TECHNICAL
NOTE
Engineering considerations
group effects. Because the dynamic
response of a pile group is very
complex, simplified engineering
approximations are accepted in
practice.
for design of wind farm
foundations
The nature of wind farminduced loading
Information on the magnitude and
the characteristics of the dynamic
loads imposed by the turbine on the
foundation are specified by the turbine manufacturer. The maximum
turbine-induced loads at the foundation base are commonly the coupled
bending moment My and translation
force Fx (Figure 2). In most cases,
rocking vibration dominates the
foundation response; the rotor frequency, f, is usually within the low
frequency range (f ≤ 1Hz).
The direct consequence of the
nature of the dynamic excitation
from a turbine is that a rocking-dominated shallow foundation may induce
large strains directly under its edges.
Also, under low frequency vibration,
a laterally oscillating pile foundation
may generate large strains, particularly in cohesive soil layers.
The degradation of pile capacity
as a result of cyclic loading is an
important factor and has been discussed by Zeevaert (1991).
By David S Bu, Haskoning UK
Introduction
It should be noted the magnitudes
of vibration satisfying serviceability
usually involve relatively small
dynamic displacement amplitudes,
compared to the several centimetres
that is the usual limitation for static
foundation settlements.
As a result, soils can be consid­ered
to behave approximately as linear
elastic materials for small amplitudes
of strain. Soil properties can then be
defined by the mass density, ρ, Poisson’s ratio, ν, and the shear modulus,
G.
Established soil models for analy­
sing foundations subject to dynamic
loads include homogeneous half
space, homogeneous soil stratum
underlain by bedrock and inhomogeneous profiles, in which the shear
modulus increases linearly with
depth.
Alternatively, the actual beha­viour
of cyclically loaded soils can be
approximated
by
equivalent
linear soil properties. For example,
Shake analysis software (Schnabel et
Twenty one gigawatts worth of large
renewable power projects are being
planned in the UK over the next five
years (The Economist 5 February
2005). If all the projects intended,
plus those currently being consid­ered,
are built, this would mean about 200
extra wind farms. The design of wind
farm foundations is, therefore, a subject of great importance.
This technical note highlights the
major issues that need to be considered when designing wind farm
foundations. An illustrative example
is also given.
Soil models
Foundations for wind farms should
be reasonably capable of providing
sufficient static-bearing capacity; in
practice, a factor of safety of three.
An important part of successful
foundation design is the analysis
of the foundation response to the
dynamic loads from the anticipated
operation of the turbine.
1
al, 1972) adopts the equivalent linear
approach to determine the equivalent
shear wave velocity of layered ground
(Figure 1). The equivalent shear
modulus can then be approximately
determined from the Shake results.
Shallow foundations and pile
foundations for wind farms
Large, square, shallow foundations
are frequently used for wind farms.
There are few practical cases where
the use of piles is necessary. But if a
piled foundation has to be used – for
example, because the design loading
exceeds the bearing capacity of a
shallow foundation – then static pile
design methods are appropriate.
The design calculation requires
particular consideration of pileto-pile interaction, when a pile
group is needed to increase the natural frequency of the vibratory system
and to decrease the vibration amplitude.
In fact, dynamic pile group effects
differ considerably from static pile
Lumped-parameter mass
spring-dashpot system
For flexibly supported founda­tions,
the coupled horizontal-rocking vibra­
tion can be analysed by means of
Incident
wave
For each sublayer, m:
shear modulus = Gm
damping ratio = λm
mass density = ρm
m
m+1
Reflected
wave
N
(half space)
Figure 1: Nomenclature for layered soil deposits.
28
z
x
y
Figure 2: Definition of co-ordinate system.
ground engineering december
2005
the lumped-parameter mass-spring
dash­pot system (Figure 3) with frequency-dependent stiff­
ness and
damping co-efficients (Richart et al,
1970). The manufacturer will specify
the required foundation impedance
Kd, which effectively defines the performance criteria of the foundation.
Foundation impedance Kd can be
defined by:
Kd = Kst (kd+ia0cd )
where d = horizontal vibration,
rocking vibration, or coupling term;
Kst is the static foundation stiffness;
kd is the stiffness co-efficient; cd is the
damping co-efficient; i is the imaginary number.
The dimensionless frequency a0 is
defined by: a0 = ωB
vs
where: ω = the circular frequency
of excitation; Vs = the shear wave
velocity of soils; B = half the width
of a square foundation.
Available techniques for evalu­
ating foundation impedances are
analytical methods (Arnold et al,
1955), boundary element methods
(Bu, 1997), finite element methods
(Kausel and Roesset, 1975) and hybrid
methods (Mita and Luco, 1987).
