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ABSTRACT
Non-prismatic piles are typically used in cases where large lateral loads must be resisted. In many applications, piles are partially or fully embedded in multi-layered non-homogeneous soil, with each layer having its own set of properties. Analytical, simple solutions to study this problem are more limited and complex than that of prismatic ones. The analysis becomes even more complicated when both the variation of the cross-sectional area of the element and the soil inhomogeneity are included in the formulation. This work presents the derivation of the stiffness matrix and load vector of a non-uniform section of pile partially or fully embedded in non-homogeneous soil. The analysis of non-uniform piles in multi-layered soil is carried out by dividing the pile into multiple sub-elements and then assembling them using conventional matrix methods. Four examples, encompassing partially and fully embedded piles, are presented to validate the simplicity and accuracy of the proposed solution.
Disclosure statement
No potential conflict of interest was reported by the author(s).
List of Symbols
| A(x) | = | Area of the element at a depth x |
| B(x) | = | Diameter of the element at a depth x |
| E | = | Young’s modulus of the element |
| Gp | = | Shear modulus of the pile |
| I(x) | = | Second moment of inertia of the element at a depth x |
| KL | = | First-parameter of the Pasternak foundation |
| Ko | = | Modulus of subgrade reaction |
| Le | = | Embedded length of the pile |
| Lp | = | Total length of the pile |
| Lu | = | Unembedded length of the pile |
| M | = | Bending moment |
| m | = | Taper ratio |
| mh | = | Variation of the modulus of subgrade reaction with depth |
| Po | = | Axial load |
| q(x) | = | Applied transverse load |
| rb | = | Radius at the bottom of the element |
| req | = | Equivalent radius at half of the length of the element |
| rt | = | Radius at the top of the element |
| Sa, Sb | = | Shear stiffness of the linear transverse springs at ends A and B, respectively. |
| V | = | Shear force |
| x | = | Coordinate along the longitudinal axis |
| y | = | Transverse deflection |
| Y | = | Non-dimensional term for the transverse deflection |
| kg | = | Second-parameter of elastic foundation |
| κa, κb | = | Flexural stiffness of the flexural springs at ends A and B, respectively. |
| ξ | = | Non-dimensional term for the length |