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Constitutive modelling of soil (Duncan-chang Model)

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Mostafa Abedi
Mostafa Abedi

This file describes the hyperbolic constitutive model based on Duncan Chang's theory. Prepared by Mostafa Abedi

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Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi 惘忰 悋 惘忰悋 悋 1
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Comparison Duncan-Chang with other hyperbolic models Shear Modulus (G): Determination G (Shear Modulus) relative to (shear starin) 2 Ramberg-Osgood Model (1992) Hardin-Drnevich Model (1972) Davidenkov Model (1953) and etc.
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Comparison Duncan-Chang with other hyperbolic models Tangent Modulus (Et): Determination Et (tangent Modulus) relative to - (axial stress-strain) 3 Duncan-Chang(1960)
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Kondner and et al. (1963) have shown that the nonlinear stress-strain curves of both clay and sand may be approximated by hyperbolae with a high degrss of accuracy. The hyperbolic equation propose by Kondner was: 1 3 = + . 4
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 5 E0 or Ei Et Esec
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations = 1 3 = + . lim + . = 1 = = (1 3) = = (1 3) = + . 2 lim 0 + . 2 = 1 = 乞 = 0 6
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 7
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 8 The a and b values should be calculate in 70% to 95% ( - /1-3) chart
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Failure ratio (Rf): = 1 3 1 3 1.0 independent of confining pressure Rf = 0.75 1.0 9
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations If the parameters a and b are expressed in terms of E0, Rf, and (1-3): 1 3 = 1 0 + . 1 3 10
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Janbu (1963): 0 = . 3 11
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Mohr-Coulomb failure criterion: 1 3 = 2. + 23. 1 12
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Tangent modulus values (Et): 乞 = 1 (1 )(1 3) 2(. + 3. ) 2 . 3 13
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Tangent modulus values (Et): 乞 = 1 (1 )(1 3) 2(. + 3. ) 2 . 3 14
Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 15 The incremental models described cannot account for the strain softening behavior after peak strength (e.g., for dense sands and overconsolidated clays).

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Constitutive modelling of soil (Duncan-chang Model)

  • 1. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi 惘忰 悋 惘忰悋 悋 1
  • 2. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Comparison Duncan-Chang with other hyperbolic models Shear Modulus (G): Determination G (Shear Modulus) relative to (shear starin) 2 Ramberg-Osgood Model (1992) Hardin-Drnevich Model (1972) Davidenkov Model (1953) and etc.
  • 3. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Comparison Duncan-Chang with other hyperbolic models Tangent Modulus (Et): Determination Et (tangent Modulus) relative to - (axial stress-strain) 3 Duncan-Chang(1960)
  • 4. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Kondner and et al. (1963) have shown that the nonlinear stress-strain curves of both clay and sand may be approximated by hyperbolae with a high degrss of accuracy. The hyperbolic equation propose by Kondner was: 1 3 = + . 4
  • 5. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 5 E0 or Ei Et Esec
  • 6. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations = 1 3 = + . lim + . = 1 = = (1 3) = = (1 3) = + . 2 lim 0 + . 2 = 1 = 乞 = 0 6
  • 7. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 7
  • 8. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 8 The a and b values should be calculate in 70% to 95% ( - /1-3) chart
  • 9. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Failure ratio (Rf): = 1 3 1 3 1.0 independent of confining pressure Rf = 0.75 1.0 9
  • 10. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations If the parameters a and b are expressed in terms of E0, Rf, and (1-3): 1 3 = 1 0 + . 1 3 10
  • 11. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Janbu (1963): 0 = . 3 11
  • 12. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Mohr-Coulomb failure criterion: 1 3 = 2. + 23. 1 12
  • 13. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Tangent modulus values (Et): 乞 = 1 (1 )(1 3) 2(. + 3. ) 2 . 3 13
  • 14. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations Tangent modulus values (Et): 乞 = 1 (1 )(1 3) 2(. + 3. ) 2 . 3 14
  • 15. Constitutive Modelling of Soil (Duncan-Chang Model) Mostafa Abedi /15 Duncan-Chang constitutive equations 15 The incremental models described cannot account for the strain softening behavior after peak strength (e.g., for dense sands and overconsolidated clays).