A Unified Formulation for the Study of Non-Uniform Cylindrical Timoshenko Piles: Lateral Deformation, Dynamic, and Buckling
摘要
Analytical, simple solutions to investigate the lateral deformation, dynamic, and stability responses of Timoshenko piles (i.e., prismatic, tapered, and stepped piles), partially or fully embedded in an inhomogeneous multi-layered elastic soil are limited. This paper introduces a unified stiffness matrix formulation that allows these analyses to be performed efficiently. For this purpose, the governing differential equation (GDE) and the corresponding stiffness matrix of a tapered segment are derived using the classical Timoshenko theory. Here, the well-known direct stiffness matrix method (i.e., commonly used by structural engineers) is employed to investigate the response of non-uniform cylindrical piles in multi-layered soil. Examples are presented to show the simplicity, capacities, and validity of the proposed method. The results of the proposed formulation show excellent agreement with those of FE software (i.e., SAP2000) and other analytical approaches. The results showed that i) the buckling load capacity of the pile is highly influenced by the stiffness of the surrounding soil and the effect of shear deformations and ii) the shape of the pile significantly influences the natural frequency of piles, particularly under soft soil conditions.