Predicting undrained static response of sand with non-plastic fines in terms of equivalent granular state parameter

  • D. D. PorcinoEmail author
  • V. Diano
  • T. Triantafyllidis
  • T. Wichtmann
Research Paper


The influence of non-plastic fines on undrained monotonic behaviour of sand was investigated over a wide range of fines content (FC = 0–40%), global void ratio and initial mean effective stress (\( p_{0}^{\prime } \) = 100 kPa to 500 kPa), by performing triaxial compression tests with isotropic and anisotropic consolidation. For the sand–silt mixtures, steady-state line in the e − log(p′) space was found to be dependent on fines content with the existence of a limiting fines content, which defines the transition from a “fines in sand” to a “sand in fines” soil fabric. It is demonstrated that by means of the concept of equivalent granular void ratio, e*, all steady-state/critical state data points can be well described by a unique relationship in the e* − log(p′) space called the equivalent steady-state line (EG-SSL), regardless of fines content. The equivalent granular state parameter (ψ*), defined in terms of e*, and the EG-SSL can be effectively adopted for predicting the undrained monotonic behaviour of sand–silt mixtures and the onset of static instability, irrespective of fines content and initial state of the sand–silt mixtures.


Critical state Equivalent granular state parameter Instability Non-plastic fines Sands 