In general, kd and cd depend
upon the nature of the turbineinduced dynamic excitation; the
geometry and inertia of the foundation and superstructure; and the
nature and deformability of the
ground.
Once the geotechnical parameters
have been defined, the target founda­
tion impedance, specified by the
manufacturer, can be calculated by
using published engineering formu­
lae and dimensionless charts (see,
for example, Gazetas, 1991).
It should be noted that the simple
half-space idealisation is reasonably
applicable to not-very-deep soil
deposits.
As horizontal and rocking vibra­
tions are known to generate relativ­
ely shallow dynamic pressure bulbs
(one foundation width or less, in
general), it is recommended that
pub­
lished results for half space
models are adopted for the design of
wind farm foundations.
The lumped-parameter massspring-dashpot approach is also
applicable to pile foundations. However, if the prediction of the pile
head impedances (Figure 4) of
single piles is difficult, the prediction of the pile head impedance of
pile groups, accounting for pileto-pile interaction, is even more
problematic.
Again, because the dynamic
response of a pile group is very
complex, simplified engineering
approximations have to be adopted
in practice (see, for example, Gazetas, 1991; Prakash and Puri, 1988).
Site investigation shows that the
ground profile is a few metres of
clay above weathered rock, where it
is assumed the foundation will sit.
The effect of the clay layer and the
foundation embedment are conservatively ignored.
The design parameters are:
• The equivalent shear wave
velocity predicted by Shake is
350m/s
• The Poisson’s ratio is 0.25
• The equivalent shear modulus
G of the half space model is
250MPa
• The turbine operating
frequency is 1Hz
By using a trial and error process,
it can be demonstrated that a square
foundation with B = 7.5m (ie the
width of the foundation is 15m) satisfies the static design requirements
and can provide sufficient foundation stiffness:
Dimensionless frequency:
a0 = ωB
v s = 0.14
Using the published results (Bu
and Lin, 1999), it can be shown
that the foundation stiffness Kr = 58
× 1010Nm/rad is greater than
the required stiffness, 10.0 ×
1010Nm/rad.
Design example
Conclusion
A shallow square foundation is to be
designed for a proposed turbine. It
is assumed that the foundation stiffness specified by the manufacturer is
Kr = 10.0 × 1010Nm/rad.
Rigid block having equivalent
mass and moment of inertia
about horizontal axis
Equivalent
horizontal spring
Equivalent
horizontal damping
Generally, foundations for wind
turbines are low-frequency machineloaded foundations subjected to
coupled horizontal-rocking vibration. Turbine-induced vertical and
torsional dynamic loads imposed
directly on the foundation are practically negligible.
In practice, methodology for the
design of machine foundations is
equally applicable to the design
of wind farm foundations.
References
Arnold RN, Bycroft, GN, and Warburton GB
(1955). Forced vibrations of a body on an infinite elastic solid. J. of Appl. Mech. Vol 77, pp
391-400.
Bu S (1997). Infinite boundary elements for the
dynamic analysis of machine foundations. Int.
J. for Num. Meth. In Engrg., Vol 40, pp 39013917.
Bu S and Lin CH (1999). Coupled horizontalrocking impedance functions for embedded
square foundations at high frequency factors.
Journal of Earthquake Engineering, Vol 3, pp
561-587.
Gazetas, G (1991). Foundation Vibrations.
Chapter 15, Foundation Engineering Handbook, ed. Fang HY, Chapman & Hall.
Kausel E and Roesset JM (1975). Dynamic stiffness of circular foundations. J. Engrg. Mech.,
ASCE, Vol 101, pp 771-785.
Mita A and Luco JE (1987). Dynamic response
of embedded foundations: a hybrid approach.
Comput. Meth. Appl. Mech. Engrg., Vol 63, pp
233-259.
Richart FE, Hall JR, and Woods RD (1970).
Vibrations of Soils and Foundations. PrenticeHall, Englewood Cliffs.
Prakash S and Puri VK (1988). Foundations for
machines: analysis and design. John Wiley and
Sons.
Schnabel PB, Lysmer J and Seed HB (1972).
Shake: a computer program for earthquake
response analysis of horizontally layered site.
Report EERC 72-12, University of California,
Berkeley.
Zeevaert, L (1991). Foundation problems in
earthquake regions. Chapter 17, Foundation
Engineering Handbook, ed. Fang HY, Chapman & Hall.
KMH
KHM
KHH
KMM
eiωt
eiωt
Equivalent
rotational spring
Equivalent
rotational damping
Figure 3: Lumped-parameter mass-spring-dashpot system.
ground engineering december
2005
Figure 4: Definition of pile head impedances.
29