TECHNICAL PAPER A New Analytical Model for Estimating the Natural Frequency of Pile-Supported Bridges Rasoul Gholami 1 & Vahid Shirgir 1 & Ali Ghanbari 1 & Mohsen Shahrouzi 1 Accepted: 15 January 2018 # Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The common design for earthquake loading assumes that bridges are fixed at their bases. In reality, interaction between soil and structure decreases the overall stiffness of the structural system. This is not always desirable and may elevate the fundamental period of the system. The current study set to assess soil-structure interaction (SSI) impacts on dynamic performance of pile-supported bridge piers. The bridge foundation is assumed as a distributed mass pile, and a new analytical model is proposed to predict seismic analysis of pile-supported bridges. Applying the dynamic equations of motion for system and using virtual work principles, SSI effects were estimated. Based on the analytical model, a new equation is proposed for calculating the natural frequency of pile-supported bridges. Since the proposed model is very similar to real soil-pile-pier systems, this equation can be used to estimate the fundamental period of the single-pier bridges. Keywords Soil-structureinteraction . Analytical model . Bridge pier . Natural frequency . Single-pile-supported bridges Transp. Infrastruct. Geotech. https://doi.org/10.1007/s40515-018-0049-y * Rasoul Gholami Rasoul.gholami@gmail.com Vahid Shirgir v.shirgir@gmail.com; std_shirgir@khu.ac.ir Ali Ghanbari Ghanbari@khu.ac.ir Mohsen Shahrouzi Shahruzi@khu.ac.ir 1 Faculty of Engineering, Kharazmi University, No. 49 Mofatteh Ave, Tehran, Iran