Scale-dependent recursive analysis of topographical roughness: A methodology for differentiating geological and geomechanical features from point cloud data

Abstract

Exposed rock surfaces reflect diverse topographical features shaped by underlying geological and geomechanical conditions, such as mineral composition, weathering, excavation methods, and structural geology. These features directly influence the mechanical behavior of in-place materials, providing a robust basis for differentiating geological and geomechanical units in engineering. Their explicit spatial differentiation relies on time-consuming and subjective visual assessments, or the inefficient and difficult to reproduce measurement of topographical features (e.g., roughness, undulation) at arbitrary scales. This work aims to offer an objective, reproducible, and efficient topographical analysis framework to differentiate geological and geomechanical features arising from natural and man-made origins. This study introduces a scale-dependent recursive analysis method to systematically evaluate and characterize roughness conditions of exposed rock surfaces. By analyzing point clouds across multiple scales, the method derives scale-dependent trends and computes parameters that distinguish topographical features associated with specific geological and operational settings. A moving-window algorithm is applied as a second layer of analysis to capture localized trends, integrating these as an explicit scalar field within point clouds for direct differentiation of features. This methodology improves accuracy and efficiency compared to traditional roughness measurement techniques by reducing biases and subjectivity associated with visual-based assessments. The approach is demonstrated using four datasets from diverse geological and geomechanical contexts, showcasing its applicability and the insights gained. The influence of point cloud density and moving-window size on the recursive analysis is further discussed, highlighting the method's potential to provide objective and quantifiable topographical differentiation for mining, tunneling, and construction applications.