Journal of the Franklin Institute 348 (2011) 1470–1487 www.elsevier.com/locate/jfranklin
Optimized frequency-based foundation design for wind turbine towers utilizing soil–structure interaction$ Mohammad AlHamaydeha,, Saif Hussainb a
Assistant Professor, Department of Civil Engineering, American University of Sharjah, Sharjah, UAE b President, Seismic Structures International, Los Angeles, CA, USA Available online 24 April 2010
Abstract This study illustrates design optimization for multiple wind towers located at different villages in Alaska. The towers are supported by two different types of foundations: large mat or deep piles foundations. Initially, a reinforced concrete (RC) mat foundation was proposed. Where soil conditions required it, a pile foundation solution was devised utilizing a 30 in thick RC mat containing an embedded steel grillage of W18 beams and supported by 20–24 in grouted or ungrouted piles. For faster installation and lower construction cost, all-steel foundations were proposed for these remote Alaska sites. The new all-steel design was found to reduce the natural frequencies of the structural system due to softening the foundation. Thus, the tower–foundation system could potentially become near-resonant with the operational frequencies of the wind turbine. Consequently, the likelihood of structural damage or even the collapse is increased. A detailed 3D finite-element model of the tower–foundation–pile system with RC foundation was created using SAP2000. Soil springs were included in the model based on soil properties obtained from the geotechnical investigation. The natural frequency from the model was verified against the tower manufacturer analytical and experimental values. When piles were used, numerous iterations were carried out to eliminate the need for the RC and optimize the design. An optimized design was achieved with enough separation between the natural and operational frequencies. The design
$
This paper appeared in a preliminary form in the Proceedings of The Third International Conference on Modeling, Simulation and Applied Optimization (ICMSAO’09), Sharjah, UAE, 2009. Corresponding author. Tel.: þ971 6 515 2647; fax: þ971 6 515 2979. E-mail addresses:
[email protected] (M. AlHamaydeh),
[email protected] (S. Hussain). 0016-0032/$32.00 & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2010.04.013
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successfully avoids damage to the structural system, while eliminating the need for any RC in most cases. & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Wind; Turbine; Tower; Foundation; Design; Soil; Structure; Interaction
1. Introduction Wind towers have to sustain continuous vibration-induced forces throughout their operational life. The operating frequency of the three-blade turbine could potentially cause dynamic amplification of these forces significantly posing a threat to the overall structural integrity. Sufficient separation of the structural system natural frequency from the turbine operational frequencies is a key to avoiding potentially catastrophic failures. The turbine operating frequency is typically different from the structural system natural frequency, but could approach it as higher turbine output is obtained. Idealized assumptions of fixity at the base of the tower are un-conservative; a more realistic analysis accounting for foundation flexibility yields lower estimates for the natural frequency of the system. In such cases, soil–structure interaction (SSI) needs to be considered [1]. SSI is increasingly becoming part of the design codes. Several modern codes provide SSI guidelines and provisions as well as foundation design for dynamic loads. For example, wind turbine foundations could be designed using the British Standards, Eurocodes or American standards. However, considerably more refined wind loading data can be utilized for foundation design using a more specific code: IEC 61400-01 [2]. An elaborate discussion of wind turbine foundation analysis and design is well presented by Bonnett [3]. One of the investigations of the wind turbine foundations was conducted by Gill et al. [4] in 2002. Some of the challenges in making a monopole foundation solution work on offshore arctic conditions were presented. A detailed finite element analysis (FEA) was conducted using ABAQUS to simulate the soil–structure interaction. Cyclic loading on the foundation was generated due to a combination of aerodynamic and hydrodynamic conditions. Time domain simulations were also generated by the GH BLADED software. Practical solutions to the mentioned challenges were introduced. Fei et al. [5] presented a FEA model of a wind tower with fixed base and attempted to evaluate the natural frequencies of the first few modes of vibration. Assuming a fixed base could potentially overestimate the system stiffness, and thus overestimate the natural frequency. Consequently, unless the separation between the operational and natural frequencies is large, this assumption should not be used. In 2006, Zaaijer [6] presented an investigation of the sensitivity of the natural frequency for the support structure of offshore wind turbines to several parameters and modeling variations. Different foundation systems and analysis methods were presented and compared. Final modeling results were verified against experimental data for five offshore towers. Recommendations were given for foundation modeling that could be implemented in design. In a more recent study, Xu et al. [7] performed static and dynamic analyses on wind turbine models assuming a fixed base as well as elastic subgrades. The first six natural
