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Small strain stiffness anisotropy of natural sedimentary clays: review and a model

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Abstract

Very small strain stiffness anisotropy of sedimentary clays is investigated. First, a general formulation of transversely isotropic elastic model is summarised, followed by a description of its complete parameter identification using transversal and longitudinal wave velocity measurements. Then, an extensive experimental database from the literature is reviewed. A number of general trends in the anisotropy evolution is identified, based on which a model is developed describing the dependency of the ratio of in-plane and transversal very small strain shear moduli on the stress state and overconsolidation ratio. Subsequently, an empirical relation between the ratios of shear moduli and Young moduli is quantified. The most problematic tends to be the evaluation of Poisson ratios and evolution of stiffness anisotropy under general stress conditions. These issues remain to be investigated experimentally in future work.

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Notes

  1. The notion of very small strain stiffness represents stiffness measured in the strain range approximately below 10−5. In this strain range, the stiffness is approximately constant, independent of the strain magnitude [2, 6, 7].

References

  1. Addenbrooke T, Potts D, Puzrin A (1997) The influence of pre-failure soil stiffness on the numerical analysis of tunnel construction. Géotechnique 47(3):693–712

    Article  Google Scholar 

  2. Atkinson JH (2000) Non-linear soil stiffness in routine design. Géotechnique 50(5):487–508

    Article  Google Scholar 

  3. 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 

  4. Cho W, Finno RJ (2010) Stress–strain responses of block samples of compressible Chicago glacial clays. J Geotech Geoenviron Eng ASCE 136(1):178–188

    Article  Google Scholar 

  5. 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 

  6. Clayton CRI (2011) Stiffness at small strain: research and practice. Géotechnique 61(1):5–37

    Article  Google Scholar 

  7. Clayton CRI, Heymann G (2001) Stiffness of geomaterials at very small strains. Géotechnique 51(3):245–255

    Article  Google Scholar 

  8. Ezaoui A, DiBenedetto H (2009) Experimental measurements of the global anisotropic elastic behaviour of dry Hostun sand during triaxial tests, and effect of sample preparation. Géotechnique 57(7):621–635

    Article  Google Scholar 

  9. Franzius JN, Potts DM, Burland JB (2005) The influence of soil anisotropy and K 0 on ground surface movements resulting from tunnel excavation. Géotechnique 55(3):189–199

    Article  Google Scholar 

  10. Fu-Chen T (2010) Prediction of ground movement induced by excavation using the numerical method with the consideration of inherent stiffness anisotropy. PhD thesis, National Taiwan University of Science and Technology

  11. Gasparre A (2005) Advanced laboratory characterisation of London Clay. PhD thesis, University of London, Imperial College of Science, Technology and Medicine

  12. Gasparre A, Nishimura S, Minh NA, Coop MR, Jardine RJ (2007) The stiffness of natural London Clay. Géotechnique 57(1):33–47

    Article  Google Scholar 

  13. Giot R, Giraud A, Guillon T, Auvray C (2012) Three-dimensional poromechanical back analysis of the pulse test accounting for transverse isotropy. Acta Geotechnica 7:151–165

    Article  Google Scholar 

  14. Graham J, Houlsby GT (1983) Anisotropic elasticity of a natural clay. Géotechnique 33(2):165–180

    Article  Google Scholar 

  15. Greening PD, Nash DFT (2004) Frequency domain determination of G 0 using bender elements. Geotech Test J 27(3):288–294

    Google Scholar 

  16. Gunn MJ (1993) The prediction of surface settlement profiles due to tunnelling. In: Houlsby GT, Schofield AN (eds) Predictive soil mechanics. Proceedings of the Worth Memorial symposium, London. Thomas Telford, London, pp 304–316

  17. Jamiolkowski M, Lancellotta R, Lo Presti DCF (1999) Remarks on the stiffness at small strains of six Italian clays. In: Jamiolkowski L, Presti L (eds) Pre-failure deformation characteristics of geomaterials. Balkema, Rotterdam, pp 817–836

