Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

A theoretical analysis of vertical dynamic response of large-diameter pipe piles in layered soil

Considering the viscous damping of the soil and soil-pile vertical coupled vibration,a computational model of large-diameter pipe pile in layered soil was established.The analytical solution in frequency domain was derived by Laplace transformation method.The responses in time domain were obtained by inverse Fourier transformation.The results of the analytical solution proposed agree well with the solutions in homogenous soil.The effects of the shear modulus and damping coefficients of the soil at both outer and inner sides of the pipe pile were researched.The results indicate that the shear modulus of the outer soil has more influence on velocity admittance than the inner soil.The smaller the shear modulus,the larger the amplitude of velocity admittance.The velocity admittance weakened by the damping of the outer soil is more obvious than that weakened by the damping of the inner soil.The displacements of the piles with the same damping coefficients of the outer soil have less difference.Moreover,the effects of the distribution of soil layers are analyzed.The results indicate that the effect of the upper soil layer on dynamic response of the pipe pile is more obvious than that of the bottom soil layer.A larger damping coefficient of the upper layer results in a smaller velocity admittance.The dynamic response of the pipe pile in layered soil is close to that of the pipe pile in homogenous soil when the properties of the upper soil layer are the same.