Simplified frequency-independent model for vertical vibrations of surface circular foundations

Abstract

Purpose This paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper. Design/methodology/approach The proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established. Findings The validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models. Originality/value Using this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).