Numerical Modelling: The Hardening Soil Model

The following was prepared by Dr. Ronald B.J. Brinkgreve, and first presented by Virtuosity.

In a previous blog, the importance of using advanced soil models for geotechnical finite element calculations, was discussed. The Hardening Soil model is a model that captures several features of real soil behavior; both for sandy soils as well as for clays and silts. In this article, some practical details of the Hardening Soil model will be further presented, with the purpose to take away some fear and encourage engineers to use this model in their geotechnical applications.

Features of Soil Behavior

As mentioned in the blog on The Importance of an Appropriate Soil Model, simple models lack some important features of soil behavior. The Hardening Soil (HS) model (Schanz et al., 1999), or even better, the HS model with small-strain stiffness (HSsmall) (Benz, 2007) includes several features of soil behavior that are relevant for many practical applications, such as:

• Stress-dependency of stiffness and strength
• Strain-dependency of stiffness (modulus reduction)
• Memory of preloading
• Distinction between primary loading and unloading or reloading stiffness
• Realistic non-linear behavior instead of bi-linear stress-strain response
• More accurate pore pressure development in undrained loading

In contrast to other engineering materials, soil stiffness cannot simply be defined by a single Young’s modulus (E). Different loading directions (compression, shear, unloading) will cause a different stiffness response. Therefore, the Hardening Soil model has different stiffness parameters for different loading directions. They can be obtained from different soil lab tests.

“Do I need to perform all those tests to be able to use the Hardening Soil model?”

Ideally, yes, but not necessarily. Stiffness can also be obtained from field test data (CPT, SPT) by means of correlations. And there are typical ratios between the various stiffness parameters for different types of soil, so once you have determined a single stiffness parameter, you can usually have a good estimate of the others.

Model Parameters

A constitutive model, together with its set of model parameters, is supposed to be representative of a particular soil. For the HS(small) model this is probably true. The model itself will take care of stress-and-strain-dependency of stiffness and strength without changing the parameters. You can build a database of parameter sets for different soils, irrespective of the loading conditions; something that does not make sense when using simple models like the linear elastic perfectly plastic Mohr-Coulomb model, because for such models, changing loading conditions require different parameter values.

In 2010, Brinkgreve et al. published a paper with correlations providing a first estimate of all HSsmall model parameters for sandy soils, just based on Relative Density (Brinkgreve et al., 2010). This can be very useful in an early stage of a project, when only limited soil data are available. It generally provides more accurate results than using a simple model, based on the same limited data. Hence, the ‘fear’ for the Hardening Soil model and its numerous parameters to be determined, is simply not justified.

Soil Test Facility

Once you have determined your set of model parameters for the Hardening Soil or HSsmall model, you can test your ‘digital soil’ in the PLAXIS 2D/3D Ultimate Soil Test facility. This is a very convenient tool in which you can quickly check the model’s response under loading conditions similar to real soil lab tests. If you have real lab test data available, you can do a further calibration and validation of your model parameters. There is even a parameter optimization tool available.

Lear More about PLAXIS

Besides calibration of model parameters, the Soil Test facility is a very nice ‘learning tool’. It enables students and young engineers to understand various features of soil behavior, and it will show the capabilities and limitations of your soil model. Using this tool will really make you appreciate the Hardening Soil and HSsmall model for its authentic representation of real soil behavior. On the other hand, it may also warn you about the limitations of the Mohr-Coulomb model, since it clearly demonstrates its linear or bi-linear behavior under various loading conditions.

Are you convinced?

Hopefully, after reading this blog, practicing engineers will be convinced that the Hardening Soil and HSsmall models are better alternatives to use as soil models in geotechnical applications. The ‘fear’ for its parameter determination based on limited soil data is unnecessary. Simple correlations for sandy soils have been provided, and there is more to come for clays and silts. A finite element analysis using the Hardening Soil model is more accurate and realistic than when using a simple model.

PLAXIS Soil Model Talk with Dr. Ronald Brinkgreve

Credits: Virtuosity Software 

Learn more about this event here.

References

Schanz T, Vermeer PA, Bonnier PG (1999). The Hardening Soil model: Formulation and Verification. In: Beyond 2000 in Computational Geotechnics, Brinkgreve (ed). Rotterdam: Balkema. 281-296.

Benz T (2007). Small-Strain Stiffness of Soils and its Numerical Consequences. PhD thesis. Geotechnical Institute – University of Stuttgart.

Brinkgreve RBJ, Engin E, Engin HK (2010). Validation of empirical formulas to derive model parameter for sands. In: NUMGE 2010, Benz & Nordal (eds). Leiden: CRC press. 137-142.