    Google Scholar 

  18. Jovičić V, Coop MR (1998) The measurement of stiffness anisotropy in clays with bender element tests in the triaxial apparatus. Geotech Test J 21(1):3–10

    Google Scholar 

  19. Kawaguchi T, Yamashita S, Kataoka S, Shibuya S, Kawajiri S (2008) Inherent and induced anisotropy of three natural sedimentary clays reflecting on the elastic shear modulus. In: Burns SE, Mayne PW, Santamarina JC (eds) Proceedings of 4th international symposium on deformation characteristics of geomaterials, Atlanta, pp 575–579

  20. Kim T, Finno RJ (2012) Anisotropy evolution and irrecoverable deformation in triaxial stress probes. J Geotech Geoenviron Eng ASCE 138(2):155–165

    Article  Google Scholar 

  21. Kung T-C, Ou C-Y (2004) Stress–strain characteristics of the Taipei silty clay at small strain. J Chin Inst Eng 27(7):1077–1080

    Article  Google Scholar 

  22. Kuwano R, Connolly TM, Kuwano J (1999) Shear stiffness anisotropy measured by multi-directional bender element transducers. In: Jamiolkowski L, Presti L (eds) Pre-failure deformation characteristics of geomaterials. Balkema, Rotterdam, pp 205–2012

    Google Scholar 

  23. Landon MM, DeGroot DJ (2006) Measurement of small strain shear modulus anisotropy on unconfined clay samples using bender elements. In: GeoCongress 2006: geotechnical engineering in the information technology age. doi:10.1061/40803(187)20. American Society of Civil Engineers

  24. Li Q (2013) Long-term settlement mechanisms of shield tunnels in Shanghai soft clay. PhD thesis, The Hong Kong University of Science and Technology

  25. Li Q, Ng CWW, Liu GB (2012) Determination of small-strain stiffness of Shanghai clay on prismatic soil specimen. Can Geotech J 49:986–993

    Article  Google Scholar 

  26. Lings ML, Pennington DS, Nash DFT (2000) Anisotropic stiffness parameters and their measurement in a stiff natural clay. Géotechnique 50(2):109–125

    Article  Google Scholar 

  27. Lubarda VA, Chen MC (2008) On the elastic moduli and compliances of transversely isotropic and orthotropic materials. J Mech Mater Struct 3(1):153–171

    Article  Google Scholar 

  28. Mavko G, Mukerji T, Dvorkin J (2009) The rock physics handbook: tools for seismic analysis of porous media, 2nd edn. Cambridge University Press, New York

    Book  Google Scholar 

  29. Mašín D (2012) Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotechnica. doi:10.1007/s11440-012-0199-y

  30. Mašín D (2012) Hypoplastic Cam-clay model. Géotechnique 62(6):549–553

    Article  Google Scholar 

  31. Mayne PW, Kulhawy FH (1982) K 0–OCR relationships in soil. Proc ASCE J Geotech Eng Div 108:851–872

    Google Scholar 

  32. Mitaritonna G, Amorosi A, Cotecchia F (2008) Elastic stiffness anisotropy of clay samples radially compressed along different stress ratio triaxial paths. In: Burns SE, Mayne PW, Santamarina JC (eds) Proceedings of 4th international symposium on deformation characteristics of geomaterials, Atlanta, pp 589–595

  33. Ng CWW, Li Q, Liu G (2013) Measurements of small-strain inherent stiffness anisotropy of intact Shanghai soft clay using bender elements. Chin J Geotech Eng 35(7):150–156

    Google Scholar 

  34. Ng WWC, Leung EHY (2007) Determination of shear wave velocities and shear moduli of completely decomposed tuff. J Geotech Geoenviron Eng ASCE 133(6):630–640

    Article  Google Scholar 

  35. Niemunis A, GrandasTavera CE, PradaSarmiento LF (2009) Anisotropic visco-hypoplasticity. Acta Geotechnica 4(4):293–314

    Article  Google Scholar 

  36. Nishimura S (2005) Laboratory study on anisotropy of natural London clay. PhD thesis, University of London, Imperial College of Science, Technology and Medicine

