Analytical solutions for a vertically loaded pile in multilayered soil

Monica Prezzi
School of Civil Engineering, Purdue University, West Lafayette, IN 47907-1284, USA. Email: mprezzi@purdue.edu (Corresponding author)
Hoyoung Seo
School of Civil Engineering, Purdue University, West Lafayette, IN 47907-1284, USA. Email: seoh@purdue.edu (Corresponding author)

Geomechanics and Geoengineering: An International Journal. ISSN 1748-6025 print/ISSN 1748-6033 online © 2006 Taylor & Francis

Analytical solutions for a vertically loaded pile in a homogeneous single soil layer have been obtained by a number of authors. Poulos and Davis (1968) and Butterfield and Banerjee (1971) studied the response of axially loaded piles by integrating Mindlin’s point load solution (Mindlin 1936). Motta (1994) and Kodikara and Johnston (1994) obtained closed-form solutions for homogeneous soil or rock using the load-transfer (t-z) method of analysis to incorporate idealized elastic-plastic behaviour.

Vallabhan and Mustafa (1996) proposed a simple closed-form solution for a drilled pier embedded in a two-layer elastic soil based on energy principles. Lee and Xiao (1999) expanded the solution of Vallabhan and Mustafa (1996) to multilayered soil and compared their solutionwith the results obtained by Poulos (1979) for a three-layered soil. Although Lee and Xiao (1999) suggested an analytical method for a vertically loaded pile in a multilayered soil, they did not obtain explicit analytical solutions.

Explicit analytical solutions for a vertically loaded pile embedded in a multilayered soil have been presented in this paper. The solutions satisfy the boundary conditions of the problem. The soil is assumed to behave as a linear elastic material. The governing differential equations are derived based on the principle of minimum potential energy and calculus of variations. The integration constants are determined using Cramer’s rule and a recurrence formula. In addition, solutions for a pile embedded in a multilayered soil with the base resting on a rigid material are obtained by changing the boundary conditions of the problem. The solutions provide the vertical pile displacement as a function of depth, the loadtransfer curves, and the vertical soil displacement as a function of the radial direction at any depth if the following are known: radius, length, and Young’s modulus of the pile, Poisson’s ratio and Young’s modulus of the soil in each layer, thickness of each soil layer, number of soil layers, and applied load. The use of the analysis was illustrated by obtaining load-transfer and load-settlement curves for a case available in the literature for which pile load test results are available. 

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