  1. 1.
    ASTM D4253 (2000) Standard test methods for maximum index density and unit weight of soils using a vibratory table. American Society of Testing and Materials, annual book of ASTM standards, 1–14Google Scholar
  2. 2.
    ASTM D4254 (2000) Standard test methods for minimum index density and unit weight of and calculation of relative density. American Society of Testing and Materials, annual book of ASTM standards, 1–9Google Scholar
  3. 3.
    Been K, Jefferies MG (1985) A state parameter for sands. Geotechnique 35(2):99–112. CrossRefGoogle Scholar
  4. 4.
    Been K, Jefferies MG, Hachey J (1991) The critical state of sands. Geotechnique 41(3):365–381. CrossRefGoogle Scholar
  5. 5.
    Benahmed N, Nguyen T, Hicher P, Nicolas M (2015) An experimental investigation into the effects of low plastic fines content on the behaviour of sand/silt mixtures. Eur J Environ Civ Eng 19:109–128. CrossRefGoogle Scholar
  6. 6.
    Bobei DC, Lo SR, Wanatowski D, Gnanendran CT, Rahman MM (2009) A modified state parameter for characterizing static liquefaction of sand with fines. Can Geotech J 46(3):281–295. CrossRefGoogle Scholar
  7. 7.
    Carraro JAH, Murthy TG, Loukidis D, Salgado R, Prezzi M (2007) Undrained monotonic response of clean and silty sands. Géotechnique 57(3):273–288. CrossRefGoogle Scholar
  8. 8.
    Castro G, Poulos SJ (1977) Factors affecting liquefaction and cyclic mobility. J Geotech Eng Div ASCE 103(GT6):501–516Google Scholar
  9. 9.
    Chu J, Leong WK (2002) Effect of fines on instability behaviour of loose sand. Geotechnique 52(10):751–755. CrossRefGoogle Scholar
  10. 10.
    Dash HK, Sitharam TG (2011) Undrained monotonic response of sand-silt mixtures: effects of non-plastic fines. Geomech Geoeng Int J 6(1):47–58. CrossRefGoogle Scholar
  11. 11.
    Diano V (2017) Influence of non-plastic fines on the undrained monotonic and cyclic behaviour of silty sands. PhD thesis, Mediterranean University of Reggio Calabria, ItalyGoogle Scholar
  12. 12.
    Finno RJ, Rechenmacher AL (2003) Effects of consolidation history on critical state of sand. J Geotech Geoenviron Eng 129(4):350–360. CrossRefGoogle Scholar
  13. 13.
    Forie AB, Tshabalala L (2005) Initiation of static liquefaction and the role of K0 consolidation. Can Geotech J 42(3):892–906. CrossRefGoogle Scholar
  14. 14.
    Hazirbaba K (2005) Pore pressure generation characteristics of sands and silty sands: a strain approach. PhD Thesis, University of Texas, Austin, p 232Google Scholar
  15. 15.
    Huang YT, Huang AB, Chen KY, Dou TM (2004) A laboratory study on the undrained strength of a silty sand from central western Taiwan. J Soil Dyn Earthq Eng 24(9–10):733–743. CrossRefGoogle Scholar
  16. 16.
    Ishihara K (1993) Liquefaction and flow failure during earthquakes. Geotechnique 43(3):351–415. CrossRefGoogle Scholar
  17. 17.
    Karim ME, Alam MJ (2016) Undrained monotonic and cyclic response of sand–silt mixtures. Int J Geotech Eng 10(3):223–235. CrossRefGoogle Scholar
  18. 18.
    Karim ME, Alam MJ (2017) Effect of nonplastic silt content on undrained shear strength of sand–silt mixtures. Int J Geo-Eng 8:14. CrossRefGoogle Scholar
  19. 19.
    Kato S, Ishihara K, Towhata I (2001) Undrained shear characteristics of saturated sand under anisotropic consolidation. Soils Found 41(1):1–11. CrossRefGoogle Scholar
  20. 20.
    Lade PV (1992) Static instability and liquefaction of loose fine sandy slopes. J Geotech Geoenviron Eng 118(1):51–71. CrossRefGoogle Scholar
  21. 21.
    Lade PV, Yamamuro JA (1997) Effects of non-plastic fines on static liquefaction of sands. Can Geotech J 34(6):918–928. CrossRefGoogle Scholar
  22. 22.
    Lade PV, Liggio CD, Yamamuro JA (1998) Effects of non-plastic fines on minimum and maximum void ratios of sand. Geotech Test J 21(4):336–347. CrossRefGoogle Scholar
  23. 23.
    Lashkari A (2016) Prediction of flow liquefaction instability of clean and silty sands. Acta Geotech 11(5):987–1014. MathSciNetCrossRefGoogle Scholar
  24. 24.
    Lee KL, Seed HB (1967) Drained strength characteristics of sands. J Soil Mech Found Div 93(SM6):117–141Google Scholar
  25. 25.
    McGeary RK (1961) Mechanical packing of spherical particles. J Am Ceram Soc 44(10):513–522CrossRefGoogle Scholar
  26. 26.
