The Procedure for Designing of Monopiles for Offshore Wind Farms
As the demand for clean, renewable energy in America increases, the focus of
geotechnical and ocean engineers has been greatly shifted to offshore wind farms. With
many wind farms currently in the planning stages across the east coast of the United
States, it is clear that the design of the monopiles for the wind farms could become a very
lucrative field. This paper intends to focus on one specific site off, of Block Island, RI,
and to consider the loads that the monopiles will face, and the sediment properties that
the monopile will be installed in, as well as to look at already installed monopiles in
European wind farms for a reference, and show how to design a monopile. The ultimate
goal of this paper is to create a reference for the basic design of monopiles for offshore
wind farms. However, there are two precautions. This first precaution is that while a
reduction of allowable normal force is talked about, research still needs to be done to
determine exactly how much reduction is required. The second precaution is that the
monopile designed in this instance is a straight pile, and is not tapered, which is the
preferred method of design.
Monopiles are the most commonly used structure in the design of wind
farms. In Europe, there are many functional wind farms, and nearly all of them utilize
monopiles for their structure and foundation. A brief summary of many of these wind
farms was compiled by Garrad Hassan and Partners Limited for the United States Army
Corps of Engineers [Hidgetts et. Al 2003]. Of all of his summarized wind farms, only 4
of them are similar to our site. These four can bee seen summarized in table 1.
(Table1) This table shows the basic site description for 4 European Wind Farms similar
to the Wind Farm sited for off of Block Island.
While very similar to our site, there are a few noticeable differences. The
first is that the water depth off of Block Island is well over 10 meters in most cases, and
typically upwards of 17. Also, the extreme wind and wave forcing in these areas are
considerably lower than the extremes that the Block Island site will experience. Both of
these factors will lead to the monopile being larger for the Block Island site, than for any
of these. A better estimate for the proper size comes from a paper by Kesny and
Wiemann. They use finite element analysis and created a table to demonstrate
appropriate monopile dimensions for a larger scale monopile. This can be seen in table 2.
(Table 2: This table shows appropriate monopile dimensions for monopiles ranging in
diameter from 1 meter to 6. [Lesny and Kesny])
While taking lessons from European wind farms is a very good starting
point, it alone will not suffice for designing the structural monopile. Therefore the
methodology used by European wind farms must be taken into account, and then
implemented on the Block Island parameters. Combining this method with a basic
understanding of civil engineering, one can create a monopile for a wind farm.
For reference throughout this paper, foundation refers to any part of the monopile
below the mudline, structure refers to any part of the monopile above the mudline, and
the term monopile refers to the entire monopile itself.
There are four main aspects to consider in deciding on a site for the wind
farm, and ultimately the monopiles. The site chosen must have ample winds, not have
any site restrictions ( such as maritime conflicts, legal conflicts, unusable water depths, or
anything else that would prevent the installation of a wind farm), the wave data must be
known, and finally the seafloor sediment must be researched to discover the geotechnical
properties at the site. The first two are not important for the design of the monopile (the
ultimate force and the cyclic loading of the wind will be important, but it will be
discussed later). However, the second two are crucial for the design.
To be ready to install a monopile, a geotechnical site analysis must
first be performed at the site. This investigation will give us many geotechnical
parameters, but for the design of the foundation, only the internal friction angle, bulk
density, and the depth the bedrock will matter.
To retrieve these parameters, a ship investigation will be needed. To find the
depth to bedrock, ground penetrating sonar would have to be used. The reflection of the
noise off of different sediment types, and ultimately, the bedrock, can be timed. Using
the speed of sound in the different materials (water and different sediment types), the
depth to bedrock can be calculated. To discover the internal friction angle and the bulk
density, a core sample must be taken. In this instance a simple gravity corer could be
used. Once the sample is taken, a simple bulk density test could be taken (take a sample,
find the mass, divide by the sample’s volume). To determine the internal friction angle a
triaxial test must be done. This triaxial test needs to be run for both the drained and
undrained conditions, to ensure that when the monopile is installed there will be no
failure. The drained triaxial test will provide the internal friction angle that is going to be
passed on to the design of the foundation.
The sediment in this area of Rhode Island was deposited here by the advance of
the Wisconsinan Glacier. This means that as the glacier advanced, it moved a lot of rocks
and boulders along with it. Block Island is actually and end moraine from this glacier.
Since the glacier not only forced large debris in this area, but also compacted and
consolidated any sediment it was on top of, we can expect very dense sediment.
Unfortunately, from prior inspection of this area, it is very likely that the depth of the
sediment will not be sufficient for the design of the foundation, and that drilling into the
bedrock is going to end up being the solution for the construction.
