# Non linear finite element design on wind turbine foundations

The design of wind turbine foundations is currently based on the plate theory.

“Plates” are plane structural element and the theory (or “theories” – there are at least two currently used) calculate stress and deformation when the structure is loaded.

During the analysis several difficulties emerges in satisfying equilibrium, stress-strain relations, compatibility of strains and boundary conditions. Theoretical results are often less accurate than you might expect.

These difficulties increase when the classical theory (the one usually used by foundation designer) is applied to reinforced concrete slabs.

This is due to several aspects such as:

• The non-homogeneous nature of concrete
• The nonlinear response of the material
• Cracking
• Time effects

The use of classical elastic plate theory, therefore, has been limited to reinforced concrete slabs under low levels of stress.

Classical elastic theory fails to predict either the yield moment capacity or the load-deflection behavior of reinforced concrete slabs.

Basically, the problem is that the stress distribution that we consider in our foundations project may be inaccurate due to the existance of cracks in concrete.

These cracks appear when the concrete is subjected to tensile stress.

Once the concrete cracks the stiffness of the section changes (it reduces importantly) and the forces in the section redistribute to other stiffer regions without cracks.

Subsequently, these stiffer regions may also crack after receiving these “extra loads”.

Then, that section continues the redistribution until you reach convergence and equilibrium.

Almost no wind turbine foundation designer is yet considering this effect, that should be, in most of cases, beneficial as the redistribution reduces the stress in the most loaded areas.

Why is that?

Basically because it requires a more complex and time consuming analysis.

The models required to consider these type of effects need to include the reinforcement. This can only be obtained using an iterative process.

You also need to take into consideration the crack propagations, and the bond-slip behaviour of the reinforcement (the tension in concrete, the tension stiffening of the reinforcement, and many other phenomena that may modify the final results).

Furthermore, the models used for wind turbine foundation design include always a contact non-linearity because the foundation may have a gap (that is, partially “lifting” under certain load cases creating uncompressed areas below).

Adding the sectional nonlinearity to the steel – concrete contact nonlinearity already considered may increase importantly the calculation times.

Additionally it is not completely clear how to implement the fatigue verification to the steel and reinforcement considering this type of analyses.

Nevertheless, taking into account the size of the foundations we are reaching in the market, this type of analysis may reduce the quantities in the foundations, making them more efficient.