Why does the deviatoric stress tend to infinity when modeling undrained behavior with the Hardening-Soil model?

Why does the deviatoric stress tend to infinity when modeling undrained behavior with the Hardening-Soil model?


This is because, in the original Hardening-Soil model formulation, the shear and volumetric plastic mechanisms are decoupled. The preconsolidation pressure pc, being the hardening parameter of the cap yield surface, depends solely on the accumulated volumetric plastic strain εvp produced by this mechanism. Similar assumption is adopted for the shear yield surface that expands with increasing accumulated deviatoric plastic strain γPS produced by the shear mechanism. The latter plastic mechanism may also produce volumetric plastic strain (due to dilatancy) but it is not coupled with the hardening law for preconsolidation pressure.

Evolution of the effective stress path in the undrained triaxial test assuming uncoupled shear/volumetric plastic mechanisms (OCR = 1)

The macroscopic behavior of cohesionless soils can be reproduced by the model reasonably well, regardless of drainage conditions (i.e. drained or undrained). The ability to represent undrained behavior of overconsolidated, therefore usually dilative, cohesive soils is limited.  Lack of coupling of these two plastic mechanisms leads to an unlimited undrained shear strength increase regardless of the OCR value.


The major drawback of the model is such that it is unable to appropriately reproduce the undrained shear strength in the case when dilatancy angle ψ is larger than zero. By applying a conservative assumption ψ = 0°, the computed undrained shear strength may be underestimated with respect to the true one (even a few times for larger values of OCR). On the other hand, by assuming ψ > 0°, the undrained shear strength will tend to infinity with the increasing shear strain amplitude.

The coupling of shear and volumetric mechanisms provides a general solution to the problem, it will be available in ZSoil v2016.

Why does the initial state analysis diverge for simulations with Modified Cam-Clay model

Setting the initial stresses σ0 super element for Modified Cam-Clay model is required

The Modified Cam-Clay model (MCC) requires an initial guess for the initial effective stress state to be set by the user. In the initial state computation hardening is deactivated and MCC behaves as classical elasto-plastic model with deviatoric flow rule.

Notice that once the unloading branch, that we assume does not produce any plastic strains, is linear in e-ln(p) axes the soil stiffness must depend on the effective stresses. The bulk modulus is expressed as K = (1 + eo)/p.

So every computation with Modified Cam-Clay model (also HSs) will require to set up the initial guess for the initial effective stress. No matter whether the initial state driver is active or not.

Read more:  Advanced model for soft soils. Modified Cam-Clay model (MCC)

How to define initial stresses σ0 super element

modified Cam-Clay model

How can we guess the initial stresses in that case?

modified Cam-Clay model - natural Slope

Setting the initial effective stresses can be made exclusively at the FE level through the option in right menu:

  • FE Model/Initial conditions/Initial stresses/On 4 nodes/points (for 2D cases)
  • FE Model/Initial conditions/Initial stresses/On 8 nodes/points (for 3D cases)

modified Cam-Clay model

To de fine the initial stresses in quadrilateral regions (covering our FE mesh) we can set all stress components at each vertex separately or we can use a simplified method where we fix the vertical stress at the top and we de fine the in situ Ko coefficient and soil unit weight that will produce correct σo .

modified Cam-Clay model

Note that by running the Initial State driver and assuming Ko coeficient locally at the material level we do not need to be very precise when we guess the initial in situ stress state. The driver will correct it anyway.

Read more:  Advanced model for soft soils. Modified Cam-Clay model (MCC)

How to simulate the undrained behavior?

Simulating the undrained behavior of soil can be carried out by means of three different approaches:

  1. Effective stress analysis using Consolidation driver type for Deformation+Flow problem type
  2. Effective stress analysis using Driven Load-Undrained driver type for Deformation+Flow problem type
  3. Total stress analysis using Driven Load driver type for single-phase Deformation problem type

These approaches are described below.


Driver setup:   Deformation+Flow, Time Dependent, Consolidation

Input parameters:   always effective strength and stiffness parameters


  • undrained or partially drained conditions arise naturally depending on action time and soil permeability
  • partial saturation effects are included
  • consolidation analysis can be followed by any analysis type


  • CPU time for very large boundary value problems



Driver setup: Deformation+Flow, Time Dependent, Driven Load (Undrained)

Input parameters: effective strength and stiffness parameters


  • fully undrained regime (no volume change) is obtained regardless defined soil soil permeability
  • useful for dynamics


  • Undrained driver cannot be followed by any other driver


Using Undrained driver type, special attention must be paid on appropriate selection of undrained driver settings. Undrained behavior can be disabled for material layers for which undrained behavior is not relevant.



Driver setup:   Deformation, Time Dependent, Driven Load

Input parameters:   total stress strength and stiffness parameters


  • relatively fast in terms of CPU


  • undrained shear strength c = Su is stress independent (i.e. constant over depth; typically, not the case in natural conditions)
  • although « undrained » conditions imply no volume change, model’s preconsolidation pressure pc may evolve so not relevant for normally- and lightly overconsolidated soils
  • stiffness depends on φc term because c cot φ = 0




The use of the Hardening-Soil model to simulate undrained behavior with the total stress approach demands the parameter setup which presented below.





Pore pressure

For Consolidation analysis, pore pressure values can be standardily visualized using nodal quantities. In the case of Undrained driver, the results are stored in the Gauss points and visualization of pore pressure can be done using “Undrained pressure” under continuum element results.

Suction pressure (S*p)

Magnitudes of suction pressure are stored in the Gauss points and can be read using S*p + <dp_undr> under continuum element results.