Acta Geotechnica

, Volume 14, Issue 6, pp 1757–1783 | Cite as

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

  • Dan Chang
  • Yuanming LaiEmail author
  • Fan Yu
Research Paper


The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na2SO4 contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.


Elastoplastic incremental constitutive model Frozen saline sandy soil Particle breakage Plastic mechanism Pressure melting 



This work was supported by National Key Research and Development Program of China (Grant No. 2018YFC0809605), Key Research Program of Frontier Sciences of Chinese Academy of Sciences (Grant No. QYZDY-SSW-DQC015), the National Natural Science Foundation of China (41701068, 41230630), and National key Basic Research Program of China (973 Program No. 2012CB026102).


  1. 1.
    Bandini V, Coop MR (2011) The influence of particle breakage on the location of the critical state line of sands. South Atl Q 51(4):591–600Google Scholar
  2. 2.
    Bardet JP (1997) Experimental soil mechanics. Prentice-Hall, Englewood CliffsGoogle Scholar
  3. 3.
    Been K, Jefferies MG, Hachey J (1991) The critical state of sands. Géotechnique 41(3):365–381Google Scholar
  4. 4.
    Challamel N, Rajagopal K (2016) On stress-based piecewise elasticity for limited strain extensibility materials. Int J Non-Linear Mech 81:303–309Google Scholar
  5. 5.
    Cleja-Tigoiu S (1990) Large elasto-plastic deformations of materials with relaxed configurations-I. Constitutive assumptions. Int J Eng Sci 28(3):171–180zbMATHGoogle Scholar
  6. 6.
    Cleja-Tigoiu S (1990) Large elasto-plastic deformations of materials with relaxed configurations-II. Role of the complementary plastic factor. Int J Eng Sci 28(4):273–284MathSciNetzbMATHGoogle Scholar
  7. 7.
    Collins IF (2005) The concept of stored plastic work or frozen elastic energy in soil mechanics. Géotechnique 55:373–382Google Scholar
  8. 8.
    Collins IF, Hilder T (2002) A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. Int J Numer Anal Method Geomech 26(13):1313–1347zbMATHGoogle Scholar
  9. 9.
    Collins IF, Houlsby GT (1997) Application of thermomechanical principles to the modelling of geotechnical materials. Proc Math Phys Eng Sci 453:1975–2001zbMATHGoogle Scholar
  10. 10.
    Coop MR, Sorensen KK, Freitas TB, Georgoutsos G (2004) Particle breakage during shearing of a carbonate sand. Géotechnique 54(3):157–163Google Scholar
  11. 11.
    Daouadji A, Hicher PY (2010) An enhanced constitutive model for crushable granular materials. Int J Numer Anal Method Geomech 34(6):555–580zbMATHGoogle Scholar
  12. 12.
    Daouadji A, Hicher PY, Rahma A (2001) An elastoplastic model for granular materials taking into account grain breakage. Eur J Mech 20(1):113–137zbMATHGoogle Scholar
  13. 13.
    Einav I (2007) Breakage mechanics—part I: theory. J Mech Phys Solids 55(6):1274–1297MathSciNetzbMATHGoogle Scholar
  14. 14.
    Einav I (2007) Breakage mechanics—part II: modelling granular materials. J Mech Phys Solids 55(6):1298–1320MathSciNetzbMATHGoogle Scholar
  15. 15.
    Ghafghazi M, Shuttle DA, Dejong JT (2014) Particle breakage and the critical state of sand. Soils Found 54(3):451–461Google Scholar
  16. 16.
    Goddard JD (1990) Nonlinear elasticity and pressure-dependent wave speeds in granular media. Proc R Soc A Math Phys Eng Sci 430:105–131zbMATHGoogle Scholar
  17. 17.
    Hardin BO (1985) Crushing of soil particles. J Geotech Eng 111(10):1177–1192Google Scholar
  18. 18.
    Hashiguchi K, Ozaki S (2008) Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction. Int J Plast 24:2102–2124zbMATHGoogle Scholar
  19. 19.
    Hivon EG, Sego DC (1995) Strength of frozen saline soils. Can Geotech J 32(2):336–354Google Scholar
  20. 20.
