ISSN 0536-1028 (Print)              ISSN 2686-9853 (Online)  
УДК 519.25:622.02; 624.131.3 DOI: 10.21440/0536-1028-2019-4-33-42


Gordeev V. A. Calculation of statistical characteristics of rock strength certificate. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal = News of the Higher Institutions. Mining Journal. 2019; 4: 33–42 (In Russ.). DOI: 10.21440/0536-1028-2019-4-33-42

Introduction. At risk assessment in problems of mining geomechanics it is necessary to consider statistical characteristics of rock physical parameters variability and interconnection – mean square deviations and coefficients of correlation of these parameters for each engineering-geological element. In calculations of career slopes stability rock strength certificate parameters are used – coupling and internal friction angle. Neglection of mutual correlation between rock strength certificate parameters leads to settlement indicator errors overestimate/understating, while the neglection of the coefficient of stability and geometrical parameters of a slope leads to understating/overestimate of degree of risk. Research aim and methodology. On the basis of the regression analysis the present research aims to consider ways of receiving elements of a correlation matrix for various ways of creating rock strength certificate according to the results of laboratory researches of the samples – at monoaxial compression and stretching and by the one-plane cut method. Results. The formulae necessary to calculate rock strength certificate parameters covariance matrix are introduced in the article. It is established that the way of calculating covariance matrix depends on the applied samples laboratory test method. The examples have shown that the correlation coefficient between coupling and of internal friction coefficient can be of various signs. Scope of results. Values of rock strength certificate parameters statistical characteristics, calculated by the offered technique, can be used to solve rock geomechanics probabilistic problems.

Key words: rock strength certificate; coupling; internal friction coefficient; tests of samples; covariance matrix; correlation coefficient.



  1. Gordeev V. A. The fundamentals of geotechnical development conditions geometrization at open pits. DSc (Engineering) abstract of dissertation. St. Petersburg; 1994. (In Russ.)
  2. Popov V. N., Shpakov P. S., Iunakov Iu. L. Open pit slopes stability control. Moscow: MSMU Publishing; 2008. (In Russ.)
  3. Gordeev V. Zur parameterschätzung ausgleichender funktionen ohne fehlerfreie variable. Vermessungstechnik. 1989; 9: 310–313.
  4. Manakov A. V. Building strength certificates according to experimental data. Gornyi informatsionnoanaliticheskii biulleten (nauchno-tekhnicheskii zhurnal) = Mining Informational and Analytical Bulletin (scientific and technical journal). 2004; 11: 94–95. (In Russ.)
  5. Pevzner M. E., Iofis M. A., Popov V. N. Geomechanics. Moscow: MSMU Publishing; 2005. (In Russ.)
  6. Latyshev O. G. Rock breaking. Moscow: Teplotekhnik Publishing; 2007. (In Russ.)
  7. Baklashov I. V. Geomechanics. In 2 volumes. Volume1. The fundamentals of geomechanics. Moscow: MSMU Publishing; 2004. (In Russ.)
  8. Gordeev V. A. The theory of measurement errors and compensation computations. Ekaterinburg: UrSMU Publishing; 2004. (In Russ.)
  9. Wolf H. Ausgleichungsrechnung I. 3. Aufl. Ferd. Dümmlers Verlag, Bonn. 1998. 322 s.
  10. Draper N., Smith T. Applied regression analysis. 1998, by John Wiley & Sons, Inc. 736 p.
  11. V. V. Fursov, M. V. Baliura (eds.) Determination of soil shear resistance by the method of single-plane cut: guidelines for laboratory work on soil mechanics. Tomsk: TSUAB Publishing; 2016. (In Russ.)
  12. Borshch-Komponiets V. I. Applied rock mechanics. Moscow: Gornaia kniga Publishing; 2013. (In Russ.)
  13. Gordeev V. A. Geometrization of geotechnical development conditions at open pits: scientific monograph. Ekaterinburg: UrSMU Publishing; 2017. (In Russ.) 

Received 27 February, 2019




This email address is being protected from spambots. You need JavaScript enabled to view it.

Мы индексируемся в: