Duncan-Chang Material Properties

The Duncan-Chang material model is used to simulate soil. It assumes a hyperbolic stress-strain relation and was developed based on tri-axial soil tests. The model accommodates the variation of Poisson's ratio by means of stress-dependent Poisson's ratio (E-v model) or stress-dependent bulk modulus (E-B model).

Refer to the following page, Duncan-Chang Theoretical Description, for additional clarification and equations in which the material properties are used.

General tab:

• Mass density Enter the mass per unit volume, not the weight density. (Mass density = weight density/gravity.) This value is required for dynamic analyses where accelerations are involved, or when gravity is included in the analysis, or when the initial stress due to the self weight is included. (See the page General Options: Unit Systems: Converting Mass Units for tips on converting to the appropriate units. Alternatively, define a Display Unit system that uses the provided units for the mass.)
• Cohesion Intercept (c) This is the strength parameter c used in the Mohr-Coulomb criterion for the failure of the soil. The input must be greater than or equal to 0.
• Friction Angle (phi) This is the strength parameter f used in the Mohr-Coulomb criterion for the failure of the soil. The input must be in the range of 0 (inclusive) to 90 degrees.
• Cohesionless Soils Activate this option if the soil is considered cohesionless, in which case the Mohr failure criterion is based on the friction angle.
• Friction Angle (dphi) This value,Df₀, is the reduction in the strength parameter f for a 10-fold increase in the minor principal stress s₃. The input must be in the range of 0 (inclusive) to 90 degrees.
• Failure Ratio (Rf) The failure ratio relating the stress intensity range (s₁-s₃) for failure to the ultimate. The typical range is 0.75 to 1, but values between 0 and 1 (inclusive) are acceptable.
• Modulus Number (K) Modulus number used to define the initial modulus. This value must be greater than 0.
• Modulus Number (Kur) Modulus number when the model has been unloaded. The stress intensity range (s₁-s₃) is less than the historical maximum. This value is greater than or equal to the modulus number K.
• Modulus Exponent (n) Modulus exponent used to define the initial modulus.
• Formulation Choose the formulation to use to account for the variation of Poisson's ratio.
  • E-B is the stress-dependent bulk modulus method
  • E-v is the stress-dependent Poisson's ratio method
• Bulk Modulus Number (Kb) Bulk modulus number used with the E-B formulation. The value must be greater than 0.
• Bulk Modulus Exponent (m) Bulk modulus exponent used with the E-B formulation.
• Poisson's Ratio Parameters (G) Material parameter used with the E-v formulation.
• Poisson's Ratio Parameters (F) Material parameter used with the E-v formulation.
• Poisson's Ratio Parameters (D) Material parameter used with the E-v formulation.
• Atmospheric Pressure The default is based on 14.696 psi, converted to the same units as the model.

Advanced tab:

The following material properties are used to stabilize the analysis at time zero and if the minor principal stress (s₃) become less than or equal to zero. Values for time 0 (and before failure) and after failure are entered.

• Elastic Moduli at Rest: Young's Modulus: A reasonable default is 0.01*K*Pa, where K is the Modulus Number and Pa is the atmospheric pressure (both entered on the General tab).
• Elastic Moduli at Rest: Poisson's Ratio: Enter the Poisson's Ratio for the soil in the rest condition.
• Elastic Moduli at Failure: Young's Modulus: A reasonable default is 0.001*K*Pa, where K is the Modulus Number and Pa is the atmospheric pressure (both entered on the General tab).
• Elastic Moduli at Failure: Poisson's RatioEnter the Poisson's Ratio for the soil in the failed condition.