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Kinematic response of single piles for different boundary conditions: Analytical solutions and normalization schemes

Anoyatis, George; Di Laora, Raffaele; Mandolini, Alessandro; Mylonakis, George


George Anoyatis

Raffaele Di Laora

Alessandro Mandolini

George Mylonakis


Kinematic pile-soil interaction is investigated analytically through a Beam-on-Dynamic-Winkler-Foundation model. A cylindrical vertical pile in a homogeneous stratum, excited by vertically-propagating harmonic shear waves, is examined in the realm of linear viscoelastic material behaviour. New closed-form solutions for bending, displacements and rotations atop the pile, are derived for different boundary conditions at the head (free, fixed) and tip (free, hinged, fixed). Contrary to classical elastodynamic theory where pile response is governed by six dimensionless ratios, in the realm of the proposed Winkler analysis three dimensionless parameters suffice for describing pile-soil interaction: (1) a mechanical slenderness accounting for geometry and pile-soil stiffness contrast, (2) a dimensionless frequency (which is different from the classical elastodynamic parameter a0=ω d/Vs), and (3) soil material damping. With reference to kinematic pile bending, insight into the physics of the problem is gained through a rigorous superposition scheme involving an infinitely-long pile excited kinematically, and a pile of finite length excited by a concentrated force and a moment at the tip. It is shown that for long piles kinematic response is governed by a single dimensionless frequency parameter, leading to a unique master curve pertaining to all pile lengths and pile-soil stiffness ratios. © 2012 Elsevier Ltd.


Anoyatis, G., Di Laora, R., Mandolini, A., & Mylonakis, G. (2013). Kinematic response of single piles for different boundary conditions: Analytical solutions and normalization schemes. Soil Dynamics and Earthquake Engineering, 44, 183-195.

Journal Article Type Article
Acceptance Date Sep 20, 2012
Online Publication Date Nov 3, 2012
Publication Date Jan 1, 2013
Journal Soil Dynamics and Earthquake Engineering
Print ISSN 0267-7261
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 44
Pages 183-195
Keywords pile, kinematic interaction, subgrade reaction, Winkler model, closed-form solution
Public URL
Publisher URL
Additional Information Additional Information : The final publication is available at


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