Gravitational and tectonic stresses in the rock mass and their determination by measurements in separate points
1Saint-Petersburg Branch of the Federal State Budgetary Institution of Science of the Institute of Geoecology named after E.M. Sergeev of the Russian Academy of Sciences, Saint-Petersburg, Russia
Min. miner. depos. 2017, 11(3):56-69
Full text (PDF)
Purpose.Stress state in rock mass is the most important factor affecting processes around mine working. The methods used for calculation of stresses based on hypotheses of elastic thrust, hydrostatic state or spherical equilibrium of the earth crust do not consider tectonic processes and influence of rocks’ viscous properties on formation of stress fields. The goal is to develop methods of calculating stress state in rock masses depending on the elastic and viscous rock properties and interaction of tectonic plates considering stresses measured in individual points.
Methods. Conditions of stress state formation in rock masses due to gravitation effect are modeled under axial compression of a cylindrical sample with forbidden lateral movements. Solution of the problem about deformation of such sample allowed to obtain the ratio between lateral stresses and axial stresses. This ratio determines the lateral thrust coefficient in the rock mass. Tectonic component of stress state in rock mass is determined by values of deformations in the horizontal plane caused by interaction of tectonic plates. Tectonic components of stresses depend on tectonic deformations in the horizontal plane. Due to the length of tectonic processes the tectonic component of lateral stresses also depends on viscous and elastic deformations.
Findings. Gravitation component of the lateral thrust coefficient does not vary with depth, while the tectonic component is inversely proportional to depth. Growth of lateral thrust coefficient as its measurements are approaching the surface is explained by the effect of tectonic component of stresses.
Originality.Experimental measurements of stresses are possible only in a limited number of points. There is no other method to determine stresses in masses with non-horizontal bedding, non-uniformities and folds except for mathematical modeling. Within the frames of hypothesis describing a medium with limited linear viscous deformations, we have obtained equations relating the stress components with full and elastic deformations. The method is developed for formulation and solution of problems for modeling stress state using equations of rock mass state as the medium with quasi-elastic properties. Gravitation component is set by the rocks' weight, and effect of tectonics is set by the tensor of tectonic deformations.
Practical implications. A method for solving the problem for determination of stresses in rock mass considering measured stresses in individual points is proposed.
Keywords: rocks, stressed state, lateral expansion, tectonic deformations, tectonic stresses, mathematical modeling
Amadei, B. (1996). Importance of Anisotropy When Estimating and Measuring in situ Stress in Rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33(3), 293-325.
Amadei, B., & Stephansson, O. (1997). Rock Stress and Its Measurement. London and New York: Chapman & Hall.
Baryakh, A.A., Konstantinova, S.A., & Asanov, V.A. (1996). Deformirovanie solyanykh porod. Ekaterinburg: UrO RAN.
Brady, B., & Brawn, E. (2004). Rock Mechanics for Underground Mining. Dordrecht: Kluwer Academic Publishers.
Brown, E.T., & Hoek, E. (1978). Trends in Relationships Between Measured in-situ Stresses and Depth. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 15(4), 211-215.
Cartwright, P.B. (1997). A Review of Recent in situ Stress Measurements in United Kingdom Coal Measure Strata. In Proceedings of the International Symposium on Rock Stress (pp. 469-482). Rotterdam: CRC Press/Balkema, Taylor & Francis Group.
Glushko, V.T., & Vinogradov, V.V. (1982). Razrushenie gornykh porod i prognozirovanie proyavleniy gornogo davleniya. Moskva: Nedra.
Gzovskiy, M.V. (1975). Osnovy tektonofiziki. Moskva: Nauka.
Heim, A. (1878). Untersuchungen uber den Mechanismus der Gebirgsbildung. Basel: Schwabe.
Herget, G. (1987). Stress Assumptions for Underground Excavations in the Canadian Shield. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 24(1), 95-97.
Jaeger, J.C., Cook, N.G.W., & Zimmerman, R.W. (2007). Fundamentals of Rock Mechanics. Hoboken: Blackwell Publishing.
Kartashov, Yu.M., Matveev, B.V., Mikheev, G.V., & Fadeev, A.B. (1979). Prochnost’ i deformiruemost’ gornykh porod. Moskva: Nauka.
Leont’yev, A.V. (2001). Analiz estestvennykh napryazheniy po rezul’tatam izmereniy v rudnikakh na territorii Severnoy Evrazii. Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, (1), 31-40.
Lo, K.Y. (1978). Regional Distribution of in-situ Horizontal Stresses in Rocks of Southern Ontario. Canadian Geotechnical Journal, 15(3), 371-381.
Markov, G.A. (1977). Tektonicheskie napryazheniya i gornoe davlenie v rudnikakh Khibinskogo massiva. Leningrad: Nauka.
McCutchen, W. R. (1982). Some Elements of a Theory of in situ Stress. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 19(4), 201-203.
Olovyannyy, A.G. (2012). Mekhanika gornykh porod. Modeli-rovanie razrusheniy. Sankt-Peterburg: IPK Kosta.
Olovyannyy, A.G. (2016). Bokovoy raspor i tektonicheskie napryazheniya v massive gornykh porod. Gornyy Zhurnal, (6), 25-31.
Petukhov, I.M., & Batugina, I.M. (1999). Geodinamika nedr. Sankt-Peterburg: Mig.
Savchenko, S.N., Kozyrev, A.A., & Mal’tsev, V.A. (1994). Napryazhennoe sostoyanie porod blochnogo stroeniya razlichnykh masshtabnykh urovney. Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, (6), 24-29.
Savchenko, S.N. (2004). Otsenka napryazhennogo sostoyaniya gornykh porod v rayone bureniya Kol’koy sverkhglubokoy skvazhiny. Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, (1), 27-34.
Sheorey, P.R. (1994). A Theory for in situ Stresses in Isotropic and Transversely Isotropic Rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 31(4), 193.
Sheorey, P.R., Murali Mohan, G., & Sinha, A. (2001). Influence of Elastic Constants on the Horizontal in situ Stress. International Journal of Rock Mechanics and Mining Sciences, 38(8), 1211-1216.
Zoback, M.D., Barton, C.A., Brudy, M., Castillo, D.A., Finkbeiner, T., Grollimund, B.R., … & Wiprut, D.J. (2003). Determination of Stress Orientation and Magnitude in Deep Wells. International Journal of Rock Mechanics and Mining Sciences, 40(7-8), 1049-1076.