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

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.