How to optimize the design of WTG foundations?

As wind turbine loads and foundations size keep increasing year after year sharpening the geotechnical calculations and modelling correctly the interaction between soil and foundation is becoming a priority.

The cost of foundations can represent a significant percentage of the investment in a new wind farm - even more in 2021, when steel and concrete are becoming every day more expensive.

An important topic that is becoming the focus of detailed studies is the soil bearing capacity degradation under cyclic loads.

This subject has been incorporated in the new version of the standard IEC61400-6 on Wind energy generation systems in Part 6: Tower and foundation design requirements.

Now, under certain conditions, a certain amount of "gap" below the foundation may be allowed.

“Gap” means that under certain situations the ground below part of the foundation might become uncompressed – as if the foundation was partially lifted, creating a "gap" (i.e., a separation between the structure and the soil).

This is something that previously was not allowed (unless the foundation was on rock).

The reason is that if the soil goes through several cycles of compression and decompression its bearing capacity might deteriorate. Basically the bearing capacity becomes lower and lower, putting at risk the stability of the structure.

This is a relevant change, as the IEC standard is one of the most important document (if not the most important) used in wind turbines foundation design.

The key idea behind the change is that if the soil below the turbine is not susceptible to the phenomenon of degradation under cyclic loads a certain amount of gap can be allowed.

Removing this “no gap” requirement means that a significant reduction in the diameter of the foundation can be achieved.

This happens because otherwise the foundation would have been bigger only to keep the soil below it always compressed.

The “no gap” requirement used to be one of the dimensioning constraints in wind turbines foundation design when the soil was good.

The key to allow some gap in the foundation design (and as a result, a smaller foundation and savings in concrete and steel) is to be able to justify that the soil characteristics will not will not degrade under cyclic loads.

This involves dynamic tests, which are time consuming, expensive, difficult to implement on site, unusual for most geotechnical companies and difficult to post process and interpret.

In some cases, even with a robust testing campaign, additional finite elements models have to be created to validate the design.

Will we see smaller foundations after this change in the IEC? We will need to wait several months to answer this question.

Since some years ago almost all wind turbine manufacturers (“OEM” - I hate acronyms) have modified their tower to foundation interface.

The previous technical solution to connect tower and foundation was based on an embedded steel section (like a “ring” inside the foundation).

It did not work properly and the issues caused by this element might be easily subject of several articles, about the problems caused by the ring and on the solutions developed to fix those problems (i.e. retrofitting and repairs works necessary to ensure the necessary lifetime of the turbine foundations).

In the last years (I would say since around 2010) the embedded ring has been replaced with a pre-stressed anchor cage, as shown in the following picture:

The design methodology for this element is usually based on simplified hypothesis:

The first assumption is that the tensile/compression strength on each element is calculated assuming a uniform load distribution, usually using formulas such as:

T = 4Md / (n*D) + N/n

Being

T = Maximum tension force on the more loaded bolt

Md = Bending moment from the tower

n = Number of anchors

D = Average diameter of the anchor cage

N = Axial force

This is usually known as the “Petersen approach”.

Petersen is a German engineer who wrote a book about steel structure design appropriately titled “Stahlbau” (“steel construction” in German) where this calculation method is presented.

The second assumption is that the tensile force is distributed between concrete and steel if there is no decompression.

If decompression happens (something that will always happen under ultimate limit state factored loads) all the tensile force will be taken by the steel.

The only problem with this approach is that the first assumption is only true in case there is no decompression.

This approach leads to conservative results, as it does not account for the force re-distribution due to the stiffness change when decompression occurs.

However, it is very easy to obtain the maximum tension the more loaded bolt or to calculate the needed number bolts or their dimensions for a given tension.

When decompression occurs the stiffness in the “compressed” side and in the “tensioned” side stops having the same value, as the concrete stops providing its stiffness (this is the magic of pre-stressing, before de-compression the concrete is somehow taking some tension, a thing that concrete rarely does).

In the compressed side we will have an area of concrete under compression and bolts in tension (due to the prestressing), that take the compression by de-tensioning.

In the tensioned side we will only have the bolts in tension.

Similarly to a hyper static structure the stiffer side (in this case the one under compression) is able to take more load.

This works like a beam supported by springs:

In the picture on the left all the springs have the same stiffness. This would be the current design model, as in the formula shown above.

In the picture on the right the tension springs (right side of the beam) have only half the stiffness.

This is just to show how stiffness affects the force distribution, in a real anchor cage the loss of stiffness when decompression occurs might be over 80% as the concrete area contribution it is much bigger than the bolts area (total stiffness would be Es*As+Ec*Ac, being Es and As the area and elastic modulus of steel, and Ec, Ac the ones from concrete).

The “softer springs” on the right take less load, that is redistributed to the more rigid area on the left.

Please note that this would not happen in an isostatic structure (with only two supports)

As the neutral axis moves, the redistribution of forces changes. This lead to a non-linear calculation.

To perform this analysis we can implement a model with a homogenized concrete-steel section, and with variable parameters depending of the location of the neutral axis. Using this type model, we would be able to obtain the maximum stress on concrete and the tensile force on the pre-stressing element.

This way the anchors size may be adjusted, and we will get a more accurate value for the concrete compression which is slightly underestimated with the current models.

I am not going more deep into this boring details about calculations but I think that it is interesting to know that there is still room for optimization in anchor cage design.