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.

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How to visualize the color map of modulus of subgrade reaction ks ?

You can visualize the color map of modulus of subgrade reaction ks using Paraview which is an open source, multi-platform data analysis and visualization application. ParaView is known and used in many different communities to analyze and visualize scientific data sets. It can be used to build visualizations to analyze data using qualitative and quantitative techniques. ParaView runs on distributed and shared memory parallel and single processor systems making the data analysis for large scale models very effective. ParView is is a multi-platform application ZSoil-produced data sets can be visualized using different operational systems (Windows, Mac OS X, Linux, etc).

Since 2016, ZSoil has been offering the new feature that allows ZSoil results to be exported to the file formats that ParaView understands.

The modulus of subgrade reaction coefficient should can be calculated based on the results retrieved from the interface elements according to the following basic equation:

– total stress increment which induces the deformation
– normal displacement increment corresponding to the applied total stress increment

In order visualize the color map of modulus of subgrade reaction ks, follow these steps:
1. In ZSoil, export interface data to ParaView format (you don’t have to export all data but you can if you need them for other purposes); consider the reference time step if needed (contact typically appears with the structure).
2.  In ParaView, open file “filename_cn_timeInstance.vtu”. These are interface results only for a given time instance. Click on Apply to plot the data.
3.  Apply “Cell Data to Point Data” filter. It allows to interpolate normal total stresses from central Gauss points (average value for 4 Gauss points) to the nodes at which displacements are computed
4. Apply the “Calculator” filter. It allows to define a custom output based on data which are collected in data vectors or scalars.

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