Vibration Analysis Of A Single Pile Under Time-harmonic Torsional Loading In Inhomogeneous Soil

With the rapid development of infrastructure in China,major projects such as offshore wind turbines,offshore work platforms and bridges across ocean continue to be constructed.The pile foundation is widely used in the above projects due to its advantages such as high bearing capacity and convenient for construction.Most of these pile foundations are subjected to both static loads(weight of upper structure and foundation,etc.)and dynamic loads such as running loads of machine,wind loads and wave loads,which results in complex dynamic problems of pile-soil system.At present,the research of torsional vibration mostly assumes that the surrounding soil is homogeneous and isotropic,while the actual foundation soil tends to be inhomogeneous.Therefore,based on the existing research results and supported by the National Natural Science Foundation of China(NO:51578231&51378197),this study investigated torsional vibration of an elastic pile embedded in inhomogeneous soil and subjected to a time-harmonic torsional loading.At first,considering the radial inhomogeneous of layered foundation,dynamic equilibrium equation of soil and pile were established based on three-dimensional continuum model and the dynamic elastic theory.Using the variables separation method to solve the equation of soil from inside to outside and from bottom to top,the circumferential shear stress on the pile generated by surrounding soil is then obtained by considering continuity conditions of stress and displacement on the contact surface.Then putting the circumferential shear stress into the equation of pile,and the analytical expression of the complex stiffness at pile head is obtained due to solving the equation of pile and the corresponding boundary conditions.In order to verify the feasibility of the solution,the above inhomogeneous foundation model was degenerated to homogeneous foundation model and radial inhomogeneous foundation model respectively,and compared with the existing research results.Secondly,the calculation program by Mathematica was completed based on above solution and used to analyze the influence of radial and vertical inhomogeneous of soil,shear wave velocity ratio V_p/V_s and length-diameter ratio H/r0 on the complex stiffness at pile head.Finally,assuming a nonlinear distribution of the shear modulus of soil with the depth defined by the exponential function,the dynamic equilibrium equation of soil under a time-harmonic buried torsional loading was established by using the Biot’s consolidation theory and the dynamic elastic theory.The expressions of stress and displacement then were acquired by solving the soil equation with the method of Hankel transform.Then,the influence of load frequency,load depth,non-uniform distribution factor of shear modulus and permeability coefficient of soil on the dynamic response of saturated soil are analyzed.