Advertisement

Acta Geotechnica

, Volume 14, Issue 2, pp 329–345 | Cite as

A critical state constitutive model for clean and silty sand

  • X. Wei
  • J. YangEmail author
Research Paper

Abstract

The mechanical behavior of silty sand is highly dependent on the percentage of fines in addition to the packing density and confining pressure. Properly modeling the diverse behavior of silty sand remains an area of difficulty and uncertainty. This paper presents an attempt to formulate a critical state-based constitutive model for sand with varying fines content based on several new laboratory findings. A marked feature of the model is a unified description of the state-dependent elastic modulus as well as a unified description of plastic hardening modulus such that only one set of elastic and hardening parameters is required for sand with different fines contents. The model is calibrated and validated using the results from a structured experimental program. It shows that the model can produce reasonably good predictions for undrained shear responses of sand specimens under a range of void ratios, confining stresses and fines contents. In particular, it successfully predicts the laboratory observation that under otherwise similar conditions, the presence of non-plastic fines increases the liquefaction susceptibility of sand.

Keywords

Constitutive modeling Critical state Liquefaction Silty sands State parameter 

List of symbols

Ae

Fitting parameter of G using F(e)

ae

Fitting parameter of G in F(e)

Aψ

Fitting parameter of G using F(ψ)

aψ

Fitting parameter of G in F(ψ)

C0

Model parameter in Cr

Cr

Reduction factor for elastic shear modulus

D

Dilatancy

d0

Dilatancy parameter

dεq

Deviatoric strain increment

dεqe

Elastic deviatoric strain increment

dεqp

Plastic deviatoric strain increment

dεv

Volumetric strain increment

dεve

Elastic volumetric strain increment

dεvp

Plastic volumetric strain increment

e

Void ratio

e0

Initial void ratio prior to shearing (i.e., post-consolidation void ratio ec)

eΓ

Intercept of critical state line (CSL) in the e − (p′/Pa)ξ plane

F(e)

Void ratio function

f(X1, X2, X3…)

Function of X1, X2, X3

F(ψ)

State parameter function

FC

Fines content (%)

fc

Fines content in decimal

G

Elastic shear modulus

h, h1, h2

Hardening parameters

K

Elastic bulk modulus

k

Pressure exponent of modulus

k1

Model parameter in Cr

Kp

Plastic hardening modulus

L

Loading index

m

Dilatancy parameter

M

Stress ratio (η) at critical state

n

Hardening parameter

p′

Mean effective stress

pc

Post-consolidation pressure (i.e., initial mean effective stress)

Pa

Reference stress equaling to 1 atm

PSD

Particle size distribution

PTS

Phase transformation state

q

Deviatoric stress

R

Roundness of sand particle

Rcomb

Combined roundness

UIS

Undrained instability state

α

Model parameter in Kp

εq

Deviatoric strain

εqe

Elastic deviatoric strain

εqp

Plastic deviatoric strain

εv

Volumetric strain

εve

Elastic volumetric strain

εvp

Plastic volumetric strain

ζ

Accumulated plastic deviatoric strain

η

Stress ratio q/p′

ηpeak

Stress ratio (η) at peak state

ηPTS

Stress ratio (η) at phase transformation state

λc

Magnitude of the slope of CSL

ν

Poisson’s ratio

ξ

Pressure exponent of CSL formulation

φcs

Critical state friction angle

ψ

State parameter

ψ0

Initial state parameter prior to shearing

Notes

Acknowledgements

This work was supported by the Research Grants Council of Hong Kong through the General Research Fund (17250316, 17205717). This support is gratefully acknowledged.