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frequencies and corresponding mode shapes were investigated and compared for different conditions accounting and neglecting the door opening and its orientation. It was concluded that simplified FEA models can predict overall behavior with reasonable accuracy. 2. Wind–structure interaction By nature, air flow is generally unsteady causing induced forces on structures to fluctuate with time. In some cases, however, winds would be steady which causes acrosswind harmonic vibrations due to the vortex shedding phenomenon. Along-wind response is also of concern due to wind gust on the structure and possible vibration amplification or even resonance. Extreme wind conditions may cause significantly high stresses and possible yielding in the structure. Another complication is the general transient nature of wind at low velocities, which could cause strain cycling and eventually high cycle fatigue. 2.1. Behavior under steady winds Slender structures obstructing steady air flow will experience aerodynamic forces in both directions along-wind and across-wind (or drag and lift forces, respectively). If the structure has a symmetric cross-section, the dominant force would be the drag force. When the vortex shedding phenomenon is exhibited, the lift force increases and becomes significant. To illustrate this, the Bernoulli’s equation can be used to determine the pressure on a structure due to steady wind as shown below 1 P ¼ rv2 ð1Þ 2 where P is the pressure, n is the velocity and r is the standard air density which is 0.0761 pcf at 15 1C and 760 mm of mercury. The equivalent static pressure representing the mean dynamic pressure is then evaluated as Ps ¼ 0:00256V 2
ð2Þ
where Ps is the static pressure in psf and V is the velocity expressed in mph as traditionally done in the structural engineering industry [8,9]. The Drag Force (FD) and the Lift Force (FL) can be found by FD ¼ 0:00256V 2 CD B
ð3Þ
FL ¼ 0:00256V 2 CL B
ð4Þ
where FD and FD are in lb/ft, B is the effective width in ft, and CD and CL are the Drag and Lift coefficients, respectively, which depend on the obstruction shape as well as Reynolds number, Re, which in turn is defined as the ratio of inertial forces to viscous forces. vB ð5Þ Re ¼ n where n is the velocity in ft/s, B is the section width and n (Greek letter nu) is the kinematic viscosity of air, which are 1.46 105 m2/s at 15 1C and 760 mm of mercury. For a circular section, B in Eq. (5) would be taken as the diameter D. Thus, Eq. (5)
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can be rewritten as Re ¼ 9350VD
ð6Þ
where V is the velocity in mph and D is the diameter in ft. 2.1.1. Along-wind forces in steady wind The Drag coefficient CD for a bluff body with circular cross-section depends on the Reynolds number due to the wake developed behind the body. At low to intermediate values of Reynolds number (less than 3 104), the flow is subcritical and CD is determined experimentally to be 1.2 [10]. As the Reynolds number further increases, supercritical flow is exhibited and CD reduces to about 0.45. CD will gradually increase to a constant value of 0.75 at very high Reynolds numbers (greater than 8 107). 2.1.2. Across-wind forces in steady wind For a relatively wide range of Reynolds numbers (140oReo5 105), a bluff body with circular cross-section will experience asymmetric vortex shedding causing significant vibrations normal to the wind direction. This phenomenon is approximated as sinusoidal motion producing harmonic Lift Forces [11] which could be expressed as 1 FL ¼ rV 2 CL B sinð2pftÞ ð7Þ 2 where f is the vortex shedding frequency in Hz from the Strouhal number Sn fD ð8Þ v where n is the velocity in ft/s and D is the diameter of the cross-section [11]. It is worth mentioning here that the vortex shedding phenomenon occurs at exactly half the frequency of the along-wind impulse [12]. Thus, if the vortex shedding frequency happens to coincide with the structure’s natural frequency, the peak transverse wind force can be found as FL Ft ¼ ð9Þ 2x Sn ¼
where x is the damping ratio. 2.2. Behavior under unsteady winds Despite the apparent complexity of the vibration behavior of the wind–turbine–tower system, the problem could be studied as a Single Degree of Freedom (SDOF) [13]. Fig. 1 below illustrates the SDOF representation of the system. Utilizing Newton’s second law, the equation of motion for the SDOF can be written as mu€ þ cu_ þ ke u ¼ F ðtÞ
ð10Þ
where F(t) is the time-dependent load acting on the system mass m, k is the tower stiffness, ks is the support stiffness, ke is the equivalent stiffness and c is the damping coefficient. For convenience, Eq. (10) can be rewritten as u€ þ 2xon u_ þ o2n u ¼
F ðtÞ m
ð100 Þ
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ut
us F(t)
m
u m
m
θt θs θ ks θs Fig. 1. Simplified SDOF model with support rotation.
