Study On Vertical Dynamic Characteristics Of Single Pile With Cushion Cap Based On Fictitious Soil Pile Method

In this paper,the fictitious soil pile model is used to simulate the different properties of pile subsoil,so as to make up the shortcomings of existing model.In order to better understand the vertical dynamic characteristics of cap-pile-soil system,the surrounding soil's stratification is considered by generalized Voigt model,pile-soil coupling model and plane strain model,and the vertical dynamic equation of single pile with cushion cap is solved by Laplace transform and impedance recursion theory.This paper mainly includes the following aspects:(1)Based on fictitious soil pile and generalized Voigt model,the vertical dynamic characteristics of single viscoelastic pile with exposed cushion cap are studied.The pile subsoil and surrounding soil are modeled as fictitious soil pile and generalized Voigt model based on their vertical stratification,the dynamic equilibrium equations of pile and cushion cap are established in the vertical vibration.First,the frequency domain solution of the impedance is obtained on the pile top by the Laplace transform and impedance recursive equation.Secondly,the impedance function of pile is substituted into the dynamic balance equation of exposed cushion cap,and the velocity and displacement frequency domain solutions of exposed cushion cap are obtained,the response time domain solutions are obtained by inverse transform.Then,the influences of single pile subsoil on the vertical dynamic characteristics of exposed cushion cap are discussed under the conditions of different pile length,diameter,and longitudinal wave velocity.Finally,compared with single Voigt model of pile subsoil and actual engineering curves,the results show that fictitious soil pile model can accurately simulate the role of weak substratum and calculation is more close to the measured data.(2)Based on fictitious soil pile and pile-soil coupling model,the influences of pile subsoil on the vertical dynamic characteristics of single flexible pile with exposed cushion cap are studied.The pile subsoil and surrounding soil are modeled as fictitious soil pile and pile-soil coupling model,the dynamic equilibrium equations of pile and cushion cap are established in the vertical vibration.First,the vertical displacement of surrounding soil is obtained by solving the dynamic equilibrium equation of soil-pile coupling model.Secondly,the vertical displacement of surrounding soil is substituted into the vertical dynamic balance equation of pile,the frequency domain solution of the impedance is obtained on the pile top by the Laplace transform and impedance recursive equation.Finally,the impedance function of pile is substituted into the dynamic balance equation of exposed cushion cap,and the velocity and displacement frequency domain solutions of exposed cushion cap are obtained,the response time domain solutions are obtained by inverse transform.Based on the results,the influences of single layered,double layered pile subsoil thickness,shear wave velocity and longitudinal wave velocity on the vertical dynamic characteristics of single flexible pile with exposed cushion cap are studied.(3)Based on fictitious soil pile and plane strain model,the vertical dynamic characteristics of single viscoelastic pile with buried cushion cap are studied.The pile subsoil and surrounding soil are modeled as fictitious soil pile and plane strain model based on their vertical stratification,the dynamic equilibrium equations of pile and cushion cap are established in the vertical vibration.First,the vertical displacement of pile surrounding soil is obtained by solving the displacement control equation of plane strain model,and the corresponding shear stiffness of soil is obtained.Secondly,the shear stiffness of soil is substituted into the vertical dynamic balance equation of pile,the frequency domain solution of the impedance is obtained on the pile top by the Laplace transform and impedance recursive equation.Finally,the impedance function of pile and shear stiffness of soil are substituted into the dynamic balance equation of buried cushion cap,and the velocity and displacement frequency domain solutions of buried cushion cap are obtained,the response time domain solutions are obtained by inverse transform.Based on the results,the influences of cushion cap surrounding soil and sediment on the vertical dynamic characteristics of single viscoelastic pile with buried cushion cap are studied.