Study On Torsional Dynamic Interactions Of Transversely Isotropy Satruated Soil And Circular Foundation

Basing on the stress-strain relationships of transversely isotropic medium, the basic dynamic equations of saturated soil, combining the torsional characteristic of foundation in cylindrical coordinates, and using the contact boundary conditions of the soil and foundation, the torsional dynamic interactions of transversely isotropic saturated soil and circular foundation have been analysed systematically in this dissertation.For a rigid circular foundation, the dynamic governing equations are solved by using Hankel transform first. Then, the general solutions for saturated half space and overlaying bedrock saturated soil in Hankel transform domain are formulated separately. Combining the mixed boundary conditions at the bottom surface of the foundation, the dual integral equations of the torsional vibrations of a rigid circular foundation resting on transversely isotropic saturated soil are established, which are further converted to a Fredholm integral equation of the second kind. By numerical method, the dynamic compliance coefficients of the foundation and the contact shear stress under the foundation are studied.When the level of the groundwater is below the surface of the soil, we treat the soil above the groundwater level as an elastic single-phase medium and the soil below the groundwater level as saturated medium. After considering the anisotropy of the soil, the torsional vibrations of a rigid circular plate on partial saturated transversely isotropic soil are presented. Both the saturated half space and overlaying bedrock saturated soil are considered in the selected examples.Furthermore, under the action of harmonic torque, the torsional vibrations of a rigid circular plate embedded in transversely isotropic saturated soil is also discussed in this dissertation.On the basis of the differential equations of an elastic foundation under the action of dynamic torque and the contact boundary conditions of the soil and foundation, the dual integral equations of an elastic cylindrical foundation subjected to harmonic torque are obtained under the help of Hankel transform. We can get the solutions of torsional dynamic interactions after solving the dual integral equations. Selected numerical examples are presented to investigate the influence of relevant parameters on the results.When a cylinder foundation is embedded in transversely isotropic saturated soil, assuming both the side face and the bottom surface of the foundation are perfectly bonded to the soil, we can get the reaction torques that the side soil and the bottom soil acted on the foundation. According to the dynamicequilibrium equations of a foundation under dynamic torque, the torsional vibrations of an embedded cylinder foundation are presented. Both the embedded foundation is rigid and elastic are considered in this dissertation. By numerical method, both the saturated half space and overlaying bedrock saturated soil are considered. By comparison the experimental results with the theoretical results of an embedded rigid cylindrical foundation, the difference of resonant angular displacement amplitude and resonant frequency are also studied.Finally, the dynamic response of transversely isotropic saturated soil under the action of transient torque are solved. By the technique of Laplace-Hankel transform, the solutions of tangential displacement and shear stresses in transversely isotropic soil are expressed in integral form. Selected examples are presented to investigate the characteristics of the displacement and shear stresses in transversely isotropic saturated soil when two different impulsive loadings are applied on the surface of the soil.