Rock and Soil Mechanics ›› 2020, Vol. 41 ›› Issue (4): 1259-1269.doi: 10.16285/j.rsm.2019.5788

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Methods of determining the minimum number of samples for statistical measurement of rock joint roughness

HOU Qin-kuan, YONG Rui, DU Shi-gui, XU Min-na, CAO Ze-min   

  1. Shaoxing University, Shaoxing, Zhejiang 312000, China
  • Online:2020-04-27 Published:2020-09-27
  • Contact: YONG Rui, male, born in 1987, Post-doctor, associate Professor, research interests include the mechanical properties of rock mass joints and slope engineering stability evaluation. E-mail:
  • About author:HOU Qin-Kuan, male, born in 1995, Master degree candidate, research interests include the mechanical properties of rock mass joints and slope engineering stability evaluation.
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (41502300, 41427802) and the Natural Science Foundation of Zhejiang Province (LQ16D020001).

Abstract: The rock joint roughness has many characteristics like heterogeneity, anisotropy, nonuniformity and scale effect. In engineering practice, different statistical methods are utilized for analyzing the rock joint roughness due to its uncertainty. However, previous studies often neglected the impact of insufficient samples on statistical results. To solve the problem that reasonable number of samples cannot be determined during the statistical measurement of joint roughness, the methods based on the coefficient of class ratio analysis and the simple random sampling principle are proposed for determining the minimum number of samples (MNS), respectively. In the case study, the MNS of statistical measurements is determined based on the proposed methods. The results of rock joint samples are compared and analyzed with different sample sizes. The results indicate that the coefficient of variation (COV) value of the small samples is significantly larger than that of large ones, and the COV value decreases with increasing size of samples. The COV values of the joint samples with the sizes of 10?50 cm basically are in a range of 0.31?0.47, and the values for those of 60?100 cm samples are between 0.21?0.31. The relationship between MNS and sample size basically satisfies the power function relationship, and the MNS decreases with the sample size. The MNS determined by the former method with an allowable error of ±2% is consistent with that calculated by the latter with a maximum allowable error of 10% and a confidence level of 95%. The similarity of the results based on these two methods is greater than 0.997. This study can provide basis for quantitatively obtaining the MNS in rock joint roughness statistical measurement, and can ensure the accuracy of JRC statistical analysis. It is of great significance to accurately obtain mechanical parameters of rock joints in rock mass stability evaluation.

Key words: joint roughness coefficient (JRC), class ratio analysis, simple random sampling principle, minimum number of samples (MNS)