Characterization of the surface roughness of sand particles using an advanced fractal approach

Abstract

The surface roughness of soil grains affects the mechanical behaviour of soils, but the characterization of real soil grain roughness is still limited in both quantity and quality. A new method is proposed, which applies the power spectral density (PSD), typically used in tribology, to optical interferometry measurements of soil grain surfaces. The method was adapted to characterize the roughness of soil grains separately from their shape, allowing the scale of the roughness to be determined in the form of a wavevector range. The surface roughness can be characterized by a roughness value and a fractal dimension, determined based on the stochastic formation process of the surface. When combined with other parameters, the fractal dimension provides additional information about the surface structure and roughness to the value of roughness alone. Three grain sizes of a quarzitic sand were tested. The parameters determined from the PSD analysis were input directly into a Weierstrass-Mandelbrot function to reconstruct successfully a fractal surface.

The Use of the Surface Roughness Value to Quantify the Extent of Supercritical CO2 Involved Geochemical Reaction at a CO2 Sequestration Site

“…The SPM included a cantilever tip connected to a probe with the laser beam, which was used to measure the height difference at each point and at the standard level (mean height), in nanometers, finally acquiring a 3-dimensional surface image profile for the certain surface domain of a slab ( Figure 3). The information acquired from SPM analysis is useful not only for the surface image but also for more quantitative parameters to evaluate the roughness degree of the surface [50,51]. Several surface roughness parameters have been developed, and in this study, a surface roughness value (SR RMS ) was used to reduce all of the information in the 3-dimensional surface image to a single number representing the degree of the surface roughness [52,53].…”

3D Analysis of gravel surface texture

“…So far, a 3D analysis of surfaces has been made possible with the development of suitable testing apparatus, such as optical interferometry (e.g. [2,4,[20][21][22][23]) and X-ray micro Computed-Tomography (CT) [24]. However, all of these are limited to sand-sized particles.…”

“…[25]). To enable the surface measurements to be compared at the two scales a new method is proposed whereby an open surface from digitized particles is defined and analyzed by fractal analysis using the power spectral density method [22].…”

“…Optical interferometers have been used for scanning small sand-sized particles (e.g. [20,22]). Here, we used the white light interferometry of an optical microscope (M3D 3000, Fogal Nanotech, France).…”

“…The surface topography is described by an interferogram that is a function of the sample height at discrete points. The measuring area is up to 141.3 × 106.6 µm with the best in-plane (perpendicular to surface height) resolution being 0.184 µm and 3 nm resolution in the surface height direction [22].…”