    Hu W, Yin ZY, Dano C, Hicher PY (2011) A constitutive model for granular materials considering grain breakage. Sci China Technol Sci 54(8):2188–2196zbMATHGoogle Scholar
  21. 21.
    Kan ME, Taiebat HA (2014) A bounding surface plasticity model for highly crushable granular materials. Soils Found 54(6):1188–1201Google Scholar
  22. 22.
    Kikumoto M, Wood DM, Russell A (2010) Particle crushing and deformation behaviour. Soils Found 50(4):547–563Google Scholar
  23. 23.
    Lade PV, Yamamuro JA, Bopp PA (1996) Significance of particle crushing in granular materials. J Geotech Engineering 122(4):309–316Google Scholar
  24. 24.
    Lai YM, Jin L, Chang XX (2009) Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil. Int J Plast 25(6):1177–1205zbMATHGoogle Scholar
  25. 25.
    Lai YM, Liao MK, Hu K (2016) A constitutive model of frozen saline sandy soil based on energy dissipation theory. Int J Plast 78:84–113Google Scholar
  26. 26.
    Lai YM, Yang YG, Chang XX, Li SY (2010) Strength criterion and elastoplastic constitutive model of frozen silt in generalized plastic mechanics. Int J Plast 26(10):1461–1484zbMATHGoogle Scholar
  27. 27.
    Lai YM, Xu XT, Dong YH, Li SY (2013) Present situation and prospect of mechanical research on frozen soils in China. Cold Reg Sci Technol 87:6–18Google Scholar
  28. 28.
    Lai YM, Xu XT, Yu WB, Qi JL (2014) An experimental investigation of the mechanical behavior and a hyperplastic constitutive model of frozen loess. Int J Eng Sci 84:29–53Google Scholar
  29. 29.
    Leblanc C, Hededal O, Ibsen LB (2008) A modified critical state two-surface plasticity model for sand-theory and implementation. Department of Civil Engineering, Aalborg University 8, AalborgGoogle Scholar
  30. 30.
    Lee KL, Farhoomand I (1967) Compressibility and crushing of granular soil. Can Geotech J 4(1):68–86Google Scholar
  31. 31.
    Liao MK, Lai YM, Wang C (2016) A strength criterion for frozen sodium sulfate saline soil. Can Geotech J 53(7):1176–1185Google Scholar
  32. 32.
    Liao MK, Lai YM, Yang JJ, Li SY (2016) Experimental study and statistical theory of creep behavior of warm frozen silt. KSCE J Civil Eng 20(6):2333–2344Google Scholar
  33. 33.
    Liu MC, Liu HL, Gao YF (2012) New double yield surface model for coarse granular materials incorporating nonlinear unified failure criterion. J Central South Univ 19(11):3236–3243Google Scholar
  34. 34.
    Loukidis D, Salgado R (2009) Modeling sand response using two-surface plasticity. Comput Geotech 36(1–2):166–186Google Scholar
  35. 35.
    Ma W, Wu ZW, Zhang LX, Chang XX (1999) Analyses of process on the strength decrease in frozen soils under high confining pressures. Cold Reg Sci Technol 29(1):1–7Google Scholar
  36. 36.
    Marsal RJ (1967) Large scale testing of rockfill materials. J Soil Mech Found 93(2):27–43Google Scholar
  37. 37.
    Mendes PRDS, Rajagopal KR, Thompson RL (2013) A thermodynamic framework to model thixotropic materials. Int J Non-Linear Mech 55(10):48–54Google Scholar
  38. 38.
    Miura N, Yamamoto T (1976) Particle-crushing properties of sands under high stresses. Technol Rep Yamaguchi Univ 1(4):439–447Google Scholar
  39. 39.
    Miura S, Yagi K, Asonuma T (2003) Deformation-strength evaluation of crushable volcanic soils by laboratory and in situ testing. Soils Found 43(4):47–57Google Scholar
  40. 40.
    Nguyen LD, Behzad F, Hadi K (2014) A constitutive model for cemented clays capturing cementation degradation. Int J Plast 56:1–18Google Scholar
  41. 41.
    Nguyen GD, Einav I (2009) The energetics of cataclasis based on breakage mechanics. In: Mechanics, Structure and Evolution of Fault Zones. Birkhäuser Basel, pp 1693–1724Google Scholar
  42. 42.
    Parameswaran VR, Jones SJ (1981) Triaxial testing of frozen sand. J Glaciol 27(95):147–155Google Scholar
  43. 43.
