Dynamic Vibrations Of Circular Foundation In Poroelastic Soil Subjected To Elastic Waves

The problem of soil-foudation interaction has been studied by many reseachers. Seismic loads and other vibrations generated by ariticfial loads propagate in the form of waves in soil. The dynamic soil-foudation-structure interaction is caused when the foundation is excited by seimic waves. So the study of dynamic response of the foundation subjected to seimis waves not only is helpfu to rearch the mechanism of waves in soil, but also has significant application value.Firstly, based on Biot's dynamic poroelastic theory, an investigation is put into the vertical dynamic response of a rigid circular foundation on the poroelastic soil excited by incident fast P waves and SV waves in this paper. The incident and reflect wave fields are obtained by intrudcing potential functions. The radiation field and rigid-body scattering field are introduced in order to consider the dynamic interaction between the foundation and the underlying soil, as well as the scattering phenomena caused by the existence of the foundation. The motion of the soil is supposed to be governed by Biot's dynamic poroelastic theory, while the boundary conditions along the contact surface between the soil and bottom of the foundation are assumed to be perfectly bonded for the skeleton and hydraulically drained for the fluid. Combining with the mixed boundary-value condition and the dynamic equilibrium equation of the foundation, the expression of the vertical dynamic amplitude of the foundation subjected to the incident plane waves is obtained by solving the control equations using Hankel transforms. The influences of incident angle, the mass of the foundation and the permeability of the soil on the vertical vibrations of the foundation are thus determined through numerical calculations. Significant differences are found between the responses of the foundation, which is excited by fast P waves and SV waves respectively.Secondly, the rocking vibration of a rigid circular foundation on the poroelastic soil excited by incident fast P waves and SV waves is studied. Together with the Fourier expansion and the linear independence of trigonometric functions, two sets of dual integral equations elaborating the mixed boundary-value conditions are established by adopting the method similar to that used in analyse the problem of the vertical vibration. Numerical results show the influences of the incident waves and soil properties on the rocking vibrations.Thirdly, the torsional vibration of the foundation to SH waves and the vertical, rocking vibration of the foundation to Rayleigh waves are researched, and effects of related coeffiecents are discussed.Finally, considering the engineering practice, the vertical and rocking vibrations of the circular foundation embedded in poroelastic soil are studied. The Novak model is introduced. Namely, the soil along the foundation vertical side is composed of series of infinitesimally thin poroelastic layers, and the soil under the foundation base is regard as the poroelastic half space which independent of the overlying soil. By the integration along the foundation side, the force acting on the foundation side can be obtained, and by the dual integral equations, the force actiong on the foundation base is derived. Combing the dynamic equilibrium equation of the foundation, the expressions of the vertical and rocking vibration amplitudes of the embedded foundation subjected to the incident plane waves are acquired. Numerical results are presents to demonstrate the influcences of related coeffiecnts.