3. Load combinations and design checks for monopile foundation

This section describes how we combine the simultaneously acting loads in order to derive the design load effects (M, V, N). It also shows the basic design checks for the verification of the structural integrity of the OWSS.

3.1. Loads Combinations

3.1.1. Preliminary design

For the preliminary design, only the ULS is considered and the loads are considered static.

The environmental loads calculated in Section 2, act simultaneously on the structure. In order to find their total effect we should combine them in such a way that the resultant loading has a return period of 50 years. According to DNV the characteristic combined effect will result from the load combinations shown in table F1. When considering a specific part of the structure, the characteristic environmental load effect at that part is the highest from the 5 combinations.

After deriving the characteristic load effect due to environmental loads, we further combined it with the characteristic load effects from the other load categories as shown in Table 1. Three set of load factors are applicable for the ULS.

3.1.2. Detail design

During the detail design of the jacket structure, more load combinations are taken into account and time-domain analysis is used to simulate the dynamic nature of the loads. Simulated time series of the simultaneously applied wind and wave load are used to load the model along with the loads from current, gravity etc. As per DNV-Table E1, the designer should consider 31 load cases for wind turbine load conditions and their companion wave load conditions, current conditions and water level conditions in order to capture the 50-year loading on the structure (50-year return period = 0.02 probability of exceedance). For the purposed of this example, we assess the structure for two load cases:

  • DLC 1.3 power production with Extreme Turbulence
  • DLC 6.1 Idling with 50 year wind conditions

3.2. Check of resonance frequencies

It is very important to check that resonance does not occur. The excitation frequencies of the main dynamic loads should not coincide with the natural frequencies of the structure. The stiffness of the monopile and that of tower greatly affect the natural frequencies to the structure thus we should make sure that the stiffness is such that the natural frequency of the structure is far from that of the loads in order to avoid resonance excitation.

The excitation frequencies that must be avoided are those:
(1) related to the range of rotational frequencies of the rotor and passing frequencies of the blades.
(2) from the excitation by waves. The low frequencies of short waves (T= 4-5 s) should be avoid because of their high influence on the fatigue lifetime.

Based on the previous considerations, for the REPower 5M turbine, the first natural frequency of the structure should be in the range of 0,22 – 0,31 Hz and the second natural frequency above 0,67 Hz. A 10% margin has been applied on the rotor speed range.

The allowable frequency range is derived from the rotational speed of the turbine:

  • Rotational speed: 6.9 – 12.1 rpm
  • 10% safety margin: 6.21 – 13.31 rpm equals to 0.10 – 0.22 Hz
  • 1P frequency: 0.10 – 0.22 Hz
  • 3P frequency: 0.31 – 0.67 Hz

The 1P range is determined by the rotation speed of the rotor and the 3P range by the passing frequencies of the blades. For a three-blade turbine, the 3P range is equal to the lower and upper rotational frequencies of the rotor divided by three.

3.3. Structural checks

3.3.1. Yield stress check

The stress in the structure should not exceed the yield stress of steel

The above condition should be checked at all sections of the structure. In this example, we only check the condition at the following locations:

  • Top of the tower
  • Bottom of the tower
  • Transition piece at elevation +5,00 (just above the end of the monopile)
  • Pile at seabed level

3.3.2. Buckling check

Buckling can be critical since it can occur before the yield stress is reached. Two types of buckling are possible:

(1) Global buckling: in order to verify that the structure does not collapse under compressive axial load and bending moment. The check is:

– Nd: axial compressive force from the most severe load combination
– Md: bending moment acting together with Nd
– Np: plastic axial resistance of the section under consideration
– Mp: plastic resistance moment of the section under consideration
– k: reduction factor for flexural buckling
– βm: bending moment coefficient
– Δn:  0.25 * κ * λ² ≤ 0,1
– λ:  slenderness

(2) Local (or shell) buckling: if the section is not stiff enough it can fail locally. When designing a monopile, this check can be critical during pile driving, when the pressure in the outer side of a tubular section in greater than that of the inner side. However, it is decided not to do this check since the soil is predominantly sand and it is not expected to have high pressure differences. When designing a jacket, the local buckling check is important for the braces, since they are not flooded. Especially, the lower braces because the pressure difference and axial compressive stresses are usually greater at those braces. The check is:

σx : axial compressive stress
σφ : circumferential compressive stress
σxu: ultimate compressive
σφu: the ultimate circumferential stresses

3.4. Fatigue checks

From the time-domain simulation of the structure in Bladed the number of cycles that each part of the structure undergoes is obtained at every strength range.  Using the S-N curve (Figure 6) from the DNV we can find the fatigue damage (rule of Miner) and then the Fatigue lifetime for every part of the structure. If the fatigue lifetime is smaller than the design lifetime then the dimensions of the members will be increased until the fatigue lifetime is greater that the design lifetime (fatigue damage D = 1)

Particularly, for the fatigue check of welded joints the stress concentration factor (SCF) are calculated of the detail and the stress is multiplied for which we want the fatigue capacity (Ni cycles to failure) with the SCF before going to the S-N curve to get the capacity Ni.

Figure 6: S-N curve

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