    People’s Republic of China National Standard GB/T 50123–1999 (1999) Standard for soil test method. China Planning Press, BeijingGoogle Scholar
  44. 44.
    Qi JL, Ma W (2007) A new criterion for strength of frozen sand under quick triaxial compression considering effect of confining pressure. Acta Geotech 2(3):221–226Google Scholar
  45. 45.
    Quintanilla R, Rajagopal KR (2011) Mathematical results concerning a class of incompressible viscoelastic solids of differential type. Math Mech Solids 16(2):217–227MathSciNetzbMATHGoogle Scholar
  46. 46.
    Rajagopal KR, Srinivasa AR (2013) An implicit thermomechanical theory based on a Gibbs potential formulation for describing the response of thermoviscoelastic solids. Int J Eng Sci 70(9):15–28Google Scholar
  47. 47.
    Roscoe KH, Burland JB (1968) On the generalized stress-strain behavior of wet clay. Engineering Plasticity. Cambridge University Press, Cambridge, pp 535–609zbMATHGoogle Scholar
  48. 48.
    Salim W, Indraratna B (2004) A new elastoplastic constitutive model for coarse granular aggregates. Can Geotech J 41:657–671Google Scholar
  49. 49.
    Sammis CG, King G, Biegel R (1987) The kinematics of gouge deformations. Pure appl Geophys 125:777–812Google Scholar
  50. 50.
    Selvadurai APS, Yu Q (2006) Constitutive modeling of a polymeric material subjected to chemical exposure. Int J Plast 22:1089–1122zbMATHGoogle Scholar
  51. 51.
    Shen CM, Liu SH, Wang LJ, Wang YS (2018) Micromechanical modeling of particle breakage of granular materials in the framework of thermomechanics. Acta Geotechnica. CrossRefGoogle Scholar
  52. 52.
    Shen WQ, Shao JF, Kondo D, Gatmiri B (2012) A micro-macro model for clayey rocks with a plastic compressible porous matrix. Int J Plast 36:64–85Google Scholar
  53. 53.
    Shojaei A, Voyiadjis GZ, Tan PJ (2013) Viscoplastic constitutive theory for brittle to ductile damage in polycrystalline materials under dynamic loading. Int J Plast 48:125–151Google Scholar
  54. 54.
    Srinivasa AR (2010) Application of the maximum rate of dissipation criterion to dilatant, pressure dependent plasticity models. Int J Eng Sci 48(11):1590–1603MathSciNetzbMATHGoogle Scholar
  55. 55.
    Steinhauser MO, Grass K, Strassburger E, Blumen A (2009) Impact failure of granular materials—non-equilibrium multiscale simulations and highspeed experiments. Int J Plast 25:161–182zbMATHGoogle Scholar
  56. 56.
    Tengattini A, Das A, Einav I (2016) A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation. Géotechnique 66(9):1–16Google Scholar
  57. 57.
    Terzaghi K, Peck RB (1948) Soil mechanics in engineering practice. Wiley, New YorkGoogle Scholar
  58. 58.
    Torrance JK, Elliot T, Martin R, Heck RJ (2008) X-ray computed tomography of frozen soil. Cold Reg Sci Technol 53(1):75–82Google Scholar
  59. 59.
    Vorobiev S, Kaneko K (2008) Constitutive response of idealized granular media under the principal stress axes rotation. Int J Plast 24:1967–1989zbMATHGoogle Scholar
  60. 60.
    Tsytovich NA, Zhang CQ, Zhu YL (1985) The mechanics of frozen ground. Science Press, BeijingGoogle Scholar
  61. 61.
    Ueng TS, Chen TJ (2000) Energy aspects of particle breakage in drained shear of sands. Géotechnique 50(1):65–72Google Scholar
  62. 62.
    Vermeer PA (1978) Double hardening model for sand. Géotechnique 28(4):413–433Google Scholar
  63. 63.
    Viggiani G, Atkinson JH (1995) Stiffness of fine-grained soil at very small strains. Géotechnique 45(2):249–265Google Scholar
  64. 64.
    Vorobiev O (2008) Generic strength model for dry jointed rock masses. Int J Plast 24:2221–2247zbMATHGoogle Scholar
  65. 65.
    Voyiadjis GZ, Shojaei A, Li G (2011) A thermodynamic consistent damage and healing model for self healing materials. Int J Plast 27(7):1025–1044zbMATHGoogle Scholar
  66. 66.
