Yes, sometimes the diameter of your gravity foundation is not governed by soil bearing capacity…
Sometimes, when you run all the foundation design checks (bearing capacity, sliding, overturning, settlement…) you discover that the one that actually sizes the foundation is none of the above.
It is rotational stiffness. This is the check that could drive your diameter some metres beyond what bearing capacity alone would require, and yet it is something you might not be familiar with.
Why stiffness and not strength
In conventional building design, you size a shallow foundation based on bearing capacity. Settlements matter too, but they are a serviceability check. For a wind turbine, the picture is fundamentally different.
A wind turbine is a tall, slender, dynamically loaded structure. The rotor spins at a certain frequency (the 1P frequency), and the blades pass the tower at three times that frequency (the 3P frequency). The entire system — rotor, nacelle, tower, foundation, and soil — has a natural frequency that depends on the stiffness of every component. If that frequency gets too close to 1P or 3P, the structure resonates, and resonance means accelerated fatigue and eventually structural failure.
The OEM specifies a minimum rotational stiffness for the foundation-soil system, expressed in GNm/rad. This ensures the natural frequency stays safely between 1P and 3P (the soft-stiff design range, where many modern onshore turbines operate).
If the rotational stiffness falls below the OEM’s minimum, the natural frequency drops into the 1P range and the turbine cannot be certified for that position.
This is why rotational stiffness in some cases governs design. Bearing capacity might be satisfied with a 18-metre diameter, but the stiffness check might demand 20+ metres.
And you cannot negotiate with a frequency — either you are outside the resonance range or you are not.
The formula
For a rigid circular foundation on an elastic half-space, the rotational stiffness is:
K = 8 G r₀³ / 3(1 – v)
Where G is the shear modulus of the soil, r₀ is the equivalent radius of the foundation, and v is Poisson’s ratio.
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