    Murthy TG, Loukidis D, Carraro JAH, Prezzi M, Salgado R (2007) Undrained monotonic response of clean and silty sands. Geotechnique 57(3):273–288. CrossRefGoogle Scholar
  27. 27.
    Naeini SA, Baziar MH (2004) Effect of fines content on steady-state strength of mixed and layered samples of a sand. Soil Dyn Earthq Eng 24(3):181–187. CrossRefGoogle Scholar
  28. 28.
    Ni Q, Tan TS, Dasari GR, Hight DW (2004) Contribution of fines to the compressive strength of mixed soils. Geotechnique 54(9):561–569. CrossRefGoogle Scholar
  29. 29.
    Papadopoulou A, Tika T (2008) The effect of fines on critical state and liquefaction resistance characteristics of non-plastic silty sands. Soils Found 48:713–725. CrossRefGoogle Scholar
  30. 30.
    Phan VTA, Hsiao DH, Nguyen PTL (2016) Effects of fines contents on engineering properties of sand-fines mixtures. Proc Eng 142:213–220. CrossRefGoogle Scholar
  31. 31.
    Porcino DD, Diano V (2017) The influence of non-plastic fines on pore water pressure generation and undrained shear strength of sand-silt mixtures. Soil Dyn Earthq Eng 101:311–321. CrossRefGoogle Scholar
  32. 32.
    Rabbi ATMZ, Rahman M, Cameron DA (2018) Undrained behavior of silty sand and the role of isotropic and K0 consolidation. J Geotech Geoenviron Eng 144(4):04018014. CrossRefGoogle Scholar
  33. 33.
    Rahman MM, Lo SR (2008) The prediction of equivalent granular steady state line of loose sand with fines. Geomech Geoeng 3(3):179–190. CrossRefGoogle Scholar
  34. 34.
    Rahman MM, Lo SR (2012) Predicting the onset of static liquefaction of loose sand with fines. J Geotech Geoenviron Eng 138(8):1037–1041. CrossRefGoogle Scholar
  35. 35.
    Rahman MM, Lo SR (2014) Undrained behaviour of sand-fines mixtures and their parameter. J Geotech Geoenviron Eng 140(7):04014036. CrossRefGoogle Scholar
  36. 36.
    Rahman MM, Lo SR, Baki MAL (2011) Equivalent granular state parameter and undrained behaviour of sand-fines mixtures. Acta Geotech 6(4):183–194. CrossRefGoogle Scholar
  37. 37.
    Rahman MM, Lo SR, Dafalias YF (2014) Modelling the static liquefaction of sand with low-plasticity fines. Geotechnique 64(1):881–894. CrossRefGoogle Scholar
  38. 38.
    Rees S (2010) Effects of fines on the undrained behaviour of Christchurch sandy soils. PhD thesis, University of Canterbury, Christchurch, New ZealandGoogle Scholar
  39. 39.
    Riemer MF, Seed RB (1997) Factors affecting apparent position of steady-state line. J Geotech Geoenviron Eng 123(3):281–288. CrossRefGoogle Scholar
  40. 40.
    Sladen JA, D’Hollander RD, Krahn J (1985) The liquefaction of sands, a collapse surface approach. Can Geotech J 22(4):564–578. CrossRefGoogle Scholar
  41. 41.
    Thevanayagam S (1998) Effect of fines and confining stress on undrained shear strength of silty sands. J Geotech Geoenviron Eng 124(6):479–491. CrossRefGoogle Scholar
  42. 42.
    Thevanayagam S (2007) Intergrain contact density indices for granular mixes-I: framework. Earthq Eng Eng Vib 6(2):123–134. CrossRefGoogle Scholar
  43. 43.
    Thevanayagam S, Shenthan T, Mohan S, Liang J (2002) Undrained fragility of clean sands, silty sands, and sandy silts. J Geotech Geoenviron Eng 128(10):849–859. CrossRefGoogle Scholar
  44. 44.
    Yamamuro JA, Lade PV (1997) Static liquefaction of very loose sands. Can Geotech J 34:905–917CrossRefGoogle Scholar
  45. 45.
    Yamamuro JA, Lade PV (1998) Steady-state concepts and static liquefaction of silty sands. J Geotech Geoenviron Eng 124(9):868–877. CrossRefGoogle Scholar
  46. 46.
    Yang J, Wei LM (2012) Collapse of loose sand with the addition of fines: the role of particle shape. Géotechnique 62(12):111–1125. CrossRefGoogle Scholar
  47. 47.
    Yang SL, Sandven R, Grande L (2006) Steady-state lines of sand-silt mixtures. Can Geotech J 43(11):1213–1219. CrossRefGoogle Scholar
  48. 48.
    Yang J, Wei LM, Dai BB (2015) State variables for silty sands: global void ratio or skeleton void ratio? Soils Found 55(1):99–111. CrossRefGoogle Scholar
  49. 49.
    Zuo L, Baudet BA (2015) Determination of the transitional fines content of sand-non plastic fines mixtures. Soils Found 55(1):213–219. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department DICEAMUniversity “Mediterranea” of Reggio CalabriaReggio CalabriaItaly
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Bauhaus-Universität WeimarWeimarGermany

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