Study On The Torsional Vibrations Of Foundations Resting On Saturated Grounds

The study of dynamic interactions of foundations and grounds on half space has been the focus on the mechanics and engineering fields. It is of great value to the development of the elastodynamics and is very helpful to the analysis and design of foundations subjected to dynamic loads, such as vibrating machines and seismic waves.This dissertation is based on the practical saturated governing equations of elastic waves in saturated soils established by Longzhu Chen, ect.. On the basis of the existing work, the torsional vibrations of foundations resting on saturated grounds are studied analytically or semi-analytically in details for the first time. The main work includes:For the torsional vibrations of a rigid disk on saturated media, first, the dynamic governing equations are solved by the use of Hankel transform and the general solutions in the Hankel transform fields are formulated. Then, considering the mixed boundary-value condition, the dual integral equations of the torsional vibrations of a rigid disk on saturated grounds are obtained, which can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient curves and the torsional angle amplitude curves versus the dimensionless frequency are presented and contrasted to that of the elastic one.Then, considering the existing of the ground water, we can treat the soil layer below the water level as the saturated one and the soil layer above the water level as the single-phased elastic one. Using this model, the torsional oscillations of the rigid disk resting on the saturated ground with an elastic layer is studied and the effects of the elastic layer on the foundation's vibration are discussed.Considering the elasticity of the foundation, the author uses the same integral transform method and analyses the presence of the pore water and the effect of the rigidity of the foundation on the dynamic response of the foundation.It is necessary to study the torsional vibrations of foundations on layered saturated grounds, since layered property is one of the main characteristics of grounds. This question is studied in details by means of recurrence laws of matrices and integral transform technique.In this dissertation, the author also uses the same integral transform technique and analyses the torsional vibration of a rigid disk embedded in a saturated half space. The numerical results indicate that the response of the rigid disk and the foundation strongly depends on the material and geometrical properties of the saturated soil and the embedded depth.Finally, the torsional vibration of a rigid disk resting on the saturated grounds under the general torque is primarily discussed by the means of Laplace-Hankel transform. The general solutions of the torsional moment, stress and displacement are given and the numerical solutions in special cases are also obtained.The work presented in this paper is part of the contents of the project Study on the Dynamic Properties of Compound Foundation and it's Application (Grant. Number 50079027), which is supported by the National Natural Science Foundation of China.