Dynamic Pile-Soil-Pile Interaction Based on a Lagrangian Functional Approach

Josue Labaki¹; Euclides Mesquita¹

¹ Unicamp

doi:10.20906/CPS/CON-2016-1653

Resumo

This paper presents a semi-analytical formulation of the problem of time-harmonic vertical vibration of two elastic bars interacting with each other through and with their surrounding transversely isotropic half-space. The formulation is presented within the framework of linear theory of elastic wave propagation that is applicable for most cases of inertial response of embedded elastic buries under external excitations. The embedding medium is described by a classical Green's functions corresponding to buried distributed vertical loading in a homogeneous half-space. The motion of the bar is represented by a time-harmonic polynomial function containing a set of generalized coordinates. The body force field in the half-space corresponding to each polynomial shape function of the bar is obtained numerically by solving a flexibility equation system based on the Green's functions corresponding to buried distributed vertical body forces in the half-space. The generalized coordinates of the bar's displacement function are thereafter computed by formulating the Lagrange's equations of motion for the bar. Numerical solution of the equation of motion results in the solutions for generalized coordinates. The bar displacements and axial load profiles are determined from the solutions for generalized coordinates. The influence of the bars on each other is obtained by considering that the bar at the measuring end is a one-dimensional line within the half-space. This is an adequate hypothesis, given that the distance between piles is much larger than their radii in most engineering applications. This technique adequately incorporates the wave propagation through the half-space from one bar to the other. Vertical impedance of the two-bar system is presented for different frequency of excitations and distances between bars. The present formulation can be readily extended for the case of a larger pile group.

Palavras-chave: Soil-foundation interaction; Pile groups