Dynamic Responses Of The Saturated Poro-elastic Half-space Due To A Moving Loads And Analysis Vibration Isolation Effectiveness With Pile Rows

Based on Biot's theory, dynamic responses of a homogeneous and layered poroelastic half space subjected to a moving loads as well as the effect of vibration isolation using pile rows embedded in a poroelastic half space is investigated with the semi-analytical methods. The studies of the paper consist of the following parts.1. Using the potential method and applied Fourier transform, the free field solution for a moving load traveled on the surface of a poroelastic half space are derived first. Utilizing the stress and displacement boundary conditions, the frequency wave-number domain solutions for the displacements, the pore pressures and the stresses are established. The time domain solutions for the half space are obtained by the inverse Fourier transform method. As soil inhomogeneity has a significant influence on the dynamic responses the ground and the structures, especially on the case of the high speed, high frequency and large layer thickness, which are difficult to be addressed by the conventional propagator matrix method. Consequently, the transmission and reflection matrices (TRM) method is used in solving the layered water-saturated poro-elastic half space subjected to a moving load. The present methodology was validated by comparing solutions with some known results. Moreover, some numerical examples and corresponding analysis are presented the influences of the load speed, frequency and material parameters of the poro-elastic half space on the responses of ground.2. Based on the obtained general solutions for the displacements, the stresses and the pore pressure for a homogeneous and layered poroelastic half space, the equivalent stiffness of the layered poroelastic half space interacting with an infinite beam to harmonic moving loads is obtained via the transmission and reflection matrices (TRM) method in the frequency wave-number domain. Also, the influences of the load speed and material parameters of the poroelastic half space on the deflection, the bending moment and the shear force of the beam as well as the dynamic response of layered half space are investigated.3. Utilizing Muki's method and the transmission and reflection matrices (TRM) method for the layered poroelastic half space, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half space and the pile is constructed. The integral equations are solved by using the discretization method and the dynamic response of a single pile or pile groups embedded in a layered poroelastic half space subjected to harmonic axial or lateral load are yielded. Based on numerical results of this paper, the TRM method used in this study for the analysis of the piles embedded in a layered poroelastic half-space have the advantages that it can address the layered poroelastic half-space with arbitrary layer thicknesses and arbitrary modulus differences very efficiently. Also, it can deal with high frequency case due to high speed of moving loads without any additional efforts. The numerical results of this study also demonstrate that the soil inhomogeneity has a significant influence on the response of the pile and the half space. For example, that the presence of a stiffer and softer middle layer in the layered half space will affect the impedance of the pile considerably and the inhomogeneity of the half space will enhance the pore pressure significantly.4. According to the free field solution for a moving load or Rayleigh waves applied on the surface of a poroelastic half space, the second kind of Fredholm integral equation in the frequency domain describing the dynamic interaction between pile rows and the poroelastic half space is developed. After numerical solution of the frequency domain integral equation and inversion of the Fourier transform, the amplitude reduction ratio used to assess the vibration isolation effect of pile rows is obtained. Then, the effect of isolation the vibration due to harmonic Rayleigh waves, a harmonic vertical point force and the moving loads by using pile rows embedded in a poroelastic half space is investigated in this study. The influences of the soil inhomogeneity, pile length, Young's modulus of the pile, the net spacing between two neighboring piles in a row are investigated by numerical simulation. Also, the influence of the number of pile rows and spacing between pile rows are examined. The semi-analytical nature of the proposed method avoids the discretization of the whole calculation domain which is necessary for finite element method, and thus it reduces the CPU time for the current problem substantially. Results suggest that the pile length, the number of pile rows, the spacing between neighboring piles in each pile row and the stiffness of piles have significant influence on the vibration isolation effect of pile rows. The spacing between the neighboring pile rows may have little influence on the vibration isolation effect. It also show that speed of moving loads has an important impact on the isolation vibration effect of pile rows: the same pile rows can achieve better vibration isolation effect for lower speed loads than for higher speed loads. Moreover, for the same pile rows and the vibration source, the poroelastic medium often leads to a better vibration isolation effect than the single phase elastic medium does.