Study On Vertical Dynamic Response Of Pile-soil Coupling Vibration Embedded In Radial Inhomogeneous Soil Layers

Dynamic response analysis of a pile considering soil radial inhomogeneity under vertical vibration load is presented on the basis of constitutive relations of soil and pile,adopting three dimensional axisymmetric soil model and taking consideration of the vertical wave effect of soil around pile,dynamic wave equations of three-dimensional axisymmetric inhomogeneous soil and one-dimensional viscoelastic pile are constructed.Then leading-in boundary conditions and pile-soil contact condition,the dynamic equations of viscoelastic solid pile and tubular pile are solved by analytical solution methods under arbitrary exciting force in the longitudinal direction.The principal contents and original work are as the following:1.Under the condition of considering the radial heterogeneity of soil,the soil around pile is regarded as three-dimensional axisymmetric model,combined with boundary condition and complex stiffness of viscoelastic soil mass from outer zone to inner zone,the complex stiffness of soil is obtained between the contact interface of solid pile and soil,then the vibration equation's expression of single pile in frequencydomain is deduced under the vertical load from the top of the pile.Next,a semi-analytical solution for the velocity response of the pile subjected to a semi-sine wave exciting force was derived by using convolution formula,Laplace inverse transformation and iterative theory of the impedance function.basing on these solutions,pile-soil interactions and dynamic characteristics of soil are obtained by investigating the influences of soil inhomogeneity caused by construction,it manifests that soil radial inhomogeneity is necessary to take into account and has an apparent effect on the pile-soil system on the dynamic properties.2.Under the condition of three-dimensional axisymmetric soil model,a radial inhomogeneous continuum medium model is presented,the vertical dynamic response of tubular pile-soil coupling oscillation in radial heterogeneous soil layers is studied,in which the soil rounding the pile is subdivided into arbitrary numerous annular zones to consider the heterogeneity.Then combining the boundary conditions and continuum conditions of stress and displacement between adjustment soil zones,the dynamic equilibrium equations of every soil zone are solved one by one from outer zone to inner zone.Next,taking advantage of the coupled condition of pile-soil interface,the dynamic equilibrium equation of pile is solved and analytical in frequency domain and semi-analytical solutions in time domain are derived,then the complex stiffness,displace admittance and velocity admittance curve are obtained by programming with Matrix Laboratory software.At last,analyzing the influence of thickness of pipe,pile-soil shear modulus ratio,shear modulus ratio of inner soil and outer soil,thickness of soil layer and shear modulus of soil layer on vertical vibration of a single pile were investigated with numerical examples.The theory with pile-soil vertical coupling vibration developed in this paper is more reasonable in theory.It not only makes the theory of pile vibration more practical,but also provides more theoretical support for anti-seismic design of piles foundation and dynamic testing of piles.