    Wang N, Yao Y (2008) A generalized constitutive model considering sand crushing. Soils Found 48(2):12–15Google Scholar
  67. 67.
    Wood DM, Maeda K (2008) Changing grading of soil: effect on critical states. Acta Geotech 3(1):3–14Google Scholar
  68. 68.
    Xiao H (2014) Thermo-coupled elastoplasticity models with asymptotic loss of the material strength. Int J Plast 63(9):211–228Google Scholar
  69. 69.
    Xiao Y, Liu HL (2017) Elastoplastic constitutive model for rockfill materials considering particle breakage. Int J Geomech 17(1):04016041Google Scholar
  70. 70.
    Xiao Y, Liu HL, Chen QS, Ma QF, Xiang YZ, Zheng YR (2017) Particle breakage and deformation of carbonate sands with wide range of densities during compression loading process. Acta Geotech 12(5):1177–1184Google Scholar
  71. 71.
    Xiao Y, Liu HL, Desai CS, Sun YF, Liu H (2015) Effect of intermediate principal-stress ratio on particle breakage of rockfill material. J Geotech Geoenviron Eng 142(4):06015017Google Scholar
  72. 72.
    Xiao Y, Liu HL, Yang G, Chen YM, Jiang JS (2014) A constitutive model for the state-dependent behaviors of rockfill material considering particle breakage. Sci China Technol Sci 57(8):1636–1646Google Scholar
  73. 73.
    Xiao Y, Sun YF, Fikry HK (2015) A particle-breakage critical state model for rockfill material. Sci China Technol Sci 58(7):1125–1136Google Scholar
  74. 74.
    Xie SY, Shao JF (2006) Elastoplastic deformation of a porous rock and water interaction. Int J Plast 22(12):2195–2225zbMATHGoogle Scholar
  75. 75.
    Xu XT, Fan CX, Zhang TY (2014) A constitutive model with effect of temperature for frozen soil. Adv Mater Res 919–921:627–631Google Scholar
  76. 76.
    Yang YG, Gao F, Lai YM, Cheng HM (2016) Experimental and theoretical investigations on the mechanical behaviors of frozen silt. Cold Reg Sci Technol 130:59–65Google Scholar
  77. 77.
    Yang YG, Lai YM, Dong YH, Li SY (2010) The strength criterion and elastoplastic constitutive model of frozen soil under high confining pressures. Cold Reg Sci Technol 60:154–160Google Scholar
  78. 78.
    Yang YG, Lai YM, Li JL (2010) Laboratory investigation on the strength characteristic of frozen sand considering effect of confining pressure. Cold Reg Sci Technol 60(3):245–250Google Scholar
  79. 79.
    Yin ZY, Hicher PY, Dano C, Jin YF (2016) Modeling mechanical behavior of very coarse granular materials. Journal of Engineering Mechanics 143:C4016006Google Scholar
  80. 80.
    Yin ZY, Xu Q, Hicher PY (2013) A simple critical-state-based double-yield-surface model for clay behavior under complex loading. Acta Geotech 8(5):509–523Google Scholar
  81. 81.
    Yu FW, Su LJ (2016) Particle breakage and the mobilized drained shear strengths of sand. J Mt Sci 13(8):1481–1488Google Scholar
  82. 82.
    Zhang D, Liu EL, Liu XY, Zhang G, Song BT (2017) A new strength criterion for frozen soils considering the influence of temperature and coarse-grained contents. Cold Reg Sci Technol 143:1–12Google Scholar
  83. 83.
    Zhang JW, Wang C, Zheng QW (2011) Particle breakage of gypsum granular materials in triaxial compression tests. Adv Mater Res 374–377:2261–2264Google Scholar
  84. 84.
    Zhao Y, Zhou H, Feng XT, Cui YJ (2012) Effects of water content and particle crushing on the shear behaviour of an infilled-joint soil. Géotechnique 62(12):1133–1137Google Scholar
  85. 85.
    Zhu ZW, Ning JG, Ma W (2010) A constitutive model of frozen soil with damage and numerical simulation for the coupled problem. Sci China (Phys Mech Astron) 53(4):699–711Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and ResourcesChinese Academy of SciencesLanzhouChina
  2. 2.School of Civil EngineeringBeijing Jiaotong UniversityBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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