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Mathematical Problems in Engineering
Volume 2018, Article ID 9835341, 14 pages
Research Article

A Method for Estimating the Surface Roughness of Rock Discontinuities

1Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
2Three Gorges Research Center for Geo-Hazard, Ministry of Education, Wuhan 430074, China

Correspondence should be addressed to Hui-ming Tang; nc.ude.guc@mhgnat

Received 19 October 2017; Revised 26 January 2018; Accepted 8 February 2018; Published 18 March 2018

Academic Editor: Fabrizio Greco

Copyright © 2018 Yi Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The primary objective of this study is to develop a parameter with a clear physical meaning to estimate the surface roughness of rock discontinuities. This parameter must be closely related to the shear strength of rock discontinuities. The first part of this study focuses on defining and computing this parameter. The estimation formula for the shear strength of a triangle within a discontinuity surface is derived based on Patton’s model. The parameter, namely, the index of roughness (), is then proposed to quantitatively estimate discontinuity roughness. Based on laser scanning techniques, digital models of discontinuities and discontinuity profiles are constructed, and then their corresponding values are computed. In the second part of this study, the computational processes and estimated effects of the two-dimensional (2D) and three-dimensional (3D) values of the discontinuities are illustrated through several applications. Results show that the 2D and 3D values of these discontinuities indicate anisotropy and sampling interval effects. In addition, a strong linear correlation is detected between and the joint roughness coefficient (JRC) for seventy-four profiles and eleven discontinuity specimens, respectively. Finally, the proposed method, back analysis method, root mean square () method, and Grasselli’s method are compared to study the use of the parameter .