  37. Pennington DS, Nash DFT, Lings ML (1997) Anisotropy of G 0 shear stiffness in Gault Clay. Géotechnique 47(3):391–398

    Article  Google Scholar 

  38. Pickering DJ (1970) Anisotropic elastic parameters for soil. Géotechnique 20(3):271–276

    Article  Google Scholar 

  39. Piriyakul K (2006) Anisotropic stress–strain behaviour of Belgian Boom clay in the small strain region. PhD thesis, Ghent University

  40. Ratananikom W, Likitlersuang S, Yimsiri S (2013) An investigation of anisotropic parameters of Bangkok Clay from vertical and horizontal cut specimens. Geomech Geoeng Int J 8(1). doi:10.1080/17486025.2012.726746

  41. Raymond GP (1970) Discussion: stresses and displacements in a cross-anisotropic soil, by l. barden. Géotechnique 20(4):456–458

    Article  Google Scholar 

  42. Salager S, François B, Nuth M, Laloui L (2013) Constitutive analysis of the mechanical anisotropy of Opalinus Clay. Acta Geotechnica 8:137–154

    Article  Google Scholar 

  43. Santagata M, Germaine JT, Ladd CC (2005) Factors affecting the initial stiffness of cohesive soils. J Geotech Geoenviron Eng ASCE 131(4):430–441

    Article  Google Scholar 

  44. Shibuya S, Hwang SC, Mitachi T (1997) Elastic shear moduli of soft clays from shear-wave velocity measurement. Géotechnique 47(3):593–601

    Article  Google Scholar 

  45. Shirley DJ, Hampton LD (1978) Shear-wave measurements in laboratory sediments. J Acoust Soc Am 63(2):607–613

    Article  Google Scholar 

  46. Spencer AJM (1982) The formulation of constitutive equation for anisotropic solids. In: Boehler JP (eds) Mechanical behaviour of anisotropic solids, 2nd edn. Martinus Nijhoff Publishers, The Hague

    Google Scholar 

  47. Teachavorasinskun S, Lukkanaprasit P (2008) Stress induced and inherent anisotropy on elastic stiffness of soft clays. Soils Found 48(1):127–132

    Article  Google Scholar 

  48. Teng F-C, Ou C-Y, Chien S-C (2013) Investigations on stiffness anisotropy of soft clay with electro-osmosis chemical treatment. In: Coutinho Mayne (eds) Geotechnical and geophysical site characterisation 4. Taylor and Francis Group, pp 1551–1557

  49. Viggiani G, Atkinson JH (1995) Stiffness of fine-grained soil at very small strains. Géotechnique 45(2):245–265

    Article  Google Scholar 

  50. Wroth C, Houlsby G (1985) Soil mechanics—property characterisation, and analysis procedures. In: Proceedings of 11th conference on soil mechanics, San Francisco, vol 1, pp 1–55

  51. Yamashita S, Hori T, Suzuki T (2005) Anisotropic stress–strain behavior at small strains of clay by triaxial and bender element tests. In: Lade PV, Nakai T (eds) Proceedings of the second Japan–U.S. workshop on testing, modeling, and simulation in geomechanics, Kyoto, Japan; ASCE Geotechnical Special Publication 156, pp 44–57

  52. Yimsiri S, Soga K (2011) Cross-anisotropic elastic parameters of two natural stiff clays. Géotechnique 61(9):809–814

    Article  Google Scholar 

Download references

Acknowledgments

The research presented in this paper has been funded by the Grant P105/12/1705 of the Czech Science Foundation.

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  1. Faculty of Science, Charles University in Prague, Albertov 6, 12843, Prague 2, Czech Republic

    David Mašín & Josef Rott

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  1. David Mašín
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Correspondence to David Mašín.

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Mašín, D., Rott, J. Small strain stiffness anisotropy of natural sedimentary clays: review and a model. Acta Geotech. 9, 299–312 (2014). https://doi.org/10.1007/s11440-013-0271-2

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