2. Environmental Loads – Static, hydrodynamic and wind load on monopile foundation.

2.1. Ice loading

Sea ice is not expected, thus ice loads from laterally moving ice is zero. In this example ice loading occurs from:

(1) Atmospheric ice formation of 30 mm (from HSWL to + 85 m). This results in:
– Increase of the self weight by: ≈ π * 5.25 *0,03 * 80 * 9 ≈ 380kN
– Increase in the aerodynamic load on the tower because the diameter gets larger. This effect is insignificant and we can neglect it.

(2) Ice formation due to sea water spray from MSL to HSWL. This results in:
– Increase of the self weight of: ≈ π * 6 *0,1 * 3 * 9 ≈ 50 kN
– Increase in the hydrodynamic load on the TP (when considering the monopile). However, this is minor and it is chosen to neglect it.

(3) Ice formation due to sea water spray from HSWL up to 60m above MSL Thickness: decreasing linearly to 30mm
– It results in an increase of the self weight of: ≈ π * 5.25 *0,015 * 57* 9 ≈ 125 kN

2.2. Hydrodynamic Loading

Waves and current cause the movement of water around the monopile which results in hydrodynamic loads. Hydrodynamic loading consists of two forces.
– The drag force, due to the velocity of the water particles
– The inertia force, due to the acceleration of the water particles.

We apply Morison equation to calculate the hydrodynamic load:


The calculation is repeated three times using the following three combinations of wave and current values (5-year return period values and 50-year return period values). These combinations will be needed later when the load combinations for the ULS are considered.

  • Combination 1: Wave (5-year) + Current (5-year)
  • Combination 2: Wave (50-year) + Current (5-year)
  • Combination 3: Wave (5-year) + Current (50-year)
  • Vmax, 5y = 0.6 m/s (current velocity, 5-year return period)
  • Vmax, 50y = 1.1 m/s (current velocity, 50-year return period)
  • Hmax, 5y = 13,21 m (wave, 3-hour storm, 5-year return period)
  • Hmax, 50y = 15,07 m (wave, 3-hour storm, 50-year return period)

The water level for the hydrodynamic calculation is at the 50-year max of 3.1 m above MLS (DNV, 2011). The period of the wave is Tp=7 s. Linear wave theory and wheeler stretching is used. Marine growth is 100 mm. The assumption for the drag coefficient is Cd=1 and for the inertia coefficient Cm=2. Those coefficients were further increased to account for the boat landing and the J-tubes. The following formulas apply:

The modified CD and CM to account for the boat landing and the J-tubes are:

Transition Piece: Diameter = 6 m, CD,eq = 1.12, CM,eq = 2.01
Monopile: Diameter = 6.2 m, CD,eq = 1.12, CM,eq = 2.01

The total hydrodynamic Force & Moment at seabed level is calculated using the stick model. The structure is divided in 50 cm long pieces and the calculation is performed in many time steps until the maximum hydrodynamic force and moment is found. This is necessary since the maximum inertia and drag force do not occur simultaneously.

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-yearwater level, 5-year wave,  50-year current4800106

The results are validated using the guidance note under Section 4, 408 of DNV (DNV, 2011) which states that for linear waves, the maximum horizontal force on a vertical cylinder of diameter D installed in water of depth d and subjected to a wave of amplitude AW, can be calculated as:

and its arm measured from the seabed is:

The total horizontal load is 6000 kN which is in the order of magnitude of the results.

2.3. Aerodynamic loading

Wind loads are considered both for the wind turbine in operation (power production) and when the wind turbine is parked (idling of standing still). The drag force on the tower is also considered.

2.3.1. Wind turbine in operation

The trust force is:  

C­­­­­­Dax­­ and Dax are calculated using the blade element momentum theory.

The maximum Dax= 780 kN, applied at +85 (from MSL). This value is used for the load cases considered in the preliminary design.

However, during the various simulations that are necessary for the detail design the thrust force is calculated using Bladed (GH Bladed, 2012)

2. Parked wind turbine (idling of standing still)

The loading is calculated during the detail design of the jacket structure using Bladed.

3. Air Drag Force on the Tower

Due to the flow of air around the turbine’s tower, a drag force acts on the tower. This force is given by:

That drag force varies over the tower height. However, in these calculations it is assumed that the drag force has a constant value over the whole length of the structure, equal to the value calculated using the velocity at z = +45 m. Assumed is: Cd=0.8 and ρ=1,25 kg/m3

Two wind conditions are considered:

Air Drag  force on Tower [kN]
Force [kN]Acting at
50-year wind (@+45)28.8m/s18345 m Above MSL
5-year wind (@+45)26.5m/s15545 m Above MSL

Leave a Comment

Scroll to Top