Dynamic Stress Analysis of a Ballasted Railway Track Bed during Train Passage

Scientific design of a railway track formation requires an understanding of the subgrade behavior and the factors affecting it. These include the effective resilient stiffness during train passage, which is likely to depend on the stress history and the stress state of the ground, and the stress path followed during loading. This study investigates the last of these, by means of a two-dimensional dynamic finite-element analysis. The effects of train speed, acceleration/braking, geometric variation in rail head level, and a single unsupported sleeper are considered. Results indicate that dynamic effects start to become apparent when the train speed is greater than 10% of the Rayleigh wave speed, vc, of the subgrade. At a train speed of 0.5vc, the shear stresses will be underestimated by 30% in a static analysis, and at train speeds greater than vc the stresses due to dynamic effects increase dramatically. Train acceleration/braking may increase shear stresses and horizontal displacements in the soil, and hence the requirement for track maintenance at locations where trains routinely brake or accelerate. For heavy haul freight trains, long wavelength variations in rail head level may lead to significantly increased stresses at passing frequencies (defined as the train speed divided by the wavelength of the variation in level) greater than 15, and short wavelength variations at passing frequencies of 60–70. Stress increases adjacent to an unsupported sleeper occur in the ballast and subballast layers, but rapidly become insignificant with increasing depth.