’s function,respectively.Analyses show that neglecting the existence of underground water changes the characteristics of time histories and increases the dynamic response amplification ratio caused by bidirectional train operation.The cut-off speed of the ground is a key parameter determining the vibration characteristics and is influenced by transverse isotropy.The dynamic response induced by a single-line subgrade is intenser than that by a double-line subgrade when the train speed exceeds the cut-off speed.The variation of vibrations due to one train operation with train speed is the same as that due to two trains meeting each other.The distribution characteristics of amplification coefficients of dynamic responses along the ground surface depend on the relationship between train speed and the cut-off speed.The amplification coefficient of excess pore pressure in the ground under the track is larger than 1.6.The influence of rail irregularity is moderate on the displacement and gradually increases on the velocity and acceleration of the subgrade surface.The influence of rail irregularity on the velocity and acceleration of the ground surface is related to the cut-off speed.When the train speed is higher than the cut-off speed,the influence of rail irregularity decreases,and the ground velocity is dominated by the axle load.The effect of axle load on excess pore pressure is more significant than rail irregularity.（5）Based on the train-ballastless track-subgrade-layered TI ground model,the model of the vibration mitigation measure of subgrade replacement is developed.The effects of two kinds of measures,subgrade replacement under the concrete base and along the subgrade slope,are investigated by adopting a hybrid method of 2.5-D FEM and 2.5-D Green’s function.Analyses show that hard material is more appropriate than soft material in the subgrade replacement.The mitigation effect is enhanced with increasing train speed.Subgrade replacement under the concrete base serves to mitigate vibrations both in the subgrade and on the ground surface,while replacement along the subgrade slope serves to mitigate vibrations on the ground surface.The mitigation efficiencies of the two measures on ground surface responses are dependent on the transverse isotropy of the ground,and the mitigation efficiencies are higher when the ratio of the horizontal elastic modulus to the vertical one is lower.