Dynamic Responses Of Saturated Ground And Environmental Vibrations Caused By Elevated High-speed Railways

With a large number of high speed railway lines being built and the running speed on existed main railway lines being increased in China, the train-induced environmental vibration pollutions have been increasingly significant. Especially in southeastern coastal areas, where the ground soil is soft and saturated, the train operation speed can easily exceed the Rayleigh wave speed of ground to generate excessive ground vibrations. Among the high speed railways lines with an operation speed of more than300km/h in China, such as the Jing-Jin, Jing-Hu, Hu-Hang, Hu-Ning and Hang-Yong railway lines, the elevated railway lines constitutes80%of the total railway length. However, little research has been conducted on the environmental vibrations caused by elevated high-speed railway line on saturated ground. Based on Biot's theory, the following researches concerning calculations of the responses of three-dimensional saturated ground both in time and frequency domains as well as predictions of the environmental vibrations caused by elevated high-speed railway lines are conducted:1. Under the action of a moving harmonic point load, the soil skeleton displacements and pore pressures are solved for a saturated half-space governed by the simplified u-p formulations, the fully undrained formulations and the fully drained formulations, and then compared with Biot's complete u-w formulation to determine in which circumstances the simplified formulation can be used to replace to the complete formulation. To do so, a dimensionless parameter R?, named maximum frequency ratio, is proposed to quantify the application scopes of the various formations.2. Based on the complete u-w formulation of Biot's theory, the governing equations of the three-dimensional finite element of the saturated soil are derived by using Galerkin method. Accordingly, the two-and three-dimensional finite elements of the saturated soil are programed and inserted into a self-developed finite element solver. The consolidations and wave-propagations in a saturated soil column as well as the dynamic responses of a two-dimensional saturated ground are studied and then compared with analytical and published results to testify the correctness of the developed saturated-soil finite elements. Meanwhile, the effects of the load speed and the soil permeability on displacements of the soil skeleton and the pore fluids are studied for a plan-strain saturated ground under the action of a moving point load.3. The multi-transmitting formula (MTF), which is originally proposed for the single-phase medium, is generalized and applied to the finite-element modellings of the saturated-ground dynamic responses. Firstly, expressions of the refection coefficients of the second-order MTF boundary condition, which is applied at boundaries of a finite element grid discretizing a saturated ground governed by the u-w formulation, are analytically derived in frequency domain for incidences of the plain P1, P2and SV waves, respectively. The effects of the dimensionless frequency ratio, grid size and time step length on the boundary reflection coefficients and the reflection angles are investigated. Then, the second-order MTF boundary condition is implemented into the self-developed finite element solver. By comparing with the analytical solutions and the reference results obtained from setting the boundary far away from the studied area, the effectiveness of the second-order MTF boundary condition are testified for the finite-element modellings of the one-dimensional, two-dimensional and three-dimensional saturated ground and of the dynamic responses of saturated ground under the actions of moving loads.4. A three-dimensional layered-saturated ground model is established with non-reflection boundary conditions applied at the ground bottom to simulate the ground's infinity. Note that the ground bottom should be fixed if there were overlying rigid rocks. The model is solved by using the thin layer element method to obtain the dynamic Green function of the three-dimensional layered saturated ground in frequency domain. By comparing with published results, the obtained Green function is proved to be correct in reproducing the dynamic responses of the three-dimensional saturated ground under harmonic loadings with different oscillating frequency and at different depths. It is noted that the obtained Green function involves no numerical integral inversions of the Hankel functions and can take the soil stratification into account in an easy way.5. An analytical model incorporating the pile groups and the three-dimensional saturated ground is established basing on the flexible volume method. The piles are discretized by three-dimensional Euler-Bernoulli beam elements. The stiffness matrix of the saturated ground is obtained by inversing the receptance matrix, which is formed among the pile-soil interaction nodes by using the obtained Green function. By comparing with published results, the correctness of the established model is justified. Then the horizontal, vertical, rocking and torsional impedances of the pile groups embedded in three-dimensional saturated ground are studied for different combinations of the soil permeability and the excitation frequency. Specially, the free-field displacements and pore pressures of the saturated ground are investigated for unit forces and unit bending moments applied at the pile-cap center, respectively.6. A vertically-coupled analytical model incorporating the moving oscillating point load, the multi-span elastically supported bridge girders and the slab track carrying an infinite rail beam is established and solved by using the periodic structure theory. The displacement spectrums of the rail, the slab and the box girder are studied for different sets of load oscillating frequencies and load velocities. Meanwhile, both the rail displacements and the reaction forces of the girder supports are investigated for different combinations of the load velocities, oscillating frequencies and initial positions in time-domain. It is concluded that the deformations and the vibration energy will be confined in the rail and the railpads when the quasi-receptance of the rail is lower than that of the railpad, then the loads being transferred into the girder supports will be substantially reduced. Two characteristic frequencies of the elevated railway bridge are identified:(i) the first flexural natural frequency of the girder on springs representing the elastic bearings;(ii) the resonance frequency of the slab on springs account for the under-slab CA cushion layer.7. As a common type of elevated railway bridges in China, a structure pattern of a single-box girder carrying double slab tracks, which is supported by pile foundations, is often utilized. For studying the environmental vibrations caused by the above-mentioned elevated bridges, a vertically-coupled analytical model is proposed to reproduce the transmission processes of the moving train load to the girder supports by the rail, the railpads, the slabs, the CA cushion layer and the box girder, and then to the saturated ground via the piers and the pile foundations. Three key parameters of the proposed model are studied firstly in both frequency and time domains. Then the loads on pile cap center, the soil skeleton displacements and the pore pressures are investigated for different combinations of the load velocities, oscillating frequencies and initial positions. Also the decreasing of the velocities at the ground surface with the increasing of the transverse distance between the observation point and the railway central line is studied. Three characteristic frequencies are revealed, for the first time, for the dynamic responses of the saturated ground:(i) the first flexural natural frequency of the girder on springs representing the elastic bearings;(ii) the resonance frequency of the slab on springs account for the under-slab CA cushion layer;(iii) the first flexural natural frequency of the pier on springs representing impedances of the pile foundation.The present work enriches the analysis methods for the dynamic responses of the saturated soil, and is of theoretical significance and application prospect in solving the environmental vibration problems caused by the elevated high-speed railway lines.