Closed-form dynamic stiffness formulation for modal and dynamic response analysis of pile group foundations

A closed-form dynamic stiffness (DS) formulation is proposed for pile group foundations. This model consists of a rigid cap and an arbitrary number of flexible piles. The rigid cap, connecting to all piles, is modeled as a rigid body resting on an elastic foundation. For each pile, a longitudinal soil–pile model and a preloaded Timoshenko beam on viscoelastic Pasternak foundation are adopted to describe the longitudinal and transverse vibration, respectively. The piles can be either friction piles or end-bearing piles, and pile sections surrounded by different soil layers can be easily modeled by the assembly of pile elements with different parameters. The proposed DS formulations essentially use very few degrees of freedom to, nevertheless, describe the broadband dynamic behaviors of complex pile group foundations in a highly accurate manner. The DS formulation is then used for modal and dynamic response analysis. For modal analysis, the Wittrick–Williams algorithm is applied, with the key issue J0 count problems resolved. The proposed method is verified against some existing results. This research provides an exact and highly efficient modal and response analysis tool for pile group foundations, which can be used for the dynamic analysis of pile foundations subjected to earthquake or traffic excitations.