Evidence that surface roughness influences the inter-particle contact behaviour as well as the continuum behaviour of soils prompts us to develop advanced means of roughness characterisation for soil grains. Due to the complex nature of the soil forming process, the surface of a soil grain usually exhibits random features, unlike engineered surfaces.
Existing advanced metrology technologies are difficult to apply to real soil grains, in particular because of the irregular shape of soil grains, which can influence the measurements. For example, roughness measurements are generally made by interferometry. Using a built-in programme to separate shape and roughness may not be appropriate for irregular shapes and does not usually give a scale for roughness.
In this research we are proposing a new method, partly borrowed from tribology and uniquely applied to soil grains, which uses unaltered measurements of the soil grain surface morphology obtained by interferometry. We show that by first calculating the surface area by triangulation at various discretisation lengths, it is possible to determine a cut-off length between roughness and local shape.
Assuming an auto-correlation function for heights formed by random processes, the data can also be expressed in terms of power spectral density (PSD), so that the spatial surface height data are transformed into a spatial frequency domain. The statistical roughness can be calculated from the PSD, while the self-affine nature of the surface allows determining fractal dimensions which, when combined with other parameters, provide additional information about the surface structure and roughness to the value of roughness alone. The parameters characterising the roughness can be used to reconstruct the surface of soil grains by using the Weierstrass-Mandelbrot function, for example for constructing realistic numerical particles for discrete element models of soils
Authors
Béatrice Baudet, Ting Yao (University of Hong Kong), Hongwei Yang (formerly University of Hong Kong)
