Closed‐form solution for natural frequency of flexible combined pile‐raft foundation

Dynamic attributes of flexible combined pile‐raft foundation (CPRF) hold paramount importance in assessing the behavior of it, especially in an earthquake prone area. The present study proposes a closed‐form solution for obtaining the natural frequency of flexible CPRF, where the piles and raft are represented as beam and thin plate respectively, lying on a two‐parameter Pasternak medium. Two simultaneous governing differential equations for the components are formulated and closed form solutions are obtained for finding the natural frequency and transient horizontal displacement of the foundation system. The complex soil‐structure interactions associated with the load‐bearing mechanism of CPRF is incorporated in the analysis scheme. The proposed method is validated with available centrifuge test result. Further parametric studies showcase that with decrease in raft thickness, the spectral acceleration response of the raft decreases. Also, for CPRF with high raft flexibility, the natural frequency of the foundation in dense sand is 34% and 53% higher compared to medium dense and loose sands, respectively. Thus, the present method can be reckoned as a notable contribution in comprehending the dynamic behavior of flexible CPRF.