Study On 3D Analytical Solutions And Dynamic Properties Of Pile Torsional Vibration Under Axisymmetric Condition

A three-dimensional axisymmetric dynamic model of pile torsional vibration is presented in the paper.The longitudinal stress gradient of soil around the pile is ignored and the soil is assumed as a plane strain model,the transform domain solution of the governing equation is solved via variable separation and Laplace transform.Combining with the coupling conditions and the boundary conditions of the pile-soil system,transform domain expression for dynamic response and dynamic impedance at an arbitrary point of the pile top is obtained.By using inverse Laplace transform,the time domain dynamic response of pile torsional vibration under 3D axisymmetric condition is obtained.It is compared with the one-dimensional theory and measured results by simulation and the time domain characteristics of 3D dynamic response are analyzed.In addition,the sources and influencing factors of three-dimensional effect for pile torsional vibration is studied in detail and the methods to reduce three-dimensional effect is suggested.Finally,the dynamic properties of pile torsion vibration were analyzed,and the influence of pile-soil parameters on its dynamic characteristics is studied.The results show that the analytical results than the one-dimensional model solution is closer to the actual situation of pile torsional vibration;torsional vibration response is actually composed of n modal superposition results,the first mode is the basic vibration mode,two order mode is the main mode of interference;the 3D effect is mainly related with the pile diameter,elastic modulus of pile,exciting time and exciting radius;the sensor is placed at the top of pile r=0.75 R or the double velocity averaging method can be used to obtain dynamic testing curve of the minimum 3D effect;the dynamic stiffness and damping of pile-soil system will increase with the increase of length,diameter and elastic modulus of pile.The increase of shear modulus(wave velocity)of soil will increase the dynamic stiffness of pile-soil system,reduce its dynamic damping;the resonance frequency of pile-soil system is positively related to the elastic modulus of pile,and negatively correlated with the length and diameter of pile.