Vertical kinematic response of an end-bearing pipe pile in fractional viscoelastic unsaturated soil under vertically-incident P-waves

Abstract

This work investigates the kinematic response of a pipe pile embedded in a fractional-order viscoelastic unsaturated soil stratum over a rigid base subjected to vertically-propagating seismic P-waves based on a continuum model. The fractional standard line solid model is introduced to the governing equation of unsaturated soil to refine the frequency-dependent viscoelastic behavior of the soil skeleton. The Rayleigh-Love rod theory is utilized to characterize the vertical motion of the pipe pile. A rigorous series form solution for the vertical kinematic response of the end-bearing pipe pile under vertically incident P-waves is yielded theoretically with boundary conditions of pile-soil system. The proposed solution is then verified by comparing with the numerical result of the reported solution. Based on the given rigorous analyzed solution, the effects of physical parameters in pile-soil system on the vertical kinematic response of the end-bearing pipe pile under harmonic P-waves are studied in both the frequency and time domains through calculation example and parametric analysis. Finally, relevant meaningful conclusions are included and indicate that soil parameters and pipe pile dimensions have significant effect on the vertical kinematic response of the pipe pile.