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Approximate closed-form solutions are derived for the settlement of axially loaded piles embedded in inhomogeneous soil by employing an energy method based on the Winkler model of soil reaction. Simple, linear shape functions for the attenuation of pile displacement with depth result in easy-to-use formulas. Two alternative methods are discussed for selecting the slope of the linear function. The proposed methodology is compared with rigorous (yet complicated) closed form solutions and an alternative approximation using a representative homogeneous soil.

Energy Formulation for Axial Pile Head Stiffness in Inhomogeneous Soil