Acta Geotechnica

, Volume 10, Issue 1, pp 1–14 | Cite as

Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales

  • Kane C. Bennett
  • Lucas A. Berla
  • William D. Nix
  • Ronaldo I. Borja
Research Paper


Nanoindentation tests, spanning various length scales ranging from 200 nm to 5 μm deep, were performed on a sample of organic-rich Woodford shale in both the bedding plane normal and bedding plane parallel directions. Focused ion beam milling, scanning electron microscopy, and energy dispersive X-ray spectroscopy were utilized to characterize the shale at the scale of the nanoindentation testing as being comprised predominantly of clay and other silicate minerals suspended in a mixed organic/clay matrix. The nanoindentation tests reveal the mechanical properties of the relatively homogeneous constituent materials as well as those of the highly heterogeneous composite material. Loads on the order of a few millinewtons produced shallower indents and demonstrated the elastic–plastic deformation response of the constituent materials, whereas higher loads of as much as a few hundred millinewtons produced deeper indents revealing the response of the composite matrix. In both cases, significant creep was observed. We use nonlinear finite element modeling utilizing an isotropic critical state theory with creep to capture the indentation response by calibrating plastic material parameters to the laboratory measurements. The simulations provide a means of extracting plastic material parameters from the nanoindentation measurements and reveal the capabilities as well as limitations of an isotropic model in capturing the response of an inherently anisotropic material.


Anisotropy Creep FIB-SEM Heterogeneity Nanoindentation Shale 



This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program, under Award Number DE-FG02-03ER15454. L.A.B. and W.D.N. gratefully acknowledge support from the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-FG02-04ER46163. Part of this work was performed at the Stanford Nano Shared Facilities, and the authors are grateful for their training and support. The first author is grateful for support from the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. The authors wish to thank Dr. Younane N. Abousleiman of the University of Oklahoma for providing samples of Woodford shale, and Dr. Cindy Ross of Stanford’s Department of Energy Resource Engineering for assistance in preparing the samples.


