Numerical Model of Interaction and Behavior of Short Span High Speed Rail Bridge on Viscoelastic Supports

Currently in the United States, the National University Rail (NuRail) Center is leading a federally funded research program in railway engineering, including research in high speed rail (HSR) networks in which single span short bridges are integral part. Bridges with a span less than 30 m (98.43 ft.) are prone to high vertical accelerations at resonance speeds, which are proportional to the fundamental frequency, thus leading to safety issues related to track deteriorations or destabilization. The research of this dissertation aims at improving the estimate of bridge natural frequencies and dynamic behavior with a numerical model capable of incorporating the effects of bridge boundary conditions characterized by linear viscoelastic elements as well as the interaction between the train and the track-bridge subsystems. A 2D numerical model, based on the finite element method (FEM), is developed where the decoupled equations of motion of the train subsystem and the track-bridge subsystem are derived independently and solved using algorithms of the HHT alpha method of direct time integration. The interaction between the two subsystems is assumed to occur through constant contact between the wheels and the rails. The contact forces are treated as external forces and computed using dynamic condensation of the degrees of freedom of the wheels to the global deformations of the underlying structure. The accuracy of the simplified proposed model is verified against other computationally more expensive models and results show good agreements. Findings of the free vibration analysis indicate that natural frequencies of the bridge decrease when including shear deformations and rotational inertia, bridge support vertical stiffness, track vertical stiffness, and ballast mass. Consideration of the support rotational restraint however increases the natural frequencies but has insignificant effects for softer bridge vertical supports. This has a practical application since the main resonance speed depends on the fundamental frequency. Parametric studies of bridges with spans ranging from 5 m (16.4 ft) to 40 m (131.2 ft) show that shear deformations and rotational inertia can be ignored for slenderness ratio larger than 50. The train vehicle interaction and the track structure both decrease bridge dynamic responses by as much as 50% at resonance speeds for the studied cases. Bridges may be modeled as simply supported when the logarithmic value of the ratio of support vertical stiffness to bridge flexural stiffness is greater than 3. Supports with this ratio less than 1.5 are not adequate for HSR bridges. The high dynamic response of bridges with supports having this ratio between 2 and 2.5 may be significantly reduced when the inherent damping provided by the supporting elements or additional external dampers at the supports are taken into consideration.