Horizontal Vibration Of Pile And Pile Groups In Viscoelastic Soil Described By Fractional Derivative Model

Pile foundation has been widely used in practical engineering, the research of dynamic behavior of pile foundation under variety of dynamic excitation has an important application value and significance for the seismic design and dynamic testing of the pile foundation. Because of the dynamic interaction between pile and soil will lead to the dissipation and propagation of energy in soil, so the pile-soil dynamic interaction is the key point and difficulties on studying the vibration of pile. In order to consider the viscoelastic properties of the soil, the reasonable viscoelastic constitutive model needs to be used. With the development of the theory of fractional derivative viscoelastic, the application of the theory of fractional derivative viscoelastic in geotechnical engineering is more and more to be concerned, theory of fractional derivative viscoelastic applied to the vibration of pile has yet to be very few related reports. In this paper, the fractional derivation viscoelastic constitutive relationship is used to study the horizontal vibration of single pile and pile groups in soil.The horizontal vibration control equations in displacement of fractional derivative viscoelastic soil are established based on the theory of fractional derivative, theory of viscoelastic, elastodynamics and pile dynamics. The horizontal vibration of viscoelstic soil is solved by potential functions and method of separation variables. The semi-analytical solution of horizontal vibration of single pile in soil described by fractional viscoelastic model is obtained. The constitutive relationship of soil is described by fractional derivative viscoelastic constitutive model, the pile-soil dynamic interaction is modeled by Winkler dynamic elastic-damping, the attenuation function of horizontal displacement of fractional derivative viscoelastic soil and pile-pile dynamic interaction factor are obtained based on Novak plain model, then, the properties of the horizontal vibration of pile groups in fractional derivative viscoelastic soil is investigated, and analysis and discussion of related parameters are also conducted. The results indicate that the horizontal dynamic impedance of pile in fractional derivative viscoelastic soil can reduce to the solution classic viscoelastic and elastic cases. The order of fractional derivative and model parameter Tσ/Tεhave great effect on the lateral dynamic impedance of the single pile and pile groups in fractional derivative viscoelastic soil, the image part of lateral dynamic impedance of the single pile appears negative value for Tσ/Tε, and the absolute value of the image part of lateral dynamic impedance increases with the increasing of model parameter. The influence of length-radius ratio of pile on lateral dynamic impedance is smaller when the length-radius ration increases to a certain value.