A complete set of algebraic formulas and dimensionless charts is presented for readily computing the dynamic stiffnesses (\IK\N) and damping coefficients (\IC\N) of foundations harmonically oscillating on/in a homogeneous half-space. All possible modes of vibration, a realistic range of Poisson’s ratios, and a practically sufficient range of oscillation frequencies are considered. The foundations have a rigid basemat of any realistic solid geometric shape. The embedded foundations are prismatic, having a sidewall-soil contact surface of height \Id\N, which may be only a fraction of the embedment depth \ID\N. Two numerical examples illustrate the use of the formulas and charts and elucidate the role of foundation shape and degree of embedment on radiation damping for various modes of vibration. A companion paper (Gazetas and Stokoe 1991) presents supporting experimental evidence from model tests. The two papers aim at encouraging the practicing engineer to make use of results obtained with state-of-the-art formulations, when studying the dynamic response of foundations.

Formulas and charts for impedances of surface and embedded foundations

Analysis of machine foundation vibrations: State of the art

SUMMARY A simplified three-step procedure is proposed for estimating the dynamic interaction between two vertical piles, subjected either to lateral pile-head loading or to vertically-propagating seismic S-waves. The starting point is the determination of the deflection profile of a solitary pile using any of the established methods available. Physically-motivated approximations are then introduced for the wave field radiating from an oscillating pile and for the effect of this field on an adjacent pile. The procedure is applied in this paper to a flexible pile embedded in a homogeneous stratum. To obtain analytical closed-form results for both pile-head and seismic-type loading pile-soil and soil-pile interaction are accounted for through a single dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’. Final- and intermediate-step results of the procedure compare favourably with those obtained using rigorous formulations for several pile group configurations. It is shown that, for a homogeneous stratum, pile-to-pile interaction effects are far more significant under head loading than under seismic excitation.

Dynamic pile‐soil‐pile interaction. Part II: Lateral and seismic response

An inexpensive and realistic procedure is developed for estimating the lateral dynamic stiffness and damping of flexible piles embedded in arbitrarily layered soil deposits. Starting point is the determination of the pile deflection profile for a static force at the top using any reasonable method—beam‐on‐Winkler foundation, finite elements, well‐instrumented pile load tests in the field, etc. Material as well as radiation damping due to waves emanating at different depths from the pile‐soil interface are rationally taken into account; the overall equivalent damping at the top of the pile is then obtained as a function of frequency by means of a suitable energy relationship. The method is applied to study the dynamic behavior of three different piles embedded in two idealized and one actual layered soil deposit; the results of the method, obtained by hand computations, compare favorably with the results of three dimensional dynamic finite element analyses.

Horizontal Response of Piles in Layered Soils

A simple analytical solution is developed for computing the dynamic impedances of floating rigidly-capped pile groups with due consideration to pile-soil-pile interaction. The method introduces some sound physical approximations and considers the interference of cylindrical wave fields originating along each pile shaft and spreading radially outward. Axial, lateral, and rocking oscillations of rigidly-capped pile groups are studied parametri-cally. Results are presented for the dynamic stiffness and damping of the whole group, and for the distribution of dynamic loads amongst the individual piles. The predictions of the simple method for vertical and rocking oscillations compare extremely well with rigorous numerical solutions, thereby offering a valuable insight into the nature of pile-soil-pile interaction. It is demonstrated and explained how the dynamic efficiency may far exceed unity at certain resonant frequencies due to destructive wave interference. The proposed method can be readily applied by en...

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Simple method for dynamic stiffness and damping of floating pile groups

Most procedures to compute the t-z (stress-displacement) response for axial pile loading are empirical, based mostly on data for pile diameters less than 18 in. (0.15 m) and pile penetrations less than 100 ft (30 m). These procedures may not be appropriate for pile and soil conditions that differ from those on which the procedures were developed. Therefore, a theoretical procedure is developed to generate t-z curves for predicting pile movements under axial load. The procedure uses an approximate one-dimensional, elastic continuum approach to define the t-z response up to the maximum t response and laboratory simulation to define the post-peak response. The procedure was used with several case studies. Predicted response of the pile under axial loading was in good agreement with the measured response.

Theoretical t-z curves

Lateral load-deflection relationships of piles subjected to dynamic loadings

This paper presents a compilation of resonantcolumn and cyclic simpleshear test results on dynamic moduli and damping factors of soft marine clays. These tests were conducted on 38 undisturbed samp...

Moduli and Damping Factors of Soft Marine Clays

A nonlinear method for seismic soil-pile-structure interaction is presented. Primary features of the proposed method include a consistent approach to determine seismic p-y relationships and a liquefaction model that is suited to pore pressure evaluation for earthquake-type irregular loadings. The seismic- p-y relationships are determined from nonlinear stress-strain relations of soils, and include soil nonlinearity as well as pore pressure buildup effects around a pile. The performance and validity of the method were evaluated through an analysis of shaking table test on model soil-pile-structure systems. Using the proposed method, seismic response characteristics of an idealized offshore pile-supported structure at a sand site were analyzed. Results indicated that liquefaction as well as pore pressure bulidup around a pile can have a large impact on the response of pile-supported structures.

Lateral pile response during earthquakes

This paper documents three case studies that involve dynamic centrifuge tests that simulated large-scale shaking table tests on soilpile-structure systems. The large-scale shaking table tests were ...

Takaaki Kagawa

Papers

Theoretical t-z curves

Lateral load-deflection relationships of piles subjected to dynamic loadings

Moduli and Damping Factors of Soft Marine Clays

Lateral pile response during earthquakes

Centrifuge Simulations of Large-Scale Shaking Table Tests: Case Studies