Introduction

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 consid ered, 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.

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 de' ned by the mass density, . , Poisson's ratio, . , and the shear modulus, G.

Established soil models for analysing 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 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 pile-to-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 group effects. Because the dynamic response of a pile group is very complex, simplified engineering approximations are accepted in practice.

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

M y and translation force F x (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).

Lumped-parameter mass spring-dashpot system

For flexibly supported founda ons, the coupled horizontal-rocking vibration can be analysed by means of the lumped-parameter mass-spring dash pot system (Figure 3) with frequency-dependent stiffs and damping co-efficients (Richart et al, 1970). The manufacturer will specify the required foundation impedance K d, which effectively de' nes the performance criteria of the foundation.

Foundation impedance K d can be defined by:

K d = K st (k d+ia 0cd )where d = horizontal vibration, rocking vibration, or coupling term;

K st is the static foundation stiffness;

k d is the stiffness co-efficient; c d is the damping co-efficient; i is the imaginary number.

The dimensionless frequency a 0 is defined by: a 0 = .Bs v where: . = the circular frequency of excitation; V s = the shear wave velocity of soils; B = half the width of a square foundation.

Available techniques for evaluating 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, k d and c d 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 foundation impedance, specifid by the manufacturer, can be calculated by using published engineering formulae 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 vibrations are known to generate relatively shallow dynamic pressure bulbs (one foundation width or less, in general), it is recommended that pub shed 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).

Design example

A shallow square foundation is to be designed for a proposed turbine. It is assumed that the foundation stiffness specified by the manufacturer is K r = 10.0 Î 10 10 Nm/rad.

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 ò The Poisson's ratio is 0.25 ò The equivalent shear modulus G of the half space model is 250MPa ò 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: a 0 = .Bs = 0.14 v Using the published results (Bu and Lin, 1999), it can be shown that the foundation stiffness K r = 58 Î 10 10 Nm/rad is greater than the required stiffness, 10.0 Î 10 10 Nm/rad.

Conclusion

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.

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