- how we do it
- why we do it (parameters needed)
- Typical of RI
o Why its typical
When investigating a site the wave data must be known. For the
installation of a monopile in the United States, we can use WIS nodes to retrieve
hindcasted wave data, and from there predict storm waves that will occur in the future.
To do this the wave data must be retrieved and then plotted on the proper probability
paper (I will not go into the use of probability paper, for more information on this see
http://www.itl.nist.gov/div898/handbook/apr/section2/apr221.htm). You can then
determine the wave height for the 100 year design wave, and thusly determine the
ultimate wave loading on the monopile (this equation is given later). Table 1 has the
values of certain design waves for a wind farm site located off of Block Island. This is an
example of what wave data would look like when completed.
When designing a monopile, the loading of the monopile must be looked
at in two different aspects. These two aspects are static loading and dynamic loading.
Static loading refers to “the worst case scenario” loading, or the loading of the extreme
wave and wind. Dynamic loading is the constant loading of winds and waves on the
structure over a set period of time.
When considering the static loading we look at the monopile as a
cantilever beam fixed at one end. We then consider the extreme wave and extreme wind
to be point loads applied to the pile, and we consider the hydrostatic water pressure and
the force of the wind on the monopile as distributed loads. Each of these forces has a
corresponding moment force about the mud-line to be taken into account. To be more
precise, the point about which the moment force acts is the edge of the monopile on the
far side of the pile. Fig. 1 shows the free body diagram of the system, and more aptly
describes the forces, moments, and the point about which the moments would act.
Design of a Monopile:
Maximum Loading Failure Analysis of Mono-Pile Structure:
We must design the mono-pile to withstand a scenario where the extreme
design wave and wind load of a 100 year return period occur at the same time, and in the
same direction as one another. To do this we must find the critical stress that will act on
the mono-pile during this event. The critical stress is given by the equation
_c = p_2 + 4 _ &2.
In this equation sigma is defined by using the Normal stress (N), which is
the stress on the mono-pile caused by the normal force, and a stress caused by the
moments. The exact equation is,
_ = N=A +M/(S))
Where N is the normal force, A is the Cross Sectional Area, M is the sum
of all the moments, and S is given by the equation
S = I/c
Where I is the moment of inertia for a hollow cylinder, and c is the
distance from the neutral axis to the farthest portion of the beam, or in this case, half of
the diameter of the pile. When finding the critical stress we also take into account Z, or
the Von Mises stress. The Von Mises stress refers to the stress found using a theory
called the "Von Mises Hencky criterion for Ductile Failure." This theory states that while
no one stress in a three dimensional system is enough to cause failure, the combination of
the stresses into an equivalent stress, commonly referred to as the Von Mises stress, and
might be able to cause failure. This stress is found by using the equation
Z= 2 *T/A (12)
Where T is the sum of all shear forces on the mono-pile, and A is the area
found with the equation
A = 2 _ _ _ r _ t (13)
r = (D �� T)=2 (14)
Where t is the thickness and d is the diameter. Once these values are found
we can compare the critical stress to the resistance of steel divided by a factor of safety.
The factory of safety is as 2.0 [API]. The resistance of steel is also known as its ultimate
bearing capacity, which is found to be about 340 MPa.
Fatigue Failure Analysis of Mono-Pile Structure:
The next design criterion is the fatigue damage on the structure. Fatigue
damage is said to be the accumulation of damage under the ultimate stress that will
eventually lead to the failure of the structure. In this specific case, the damage caused
under the critical stress will be caused by the sea states at our mono-pile. This damage is
assumed to be linear, and thusly we can use Miner's sum to determine the damage caused
by all the sea states in one year. The equation we use for this is
DD = _nc=ND (15)
In this equation DDi is the Design Cumulative Fatigue Damage, I is our
total number of sea states, nci is the amount of occurrences for a given stress cycle (sea
state), and NDi is the number of cycles to failure at this stress cycle. To determine our n
value, we will be using a finite element analysis program called ANSYS. ANSYS will
model the mono-pile and apply our sea states and wind conditions to the mono-pile and
will then output us a time stress history. Using the rain-flow counting method we will
determine the amount of occurrences for this time period. We can then extrapolate that
out for the amount of occurrences for an entire year. The rain flow counting method is
done with the following procedure :
1. Rearrange the history to start with the highest peak
2. Starting from the highest peak, go down to the next reversal. Proceed
horizontally to the next downward range; if there is no range going down from the
level of the valley at which you have stopped, go upward to the next reversal.
3. Repeat the same procedure upward instead of downward and continue these
steps to the end.