where on is the undamped natural circular frequency (rad/s) can be found from rffiffiffiffiffi ke on ¼ m The damped natural circular frequency (rad/s) can be shown to be qffiffiffiffiffiffiffiffiffiffiffi oD ¼ on 1x2
ð11Þ
ð12Þ
The damped and undamped frequencies can be taken to be equal for low levels of damping (less than 20% of the critical damping). Since the tower and the support are connected in series, the equivalent stiffness ke can be calculated from the following equation: ke ¼
kks k þ ks
ð13Þ
This can be rewritten as ke ¼
k 1 þ kks
ð14Þ
Eq. (14) describes the effect of the support stiffness on the overall system stiffness. When the foundation is infinitely rigid, the equivalent stiffness of the system reduces down to the tower stiffness. Conversely, if the foundation is extremely soft, the system faces a stability problem. For most engineered systems, the latter is highly unlikely. The following sections will shed light on the effect of foundation modeling on the natural frequency of the entire system. 3. Structural description (wind towers, multiple village locations, Alaska) The utilized towers are out-of-commission prefabricated models that were donated to and/or purchased by the state of Alaska to generate electricity in the following remote villages: Hooper Bay, Chevak, Gambell, Savoonga, Mekoryuk, Kasigluk Akula Bay,
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Fig. 2. Operational wind towers.
Toksook Bay, Danwin and Nordtank. The tower models differ in height (23–46 m), weight and wall thickness. Furthermore, the three-bladed turbines vary in mass (7812–7909 kg), blade diameter (19–27 m) and power output (100–225 kW). All towers were supplied by the same manufacturer, Distributed Energy Systems (DES), formerly Northern Power Systems (NPS), while the turbines were supplied by NPS and Vestas. Fig. 2 below shows some of the installed towers.
4. Operational issues (hazards) During early design stages, it was determined that the along-wind and across-wind resonance phenomena will occur at relatively high frequencies, which are sufficiently separated from the natural frequencies of the system. Using Eq. (8) above, one could calculate the frequency at which vortex shedding will occur for a typical circular tower (Sn=0.2) with a diameter of 3 ft under the maximum design wind speed of 100 mph. The simple calculation yields a vortex shedding frequency of 9.78 Hz, which corresponds to an along-wind impulse frequency of 19.56 Hz. This renders both phenomena critical for the design wind loads of the super-structure, but not an operational limitation for the turbine. On the other hand, as the wind turbine blades start to rotate from rest, their circular speed increases and the induced vibration frequency increases. Depending on its power output capacity, the turbine blades rotate at maximum rotational (circular) speeds that typically range 45–60 rpm corresponding to 0.75–1.00 Hz. These operational frequencies are close to the range of natural frequencies of the entire soil–foundation–tower–turbine system. If more power output is desired, higher rotational speeds have to be accommodated. A poor design decision would involve a maximum rotational speed that is very close to the natural frequency of the structural system resulting in a high likelihood of resonant amplification. In such cases, the structure would have to endure violent resonance vibrations as the operational frequency coincides with the natural frequency. This situation would result in very high dynamic forces, which could cause immediate damage to the structure. Even if these dynamic forces do not exceed the structure’s strength capacity or elastic limit, fatigue-induced failures could also be encountered. A sound design would avoid allowing the operational frequency to approach the vicinity of the natural frequency by a certain safety factor. A safety factor of 15% of the natural frequency was recommended by the turbine vendor and adopted by the authors for this
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project. This is in agreement with the 10% separation rule-of-thumb that is typically implemented in design [2]. It is worth mentioning here that the factor of safety mentioned above is a nominal (conservative) one and is only used for the frequency comparison. Conservatively, it does not reflect the combined soil and structure damping which ranges 5–25% of the critical damping depending on the soil type, strain level and confinement pressure [14]. 5. Design objective In order to develop a sound overall structural system that meets the structural performance requirements of the wind towers, the dynamic interaction of the supporting soil, foundation and super-structure needs to be considered. Since the tower and turbine are prefabricated and manufactured, once selected for a certain installation location, only the foundation can be designed and fine-tuned in accordance with the site soil conditions and desired system frequency. Depending on the soil conditions, the optimum foundation system needs to be selected (spread footing, deep piles, micro-piles, etc.). Additionally, the foundation must have adequate stiffness in order to maximize the system natural frequency within practical limits. A suitably stiff soil–foundation–structure system will allow for higher power output generated by the turbines. 6. Foundation design Based on the geotechnical conditions at different sites, two types of foundations were selected; large spread foundation and deep piles. A 50 deep, 120 120 RC spread footing was utilized to provide the system with vertical and lateral support as well as damping and stiffness. Where soil conditions necessitated it, a pile foundation solution was devised utilizing a 30 in thick mat of RC foundation embedded with a steel grillage of W18 beams founded on 20 in grouted piles (Fig. 3 below). After some installations were made, it was determined that the mixing and casting of concrete in-situ is the major source of cost and difficulty of construction. An all-steel foundation was proposed for faster installation and lower cost, but such a foundation system impacted the natural frequency and softened the system. Consequently, the foundation design was driven by the system natural frequency rather than strength or serviceability. Multiple solutions combining different pile sizes, grouted and un-grouted and different beam sizes were devised. The optimum design was selected for each location
Fig. 3. 30 in Thick RC mat foundation embedded with W18 grillage.
