Abstract
Based on the hypothesis that shearing stresses and normal tensile stresses both play a decisive role in fracturing and brittle failure of rock material, a novel strength criterion was developed in one of the earlier works of the author. In the criterion, a certain parameter ν′ occurs which depends on the structure of the material. Originally, the parameter was treated as a constant, which resulted in a linear form of the strength function F σ 1 = f(σ 3), where σ 3 = σ 2. Although the linear strength criterion is sometimes found to be applicable to various particular rock materials, it is not, in general, of a universal character. Analysis of the triaxial test results for 75 different sandstones revealed that parameter ν′ usually increases in an exponential or linear manner as confining pressure increases, and only in isolated cases does it seem to be independent of the confining pressure. For these three types of function ν′ = f(p) appropriate strength criteria F σ 1 = f(σ 3) are given in the present paper. These criteria were used to fit all of the collected empirical data sets. In general, a very good fit to the data was obtained.
Similar content being viewed by others
References
Al-Ajmi AM, Zimmerman RW (2005) Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min Sci 42:431–439
Benz T, Schwab R (2008) A quantitative comparison of six rock failure criteria. Int J Rock Mech Min Sci 45:1176–1186
Benz T, Schwab R, Kauther RA, Vermeer PA (2008) A Hoek–Brown criterion with intrinsic material strength factorization. Int J Rock Mech Min Sci 45:210–222
Borecki M, Kwaśniewski M, Oleksy S, Berszakiewicz Z, Pacha J (1982) Deformational and strength properties of a certain Jastrzębie sandstone in the conditions of conventional triaxial compression. In: Borecki M (ed) Metody i środki eksploatacji na dużych głębokościach (Wybrane zagadnienia). Politechnika Śląska, Gliwice, pp 55–76 (in Polish)
Dunikowski A, Korman S, Köhsling J (1969) Laboratory tests on indices of physico-mechanical properties of rocks in three-axial state of stress. Przegląd Górniczy 25:523–528 (in Polish)
Franklin JA, Hoek E (1970) Developments in triaxial testing technique. Rock Mech 2:223–228
Gustkiewicz J (1985) Deformation and failure of the Nowa Ruda sandstone in a three-axial state of stress with gas under pressure in the pores. Archiwum Górnictwa 30(3):401–424
Haimson B (2009) A three-dimensional strength criterion based on true triaxial testing of rocks. In: Hudson JA et al (eds) Proceedings of the ISRM-sponsored international symposium on rock mechanics SINOROCK2009, Hong Kong, 19–22 May 2009. ISRM and The University of Hong Kong, Hong Kong, pp 21–28
Haimson B, Chang C (2000) A new triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. Int J Rock Mech Min Sci 37:285–296
Hoshino K, Mitsui S (1975) Mechanical properties of palaeogene and cretaceous rocks in Shikoku under high pressure. J Japan Assoc Petrol Technol 40:166–173 (in Japanese)
Hoshino K, Koide H, Inami K, Iwamura S, Mitsui S (1972) Mechanical properties of Japanese Tertiary sedimentary rocks under high confining pressures. Geological Survey of Japan, Report No. 244
Ilnitskaya EI, Teder RI, Vatolin ES, Kuntysh MF (1969) Properties of rocks and methods of their determination. Nedra, Moskva (in Russian)
Kwaśniewski M (1987) A new linear criterion of brittle failure for rocks. In: Herget H, Vongpaisal S (eds) Proc 6th Int Congr on Rock Mech, Montreal. Balkema, Rotterdam, 2:1031–1038
Kwaśniewski M (1989) Laws of brittle failure and of B–D transition in sandstones. In: Maury V, Fourmaintraux D (eds) Proc. ISRM-SPE Int Symp, Pau. Balkema, Rotterdam, 1:45–58
Kwaśniewski M, Szutkowski I (1988) Brittle fracture and plastic flow of dry and wet arenaceous and clay rocks from the Lublin Coal Basin in the conditions of triaxial compression. Prace Instytutu PBKiOP Politechniki Śląskiej, PB No. 206/456, Gliwice (in Polish)
Kwaśniewski M, Takahashi M (2006) Behavior of a sandstone under axi- and asymmetric compressive stress conditions. In: Leung CF, Zhou YX (eds) Rock mechanics in underground construction (Proceedings of the 4th Asian Rock Mechanics Symposium, Singapore, 8–10 November 2006). World Scientific Publishing Co. Pte. Ltd., Singapore, pp 320 (abstract) plus CD-ROM (full paper)
Kwaśniewski M, Takahashi M (2007) Effect of confining pressure, intermediate principal stress and minimum principal stress on the mechanical behavior of a sandstone. In: Ribeiro e Sousa L et al (eds) Proc 11th Congr of the ISMR, Lisbon, 9–13 July 2007. Taylor and Francis/Balkema, Leiden, 1:237–242
Kwaśniewski M, Pacha J, Oleksy S (1983) Triaxial strength of two mineralogic/diagenetic varieties of fine-mediumgrained carboniferous Pniówek and Anna sandstones. Zeszyty Naukowe Politechniki Śląskiej 778, Górnictwo 128:265–287 (in Polish)
Mogi K (1971a) Effect of the triaxial stress system on the failure of dolomite and limestone. Tectonophysics 11:111–127
Mogi K (1971b) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76(5):1255–1269
Mogi K (2007) Experimental rock mechanics. Taylor and Francis/Balkema, Leiden
Murrell SAF (1965) The effect of triaxial stress systems on the strength of rock at atmospheric temperatures. Geophys J R Astr Soc 10:231–281
von Kármán T (1911) Festigkeitsversuche unter allseitigem Druck. Zeitschrift des Vereines Deutscher Ingenieure 55(42):1749–1757
Zhang L (2008) A generalized three-dimensional Hoek–Brown strength criterion. Rock Mech Rock Eng 41:893–915
Zhang L, Zhu H (2007) Three-dimensional Hoek–Brown strength criterion for rocks. J Geotech Geoenviron Eng ASCE 133(9):1128–1135
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kwaśniewski, M. A New Approach to the Modeling of the Pressure Dependency of the Strength of Rocks. Rock Mech Rock Eng 44, 103–111 (2011). https://doi.org/10.1007/s00603-009-0080-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-009-0080-y