Vertical impedance of an end‐bearing pile in viscoelastic soil

Abstract

This paper presents a new method to derive the analytical solution for the vertical impedance of an endbearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one-dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil-pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. otherwise specified, the following parameter values are used: H = 10 m, r 0 = 0.5 m, E p = 25 GPa, VERTICAL IMPEDANCE OF AN END-BEARING PILE IN VISCOELASTIC SOIL

Development of a three‐dimensional soil model for the dynamic analysis of end‐bearing pile groups subjected to vertical loads

“…This is attributed to the fact that the plane‐strain model considers only waves propagating in the horizontal direction towards infinity, therefore resonance is not possible. On the other hand, the three‐dimensional model predicts the generation of shear and longitudinal waves; hence, resonance results from the propagation and reflection of standing waves in the soil layer: the dominant frequency, ω 2 , is associated with longitudinal waves and is equal to the natural frequency of the soil deposit for vertical vibrations; while the secondary frequency, ω 1 , corresponds to shear waves and is equal to the natural frequency of the soil deposit for shear vibrations . It must be mentioned here that the imaginary components of the attenuation function and of the interaction factor are not particularly sensitive to the second cutoff frequency ω 2 .…”

Vertical vibration of an elastic pile embedded in poroelastic soil

“…In addition, the pile shaft is assumed perfectly bonded to its surrounding soil. To introduce the stiffness of the pile in the solution, we model it as a 1D cylindrical elastic rod [1][2][3][4][5][6]. This is a reasonable approximation for slender piles (H/R⪢1) subjected to a harmonic vertical force Pe iωt .…”

“…The vibration characteristics of the soil-pile system are often quantified via the complex impedance at the pile head [4][5][6]. The vertical impedance K v is defined as the amplitude of the harmonic axial pile force that results in a unit harmonic pile head displacement, therefore the vertical dynamic impedance of the pile is calculated as…”

“…Several analytical models have been developed in the literature to quantify soil-pile interactions for piles subjected to dynamic loads, with the most widely used ones being the Winkler model [1,2], the continuum model [3,4] and the virtual pile model [5,6]. The soil resistance in Winkler model is simulated by means of a series of linear springs and dashpots.…”

A revised solution for the horizontal vibration of an end‐bearing pile in viscoelastic soil

“…In this short communication, we employ a new analytical approach, which was first proposed by the authors to treat the problem of vertical vibration of piles , to solve the problem of an end‐bearing circular pile in viscoelastic soil subjected to harmonic lateral force and bending moment. The advantage of the proposed formulation is that it does not require the introduction of potential functions.…”