Characterization of Joint Roughness Heterogeneity and Its Application in Representative Sample Investigations

Rock joint surface roughness is usually characterized by heterogeneity, but the determination of a required number of samples for achieving a reasonable heterogeneity assessment remains a challenge. In this paper, a novel method, the global search method, was proposed to investigate the heterogeneity of rock joint roughness. In this method, the roughness heterogeneity was characterized based on a statistical analysis of the roughness of all samples extracted from different locations of a given rock joint. Analyses of the effective sample number were conducted, which showed that sampling bias was caused by an inadequate number of samples. To overcome this drawback, a large natural slate joint sample (1000 mm x 1000 mm in size) was digitized in a laboratory using a high-accuracy laser scanner. The roughness heterogeneities of both two-dimensional (2D) profiles and three-dimensional (3D) surface topographies were systematically investigated. The results show that the expected value obtained from conventional methods failed to accurately represent the overall roughness. The relative errors between the population parameter and the expected value varied not only from sample to sample but also with the scale. The roughness heterogeneity characteristics of joint samples of various sizes can be obtained using the global search method. This new method could facilitate the determination of the most representative samples and their positions.