Study On The Dynamic Vibrations Of Embedded Foundation In Poroelastic Soil

The study on dynamic soil-foundation interaction problem has been of considerable interest in the field of geomechanics and civil engineering.It plays an important role in the development of the elastodynamics and has important practical applications in machine foundations design as well.Based on the Biot's poroelastodynamic theory,the dynamic vibrations of a rigid cylindrical embedded foundation in poroelastic soil are studied by analytical method in detail for the first time.The main work is as follows:For the vertical vibration of a rigid cylindrical foundation embedded in a poroelastic half-space,the foundation is subjected to vertical time-harmonic excitation along the vertical axis and is perfectly bonded to the surrounding soil.It is assumed that the contact surface between the foundation base and the poroelastic soil is smooth and fully permeable.The total dynamic reaction of the soil at the foundation is composed of a reaction acting in the foundation base and a reaction on the foundation vertical sides.To study the reaction acting in the foundation base,the Novak approximate method is introduced based on the assumption that the soil underlying the foundation base is a homogeneous poroelastic half-space which is independent of the overlying soil.First,the dynamic governing equations of poroelastic soil are solved by using the Hankel transform method and the general solutions are formulated in the Hankel transform fields.Then,considering the mixed boundary-value condition at the interface between the foundation base and the poroelastic soil,the vertical vibration of a rigid foundation is formulated in a set of dual integral equations,which are further reduced to Fredholm integral equation of the second kind.Consequently, the soil reaction acting in the foundation base is derived from solving this Fredholm integral equation.To study the reaction acting on the foundation vertical sides,the soil along foundation vertical sides is modeled as an independent stratum composed of a series of infinitesimally thin poroelastic layers.By using the force-displacement relationship of the infinitesimally thin poroelastic layers and the integration along the circumference of the cylinder,the soil reaction acting on the foundation vertical sides can be derived.Finally,the expressions for the dynamic impedance and displacement amplitude are obtained for the vertical vibration of a rigid cylindrical foundation embedded in a poroelastic half-space by combing the dynamic equilibrium equation of the foundation.The accuracy of the present solution is verified by comparisons with the existing solutions obtained by other researchers.Numerical results are presented to demonstrate the influence of nondimensional frequency of excitation, embedment depth,mass ratio of the foundation,internal friction of the poroelastic soil and pore fluid on the vertical dynamic response.In engineering applications,there are many cases in which the depth of soil layer thickness overlaying rigid base is not large enough.So the vertical vibration of rigid foundation embedded in a single-layered poroelastic soil based on rigid bedrock is then studied by using the same approximate method.The vertical dynamic impedance and dynamic response factor for different values of soil layer thickness are discussed.For the rocking vibration of a rigid cylindrical foundation embedded in a poroelastic half-space,the dynamic interaction problem is also solved by using the same approximate method.The foundation is assumed to be perfectly bonded to the surrounding soil and the contact surface between the foundation base and the poroelastic soil can be either fully permeable or impermeable.The numerical results are presented to analysis the effect of nondimensional frequency of excitation, embedment depth,mass ratio of the foundation,internal friction of the poroelastic soil, pore fluid and hydraulic boundary condition along the contact surface on the rocking dynamic impendence and angular displacement amplitude of the foundation.Considering the layered property,of soil,the author further analyse the rocking vibration of a rigid foundation embedded in a single-layered poroelastic soil based on rigid bedrock.The effect of soil layer thickness,embedment depth,internal friction of the poroelastic soil and pore fluid on the rocking dynamic soil-foundation interaction problem is studied.Finally,the torsional vibration of a rigid cylindrical foundation embedded in poroelastic soil is discussed by the same Novak approximate model.The technique is applied to the computation of torsional dynamic impedance and angular displacement of the rigid foundation embedded in a poroelastic half-space and in a single-layered poroelastic soil based on rigid bedrock.Numerical results are presented to demonstrate the effect of soil layer thickness,embedment depth,mass ratio,internal friction of the poroelastic soil and pore fluid on the torsional dynamic response.