Structural Wave Propagation in Unconsolidated Granulates

Abstract

Unconsolidated granulates exhibit complex, nonlinear behaviour when subjected to dynamic forces. The presence of granular contacts gives this type of material a relatively low stiffness and provides hysteretic energy losses. These features make unconsolidated granulates suitable for railway ballast as it provides dissipation of vibrational energy from passing trains which is important to minimise vibrational disturbance. However, simulating the response of the railway superstructure under dynamic loads becomes difficult due to then onlinearity of the ballast. In order to develop better prediction tools, the elastic behaviour of unconsolidated rocks is first investigated experimentally by quasi-static and dynamic stress-strain experiments yielding the Young's modulus, nonlinear resonance shift and analysis of harmonic generation. In addition, the transmission of structural waves through granulates is investigated by assessing the transfer function for different thicknesses of granulates, different
particle sizes and different materials with varying viscous damping. Three granulates are used, small-scale ballast, a gravel, and two sizes of uniform steel spheres. All three materials exhibit a combination of classical and hysteretic nonlinearity where the strain depends on the stress amplitude and history.

A completely new finite element approach is taken to model the hysteretic nonlinearity, based on an existing phenomenological static model. Multiple spring-slider elements with gaps are used, as opposed to implementing a homogenised material model. It is shown that only 50 elements can reproduce the hysteretic nature of the material, which is a significant advantage to a traditional material model requiring the discretisation of the entire ballast volume. Each spring-slider element is parameterised by two springs constants, a yield force and an initial gap. A distribution of these parameters across the 50 elements is found that reproduces the quasi-static stress cycles acquired experimentally. In addition, a parametric study of the model parameters during dynamic excitation reveals that key indicators of nonlinearity can be simulated. The finite element simulations prove that using a set of spring-slider elements
to model the behaviour of unconsolidated granulates is viable method. With experimental tests performed on true ballast and further work on the finite element model to understand optimal parameter distributions, a more accurate and efficient railway superstructure model can be produced.