References

  1. 1.
    Been K, Jefferies MG (1985) A state parameter for sands. Geotechnique 35(2):99–112Google Scholar
  2. 2.
    Borja RI, Andrade JE (2006) Critical state plasticity. Part VI: meso-scale finite element simulation of strain localization in discrete granular materials. Comput Methods Appl Mech Eng 195(37):5115–5140zbMATHGoogle Scholar
  3. 3.
    Fuentes W, Triantafyllidis T, Lizcano A (2012) Hypoplastic model for sands with loading surface. Acta Geotech 7(3):177–192Google Scholar
  4. 4.
    Gu X, Yang J, Huang M (2013) Laboratory measurements of small strain properties of dry sands by bender element. Soils Founds 53(5):735–745Google Scholar
  5. 5.
    Guo P, Su X (2007) Shear strength, interparticle locking, and dilatancy of granular materials. Can Geotech J 44(5):579–591Google Scholar
  6. 6.
    Huang YT, Huang AB, Kuo YC, Tsai MD (2004) A laboratory study on the undrained strength of a silty sand from Central Western Taiwan. Soil Dyn Earthq Eng 24(9–10):733–743Google Scholar
  7. 7.
    Iwasaki T, Tatsuoka F (1977) Effect of grain size and grading on dynamic shear moduli of sand. Soils Founds 17(3):19–35Google Scholar
  8. 8.
    Jefferies MG (1993) Nor-Sand: a simple critical state model for sand. Geotechnique 43(1):91–103Google Scholar
  9. 9.
    Jefferies MG, Been K (2006) Soil liquefaction: a critical state approach. Taylor & Francis, LondonGoogle Scholar
  10. 10.
    Lade PV, Yamamuro JA (1997) Effects of nonplastic fines on static liquefaction of sands. Can Geotech J 34(6):918–928Google Scholar
  11. 11.
    Li XS (2002) A sand model with state-dependent dilatancy. Geotechnique 52(3):173–186Google Scholar
  12. 12.
    Li XS, Dafalias YF (2000) Dilatancy for cohesionless soils. Geotechnique 50(4):449–460Google Scholar
  13. 13.
    Li XS, Dafalias YF (2012) Anisotropic critical state theory: role of fabric. J Eng Mech 138(3):263–275Google Scholar
  14. 14.
    Li XS, Wang Y (1998) Linear representation of steady-state line for sand. J Geotech Geoenviron Eng 124(12):1215–1217Google Scholar
  15. 15.
    Liang LB (2016) Static liquefaction of sand-fines mixtures with the presence of initial shear stress, M.Phil. Thesis, The University of Hong KongGoogle Scholar
  16. 16.
    Ling HI, Yang S (2006) Unified sand model based on the critical state and generalized plasticity. J Eng Mech 132(12):1380–1391Google Scholar
  17. 17.
    Manzari MT, Dafalias YF (1997) A critical state two-surface plasticity model for sands. Geotechnique 47(2):255–272Google Scholar
  18. 18.
    Murthy T, Loukidis D, Carraro J, Prezzi M, Salgado R (2007) Undrained monotonic response of clean and silty sands. Geotechnique 57(3):273–288Google Scholar
  19. 19.
    Ni Q, Tan TS, Dasari GR, Hight DW (2004) Contribution of fines to the compressive strength of mixed soils. Geotechnique 54(9):561–569Google Scholar
  20. 20.
    Papadimitriou AG, Bouckovalas GD, Dafalias YF (2001) Plasticity model for sand under small and large cyclic strains. J Geotech Geoenviron Eng 127(11):973–983Google Scholar
  21. 21.
    Pitman TD, Robertson PK, Sego DC (1994) Influence of fines on the collapse of loose sands. Can Geotech J 31(5):728–739Google Scholar
  22. 22.
    Potts DM, Zdravković L (2001) Finite element analysis in geotechnical engineering: theory. Thomas Telford, LondonGoogle Scholar
  23. 23.
    Rahman MM, Lo SCR, Dafalias YF (2014) Modelling the static liquefaction of sand with low-plasticity fines. Geotechnique 64(11):881–894Google Scholar
  24. 24.
    Simoni A, Houlsby GT (2006) The direct shear strength and dilatancy of sand–gravel mixtures. Geotech Geol Eng 24(3):523–549Google Scholar
  25. 25.
