4. Structural design of monopile foundation – Calculation Example

This chapter presents the design of a monopile OWSS. It is choses to design for a water depth of 28 m since this is the average water depth at the site.

4.1. Initial dimensioning

4.1.1. Dimensions of Monopile

The design starts with an initial estimate of the geometry. The monopile diameter is chosen such that the first natural frequency of the structure is within the allowable soft –stiff range. As presented in Section 3, this range is between 0,22 to 0,31 Hz so is aimed for a first natural period near 0,26 Hz. Using a stick model and formulas (1) and (2), a first estimate of the diameter is obtained. That was 6.5 m with the wall thickness set to 80 mm (D/t ≈ 80-90) and f=0.258.

The next step to improve the design is to use readily available calculations tools available (spreadsheets, ANSYS etc). Using those tools it is possible to take into account the change in diameter and thickness along the structure, the concentrated weights, the RNA, the soil properties etc. The results of such analysis show that we can use a monopile with D=6.2, and TP and tower as described in following pages. Then, the natural frequencies of the structure are within the limits set. The first natural period is 0.266 Hz (soft-stiff range) and the second natural period is 1.062 Hz (stiff-stiff range).

     Table 18: Modal frequencies of monopile support structure

f10.266  Hz f66.348  Hz
f21.062  Hz f79.680  Hz
f33.198  Hz f811.287  Hz
f45.916  Hz f911.368  Hz
f56.008  Hz f1013.349  Hz

Since the currently available hammers for driving piles are limited to diameters up to 5.5 m, a conical part is used to decrease the top diameter of the monopile to 5.5 m. The conical part extents from el. – 5 m to el. -7 m. For more dimensions, please refer to Drawing 1, Appendix 2.

The top of the monopile is at el. +4.75 m for easy installation of the transition piece. The initial thickness of the monopile is set at t = 80 mm (D/t = 80). The required thickness is determined later when performing the necessary ULS checks.

4.1.2. Dimensions of Transition Piece (TP)

The transition piece (TP) extents from just below the LSWL to the interface level. A grout connection connects the TP to the monopile. The characteristics of the connection influence our decision for the initial dimensions of the TP. The following are considered:

  • Grout length = 1,5· Dpile + grout skirt at bottom of TP = 1,5 · 5,5 + 0.5 = 8,75 m
  • Grout thickness = Min thickness + allowance for alignment (0.5°) + allowance for wall thickness variation of TP = 150 mm +230 mm + 10 mm = 390 mm
  • Transition piece diameter = Dpile + grout thickness + 2 * TP wall thickness = 5,5 + 0,39 + 0,14 ≈6 m

Given the above considerations, the TP diameter at the location of the connection should be 6 m. Since the bottom diameter of the tower is also 6 m we chose to keep the same diameter for the full height of the TP. 

4.1.3. Dimensions of Tower

For the initial geometry for the tower information is used from other wind farms (Lars Bulow, 2008).

  • @ Tower BASE: D=6 m, t=35 mm
  • @ Tower TOP: D=4,5 m, t=20 mm
  • Tower Mass =π*5.25*0.026*70*7,850 = 235 tonnes

4.2. Loads

The loads calculated in Section 2 are summarized below


Thrust Force
Dax= 780 kN at +85 (from MSL)

Drag  force on Tower
50-year wind @+45m – 28.8 m/s —> Force 183 kN acting at 45 m above MSL.
5-year wind @+45m – 26.5 m/s —> Force 155 kN acting at 45 m above MSL.


DescriptionHydrodynamic Force at seabed level [kN]Hydrodynamic Moment at seabed level [MNm]
50-year water level, 5-year wave,  5-year current4650103
50-year water level, 50-year wave,  5-year current5450122
50-year water level, 5-year wave,  50-year current4800106


Below is a breakdown of the weight of monopile

Mass (t)Weight (kN)
Tower (π*5.25*0,0275*7,850 = 3.56 t/m )2502500
Total at interface level6600 kN
Transition piece (π∙6,0∙0,08∙19∙7,850)2002000
Pile above seabed (π∙6,3∙0,08∙32∙7,850)3973970
Buoyancy (π∙6,0∙0,08∙19∙7,850)-50-500
Total Vertical action at seabed level12070 kN
≈12.07 MN
Table 20: Weight breakdown for monopile OWSS

The weight of all other parts of a wind turbine is neglected (secondary steel, platform, fittings, etc.)
The variable weight load from people, equipment, boats etc. is also neglected.

