Quantifying Failure Surface Roughness and Fractal Characteristics in Open-Pit Mining: The Case of Mashamba West Mine

Abstract

This study investigates the surface roughness and fractal properties of failure surfaces at the Mashamba West mine to enhance the understanding of the complex topographical features that influence slope stability in open-pit mining. Traditional methods for quantifying surface roughness, such as the mean absolute deviation (MAD) and standard deviation (SD), often fail to capture the multiscale and correlated behaviors typical of natural surfaces. In this research, advanced techniques, including fractal dimension calculations, semi-variogram and box-counting methods, and power spectral density (PSD) analysis, were employed to provide a more accurate characterization of the failure surface. The results revealed significant micro-roughness, with a mean absolute deviation of 0.83 and a standard deviation of 1.04, indicating a high level of surface irregularity. Geometric irregularities, such as pronounced asperities and depressions, were identified through the analysis of topographical extremes, with a mean peak height of 2.4828 and a mean valley depth of −4.7747. Fractal analysis, performed using both semi-variogram and box-counting methods, confirmed the self-affine nature of the failure surface with fractal dimensions of 1.5634 and 2.0735, respectively, indicating scale-invariant roughness patterns. The power spectral density analysis revealed a dominant frequency corresponding to periodic geological structures. These findings provide valuable insights into the surface characteristics of failure zones and offer a robust framework for future slope stability analysis. This study contributes to the field by demonstrating the utility of fractal analysis in characterizing complex failure surfaces and lays the groundwork for future research on the relationship between surface roughness and mechanical behavior in open-pit mining contexts.