Study On The Rocking Vibrations Of Foundations Resting On Saturated Grounds

The study of dynamic interaction of foundations and grounds on half space is of great value to the development of the elastodynamics and is helpful on physical geography, seismography, and rock and soil mechanics, owning practical.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 rocking vibrations of foundations resting on saturated grounds are studied analytically in details and systematically. For rigid footings, the governing equations are solved by Hankel transform and the general solutions in the Hankel transform field are formulated. Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.For the flexible circular plate or the one with a rigid core, through modifying the right term of the dual integral equations according to mixed boundary value condition, the corresponding dual integral equations are derived. The influence of the elasticity of the elastic plate, or the size of the core and the compliance of the elastic part of the elastic plate with core is analyzed by some numerical examples.Moreover, considering the existing of the ground water, the author treat the soil layer below the water lever as the saturated one and the soil layer above the water level as the single-phased elastic one. Using this model, the rocking vibrations 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.Finally, the rocking vibration of a rigid disk resting on the saturated grounds under the general moment for rocking is primary discussed by themeans of Laplace-Hankel transform. The general solutions of the moment, stress and displacement are given and the numerical solutions in special cases are also obtained.