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

http://ssi.civil.ntua.gr/downloads/journals/1984-SDEE_Seismic%20response%20of%20end%20bearing%20single%20piles.pdf

Seismic response of end-bearing single piles

An elastic analysis is presented for the horizontal displacement and rotation of a laterally loaded pile group and the distribution of horizontal forces within the group. The interaction between two identical equally loaded piles is analyzed first, and the increases in displacement and rotation of the piles, in relation to the single pile values, are expressed in terms of interaction factors. Using these interaction factors, a method for calculating the displacement and rotation of a general pile group, based on the principle of superposition, is described. An examination of the behavior of square groups of piles reveals that the displacement, rotation, and load distribution in the group is largely influenced by the length-to-diameter ratio of the piles and the relative pile flexibility. It is also found that the displacement depends on the breadth of the group rather than the number of piles in the group. A reasonable measure of agreement is found between a limited number of reported measurements and theoretical predictions of group displacements.

Closure to “Behavior of Laterally Loaded Piles: II-Pile Groups”

The paper studies the kinematic response of freehead piles. Such pile deformation has triggered structural damage in many strong earthquakes. In this Paper dimensionless parametric graphs for pile bending moments are presented which pertain to characteristic two-layer soil profiles. The results are derived by using an existing rigorous dynamic finite-element code, and by implementing a realistic beam-on-dynamic-Winkler-foundation formulation specifically developed for the kinematic response of piles in layered soil. The Winkler model is shown to reproduce quantitatively even detailed trends observed in the finite-element results; a simple analytical expression is thereby developed for estimating the Winkler stiffhess in terms of the local soil Young’s modulus and key dimensionless pile/ soil parameters. The study concludes that even relatively flexible piles may not exactly experience the wavy and abruptly changing ground deformation of the free field. The critical region of pile distress due to such kinematic loading is shown to he at or near the interface between alternating soft and stiff soil layers. The magnitude of the bending moment at such critical interface locations depends mainly on the stiffness contrast of the two layers through which the pile penetrates, the excitation frequency and the relative rigidity of the pile. A constraining cap may exert an important effect on such kinematic deformations.

http://ssi.civil.ntua.gr/downloads/journals/1993-GEOT_Kinematic%20seismic%20response%20and%20bending%20of%20free%20head%20piles%20in%20layered%20soil.pdf

Kinematic seismic response and bending of free-head piles in layered soil

Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscillating pile embedded in homogeneous soil and excited at the top. Pilesoil interaction is realistically represented through a dynamic Winkler model, the springs and dashpots of which are given values based on results of finite element analyses with the soil treated as a linear hysteretic continuum. Closed form expressions are derived for the phase velocities of the generated waves; these are compared with characteristic phase velocities in rods and beams subjected to compressionextension (axial) and flexural (lateral) vibrations. The role of radiation and material damping is elucidated; it is shown that the presence of such damping radically changes the nature of wave propagation, especially in lateral oscillations where an upward propagating (reflected) wave is generated even in a semi-infinite head-loaded pile. Solutions are then developed for the phase differences between pile displacements at various depths. For most piles such differences are not significant and waves emanate nearly simultaneously from the periphery of an oscillating pile. This conclusion is useful in analysing dynamic pile to pile interaction, the consequences of which are shown in this Paper.

/pdf/displacement-phase-differences-in-a-harmonically-oscillating-1o1utycmfy.pdf

Displacement phase differences in a harmonically oscillating pile

The Paper presents the results of a systematic parametric investigation of the static and dynamic response of single free-head piles embedded in a soil stratum, the modulus of which increases linearly with depth. The study is conducted by means of a dynamic finite-element formulation which accounts for the three-dimensionality of soil deformation while properly reproducing the radiation damping characteristics of the system. The soil is modelled as a linear hysteretic continuum and the excitation consists of a sinusoidally time-varying horizontal force or moment, applied at the pile head. Comprehensive plots of the results are presented in non-dimensional form, for a wide range of the most significant dimensionless groups of problem parameters. For the response of flexible piles, in particular, simple algebraic expressions are developed in terms of the ratio E,/E,, of the pile and soil moduli. These expressions, being valid for several values of Poisson’s ratios of the soil, compare favourably with results from previous studies and are expected to be useful in practical design calculations.

/pdf/static-and-dynamic-lateral-deflexion-of-piles-in-non-28aud7lexl.pdf

R. Krishnan

Papers

Static and dynamic lateral deflexion of piles in non-homogeneous soil stratum