Measurements of the high frequency dynamic stiffness of railway ballast and subgrade

Abstract

Conventional railway tracks are laid in a layer of crushed stone known as ballast which contributes to the resilience of the track support. Beneath it is the subgrade which also has a considerable influence on the track support stiffness. Although quasi-static measurements of track stiffness are reasonably common, the dynamic stiffness at higher frequencies is required for noise and vibration modelling. Here, a distinction is made between the dynamic stiffness of the ballast layer itself and the dynamic support stiffness which includes the underlying ground. The dynamic transfer stiffness of a ballast layer is required for ground vibration and bridge noise predictions. Two different methods for measuring this are presented, one in the laboratory and the other in the field. The laboratory method is limited to a maximum frequency of about 600 Hz due to limitations of the test rig. The field measurement, which relies on identifying the wavespeed within the medium, gives results up to 2 kHz. These methods give broadly consistent results, with a stiffness per rail seat for a 300 mm thick ballast layer of approximately 300–500 MN/m, increasing in proportion to the square root of the preload, and a damping loss factor in the range 0.15–0.3. The corresponding Young's modulus is between 200 and 700 MPa, depending on the preload. The dynamic stiffness increases above about 300 Hz with a first peak due to standing wave effects occurring at about 700 Hz. The dynamic support stiffness beneath the sleeper, on the other hand, is required for rolling noise modelling. This has been measured using two methods: a direct method for frequencies 50–500 Hz and an indirect method based on a modal analysis of a sleeper embedded in the ballast. A clear shift in natural frequencies is seen which is associated with the support stiffness. This support stiffness is strongly frequency-dependent, with the value per rail seat increasing from about 100 to 200 MN/m at 100 Hz to 2000 MN/m at 1 kHz. The support damping corresponds to a loss factor of around 1 for frequencies above 200 Hz, or a damping coefficient of 100–200 kN/m per rail seat. This damping is due to the radiation of energy into the ground rather than internal losses in the ballast. It strongly affects the modal damping of the sleeper and thus its radiated noise. The dynamic support stiffness increases roughly in proportion to the cube root of the preload. Comparison with a finite element model indicates that the underlying ground is responsible for the support stiffness and damping at low frequencies. However, above about 500 Hz it is independent of the ground and is only affected by the ballast layer. The results from the finite element model imply behaviour similar to a viscous damper. The sleeper vibration obtained using either a viscous damping or a constant loss factor is similar.