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Shear fracture energies of stiff clays and shales

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Abstract

Fracture mechanics analysis of shear band propagation requires knowledge of the material’s shear fracture energy and its related properties such as the characteristic slip displacement. Yet these properties of stiff clays and shales have not been investigated systematically. This work characterizes and analyzes the shear fracture energies and characteristic slip displacements of various stiff clays and shales based on their triaxial compression data from the literature. A methodology originally developed for hard rocks was adopted for this purpose. Results show that the shear fracture energies of stiff clays and shales generally increase with the effective normal stress on the slip plane, varying by orders of magnitude—approximately from \(4\times 10^{1}\) to \(7\times 10^{3}\) J/m\(^{2}\)—in the range of effective normal stresses from \(10^{2}\) to \(10^{5}\) kPa. An empirical equation is presented for a first-order estimate of the shear fracture energy under a given effective normal stress. The characteristic slip displacements at the laboratory scale are calculated to be smaller than 6 mm, and they appear independent of the effective normal stress. Compared with their nominal values calculated without considering the change of normal stress in triaxial tests, the shear fracture energies are approximately 70% of the nominal values, whereas the characteristic slip displacements are nearly identical to the nominal ones.

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References

  1. Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394

    Article  Google Scholar 

  2. Vardoulakis I, Goldscheider M, Gudehus G (1978) Formation of shear bands in sand bodies as a bifurcation problem. Int J Numer Anal Methods Geomech 2(2):99–128

    Article  Google Scholar 

  3. Skempton AW (1964) Long-term stability of clay slopes. Géotechnique 14(2):77–102

    Article  Google Scholar 

  4. Bjerrum L (1967) Progressive failure in slopes of overconsolidated plastic clay and clay shales. J Soil Mech Found Div 93:1–49

    Article  Google Scholar 

  5. Bishop AW (1968). Progressive failure—with special reference to the mechanism causing it. In: Proceedings of the geotechnical conference, Vol. 2. Norwegian Geotechnical Institute, pp. 142–150

  6. Palmer AC, Rice JR (1973) The growth of slip surfaces in the progressive failure of over-consolidated clay. Proc R Soc Lond A Math Phys Sci 332(1591):527–548

    MATH  Google Scholar 

  7. Puzrin AM, Germanovich LN, Kim S (2004) Catastrophic failure of submerged slopes in normally consolidated sediments. Géotechnique 54(10):631–643

    Article  Google Scholar 

  8. Puzrin AM, Germanovich LN (2005) The growth of shear bands in the catastrophic failure of soils. Proc R Soc A Math Phys Eng Sci 461(2056):1199–1228

    MathSciNet  MATH  Google Scholar 

  9. Puzrin AM, Germanovich LN, Friedli B (2016) Shear band propagation analysis of submarine slope stability. Géotechnique 66(3):188–201

    Article  Google Scholar 

  10. Puzrin AM (2016) Simple criteria for ploughing and runout in post-failure evolution of submarine landslides. Can Geotech J 53(8):1305–1314

    Article  Google Scholar 

  11. Quinn P, Diederichs M, Rowe R, Hutchinson D (2011) A new model for large landslides in sensitive clay using a fracture mechanics approach. Can Geotech J 48(8):1151–1162

    Article  Google Scholar 

  12. Quinn P, Diederichs M, Rowe R, Hutchinson D (2012) Development of progressive failure in sensitive clay slopes. Can Geotech J 49(7):782–795

    Article  Google Scholar 

  13. Viesca RC, Rice JR (2012) Nucleation of slip-weakening rupture instability in landslides by localized increase of pore pressure. J Geophys Res Solid Earth 117(B3):1–21

    Article  Google Scholar 

  14. Fei F, Choo J (2020) A phase-field model of frictional shear fracture in geologic materials. Comput Methods Appl Mech Eng 369:113265

    Article  MathSciNet  Google Scholar 

  15. Fei F, Choo J (2021) Double-phase-field formulation for mixed-mode fracture in rocks. Comput Methods Appl Mech Eng 376:113655

    Article  MathSciNet  MATH  Google Scholar 

  16. Rice JR (1980) The mechanics of earthquake rupture. In: Physics of the earth’s interior. Italian Physical Society, pp 555–649

  17. Wong T-F (1982) Shear fracture energy of Westerly granite from post-failure behavior. J Geophys Res Solid Earth 87(B2):990–1000

    Article  Google Scholar 

  18. Wong T (1986) On the normal stress dependence of the shear fracture energy. In: Earthquake source mechanics, vol 37. American Geophysical Union, pp 1–11

  19. Liu Z, Rummel F (1990) Shear fracture energy of rock at high pressure and high temperature. Phys Chem Earth 17:99–109

    Article  Google Scholar 

  20. Abercrombie RE, Rice JR (2005) Can observations of earthquake scaling constrain slip weakening? Geophys J Int 162(2):406–424

    Article  Google Scholar 

  21. Viesca RC, Garagash DI (2015) Ubiquitous weakening of faults due to thermal pressurization. Nat Geosci 8(11):875–879

    Article  Google Scholar 

  22. Mitchell JK, Soga K (2005) Fundamentals of soil behavior. Wiley, Hoboken

    Google Scholar 

  23. Bishop AW, Green GE, Garga VK, Andresen A, Brown JD (1971) A new ring shear apparatus and its application to the measurement of residual strength. Géotechnique 21(4):273–328

