Hyperbolic (Duncan-Chang)

The Hyperbolic (Ducan-Chang) model is a nonlinear elastic criterion to model the behavior of soil as it approaches failure. In the equation suggested by Duncan-Chang, the stress-strain curve is defined as a hyperbolic function and the soil parameters are the functions of confining stress and shear stress.

Applicable Modules:

General Parameters

Modulus of Elasticity (E)

The slope of the stress-strain line for a linear isotropic material.

Poisson's Ratio (u)

The ratio of the radial (or lateral) strain to the vertical strain.

Temperature Coeff. (α)

The relative change of a physical property when the temperature is changed by 1 K.

Unit Weight (Υt)

The weight of soil per unit volume.

Saturated Unit Weight (Υsat)

The weight of saturated soil per unit volume.

Cohesion (c)

It is a measure of the forces that cement particles of soil.

Internal Friction Angle (Φ)

It is a measure of the shear strength of soils due to friction.

Earth Pressure Coeff. (Ko)

The ratio of horizontal principal effective stress to the vertical principal effective stress.

Draining Condition

Drained

Dissipation of pore water pressure takes place upon the load application.

Undrained

Dissipation of pore water pressure does not take place upon the load application.

Skempton 'B' Coefficient

Enter the value of the coefficient for an 'Undrained' condition.

Additional Parameters

Initial Loading Modulus (K)

Initial Loading modulus from initial tangent gradient obtained from experiment data.

Initial Stiffness Index (n)

The parameter n is the slope of the the plot of E/Pa vs. σ3/Pa.

Failure Ratio (Rf)

It is the ratio of the asymptotic value of the hyperbolic curve (σ1-σ3)ult to the soil strength (σ1-σ3)f. Range of values: 0.75-1

Kur

The modulus used when ground is unloaded from a state of very large shear stress. Kur is independent of the level of shear stress.

Kb

The modulus used when variation of poisson's ratio is considered by means of stress-dependent Bulk Modulus. Range of values: 200-700

Mass Coefficient Index (m)

The parameter n is the slope of the the plot of Bm/Pa vs. σ3/Pa.

Min. Tangential Modulus

The minimum value of Tangential Modulus. If this value is too small, it may cause convergence problem. The default minimum value is set as Pa.

Min. Confining Pressure (σmin)

The minimum value of confining stress. If it's zero or negative then it may cause convergence problem. The default minimum value is set as 0.01*Pa.

Atmospheric Pressure (Pa)

Atmospheric pressure.

Safety Factor Calculation

The safety factor is calculated on the basis of the ratio of the current state of stress of the material to the Mohr-Coulomb failure criterion.  The Mohr-Coulomb failure criterion is most widely used criterion for brittle materials like ground.  SoilWorks uses the criterion for all the material models in the Tunnel Module.