4.3. Load Combinations

4.3.1. Combining the environmental loads

We prepared load combinations 1,2 and 3 as descript in section 4.1. We choose not to calculate the combination 4 and 5 and instead add the weight of the 50-year ice on the weight of the structure. This results in an increase of vertical load (at foundation level) of less than 5% and since we already have omitted the weight on secondary steel etc, we do not expect that this addition will lead to an overdesign that will influence the overall design of the structure.

50-year environmental load combinations - Offshore wind monopile design
Offshore Monopile load combinations
Figure: Environmental Load Combination 2
Monopile loading combinations DNVGL
Figure: Environmental Load Combination 2
Wind Turbine Monopile loading combinations DNVGL
Figure: Environmental Load Combination 3

Combining loads for the ULS

Next, we calculate the design load effects for selected sections of the structure. We choose to do this for section A, B, C, D as descript below and shown in (Figure 8):

  • Top of the tower (+ 83 m)
  • Bottom of the tower (+ 15 m)
  • Transition piece at elevation +5 m (just above the end of the monopile)
  • Pile at seabed level (- 28 m)

To find the design load effect we combine the load effects from environment load, from permanent load and from variable loads. These is done using two load factor sets (set A and set B) as descript in section 4.1. When forming those sets, for the environmental load effects we use the values that come from the most sever environmental load combination (i.e. 1, 2, 3)

4.4. Strength checks

The structure is checked to ensure that the yield stress is not exceeded and that no global buckling occurs. The equations and criteria of the check are presented in section 4.3. The results are shown in Tables 21 and 22

The applied material factors are:
– γm = 1.1 ULS stress checks (as given in C103, Sec.7, DNV for tabular members)
– γm = 1.2 ULS global buckling check  (as given in C104, Sec.7, DNV for tabular members)

Tables 21 and 22 present the main loads and strength checks at sections A,B,C and D. More specifically:

  • The load effects (M, V, N) for each load category
  • The total load effects using load factor set (a)
  • The total load effects using load factor set (b)
  • The yield stress check
  • The buckling check

Combined design load effect at the ULS due to loading from various types of loads

Load typeLoad factor Set (a)Load factor
Set (b)
Section Ael: + 83Section Bel: + 15
M [MNm]N [MN]M [MNm]V
Environmental (highest load effect from the 3 combinations)1.001.353.1200.780.55060.0900.9630.550
Total load  using load factor set a3.1200.785.67560.090.9638.790
Total load  using load factor set b4.2121.054.84381.121.3007.335
Wall thickness of section[m]0.0200.035
Section diameter[m]4.506.00
Section Area[m²]15.9028.27
Moment of Inertia[m4]0.722.97
Design stress (set a)[MPa]10.1761.03
Design stress (set b)[MPa]13.5582.23
σ yield, d (factored)304.5304.55
Buckling check0.4020.4010
Table 21: Load effects and strength checks for selected sections

Table 22:  Load effects and strength checks for selected sections (con’t)

Combined design load effect at the ULS due to loading from various types of loads
Load typeLoad factor Set (a)Load factor
Set (b)
Section Cel.: + 5Section Del.: -28
M [MNm]V [MN]N [MN]M [MNm]V  [MN]N [MN]
Environmental (highest load effect from the 3 combinations)1.001.3569.7200.9630.550221.4556.3850.550
Total load  using load factor set a69.7200.96310.078221.4556.38515.658
Total load  using load factor set b94.1221.3008.365298.9648.62012.829
Wall thickness of section[m]0.0700.080
Section diameter[m]6.006.20
Section Area[m²]28.2730.19
Moment of Inertia[m4]5.947.49
Design stress (set a)[MPa]35.5892.21
Design stress (set b)[MPa]47.85124.21
σ yield, d (factored)295.45286.36
Buckling check0.27800.492
Table 22:  Load effects and strength checks for selected sections (con’t)

Scroll to Top