Book contents
- Fundamentals of Rock Physics
- Fundamentals of Rock Physics
- Copyright page
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Density and Porosity
- 3 Stresses in Rocks
- 4 Mechanical Strain and Elastic Moduli
- 5 Permeability of Rocks
- 6 Mechanical Properties of Fluid-Bearing Rocks
- 7 Acoustic Properties of Rocks
- 8 Electric Resistivity
- 9 Dielectric Properties
- 10 Magnetic Properties of Rocks
- 11 Thermal Properties of Rocks and Minerals
- 12 Radioactive Properties of Rocks
- Index
- References
3 - Stresses in Rocks
Published online by Cambridge University Press: 19 November 2021
Book contents
- Fundamentals of Rock Physics
- Fundamentals of Rock Physics
- Copyright page
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Density and Porosity
- 3 Stresses in Rocks
- 4 Mechanical Strain and Elastic Moduli
- 5 Permeability of Rocks
- 6 Mechanical Properties of Fluid-Bearing Rocks
- 7 Acoustic Properties of Rocks
- 8 Electric Resistivity
- 9 Dielectric Properties
- 10 Magnetic Properties of Rocks
- 11 Thermal Properties of Rocks and Minerals
- 12 Radioactive Properties of Rocks
- Index
- References
Summary
Scales of rock heterogeneity are nano≪micro ≪ meso ≪ macro. In order to estimate effective physical parameters by using an averaging procedure over a certain representative reference volume, estimations of effective physical parameters may be done by taking the Reuss or the Voigt mean values or using the upper and lower Hashin–Shtrikman bounds. The fracture number per unit length of a rock is correlated with the rock quality or RQD index. Autorun analysis of rock fractures in scanlines yields a consistent criterion of rock quality. The stress tensor is defined in a symmetric matrix. In diagonal form, the elements of the stress matrix are principal normal stresses. The Mohr’s circle in 2D and 3D is used to define normal and tangential stress in an arbitrarily oriented plane. The strength of rocks depends on modes of deformation according to the failure criteria after Mohr-Coulomb, Griffith, and Hoek and Brown. The ISRM standard and four point bending tests of rock strength are designed to determine yield strength. Fracturing and failure modes in rocks are considered according to tensile fracture models after Griffith, Dugdale, Barenblatt and critical tip opening displacement. Focus Box 3.1: Percolation models in rocks.
Keywords
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- Information
- Fundamentals of Rock Physics , pp. 66 - 112Publisher: Cambridge University PressPrint publication year: 2021
References
Literature
Berryman, J. G. (1995). Mixture theories for rock properties. In: Ahrens, T. J. (Ed.) Rock Physics and Phase Relations. A Handbook of Physical Constants. 3, 205–228. doi: 10.1029/RF003p0205.Google Scholar
Blumenauer, H. & Pusch, G. (1993). Technische Bruchmechanik. Deutsche Verlag für Grundstoffindustrie, Leipzig-Stattgart, p. 244.Google Scholar
Chen, Y-L., Wang, S-R., Ni, J., Azzam, R. & Fernández-steege, T. M. (2017). An experimental study of the mechanical properties of granite after high temperature exposure based on mineral characteristics. Engineering Geology 220, 234–242.CrossRefGoogle Scholar
Christensen, K. & Moloney, N. R. (2005). Complexity and Criticality. Imperial College Press Advanced Physics Texts. Imperial College Press, 365 pp. doi:10.1142/p365.CrossRefGoogle Scholar
Deere, D. U. (1963). Technical description of rock cores for engineering purposes. Rock Mechanics and Engineering Geology 1(1), 16–22.Google Scholar
