Abstract
Rock masses are presenting an enduring challenge since the first authors began trying to model these natural structures. This modelling needs a parametrisation and a latter value assignment for those parameter value series, which show high variability, and a lack of clear patterns, in nature. Understanding the statistical nature of these values is an essential goal of rock mechanics, searching for the most appropriate probability density function (pdf) for fitting each one of those parameter values. The identification of those pdf is an aid for a better understanding of the rock mass nature and a need for correct discrete fracture network generation, or any probabilistic calculation. The parameter studied in this work is the degree of fracturing, in particular: the distances between fractures in a borehole rock core, which determines the Rock Quality Designation (RQD) value. The most accepted hypothesis is that these values fit a negative exponential pdf, however, with some criticism. Through the analysis of 1985 m of borehole rock core from five lithologies from two rock masses, this work shows the lognormality of the data series. The negative exponential does not fit correctly; however, the old approach for RQD based on this hypothesis offers satisfying results. Furthermore, it has been observed that schist presents the unclearer random pattern.
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Abbreviations
- AD :
-
Anderson Darling goodness-of-fit test
- ADF :
-
Augmented Dickey–Fuller unit root test
- KS :
-
Kolmogorov–Smirnov goodness-of-fit test
- pdf:
-
Probability density function
- RQD :
-
Rock Quality Designation
- SW :
-
Shapiro Wilk goodness-of-fit test
- t :
-
Threshold value for RQD classical calculation
- X :
-
Random vector with the distances between joints
- \(x_i\) :
-
Length of the i th fragment in a borehole core
- \(x_{it}\) :
-
Length of i th fragment in a borehole core when it is bigger than t
- \(\lambda\) :
-
Number of discontinuities per unit of length in a borehole or scanline
- \(\chi ^2\) :
-
Chi-square goodness-of-fit test
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Acknowledgements
This research was supported by: CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) funded by the Ministry of Education of Brazil; FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais) funded by the Minas Gerais Government through the research Project APQ-00478-16; CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) funded by the Brazilian Government; and PPGEM (Mining Engineering Postgraduate Program) of the Federal University of Ouro Preto.
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Bruzzi, A.F.G., Alameda-Hernández, P., Klen, A.M. et al. Probability Density Function of Rock Mass Discontinuity Distances. Geotech Geol Eng 39, 2399–2407 (2021). https://doi.org/10.1007/s10706-020-01634-6
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DOI: https://doi.org/10.1007/s10706-020-01634-6