Study On Pile Vertical Vibration In Inhomogeneous Soil

Dynamic response analysis of a pile considering soil inhomogeneity under vertical vibration load is presented. Dynamic wave equations of plane or three-dimensional axisymmetric inhomogeneous soil and one-dimensional viscoelastic or elastic pile are constructed based on constitutive relations of soil and pile. Leading-in boundary conditions and pile-soil contact condition, the dynamic equations are solved by analytical solution method, thereout a complex stiffness transfer plane-strain model or three-dimensional axisymmetric continuum medium model in inhomogeneous soil are constructed. The dynamic interactions of pile and inhomogeneous soil under vertical vibration load are systematically investigated. The principal contents and original work are as follows:1. A new model for analyzing vertical dynamic response of pile under vibration load is presented. The soil is assumed to be viscoelastic and radially inhomogeneous, by utilizing the plane strain model and combining the boundary condition, complex stiffness at the interface of pile and soil is derived by complex stiffness transfer method from outer zone to inner zone. Then, the pile is modeled as one-dimension elastic theory valid for long straight bar, the expression of the impedance function and frequency response function at pile top are derived by solving the dynamic equation. Subsequently, the relevant responses in time domain are obtained by the convolution theorem and the Inverse Fourier Transform. Finally, pile-soil interactions and dynamic characteristics of soil are obtained by investigating the influences of soil inhomogeneity caused by construction. The researched results prove that soil inhomogeneity is necessary to take into account and complex stiffness transfer plane strain model considering the soil inhomogeneity is fit for the engineering practice.2. The soil is assumed to be radially inhomogeneous and vertically layered. At first, complex stiffness at the interface of pile sections and soil is derived by complex stiffness transfer plane strain model, and then an analytical solution of dynamic response in frequency domain and a semi-solution of dynamic response in time domain are derived by solving the dynamic equations of pile sections from bottom to top step by step. Finally, rules of dynamic response in vertical layered and radially inhomogeneous soil are obtained by soil parametric analysis.3. A radially inhomogenous continuum medium model is presented. Based on the three-dimensional axisymmetric soil model, the vertical dynamic response of a pile embedded in radially inhomogeneous soil layers caused by construction effect of pile is investigated, in which the soil surrounding the pile is subdivided into arbitrary numerous annular zones to consider the inhomogeneity of soil. Then combining the boundary conditions and continuum conditions of displacement and stress between adjacent soil zones, the dynamic equilibrium equations of every soil zone are solved one by one from outer zone to inner zone. At last, by means of the coupled condition of pile-soil interface, the dynamic equilibrium equation of pile is also solved and analytical solutions in frequency domain and semi-analytical solutions in time domain are obtained. Based on the new model, dynamic response of pile in radially inhomogeneous layered soil under vertical dynamic loading is investigated. Analytical solutions in frequency domain and a semi-analytical solution in time domain are obtained. Influences of a pile with variable impedance and layered imhomogeneous soil are investigated, the rules of dynamic response of pile with variable impedance in vertical layered and radially inhomogeneous soil.4. The comparisons of complex stiffness transfer plane-strain model, series connection spring plane-strain model and precise three-dimensional continuous medium model in radially inhomogeneous soil are presented. The comparative results of the three models show that the differences between the 3-D continuum model and the complex stiffness transfer plane-strain model are small as a whole, and the precision of complex stiffness transfer plain-strain model is enough. However, the contrastive results also show that precision of the series connection spring plane-strain model is short. It can be concluded that complex stiffness transfer plane-strain model which has enough precision and relative simpleness can substitute the 3-D continuous medium model to analyze the pile-soil dynamic response in general cases.5. Based on some researches of support at the pile bottom, "fictitious soil pile" model is present, in which the finite soil layer below the pile bottom is modeled as a fictitious soil pile with soil parameters. The fictitious soil pile and pile is continuous and then the analytical solution and semi-analytical solution of dynamic response at the top of pile in frequency domain or time domain are obtained, respectively. It could be proved that the results are much more rigorous and precise by the "fictitious soil pile" model than other approximate model.The vertical pile-soil dynamic interaction models in inhomogeneous soil layers developed in this dissertation are the further theories based on existing pile-soil theories. Pile-inhomogeneous soil dynamic interaction is completely investigated to point out the rules of pile vibration.