Novel tajimi models for static and dynamic soil-pile interaction

An analytical model of the Tajimi type is developed for the response of an axially-loaded end-bearing pile in viscoelastic soil, subjected to static or dynamic harmonic head loading. Contrary to classical models pioneered by Matsuo & Ohara and Tajimi which are applicable only to homogeneous soil, the Modified Tajimi formulation proposed by the authors can treat general classes of inhomogeneous soil using pertinent eigen-expansions. The special case of two-layer soil is selected to elucidate the analytical aspects of the method, namely the solution using Fourier series involving different sets of eigen-functions for the soil and the pile media. It is shown that unlike the ordinary model, the Fourier response coefficients cannot be determined independently; a set of simultaneous equations, involving a predetermined number of coefficients should be solved instead. Closed-form solutions are obtained for: (i) the dynamic impedances at the pile head, (iii) the displacement and stress distributions along the pile, (iii) the corresponding Winkler moduli, (iv) the displacement field in the soil. The predictions of the model are validated against results from rigorous numerical solutions. Amplification of side friction close to interfaces separating layers of sharply different stiffness is highlighted. The results are presented in terms of dimensionless graphs and charts that provide insight into the physics of the problem.