A statistical analysis of geomechanical data and its effect on rock mass numerical modeling: a case study
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A statistical analysis of geomechanical data and its effect on rock mass numerical modeling: a case study Piotr Małkowski1
•
Zbigniew Niedbalski1 • Tafida Balarabe2
Received: 2 February 2020 / Revised: 31 July 2020 / Accepted: 9 September 2020 The Author(s) 2020
Abstract Geomechanical data are never sufficient in quantity or adequately precise and accurate for design purposes in mining and civil engineering. The objective of this paper is to show the variability of rock properties at the sampled point in the roadway’s roof, and then, how the statistical processing of the available geomechanical data can affect the results of numerical modelling of the roadway’s stability. Four cases were applied in the numerical analysis, using average values (the most common in geomechanical data analysis), average minus standard deviation, median, and average value minus statistical error. The study show that different approach to the same geomechanical data set can change the modelling results considerably. The case shows that average minus standard deviation is the most conservative and least risky. It gives the displacements and yielded elements zone in four times broader range comparing to the average values scenario, which is the least conservative option. The two other cases need to be studied further. The results obtained from them are placed between most favorable and most adverse values. Taking the average values corrected by statistical error for the numerical analysis seems to be the best solution. Moreover, the confidence level can be adjusted depending on the object importance and the assumed risk level. Keywords Statistical analysis Geotechnical data Laboratory tests on rocks Numerical modelling
1 Geomechanical data and their uncertainty Geomechanical data are never sufficient in quantity or adequately precise and accurate for design purposes in mining and civil engineering. This is because rock masses are naturally complex and variable at all scales. Qu (2017) stated that, in theory, the geomechanical characteristics of rock masses are not completely random variables. This is because rocks were formed and continuously modified by a variety of complex processes, causing physical heterogeneity that results in variations in measured physical & Piotr Małkowski [email protected] 1
Faculty of Mining and Geoengineering, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krako´w, Poland
2
Revoult Ltd, al. Jana Pawła II 43a, 31-864 Krako´w, Poland
properties, even within one rock type. Moreover, the presence of natural fractures creates spatial and directional variations in rock mass properties, i.e., such fractures cause a rock mass to become inhomogeneous and anisotropic (Jing 2013). Therefore, in geomechanical investigations and laboratory tests, it is necessary to statistically analyze the parametric characteristics of rock as random variables (Yegulalp and Mahtab 1983; Uzielli 2008; Mayer et al. 2014). The aim of statistical analysis is to find the most representative value of the p
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