Quantitative estimation of joint roughness coefficient using statistical parameters

Abstract

where τ is the peak shear strength of the rock joint, σ is the normal stress, JRC is the joint roughness coefficient, JCS is the strength of joint wall, φb is the basic friction angle. Over the last half century, researchers have kept working on techniques for estimating JRC of rock joints for or from this model. So far, the JRC value of a particular rock joint is most often estimated by visibly comparing it to the ten standard profiles with JRC values ranging from 0 to 20 [2]. This method was also adopted by the ISRM commission on test methods since 1981 [3]. In rock engineering practice, however, the visible comparison has been long thought to be subjective in that the user has to judge which profile his joint fits the best. The development of objective methods was gradually advanced by researchers considering quantitative estimation. Tse and Cruden [4] established regression correlations between JRC and Z2 (the root mean square of the first deviation of the profile) proposed by Myers [5] and SF (the structure function) by Sayles and Thomas [6]. As Tse and Cruden's equations have correlation coefficients as big as 0.986, they are often employed to estimate JRC [7,8], though Z2 and SF were later found by Yu and Vayssade [9] and Yang et al. [10] to be sensitive to the sampling interval. Yu and Vayssade [9] argued that Tse and Cruden's preparation of the discrete point data was improper, as an isotropic transformation (enlarging the standard profiles by 2.5 times both in xand y-coordinates) may exaggerate the roughness of the joint profiles. They manually digitized the ten standard profiles at three different sampling intervals of 0.25, 0.5 and 1.0 mm and indicated strong influences of sampling interval on JRC estimated by Tse and Cruden's equations. Yang et al. [10] reconstructed the ten standard profiles by means of Fourier transform and updated the correlations between JRC and Z2 as well as SF. Their equations display even higher correlation coefficients (0.99326) (Table 2). Besides Z2 and SF, Rp was also taken as one of the parameters to estimate JRC of a rock joint. Rp was firstly defined as roughness profile index by El-Soudani [14], which is equal to the ratio of the true length of a fracture surface trace to its projected length in the fracture plane. Maerz et al. [12] employed the ten standard profiles and related their JRCs to Rp, which gave a linear relationship with a correlation coefficient of 0.984. Yu and Vayssade [9] also proposed to estimate JRC using RL. Though RL was considered by Yu and Vayssade [9] as “real profile length”, the authors found it is identical to Rp according to its calculation provided in Yu and Vayssade's appendix. Wang [13] derived an empirical equation with R as the parameter to estimate JRC, where R was called as “elongation rate” and