Dresen, G. & Guéguen, Y. (2004). Damage and rock physical properties. In: Guéguen, Y. & Boutéca, M. (Eds.) Mechanics of Fluid-Saturated Rocks. International Geophysics Series. Elsevier, pp. 169–217.CrossRefGoogle Scholar
Eissa, E. A. & Şen, Z. (1991). Intact length correlation rock quality designation. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 28(5), 411–419.Google Scholar
Eshelby, J. D., Frank, F. C. & Nabarro, F. R. N. (1951). The equilibrium of linear arrays of dislocations. Philosophical Magazine 42, 351–364. doi: 10.1080/14786445108561060.Google Scholar
Evans, B., Fredrich, J. T. & Wong, T.‐F. (1990). The brittle‐ductile transition in rocks: Recent experimental and theoretical progress. In: Duba, A. G., Durham, W. B., Handin, J. W. & Wang, H. F. (Eds.) The Brittle‐Ductile Transition in Rocks. Geophysical Monograph Series. Vol. 56. American Geophysical Union, Washington DC, pp. 1–19.Google Scholar
Fett, T. & Munz, D. (1994). The relation between stress intensity factor and energy release rate in the presence of R-curve behaviour. Fatigue & Fracture of Engineeering Materials & Structures 17(10), 1157–1173.CrossRefGoogle Scholar
Gong, F., Zhang, L. & Wang, S. (2019). Loading rate effect of rock material with the direct tensile and three Brazilian disc tests. Hindawi Advances in Civil Engineering, Volume 2019, Article ID 6260351, 8 pages. https://doi.org/10.1155/2019/6260351.Google Scholar
Gouriet, K., Carrez, P. & Cordier, P. (2019). Ultimate mechanical properties of forsterite. Minerals 9(12), 787. doi: 10.3390/min9120787.CrossRefGoogle Scholar
Griffith, A. A. (1920). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 221, 163–198. http://doi.org/10.1098/rsta.1921.0006.Google Scholar
Guéguen, Y. & Palciauskas, V. (1994). Introduction to the Physics of Rocks. Princeton University Press, Princeton, NJ.Google Scholar
Herrmann, J., Rybacki, E., Sone, H. & Dresen, G. (2018). Deformation experiments on Bowland and Posidonia shale—Part I: strength and Young’s modulus at ambient and in situ pc–T conditions. Rock Mechanics and Rock Engineering 51, 3645–3666. https://doi.org/10.1007/s00603-018-1572-4.CrossRefGoogle Scholar
Hunt, A. G. (2005). Percolation theory and the future of hydrogeology. Hydrogeology Journal 13, 202–205. https://doi.org/10.1007/s10040-004-0405-6.CrossRefGoogle Scholar
Jaeger, J. C., Cook, N. G. W. & Zimmerman, R. W. (2007). Fundamentals of Rock Mechanics. Malden, MA: Blackwell Pub.Google Scholar
Jain, C., Korenaga, J. & Karato, S.-i. (2018). On the grain size sensitivity of olivine rheology. Journal of Geophysical Research: Solid Earth 123, 674–688. https://doi.org/10.1002/2017JB014847.CrossRefGoogle Scholar
Johnson, R. B. & DeGraff, J. V. (1988). Principles of Engineering Geology. New York: Wiley, p. 497.Google Scholar
Kimberley, J., Ramesh, K. T. & Barnouin, O. S. (2010). Visualization of the failure of quartz under quasi-static and dynamic compression. Journal of Geophysical Research 115, B08207. doi:10.1029/2009JB007006.CrossRefGoogle Scholar
Kovaleva, G. A. (1974). Mechanical properties of the principal rock-forming minerals of the Khibiny apatite – nepheline deposits. Soviet Mining Science 10, 533–537. https://doi.org/10.1007/BF02502964.CrossRefGoogle Scholar
Liu, Z., Zhang, S., Yang, J., Liu, J. Z., Yang, Y-L. & Zheng, Q-Sh. (2012). Interlayer shear strength of single crystalline graphite. Acta Mechanica Sinica 28, 978–982. https://doi.org/10.1007/s10409-012-0137-0.CrossRefGoogle Scholar
Lockner, D. A. & Beeler, N. M. (2002). Rock failure and earthquakes. International Geophysics 81 Part A, 505–537.Google Scholar
Lucian, C. & Wangwe, E. M. (2013). The usefulness of Rock Quality Designation (RQD) in determining strength of the rock. International Refereed Journal of Engineering and Science (IRJES) 2(9), 36–40.Google Scholar
