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Advances in Civil Engineering
Volume 2018, Article ID 1629039, 9 pages
https://doi.org/10.1155/2018/1629039
Research Article

Correction of Line-Sampling Bias of Rock Discontinuity Orientations Using a Modified Terzaghi Method

1Department of Engineering Geology and Geotechnical Engineering, Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430074, China
2School of Civil Engineering, Zhengzhou University, Zhengzhou, Henan 450003, China
3JiangXi Engineering Research Center of Water Engineering Safety and Resources Efficient Utilization, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

Correspondence should be addressed to Lei Huang; nc.ude.guc@ielgnauh and Changbin Yan; nc.ude.uzz@nibgnahcnay

Received 20 December 2017; Accepted 8 May 2018; Published 29 August 2018

Academic Editor: Rihong Cao

Copyright © 2018 Huiming Tang 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.

Abstract

The Terzaghi method is widely used to correct the line-sampling bias of rock discontinuity orientations. The method includes four procedures, one of which is meshing the stereographic projection diagram into cells. The method is based on the bias-compensatory factor, 1/sin θ, where θ is the angle between the scanline and the discontinuity defined at each cell center. This paper presents a modified Terzaghi method that eliminates meshing, thereby reducing the method to three steps that (1) count the frequencies, (2) weigh the frequencies by the bias-compensatory factor, and (3) round the weighed frequencies to the nearest integer. Due to the elimination of the mesh, the counting object has changed to the frequency at each pole, and θ in the bias-compensatory factor is redefined as the angle between the scanline and the discontinuity at each pole. The applicability of the redefined bias-compensatory factor is verified through a mathematical logical deduction. The accuracy of the conventional and the modified Terzaghi methods are compared using a case study in Wenchuan, China, revealing improved accuracy for the latter.