4. Repeat this procedure for all the ranges and parts of a range that were not used
in previous procedures.
Once we find the occurrences we must then find the N values, or the amount of
cycles till failure at a given stress. This will be done by using the S-N curve described in
the DNV. This equation is given as
log(N) = log(a) �� m _ log(__(t=tref )) (16)
Where _ _ is the stress range from the time stress history outputted by ANSYS, m
is the slope from the log (N)- log (S) plot, given in the DNV as m = 3, log (a) is the
intercept of the log(N) 10
axis, given by the DNV as log (a) = 12.164, tref is a reference thickness given in the
DNV as 30mm, t is the design thickness of the mono-pile, and k is the scale exponent,
given in the DNV as 2.5. We can simply sum or nn values for every sea state that will be
seen in a year. If this value is less than 1/20, then this thickness and diameter are
acceptable to survive for the full 20 year design life. Because ANSYS is such a complex
program, it has been estimated that if we use all 79 sea states, 10 different diameters, and
10 different thicknesses, it would take a considerable amount of computing time to
complete our calculations. This is unreasonable, and therefore we have devised a new
method to group the sea states into representative sea states. The forces will be taken that
each sea state imparts on the monopile, and then the sea states will be sorted by these
values, not by the period or the wave height. The forces of a wave on a monopile can be
found using the equation
ForceWave = 4*ro*g*H/2/(k^2)*sinh(k*(d+H*sin(alpha)))/tanh(k*d)*xi;
Where ro is the density of water, g is gravity, H is the wave extreme wave height,
k is the wave number, d is the depth, and alpha and xi are variables given by table. Also
the thicknesses and diameters will be reduced from 10 each, to 5 each.
Buckling Failure Analysis of Mono-Pile Structure The third design consideration
is buckling. Buckling is a form of structural failure caused by a large compression stress.
This stress is less than the maximum allowable compressive stress given by the equation
N = _2 _ E _ I=lb (17)
Where E is defined as the young's modulus, I is the moment of inertia, and lb is
the buckling length. The buckling length for a pile that is rigidly clamped on only one
end is two times the length of the pile. In buckling there is another aspect we must be
wary of; slenderness. Slenderness occurs when a structure is too tall and narrow to
support the Normal Force applied to it. It is defined as
_ = lb=i (18) and i2 = I=A (19)
I and A are the same as previously noted. If the slenderness value found exceeds
15, this is when a reduction in the allowable compressive stress occurs. While this
reduction factor is yet to be determined, it has been found that the smallest monopile
diameter necessary to avoid a need for a reduction in the normal stress is 24 meters. This
is not possible, so the reduction of the allowable stress must be researched and factored in
to the final monopile design.
Design of the foundation
When designing a foundation for a monopile we once again look at the
design as a cantilever beam with one fixed end and one free to move. This alone does not
accurately describe the behavioral properties of a monopile. Instead we attach springs
along the monopile, simulating the sediment surrounding the monopile. This method of
modeling is known as the p-y method. The equation of the p-y curve is
p(y; z) = A _ pu(z) _ tanh[(ks _ H)=(A _ pu(z)) _ y] (32)
Where pu(z), the maximum sub-grade reaction is: (use the smaller value of Pu for
pus(z) = (C1 _ H + C2 _ d) _ _ H (33)
In equation (2) the coefficients C1,C2, and C3 can be determined using Figure1 (API
pud(z) = C3 _ d _ _ H (34)
And A is a factor to account for static loading
ks= Initial Modulus Subgrade Reaction (determined from figure(2) )
H= Depth into soil (m)
A= Correction factor (Reese et al. 1974)
gamma= effective soil weight (kN=m3)
phi= Angle of Internal Friction (deg)
d= Average Pile Diameter from soil surface to depth H (m)
y= lateral deflection (m)
When this equation is fully solved, it will return the minimum penetration
depth needed for the monopile.
This method of design was created for small diameter monopiles, one to
two meters in diameter, and not the larger diameters required for the monopiles used in
off shore wind farms. When applied to large diameter monopiles, the deflection of the
monopile is more than is predicted. Because of this it is clear that the p-y method needs
some sort of scaling factor for large diameter monopiles. This scaling factor has yet to be
created and validated, but there is another way to compute the minimum penetration
depth of the monopile: finite element analysis. Using finite element analysis it is possible
to fully model the monopile and from there extract the minimum penetration depth.
What we have done
- design of structure
o need wind data, wave data, type of steel, run iterations
- design of foundation
- dimensions of structure, bulk density, p-y curves for
Must drill into bedrock
Does not take into account scour
Need to research the reduction of loads due to slenderness