How do you model geogrids in FEA?

What do you need to know, first?

The use of numerical modelling and the availability of powerful software modelling tools have enabled a major change in geotechnical design. As with all numerical methods, it is vitally important that appropriate models and material parameters are used. Not all engineers are expert in tools such as Finite Element Analysis (FEA) and it is necessary for some of us to rely on the output of those that are. However, we should be ready to examine and challenge the basic assumptions that underlie any design.

The modelling of geogrids in mechanically stabilised earth (MSE) structures in FEA illustrates how basic assumptions made on material behaviour, impact on the outcome of analysis. Those relying on the output of FEA analysis, need to ask what material behaviour has been used in the modelling and determine if it is appropriate for their needs.

Questions to ask those modelling geogrids in FEA

There are several different geogrid stiffness models that may be used to represent the tensile properties of geogrids. We need to know which has been used and why, and to be sure it’s appropriate for the purposes of the analysis. The stiffness of a polymer geogrid will depend upon four factors.

• The product: material characteristics of the polymers used to manufacture the geogrid make a difference.
   
• The load levels applied to the geogrid are important as stiffness can vary with the load level.
   
• The in-soil temperature of the geogrid can have a significant effect on tensile stiffness for some polymer types.
   
• The duration of load: most polymer materials used for geogrids will exhibit some degree of ‘creep’ under sustained load. The type of polymer and the degree of molecular orientation in the manufactured product will have a significant effect on the creep properties and the change in stiffness over time.

 

Manufacturers of geogrids certified for use in MSE structures, such as retaining walls and steep slopes, will have conducted extensive testing, at a range of temperatures and over lengthy periods of sustained loading, to fully define the tensile behaviour of their products.

Geogrid layers are usually modelled as a membrane element with no bending stiffness or compressive stiffness. Rather than attempting to model individual ribs and junctions, the tensile stiffness (EA) is taken as the average over the width of the geogrid. The membrane element may have different properties in the primary and transverse directions, as is the case with most geogrids used for MSE structures. In some cases, interface elements are introduced to model the interaction between soil and geogrid, but while this may be useful for ultimate limit state, the high degree of interlock between soil and geogrid, through the geogrid apertures means that slippage or pull out is unlikely in serviceability conditions, making the use of interface elements unnecessary for analysis of the serviceability state.

In this episode of "Ask Andrew", Andrew Lees tells us how geogrids are modelled in FEA (Finite Element Analysis)

Four stiffness models for geogrids

Each stiffness model needs to start with an understanding of the factors that impact stiffness. It is then possible to progress to the four different models.

Linear Elastic (LE)

In this case the relationship between load and strain is expressed as a straight line, in other words, the stiffness (EA) is assumed to be constant at all load levels. No account is taken of temperature variation or load duration effects. This approach is simple to model and may be suitable for initial analysis of a problem.

Linear elastic/perfectly plastic (LEPP)

This behaviour is assumed to be linear elastic with a single stiffness value (EA) up to a specific load level - and thereafter the material is assumed to behave perfectly plastic. The load strain curve is a straight line up to the maximum load level and then becomes horizontal in the plastic condition. This approach could be suitable for the ultimate limit state condition, however it is unlikely that the plastic load limit will be reached in a serviceability condition. Again, no account is taken of temperature variation or load duration.

Visco-elastic (VE)

This approach does take account of load duration, but assumes the temperature remains constant throughout. The stiffness is again assumed to be linear elastic, with a straight line relationship between load and strain. However, there are equivalent to a family of curves with decreasing gradient each representing a different period of load application. In this way the reduction in stiffness over time is modelled.

Non-linear elastic (NLE)

Instead of a straight line relationship between load and strain, this approach has a curved line, where stiffness (EA) varies with load level. This allows the stiffness to be modelled at the appropriate load level, including the varying load level that occurs along the length of any geogrid layer. This is important, because load varies considerably along the length of any geogrid layer in a MSE structure. The method does not include the effect of load duration, but there can be a family of curves, each representing a different time. These are called isochronous curves. The appropriate isochronous curve can be selected when looking at say, the end if construction, or over the full service life, which will typically be 120 years for highway structures.

Selecting the correct stiffness model

The geogrid stiffness model selected will have an effect on the predicted deformations in a structure, whichever one is used. It is therefore important for those seeking to understand and utilise the output from numerical analysis to ask and be aware of what model has been adopted and why.

Further information on FEA use in geotechnics

For further information about FEA use in geotechnics, there are several texts and areas of study available.

One key resource is the practical guide to Geotechnical Finite Element Analysis, available here.