This paper presents a new method to derive the analytical solution for the vertical impedance of an endbearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one-dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil-pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. otherwise specified, the following parameter values are used: H = 10 m, r 0 = 0.5 m, E p = 25 GPa, VERTICAL IMPEDANCE OF AN END-BEARING PILE IN VISCOELASTIC SOIL

A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

The three-dimensional finite difference method was used in this study to analyze the deformation and stresses of a passive pile under surcharge load in extensively deep soft soil. A three-dimensional numerical model was proposed and verified by a field test. The horizontal displacements of the pile agreed well with the field results. This study investigated the pile-foundation soil interaction, the load transfer mechanism, the excess pore water pressure (EPWP), and the horizontal resistance of the foundation soil. The results show that the soil in the corner of the loading area developed a large uplift deformation, while the center of the loading area developed a large settlement. The lateral displacement of the pile decreased sharply with the increase of the depth and increased with the surcharge load. The lateral displacement of the soil was negligible when the depth exceeded 30 m. The EPWP increased in a nonlinear way with the increase of the surcharge load and accumulated with the placement of the new lift. The distribution of the lateral earth pressure in the shallow soil layer was complex, and the negative value was observed under a high surcharge load due to the suction effect. The proportion coefficient of the horizontal resistance coefficient showed much smaller value in the situation of large lateral deformation and high surcharge load. The design code overestimated the horizontal resistance of the shallow foundation soil, which should be given attention for the design and analysis of the laterally loaded structures in extensively soft soil.

An analytical solution is developed in this paper to investigate the horizontal dynamic response of a large-diameter pipe pile in viscoelastic soil layer. Potential functions are applied to decouple the governing equations of the outer and inner soil. The analytical solutions of the outer and inner soil are obtained by the method of separation of variables. The horizontal dynamic response and complex dynamic stiffnesses of the pipe pile are then obtained based on the continuity conditions between the pile and the outer and inner soil. To verify the validity of the solution, the derived solution in this study is compared with an existing solution for a solid pile. Numerical examples are presented to analyze the vibration characteristics of the pile and illustrate the effects of major parameters on the stiffness and damping properties.

In recent years, the high development of high-speed railway lines cross through areas with poor geological conditions, such as soft soil, offshore and low-lying marsh areas, resulting geotechnical problems, such as large settlements and reduction of bearing capacity. As a new soil reinforcement method in high speed railway lines, the piled raft structure has been used to improve soil conditions and control excess settlement. In order to study the dynamic behavior of piled raft supported ballastless track system in soft soil, an experimental study on vibration velocities of piled raft supported embankment and foundations is presented in soft soil with different underground water levels. Vibration velocities at specified positions of the piled raft supported embankment and foundations are obtained and discussed. The vibration velocity curves on various testing locations of piled raft foundations are clearly visible and have sharp impulse and relaxation pattern, corresponding to loading from train wheels, bogies, and passages. Vibration velocity distribution in the horizontal direction at three train speeds clearly follows an exponential curves. Most of the power spectrums of vibration velocity at various locations are mainly concentrated at harmonic frequencies. The change in water level has slight impaction on the peak spectrum of vibration velocity at harmonic frequencies. The vibration power induced by train loads are transmitted, absorbed, and weakened to a certain extent through embankment and piled raft structure. The dynamic response character of embankments are affected by their self-vibration characteristics and the dynamic bearing capacity of the piled raft structure.