Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock

An axisymmetrical analytical solution is developed to investigate the vertical time-harmonic vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock. The soil is described by porous medium model established by Boer, while the pile is described by a beam vibration theory. By using separation theory of differential operator and variables to solve the dynamic governing equations for the soil, the fundamental solutions for the soil reactions on side and bottom of the pile are obtained. The dynamic impedance of the pile head is then derived by solving the vibration equation for the pile according to the compatibility condition between the pile and the soil. The proposed model is validated by comparing special cases of our model with the existing results. Numerical examples are presented to analyze the vibration characteristics of the pile.

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.