    Article  Google Scholar 

  24. Mutlu O, Bobet A (2006) Slip propagation along frictional discontinuities. Int J Rock Mech Min Sci 43(6):860–876

    Article  Google Scholar 

  25. Favero V, Ferrari A, Laloui L (2018) Anisotropic behaviour of Opalinus Clay through consolidated and drained triaxial testing in saturated conditions. Rock Mech ICS Rock Eng 51(5):1305–1319

    Article  Google Scholar 

  26. Niandou H, Shao J, Henry J, Fourmaintraux D (1997) Laboratory investigation of the mechanical behaviour of Tournemire shale. Int J Rock Mech Min Sci 34(1):3–16

    Article  Google Scholar 

  27. Shi X, Herle I, Yin J (2018) Laboratory study of the shear strength and state boundary surface of a natural lumpy soil. J Geotech Geoenviron Eng 144(12):04018093

    Article  Google Scholar 

  28. Wong RCK (1998) Swelling and softening behaviour of La Biche shale. Can Geotech J 32(2):206–221

    Article  Google Scholar 

  29. Bishop AW, Webb DL, Lewin PI (1965) Undisturbed samples of London Clay from the Ashford Common shaft: strength-effective stress relationships. Géotechnique 15(1):1–31

    Article  Google Scholar 

  30. Lo K (1972) An approach to the problem of progressive failure. Can Geotech J 9(4):407–429

    Article  Google Scholar 

  31. Parry RHG (1972) Some properties of heavily overconsolidated Oxford Clay at a site near Bedford. Geotechnique 22(3):485–507

    Article  Google Scholar 

  32. Callisto L, Rampello S (2002) Shear strength and small-strain stiffness of a natural clay under general stress conditions. Géotechnique 52(8):547–560

    Article  Google Scholar 

  33. Burland J, Rampello S, Georgiannou V, Calabresi G (1996) A laboratory study of the strength of four stiff clays. Géotechnique 46(3):491–514

    Article  Google Scholar 

  34. Mandaglio M, Moraci N, Rosone M, Farulla CA (2016) Experimental study of a naturally weathered stiff clay. Can Geotech J 53(12):2047–2057

    Article  Google Scholar 

  35. Callisto L, Rampello S (2004) An interpretation of structural degradation for three natural clays. Can Geotech J 41(3):392–407

    Article  Google Scholar 

  36. Hardin BO, Richart FE Jr (1963) Elastic wave velocities in granular soils. J Soil Mech Found Eng 89:33–65

    Article  Google Scholar 

  37. Santamarina JC, Klein KA, Fam MA (2001) Soils and waves. Wiley, New York

    Google Scholar 

  38. Rampello S, Viggiani G, Amorosi A (1997) Small-strain stiffness of reconstituted clay compressed along constant triaxial effective stress ratio paths. Géotechnique 47(3):475–489

    Article  Google Scholar 

  39. Choo J, Jung Y-H, Chung C-K (2011) Effect of directional stress history on anisotropy of initial stiffness of cohesive soils measured by bender element tests. Soils Found 51(4):737–747

    Article  Google Scholar 

  40. Atkinson J (2007) Peak strength of overconsolidated clays. Géotechnique 57(2):127–135

    Article  Google Scholar 

  41. Barton N (1976) The shear strength of rock and rock joints. Int J Rock Mech Min Sci Geomech Abst 13(9):255–279

    Article  Google Scholar 

  42. Nielsen S, Spagnuolo E, Violay M, Smith S, Di Toro G, Bistacchi A (2016) G: Fracture energy, friction and dissipation in earthquakes. J Seismol 20(4):1187–1205

    Article  Google Scholar 

  43. A. W. Skempton and D. J. Petley (1968). The strength along structural discontinuities in stiff clays. In: Proceedings of the geotechnical conference Oslo, 1967, vol 2. Norwegian Geotechnical Institute, pp 29–46

  44. Dalguer L, Irikura K, Riera J (2003) Generation of new cracks accompanied by the dynamic shear rupture propagation of the 2000 Tottori (Japan) earthquake. Bull Seismol Soc Am 93(5):2236–2252

    Article  Google Scholar 

  45. Pulido N, Kubo T (2004) Near-fault strong motion complexity of the 2000 Tottori earthquake (Japan) from a broadband source asperity model. Tectonophysics 390(1–4):177–192

    Article  Google Scholar 

  46. Tinti E, Spudich P, Cocco M (2005) Earthquake fracture energy inferred from kinematic rupture models on extended faults. J Geophys Res Solid Earth 110(B12):1–25

    Article  Google Scholar 

  47. Burjánek J, Zahradník J (2007) Dynamic stress field of a kinematic earthquake source model with k-squared slip distribution. Geophys J Int 171(3):1082–1097

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the two anonymous reviewers for their insightful and constructive comments. Financial support for this work was provided by the Research Grants Council of Hong Kong through the Early Career Scheme (27205918), General Research Fund (17201419), and the NSFC/RGC Joint Research Scheme (N_CUHK430/16).

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Correspondence to Jinhyun Choo.

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Choo, J., Sohail, A., Fei, F. et al. Shear fracture energies of stiff clays and shales. Acta Geotech. 16, 2291–2299 (2021). https://doi.org/10.1007/s11440-021-01145-5

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