A micromechanics-based analytical method for wave propagation through a granular material

This paper describes the creation and use of the stiffness and mass matrices of a granular sample to calculate its modes of vibration and natural frequencies, and obtain its transfer function. This is an important result as it is a necessary prerequisite for the application of linear systems theory to granular materials. The analytical solution for wave propagation through the material is then presented and simulations of bender element tests on an idealised two-dimensional granular sample are used as an example of the applicability of the method. Analysing wave propagation through sand and sandstone in this novel way that is explicitly particle-based can offer significant insights into phenomena such as wave dispersion. It can also offer insight into the interpretation of laboratory bender element tests, which is often challenging. Bender element tests are used to obtain the small-strain stiffness of soil for engineering design and the results generated by applying the analytical method proposed here give insight into the effects of sample aspect ratio and boundary conditions on the observed response. The model presented here allows for comparisons between the static stiffness of the sample and the stiffness value calculated through wave velocities, as obtained by a variety of methods used by experimentalists. This leads to the identification of the best procedure for extracting the small-strain stiffness value for the dry granular sample considered here.