  1. 1.
    Abaqus (2011) Abaqus documentation. Technical report, Dassault Systems, Providence, RI, USAGoogle Scholar
  2. 2.
    Abousleiman YN, Hoang SK, Liu C (2014) Anisotropic porothermoelastic solution and hydro-thermal effects on fracture width in hydraulic fracturing. Int J Numer Anal Methods Geomech 38(5):493–517CrossRefGoogle Scholar
  3. 3.
    Abousleiman Y, Tran M, Hoang S, Bobko C, Ortega A, Ulm F (2007) Geomechanics field characterization of Woodford shale: the next gas play. In: Proceedings—SPE annual technical conference and exhibition, Anaheim, CA, USA, pp 2127–2140Google Scholar
  4. 4.
    Arson C, Pereira JM (2013) Influence of damage on pore size distribution and permeability of rocks. Int J Numer Anal Methods Geomech 37(8):810–831CrossRefGoogle Scholar
  5. 5.
    Barthélémy JF, Souque C, Daniel JM (2013) Nonlinear homogenization approach to the friction coefficient of a quartz-clay fault gouge. Int J Numer Anal Methods Geomech 37(13):1948–1968CrossRefGoogle Scholar
  6. 6.
    Bennett R, O’Brien N, Hulbert M (1991) Determinants of clay and shale microfabric signatures: processes and mechanisms. In: Bennett R, Bryant W, Hulbert M (eds) Microstructure of fine-grained sediments: from Mud to Shale. Springer, New YorkCrossRefGoogle Scholar
  7. 7.
    Boggs S (2009) Petrology of sedimentary rocks. Cambridge University Press, Cambridge CrossRefGoogle Scholar
  8. 8.
    Bornert M, Vales F, Gharbi H, Minh D (2010) Multiscale full-field strain measurements for micromechanical investigations of the hydromechanical behavior of clayey rocks. Strain 46:33–46CrossRefGoogle Scholar
  9. 9.
    Brooks Z, Ulm FJ, Einstein HH (2013) Environmental scanning electron microscopy (ESEM) and nanoindentation investigation of the crack tip process zone in marble. Acta Geotech 8(3):223–245CrossRefGoogle Scholar
  10. 10.
    Cardott BJ (2012) Thermal maturity of Woodford Shale gas and oil plays, Oklahoma, USA. Int J Coal Geol 103:109–119CrossRefGoogle Scholar
  11. 11.
    Curtis M, Ambrose R, Sondergeld CH, Rai C (2011) Transmission and scanning electron microscopy investigation of pore connectivity of gas shales on the nanoscale. In: SPE North American unconventional gas conference and exhibition, Woodlands, TXGoogle Scholar
  12. 12.
    Day-Stirrat R, Dutton S, Millken K, Loucks R, Aplin A, Hillier S, van der Pluijm B (2010) Fabric anisotropy induced by primary depositional variations in the silt: clay ratio in two fine-grained slope fan complexes: Texas gulf coast and northern north sea. Sediment Geol 226:42–53CrossRefGoogle Scholar
  13. 13.
    Deirieh A, Ortega JA, Ulm FJ, Abousleiman Y (2012) Nanochemomechanical assessment of shale: a coupled WDS-indentation analysis. Acta Geotech 7(4):271–295CrossRefGoogle Scholar
  14. 14.
    Dewers T, Heath J, Ewy R, Duranti L (2012) Three-dimensional pore networks and transport properties of a shale gas formation determined from focused ion beam serial imaging. Int J Oil Gas Coal Technol 5(2–3):229–248CrossRefGoogle Scholar
  15. 15.
    Ewy RT (2014) Shale swelling/shrinkage and water content change due to imposed suction and due to direct brine contact. Acta Geotech 9:869–886CrossRefGoogle Scholar
  16. 16.
    Foster CD, Mohammad Nejad T (2013) Embedded discontinuity finite element modeling of fluid flow in fractured porous media. Acta Geotech 8(1):49–57CrossRefGoogle Scholar
  17. 17.
    Fu P, Johnson SM, Carrigan CR (2013) An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks. Int J Numer Anal Methods Geomech 37(14):2278–2300CrossRefGoogle Scholar
  18. 18.
    Hall MR, Mooney SJ, Sturrock C, Matelloni P, Rigby SP (2013) An approach to characterisation of multi-scale pore geometry and correlation with moisture storage and transport coefficients in cement-stabilised soils. Acta Geotech 8(1):67–79CrossRefGoogle Scholar
  19. 19.
    Hay J, Sondergeld CH (2010) Mechanical testing of shale by instrumented nanoindentation. Agilent Technologies App Note 5990-5816EN 1-8Google Scholar
  20. 20.
    He Z, Caratini G, Dormieux L, Kondo D (2013) Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects. Int J Numer Anal Methods Geomech 37(18):3213–3236CrossRefGoogle Scholar
  21. 21.
    Hiller S (2006) Appendix a. Mineralogical and chemical data. Geological Society, London, Engineering Geology Special Publications, vol 21, pp 449–459Google Scholar
  22. 22.
    Hu DW, Zhou H, Shao JF (2013) An anisotropic damage-plasticity model for saturated quasi-brittle materials. Int J Numer Anal Meth Geomech 37(12):1691–1710CrossRefGoogle Scholar
  23. 23.
    Hu DW, Zhang F, Shao JF (2014) Experimental study of poromechanical behavior of saturated claystone under triaxial compression. Acta Geotech 9(2):207–214CrossRefGoogle Scholar
  24. 24.
    Ingram R (1953) Fissility of mudrocks. Geol Soc Am Bull 64:869–878CrossRefGoogle Scholar
  25. 25.
    ISO-14577 (2002) Metallic materials—instrumented indentation test for hardness and materials parametersGoogle Scholar
  26. 26.
    Karim MR, Oka F, Krabbenhoft K, Leroueil S, Kimoto S (2013) Simulation of long-term consolidation behavior of soft sensitive clay using an elasto-viscoplastic constitutive model. Int J Numer Anal Methods Geomech 37(16):2801–2824Google Scholar
  27. 27.
    Kohli A, Zoback M (1983) Frictional properties of shale reservoir rocks. J Geophys Res Solid Earth 118:1–17Google Scholar
  28. 28.
    Kumar V (2012) Geomechanical characterization of shale using nano-indentation. Ph.D. thesis, OK UniversityGoogle Scholar
  29. 29.
