Hardening & softening soil models

In recent years, soil models have significantly advanced from the basic elastic perfectly plastic Mohr Coulomb soil models. The Mohr-Coulomb soil model was limited in that the stress-dependency of soil stiffness was not taken into account in addition to the yield cap being fixed in principal state.
Now we have soil models that can model soil stiffness degradation with stress in addition to having a yield surface that expands or contracts due to plastic straining.
For strain-hardening soil models (such as the Hardening Soil model in PLAXIS), the yield surface expands to accommodate plastic straining while strain-softening soil models will have a contraction of the yield surface.
At typical working loads, whether a user has adopted a strain-hardening or strain-softening soil model is often irrelevant since the soil has not reached the yield surface. For cases such as cavity expansion, however, the choice of the soil model has a significant impact on the resulting stresses and displacements since soil failure will have occurred. For clayey soils, a strain-hardening soil model will show a permanent increase in mean effective stress in the soil adjacent to the expanded cylindrical (or spherical) cavity. A strain-softening soil model, however, will show an increase in mean effective stress up to soil yielding and then exhibit a reduction in mean effective stress. After cavity expansion, a strain softening soil model can show a reduction or an increase in mean effective stress in the soil adjacent to the cavity.

The most advanced soil models at present (e.g. the SCLAY-1S soil model) have improved on this further by taking into account the destructuration of clays due to large strains. These models consider the breakdown of  inter-particle  bonds due to large strains and the destructuration of the clay structure. 

Modelling Pile and Stone Column Installation in PLAXIS

It is well know that pile and stone column installation causes large strain and deformations to occur in the soil. Large deformations can change the properties of the soil in the zone immediately around the pile or stone column (SC). This can result in a strength reduction at the interface or in some cases (for clays) a strength increase.
Although the 'Geo-Install' workshops have shown significant advances towards modelling installation, many of these methods are currently not available in commercial packages.

Cavity Expansion
A common method used to model both stone column and pile installation is cavity expansion. This is the process of expanding a cylindrical cavity of zero thickness in a radial direction until the radius of the cavity equals the radius of the pile or SC. This is an effective method for modelling the excess pore pressures, in particular, generated during pile/SC installation.

Interface Strength Reduction Factor
PLAXIS allows for an input of an 'interface strength reduction factor' in order to take into account a reduction in soil strength arising from installation. Typical values range between a value of 0.6 to 1.0 depending on the particular soil type. This strength reduction factor can only be applied when using interface elements, however, and thus may not be applicable to SCs. During the installation of SCs, the stone and soil being treated become interlocked. Thus modelling SCs using interface elements may over-predict punching of the stone columns in the soil.
In PLAXIS 3D, the user can select between volume piles and embedded piles to model a pile foundation. Embedded piles comprise of beam elements and have special interfaces. Thus strength reduction at the pile-soil interface can not be modelled using embedded piles.The differences between these two types of pile will be covered in another post in more detail. 

How to choose a soil model in PLAXIS 3D Foundation (version 2.2)

It can be difficult to choose an appropriate soil model for a certain application. PLAXIS users must always be aware of the various limitations associated with each soil model. These limitations must then be considered in design or research and results should be put into context accordingly.

LINEAR ELASTIC
The Linear Elastic (LE) soil model is the most basic and straightforward soil model. The main input parameters are the Young's modulus of the soil and Poisson's ratio. The LE soil model is perfectly elastic and thus does not account for plastic displacements, therefore soil failure is not accounted for. A LE soil model should only be applied where users are confident that elastic soil conditions are present or where there is a sufficiently high Factor of Safety (FOS) against failure. Thus a LE soil model should only be used for small strain response. When applied to pile foundations, a LE soil model considerably over-estimates pile-to-pile interaction and thus can provide an overly-conservative estimate of pile group settlement.

MOHR-COULOMB
The Mohr-Coulomb (MC) soil model is an advancement on the LE soil model in that soil failure is accounted for according to the Mohr-Coulomb failure criterion i.e.   
  \tau = \sigma~\tan(\phi) + c
An input of the cohesion strength c' and friction angle is required as PLAXIS recommends users to input drained parameters as opposed to undrained parameters. Thus the MC soil model is regarded as a perfectly elastic-perfectly plastic soil model or a bi-linear soil model. Since the MC soil model also fails to account for plastic straining before soil failure, it should be used where elastic soil conditions are present.

HARDENING SOIL
The Hardening Soil (HS) model is an advanced nonlinear soil model. This particular soil model allows for an input of the parameter 'm' which defines the stress dependency of the soil stiffness. A value of m=1 simulates a logarithmic stress dependency and is typical for soft clays. A value of 0.5 would be more suitable for sands.
Th HS model also requires the stiffness parameters Eoed (Oedometer stiffness), E50 (triaxial secant stiffness) and Eur (unload-reload stiffness).
The HS model also uses the MC failure criterion however the yield surface is not fixed but can expand to accomodate plastic straining. The HS model yields much more accurate predictions of soil behaviour compared to the previous two soil models, particularly in pile group foundations.

SOFT SOIL CREEP MODEL
The soft soil creep model (SSCM) is similar to the HS model however it can also take account of creep in soils. Although the SSCM has been known to predict unrealistic creep settlement it is still used to provide an estimate of the extent of creep settlement in soft soils. There are, however, numerous soil models currently being developed which have been shown to be a vast improvement on this soil model but are not yet avaliable commercially

Most frequently used soil models

For my PhD research on pile group foundations, I am using the advanced nonlinear Hardening Soil model in PLAXIS 3D Foundation. Although the HS model captures the nonlinear (more realistic) behaviour of soil, the more basic soil models idealising the soil as a linear elastic medium are most often used in industry.
Idealising the soil as a linear elasic medium has the effect of over-predicting pile/soil settlement thus leading to an increased factor of safety in the design. Is this extra (and often unnecessary) factor of safety necessary when the engineering profession is constantly striving for more efficient structures particularly in the current economic climate?
Vote on the poll on the right hand side and see what are the most popular soil models today.
You can also post your comments below or suggestions to soil models that should be included in the list