A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical h...A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.展开更多
Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axis...Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axisymmetric governing dynamic equation in the Biot’s theory of two-phase medium is solved. Integral solutions with the soil skeleton displacements and pore pressure as the main unknown quantity are obtained. On the basis of this solution, a systematic study on Lamb’ s problems for saturated soils is performed. Considering the case of drained surface and the case of undrained surface, the integral solutions for surface radial, vertical and circumferential direction displacements under the vertical surface force and horizontal surface force are obtained, which would be reduced to the solutions of the classical Lamb’s problem. So, the correctness of the solutions would be verified. The numerical example indicates that the two-dimensional (2-D) model cannot be applied to 3-D problem accurately.展开更多
文摘A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.
文摘Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axisymmetric governing dynamic equation in the Biot’s theory of two-phase medium is solved. Integral solutions with the soil skeleton displacements and pore pressure as the main unknown quantity are obtained. On the basis of this solution, a systematic study on Lamb’ s problems for saturated soils is performed. Considering the case of drained surface and the case of undrained surface, the integral solutions for surface radial, vertical and circumferential direction displacements under the vertical surface force and horizontal surface force are obtained, which would be reduced to the solutions of the classical Lamb’s problem. So, the correctness of the solutions would be verified. The numerical example indicates that the two-dimensional (2-D) model cannot be applied to 3-D problem accurately.