    Lee S, Hyder L, Alley P (1991) Microstructural and mineralogical characterization of selected shales in support of nuclear waste repository studies. In: Bennett R, Bryant W, Hulbert M (eds) Microstructure of fine-grained sediments: from Mud to Shale. Springer, New York, NYGoogle Scholar
  30. 30.
    Liu F, Borja RI (2013) Extended finite element framework for fault rupture dynamics including bulk plasticity. Int J Numer Anal Methods Geomech 37(18):3087–3111CrossRefGoogle Scholar
  31. 31.
    Lonardelli I, Wenk H, Ren Y (2007) Preferred orientation and elastic anisotropy in shales. Geophysics 72(2):D33–D40CrossRefGoogle Scholar
  32. 32.
    Lucas B, Oliver W, Swindeman J (1998) The dynamics of frequency-specific, depth-sensing indentation testing. In: In: Materials research society symposium proceedings vol 522, pp 3–14Google Scholar
  33. 33.
    Nedjar B, Le Roy R (2013) An approach to the modeling of viscoelastic damage. Application to the long-term creep of gypsum rock materials. Int J Numer Anal Methods Geomech 37(9):1066–1078CrossRefGoogle Scholar
  34. 34.
    Pettijohn F (1975) Sedimentary rocks, 3rd edn. Harper and Row Publishers, New York, NYGoogle Scholar
  35. 35.
    Pietruszczak S, Guo P (2013) Description of deformation process in inherently anisotropic granular materials. Int J Numer Anal Methods Geomech 37(5):478–490CrossRefGoogle Scholar
  36. 36.
    Powell J, Take W, Siemens G, Remenda V (2012) Time-dependent behavior of the Bearpaw Shale on oedometric loading and unloading. Can Geotech J 49:427–441CrossRefGoogle Scholar
  37. 37.
    Salager S, Francois B, Nuth M, Laloui L (2013) Constitutive analysis of the mechanical anisotropy of Opalinus clay. Acta Geotech 8(2):137–154CrossRefGoogle Scholar
  38. 38.
    Schaedlich B, Schweiger HF (2013) A multilaminate constitutive model accounting for anisotropic small strain stiffness. Int J Numer Anal Methods Geomech 37(10):1337–1362CrossRefGoogle Scholar
  39. 39.
    Shaw D, Weaver C (1965) The mineralogical composition of shales. J Sediment Pet 35(1):213–222Google Scholar
  40. 40.
    Shim S, Oliver WC, Pharr GM (2005) A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculation. In: Materials research society symposium proceedings vol 841, pp 39–43Google Scholar
  41. 41.
    Sondergeld C, Ambrose R, Rai C, Moncrieff J (2010) Micro-structural studies of gas shales. In: Proceedings of SPE unconventional gas conference, Pittsburgh, PA, USAGoogle Scholar
  42. 42.
    Sarris E, Papanastasiou P (2013) Numerical modeling of fluid-driven fractures in cohesive poroelastoplastic continuum. Int J Numer Anal Methods Geomech 37(12):1822–1846CrossRefGoogle Scholar
  43. 43.
    Sone H, Zoback M (2013) Mechanical properties of shale-gas reservoir rocks—part 2: ductile creep, brittle strength, and their relation to the elastic modulus. Can Geotech J 78:D393–D402Google Scholar
  44. 44.
    Tian H, Xu T, Wang F, Patil VV, Sun Y, Yue G (2014) A numerical study of mineral alteration and self-sealing efficiency of a caprock for CO2 geological storage. Acta Geotech 9(1):87–100CrossRefGoogle Scholar
  45. 45.
    Tran HTT, Wong H, Dubujet P, Doanh T (2014) Simulating the effects of induced anisotropy on liquefaction potential using a new constitutive model. Int J Numer Anal Methods Geomech 38(10):1013–1035CrossRefGoogle Scholar
  46. 46.
    Ulm F, Aboussleiman Y (2006) The nanogranular nature of shale. Acta Geotech 1(2):77–88CrossRefGoogle Scholar
  47. 47.
    Valcke S, Casey M, Lloyd G, Kendall J, Fisher Q (2006) Lattice preferred orientation and seismic anisotropy in sedimentary rocks. Geopys J Int 166:652–666CrossRefGoogle Scholar
  48. 48.
    Vallin V, Pereira JM, Fabbri A, Wong H (2013) Numerical modelling of the hydro-chemo-mechanical behaviour of geomaterials in the context of CO2 injection. Int J Numer Anal Methods Geomech 37(17):3052–3069CrossRefGoogle Scholar
  49. 49.
    Vernik L, Nur A (1992) Ultrasonic velocity and anisotropy of hydrocarbon source rocks. Geophysics 57(5):727–735CrossRefGoogle Scholar
  50. 50.
    Vitone C, Viggiani G, Cotecchia F, Hall SA (2013b) Localized deformation in intensely fissured clays studied by 2D digital image correlation. Acta Geotech 8(3):247–263CrossRefGoogle Scholar
  51. 51.
    Vu MN, Pouya A, Seyedi DM (2014) Theoretical and numerical study of the steady-state flow through finite fractured porous media. Int J Numer Anal Methods Geomech 38(3):221–235CrossRefGoogle Scholar
  52. 52.
    White JA (2014) Anisotropic damage of rock joints during cyclic loading: constitutive framework and numerical integration. Int J Numer Anal Methods Geomech 38(10):1036–1057CrossRefGoogle Scholar
  53. 53.
    Xie H, Li X, Fang Z, Wang Y, Li Q, Shi L, Bai B, Wei N, Hou Z (2014) Carbon geological utilization and storage in China: current status and perspectives. Acta Geotech 9(1):7–27CrossRefGoogle Scholar
  54. 54.
    Yin ZY, Xu Q, Hicher PY (2013b) A simple critical-state-based double-yield-surface model for clay behavior under complex loading. Acta Geotech 8(5):509–523CrossRefGoogle Scholar
  55. 55.
    Zheng P, Ding B, Zhang W, Zhao SX, Zhu Y (2014) Dynamic response to fluid extraction from a poroelastic half-space. Int J Numer Anal Methods Geomech 38(7):661–678CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Kane C. Bennett
    • 1
  • Lucas A. Berla
    • 2
  • William D. Nix
    • 2
  • Ronaldo I. Borja
    • 1
  1. 1.Department of Civil and Environmental EngineeringStanford UniversityStanfordUSA
  2. 2.Department of Materials Science and EngineeringStanford UniversityStanfordUSA

Personalised recommendations