A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities

Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds. A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities. The one-quarter car mode,1 is used to represent the train as lumped masses connected by springs. The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency. The Fourier transform is applied in the direction of train＇s movement to express the wave motion with a wave-number. The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface, including the irregularities on the track surface. Dynamic responses of the track and ground due to train＇s moving loads are obtained in the wave-number domain by solving the governing equation, using a conventional finite element procedure. The amplitude and wavelength are identified as two major parameters describing track irregularities. The irregularity amplitude has a direct impact on the vertical response for low-speed trains, both for short wavelength and long wavelength irregularities. Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases. For low-speed case, vibrations induced by track irregularities dominate far field responses. For high-speed case, the wavelength of track irregularities has very little effect on ground vibration at distances far from track center, and train＇s wheel axle weights becomes dominant.

Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds.A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities.The one-quarter car model is used to represent the train as lumped masses connected by springs.The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency.The Fourier transform is applied in the direction of train's movement to express the wave motion with a wave-number.The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface,including the irregularities on the track surface.Dynamic responses of the track and ground due to train's moving loads are obtained in the wave-number domain by solving the governing equation,using a conventional finite element procedure.The amplitude and wavelength are identified as two major parameters describing track irregularities.The irregularity amplitude has a direct impact on the vertical response for low-speed trains,both for short wavelength and long wavelength irregularities.Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases.For low-speed case,vibrations induced by track irregularities dominate far field responses.For high-speed case,the wavelength of track irregularities has very little effect on ground vibration at distances far from track center,and train's wheel axle weights becomes dominant.