Marder, M. & Fineberg, J. (1996). How things break. Physics Today 49(9): 24–29. https://doi.org/10.1063/1.881515.Google Scholar
Milton, G. W. (2002). The Theory of Composites. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge. 719 pp. https://doi.org/10.1017/CBO9780511613357.Google Scholar
Palmström, A. (1982). The volumetric joint count – a useful and simple measure of the degree of jointing. Proceedings of the International Congress of the IAEG, New Delhi, pp. V.221–228.Google Scholar
Priest, S. D. & Hudson, J. A. (1976). Discontinuity spacing in rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 13, 135–148.Google Scholar
Saberi, A. A. (2015). Recent advances in percolation theory and its application. Physics Reports 578, 1–32.CrossRefGoogle Scholar
Sahimi, M. (1995). Flow and Transport in Porous Media and Fractured Rocks. VCH, Weinheim, p. 482.Google Scholar
Şen, Z. (2000). Rock Quality Designation model formulation and simulation for correlated fracture intact lengths. Mathematical Geology 32(8), 985–999.CrossRefGoogle Scholar
Shang, J., Hencher, S. R. & West, L. J. (2016). Tensile strength of geological discontinuities including incipient bedding, rock joints and mineral veins. Rock Mechanics and Rock Engineering 49, 4213–4225. https://doi.org/10.1007/s00603-016-1041-x.CrossRefGoogle Scholar
Stauffer, D. & Aharony, A. (1994). Introduction to Percolation Theory, 2nd edn. Taylor & Francis, London.Google Scholar
Stowe, R. L. (1969). Strength and deformation properties of granite, basalt, limestone and tuff at various loading rates. Miscellaneous paper C-69-1. United States Army Engineer Waterways Experiment Station, USACE. Vicksburg, Mississippi.Google Scholar
Sun, Y., Shu, L., Lu, X., Liu, H., Zhang, X., Lin, A. & Kosaka, K. (2008). Recent progress in studies on the nano-sized particle layer in rock shear planes. Progress in Natural Science 18, 367–373.CrossRefGoogle Scholar
Taylor, G. (1934). The strength of rock salt. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 145(855), 405–415. http://www.jstor.org/stable/2935511.Google Scholar
Tullis, J. & Yund, R. (1992). The brittle-ductile transition in feldspar aggregates: An experimental study. International Geophysics 51, 89–117. https://doi.org/10.1016/S0074-6142(08)62816-8.CrossRefGoogle Scholar
Turban, L. & Guilmin, P. (1979). Correlated site percolation: Exact results on the Bethe lattice. Journal of Physics C: Solid State Physics 12, 961–968.Google Scholar
Wawersik, W. R. & Fairhurst, C. (1970). A study of brittle rock fracture in laboratory compression experiments. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 7, 561–575.Google Scholar
Weber, K. J. (1986). How heterogeneity affects oil recovery. In: Lake, L. W. and Carroll, H. B. J. (Eds.) Reservoir Characterization. Academy Press, Orlando, FL, pp. 487–544.CrossRefGoogle Scholar
Yang, G. & Park, S.-J. (2019). Deformation of single crystals, polycrystalline materials, and thin films: A review. Materials 12(2003), 1–18. doi:10.3390/ma12122003.Google ScholarPubMed
Zhang, L., Mao, X. Liu, R., Guo, X. & Ma, D. (2013). The mechanical properties of mudstone at high temperatures: An experimental study. Rock Mechanics and Rock Engineering 47 (4), 1479–1484.CrossRefGoogle Scholar
Zhou, J., Zhang, L., Yang, D., Braun, A. & Han, Z. (2017). Investigation of the quasi-brittle failure of Alashan granite viewed from laboratory experiments and grain-based discrete element modeling. Materials (Basel, Switzerland) 10(7), 835. https://doi.org/10.3390/ma10070835.CrossRefGoogle ScholarPubMed