    Stamatopoulos CA, Lopez-Caballero F, Modaressi-Farahmand-Razavi A (2015) The effect of preloading on the liquefaction cyclic strength of mixtures of sand and silt. Soil Dyn Earthq Eng 78:189–200Google Scholar
  26. 26.
    Sze HY (2010) Initial shear and confining stress effects on cyclic behaviour and liquefaction resistance of sands, Ph.D. thesis. The University of Hong KongGoogle Scholar
  27. 27.
    Sze H, Yang J (2014) Failure modes of sand in undrained cyclic loading: impact of sample preparation. J Geotech Geoenviron Eng 140(1):152–169Google Scholar
  28. 28.
    Taiebat M, Dafalias YF (2008) SANISAND: simple anisotropic sand plasticity model. Int J Numer Anal Methods Geomech 32(8):915–948zbMATHGoogle Scholar
  29. 29.
    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):849–859Google Scholar
  30. 30.
    Wang G, Xie Y (2014) Modified bounding surface hypoplasticity model for sands under cyclic loading. J Eng Mech 140(1):91–101Google Scholar
  31. 31.
    Wei LM (2012) Static liquefaction and flow failure of sandy soils, Ph.D. thesis. The University of Hong KongGoogle Scholar
  32. 32.
    Wichtmann T, Triantafylidis T (2009) Influence of the grain-size distribution curve of quartz sand on the small-strain shear modulus Gmax. J Geotech Geoenviron Eng ASCE 135(10):1404–1418Google Scholar
  33. 33.
    Wichtmann T, Hernandez M, Triantafylidis T (2015) On the influence of a non-cohesive fines content on small strain stiffness, modulus degradation and damping of quartz sand. Soil Dyn Earthq Eng 69:103–114Google Scholar
  34. 34.
    Wood DM (1990) Soil behaviour and critical state soil mechanics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  35. 35.
    Xiao Y, Liu H, Chen Y, Chu J (2014) Strength and dilatancy of silty sand. J Geotech Geoenviron Eng 140(7):06014007Google Scholar
  36. 36.
    Yang J (2002) Non-uniqueness of flow liquefaction line for loose sand. Geotechnique 52(10):757–760Google Scholar
  37. 37.
    Yang J, Li X (2004) State-dependent strength of sands from the perspective of unified modeling. J Geotech Geoenviron Eng 130(2):186–198Google Scholar
  38. 38.
    Yang J, Liu X (2016) Shear wave velocity and stiffness of sand: the role of non-plastic fines. Geotechnique 66(6):500–514Google Scholar
  39. 39.
    Yang J, Luo XD (2015) Exploring the relationship between critical state and particle shape for granular materials. J Mech Phys Solids 84:196–213Google Scholar
  40. 40.
    Yang J, Sze HY (2011) Cyclic behaviour and resistance of saturated sand under non-symmetrical loading conditions. Geotechnique 61(1):59–73Google Scholar
  41. 41.
    Yang J, Wei LM (2012) Collapse of loose sand with the addition of fines: the role of particle shape. Geotechnique 62(12):1111–1125Google Scholar
  42. 42.
    Yang J, Wei LM, Dai BB (2015) State variables for silty sands: global void ratio or skeleton void ratio? Soils Founds 55(1):99–111Google Scholar
  43. 43.
    Yang Z, Li X, Yang J (2008) Quantifying and modelling fabric anisotropy of granular soils. Geotechnique 58(4):237–248Google Scholar
  44. 44.
    Zhang JM, Wang G (2012) Large post-liquefaction deformation of sand, part I: physical mechanism, constitutive description and numerical algorithm. Acta Geotech 7(2):69–113Google Scholar
  45. 45.
    Zhao J, Gao Z (2016) Unified anisotropic elastoplastic model for sand. J Eng Mech 142(1):04015056Google Scholar
  46. 46.
    Zlatović S, Ishihara K (1995) On the influence of nonplastic fines on residual strength. In: Proceedings of the 1st international conference earthquake geotechnical engineering, Tokyo, pp 239–24Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringThe University of Hong KongHong KongChina

Personalised recommendations