Dynamic pile impedances for laterally–loaded piles using improved Tajimi and Winkler formulations

Abstract

a b s t r a c tThe analytical representation of dynamic soil reaction to a laterally-loaded pile using 3D continuum modeling is revisited. The governing elastodynamic Navier equations are simplified by setting the dynamic vertical normal stresses in the soil equal to zero, which uncouples the equilibrium in vertical and horizontal directions and allows a closed-form solution to be obtained. This physically motivated approximation, correctly conforming to the existence of a free surface, was not exploited in earlier studies by Tajimi, Nogami and Novak and leads to a weaker dependence of soil response to Poisson's ratio which is in agreement with numerical solutions found in literature. The stress and displacement fields in the soil and the associated reaction to an arbitrary harmonic pile displacement are derived analytically using pertinent displacement potentials and eigenvalue expansions over the vertical coordinate. Both infinitely long piles and piles of finite length are considered. Results are presented in terms of dimensionless parameters and graphs that highlight salient aspects of the problem. A detailed discussion on wave propagation and cutoff frequencies based on the analytical findings is provided. A new dimensionless frequency parameter is introduced to demonstrate that the popular plane-strain model yields realistic values for soil reaction only at high frequencies and low Poisson's ratios.Published by Elsevier Ltd.

Dynamic pile impedances for fixed-tip piles

“…Lemnitzer [5] examined the response of a pile with a hinged tip boundary condition using identical soil and pile system properties as described above (Fig. 1b).…”

“…Yet, similarly to rigorous elastic solutions described earlier, these expressions ( [3], [4]) fall short in their ability to accurately capture the dynamic response and are limited in their applications to "long piles" (i.e., no effect of tip fixity is considered). The performance of the Syngros and Gazetas expressions has been tested in Anoyatis and Lemnitzer [5] where an extensive parametric analysis for static pile impedances was conducted for the case of hinged-tip piles.…”

“…Note that a thorough discussion on the effect of existing Winkler moduli [dynamic stiffness and dashpots (or damping ratio )] on dynamic pile impedances is presented in Anoyatis & Lemnitzer [5],…”

“…In this paper, stiffness and damping of tip-restrained piles is investigated through an improved, analytical model, recently presented in detail by Anoyatis and Lemnitzer [5]. The improvement of the model lies in a better prediction of soil response which ultimately yields more accurate results for pile impedances.…”

“…The Authors further acknowledge that the degree of fixity intrinsically influences the ability of the pile to rotate within the embedment socket (e.g., if rock is weathered). With the assumption of a perfectly fixed tip and the solution provided in Anoyatis and Lemnitzer [5], who investigated the condition of the pile with a hinged tip, the pile response at both ends of the pile tip boundary spectrum is fully described.…”