A semi analytical model for elastic settlements of end-bearing piles in inhomogeneous soils-Paper

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The paper presents a semi-analytical method for predicting the elastic settlement and static stiffness of end-bearing piles under vertical load in soils whose shear modulus varies with depth. The pile is modelled as an elastic rod and the soil as a three-dimensional, Tajimi-type continuum. A generalized power law represents soil inhomogeneity.<br /><br />Soil displacement modes are approximated using cosine functions rather than the more computationally demanding modified Bessel functions used in an earlier analytical model. A generalized eigenvalue problem determines the modes, while coupled Fourier coefficients are solved through a system of algebraic equations. The resulting formulation predicts soil displacement and stress fields, pile displacement and normal stress along its length, and pile-head stiffness.<br /><br />Comparisons with the established model of Anoyatis et al. (2019) show excellent agreement for soil modes and very good agreement for normalized pile-head stiffness. The results also show that soil displacement and shear stress diminish with radial distance from the pile, and that pile-head stiffness decreases as pile slenderness increases.<br /><br />The approach offers a computationally simpler alternative to the earlier model while accounting for soil continuity, vertical inhomogeneity, and soil compressibility without empirical constants. Its approximations include not satisfying horizontal equilibrium or the zero-shear-stress condition at the soil surface; the authors report that these have only a minor influence on the solution. The framework could be adapted to other soil–pile interaction problems, including dynamic loading.

Keywords

end-bearing piles

elastic settlement

static stiffness

vertical load

soil inhomogeneity

shear modulus variation

Tajimi-type continuum

semi-analytical method

soil-pile interaction

pile-head stiffness