A Substructure Approach for Analyzing Pile Foundation and Soil Vibrations Due to Train Running over Viaduct and Its Validation

An efficient computational approach based on substructure methodology is proposed to analyze the viaduct–pile foundation–soil dynamic interaction under train loads. The train–viaduct subsystem is solved using the dynamic stiffness integration method, and its accuracy is verified by the existing analytical solution for a moving vehicle on a simply supported beam. For the pile foundation–soil subsystem, the geometric and material properties of piles and soils are assumed to be invariable along the azimuth direction. By introducing the equivalent stiffness of grouped piles, the governing equations of pile foundation–soil interaction are simplified based on Fourier decomposition method, so the three-dimensional problem is decomposed into several two-dimensional axisymmetric finite element models. The pile foundation–soil interaction model is verified by field measurements due to shaker loading at pile foundation top. In addition, these two substructures are coupled with the displacement compatibility condition at interface of pier bottom and pile foundation top. Finally, the proposed train–viaduct–pile foundation–soil interaction model was validated by field tests. The results show that the proposed model can predict vibrations of pile foundation and soil accurately, thereby providing a basis for the prediction of pile–soil foundation settlement. The frequency spectra of the vibration in Beijing–Tianjin high-speed railway demonstrated that the main frequencies of the pier top and ground surface are below 100 and 30 Hz, respectively.