Study Of Dynamic Green’s Functions Of Unsaturated Poroelastic Media And Poroelastodynamic Response Under Moving Loads

Soils usually exhibit a characteristic of layering due to geological sedimentation.In practical engineering,affected by some meteorological and environmental agents like rainfall and evaporation,the groundwater table in a soil medium often fluctuates dramatically with the overall saturation varying significantly,and the near-surface soil usually stays apparently unsaturated.In some more specific engineering applications(say,subgrades for high-speed trains),the above-addressed unsaturated near-surface soil may also be subjected to moving loads.Most of the existing analytical studies of soil dynamics rest on elasticity or/and saturated poroelasticity,both of which can not completely reflect the stress state and the wave propagation in a soil medium that stays in a three-phase state.Concentrating on the two crucial characteristics of soils,layering and unsaturation,this dissertation deals with a couple of valuable problems in the field of unsaturated poroelastic dynamics,which include the full-space fundamental solutions and the half-space Green’s functions for the dynamic response in unsaturated poroelastic media;wave propagation algorithm and the Lamb problem for multilayered media;and the dynamic response of a three-layered road bed subjected to moving loads.The main research contents and conclusions are as follows:1)Fundamental solutions for dynamic response in infinite unsaturated poroelastic media are derived in the frequency domain in succinctness and meanwhile without the loss of rigidity.The derivation primarily rests on the decomposition of the wave field into a rotational field and a dilatational field by the means of the wave field decomposition technique,and the decomposition technique is smartly applied to the cases of point force source,flow source and gas source.Solution for each separated wave can be directly obtained using this decomposition method and combined wave solution is then obtained using superposition principle.2)Based on the fundamental solutions derived,with the use of the u-p form governing equations of the unsaturated porous media theory that are expressed in the cylindrical coordinate system,the general solution of the Lamb problem for unsaturated porous media is derived succinctly for both axial-symmetry and non-axial-symmetry scenarios.Green’s functions of unsaturated poroelastic half-space are derived by the use of the superposition principle.A succinct dynamic Green’s function is then obtained based on the reciprocity of Green’s functions.3)A generalized transmission and reflection matrix(GTRM)method that can be used to model the acoustic response of multilayered media is proposed.The principle of the method is to decipher the wave vectors by constructing generalized T/R matrices and recursive formulas.The generalized T/R matrices are introduced to account for the contributions of multiple reflection and transmission in a global manner.This method which has desirable numerical stability appears simple and is advantageous in physical meanings interpretation.When the wave frequency is high or the layered media is greatly thick or the material combination is highly complex,the advantage of the GTRM method is more conspicuous.4)An unsaturated-saturated-bedrock model in the cylindrical coordinate system is established.Then the first-order differential equation of displacement and stress in wavenumber frequency is established.The generalized T/R matrices and recursive formulas are derived according to general solutions and interface conditions in the cylindrical coordinate system.Dynamic response of unsaturated-saturated-bedrock system subjected to a steady-state vertical concentrated force is analyzed.The results show that the saturation of unsaturated soils has a significant influence on the surface displacement,the near-surface liquid pore pressure,and the gas pore pressure,with the displacement and the equivalent pore pressure increasing with the increasing saturation,especially in the quasi-saturated state.In the case of an unsaturated soil layer,the vertical displacement increases significantly and the equivalent pore pressure decreases rapidly.5)An unsaturated-saturated-bedrock model in the three-dimensional Cartesian coordinate system is established.The first-order differential equation of displacement and stress in the Cartesian coordinate system is established.The generalized T/R matrices for the three-dimensional Cartesian coordinate system are built with the analytical solutions in the wave number domain obtained.Dynamic response of unsaturated-saturated-bedrock system subjected to a moving rectangular load is analyzed.The results show that when the load is at sub-Rayleigh wave speed,trans-Rayleigh wave speed and super-Rayleigh wave speed,the vertical displacement of the surface in the wave number domain presents elliptical,bow and hyperbolic distributions,respectively;the excitation frequency and the moving speed of the load affect the occurrence of the ground resonance in a collaborative manner;the smaller the excitation frequency,the greater the maximum vertical displacement;and the maximum vertical displacement at the ground surface increases with the saturation of unsaturated soil.6)An unsaturated-saturated-bedrock ground-track coupled system subjected to train load is established.Euler-Bernoulli beam,Timoshenko beam and a track model composed of the rail,the sleepers and the ballasts are separately used to model the track.The coupling between track and ground is materialized with the employment of the vertical displacement continuity of ground surface and ballasts.With the use of double Fourier transform,the dynamic response of the ground-track coupled system subjected to a moving load is analyzed.The results show that unlike the case of a single concentrated load,the train load increases the critical velocity of the train under the ground resonance;the higher the saturation,the smaller the critical velocity corresponding to the maximum surface vertical displacement;when the excitation frequency of the train load is relatively low,the change of saturation affects more significantly the maximum vertical displacement of the track;the maximum equivalent pore pressure in the unsaturated soil layer in the case of a quasi-saturated state is much greater than that in the case of relatively low saturation.