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Fig. 4. (a) Tapered frame element model. (b) Meshed shell element model. (c) Arbitrary mode shapes of the shell element model.
Table 1 Modulus of horizontal subgrade reaction at Hooper Bay location [14]. Soil depth below surface (ft)
Modulus of horizontal subgrade reaction (kip/in)
Soil depth below surface (ft)
Modulus of horizontal subgrade reaction (kip/in)
0 1 2 3 4 5 6 7 8 9 10 11 12
0.00 11.52 23.04 34.56 46.08 57.60 69.12 80.64 92.16 103.68 115.20 126.72 138.24
13 14 15 16 17 18 19 20 21 22 23 24 25
149.76 161.28 172.80 184.32 195.84 207.36 218.88 230.40 241.92 253.44 264.96 276.48 288.00
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based on the highest practically obtainable natural frequency and cost effectiveness of the design. 7. Modeling and analysis A detailed 3D FEA model of the tower–foundation–pile system was created using SAP2000. Initially, the tower by itself was modeled using a fine mesh of thin shell elements. The natural frequency from the model was verified against the tower manufacturer analytical and experimental values. Proper discretization of FEA elements into sub-elements is not a trivial task. Some discretizations could cause numerical difficulties during rigorous analyses. For example, during vibration analysis, abrupt changes in element size may cause spurious wave reflections and numerical noise [15]. Consequently, a simplified tapered frame element was devised to model the tower instead of the thin-walled shell elements. Negligible deviations of the results from the two modeling techniques were observed. Thus, all design
Fig. 5. Tapered frame model on RC spread footing.
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Fig. 6. Close-up of the 3D footing element.
Fig. 7. Steel tower support on top of piles which are laterally constrained by soil springs.
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optimization runs utilized the tapered frame element. Fig. 4 below shows the two different modeling techniques. For the foundation system, the steel grillage and piles were modeled using frame elements with the appropriate cross-sectional properties assigned. Thick plate elements were utilized to model the RC foundation. In order to capture the soil–foundation– structure interaction, compression-only springs were devised to mimic the soil around the piles. Dynamic soil properties could fluctuate between 30% and 80% of their nominal values depending on the strain levels [16]. Consequently, the lower-bound properties were conservatively used in estimating the soil stiffness. Table 1 lists the modulus of subgrade reaction at 1 ft intervals reaching to the point of fixity used for modeling on the Hooper Bay location. The turbine mass was lumped at the hub height above the top of the tower. The piles were meshed into 1 ft segments. The large spread footing, on the other hand, was modeled using a 3D solid element with RC properties (Figs. 5 and 6).
Fig. 8. Meshed 3D solid element with vertical and horizontal compression-only soil springs.
Fig. 9. Underside view of foundation.
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The solid element was meshed into sub-elements using an intelligent algorithm consistent with the object-based FEA modeling of the SAP2000 program. Figs. 7–9 show the discretization of the piles and footing with the application of the soil springs to the meshed surfaces.
Table 2 Influence of individual foundation components on system natural frequency. Foundation option
Natural frequency (Hz)
Difference (%)
Existing foundation 10% Grillage properties
1.2897 1.2892
10% Piles properties
1.0741
10% Concrete properties
1.2592
2.3645
75% Concrete properties
1.2881
0.1237
50% Concrete properties
1.2849
0.3718
25% Concrete properties
1.2765
1.0231
5% Concrete properties
1.2422
3.6827
2% Concrete properties
1.2191
5.4738
0% Concrete properties
1.1778
8.6738
0.0000 0.0384 16.717
Notes
Initial design Original model, reduced grillage section and mass properties by 90% Original model, reduced pile section and mass properties by 90% Original model, reduced concrete section and mass properties by 90% Original model, reduced concrete section and mass properties by 25% Original model, reduced concrete section and mass properties by 50% Original model, reduced concrete section and mass properties by 75% Original model, reduced concrete section and mass properties by 95% Original model, reduced concrete section and mass properties by 98% Original model, removed concrete
Influence of Concrete Reduction on Frequency
1.30
Natural Frequency (Hz)
1.28 1.26 1.24 1.22 1.20 1.18 1.16
0
10
20
30
40 50 60 Concrete Properties (%)
70
Fig. 10. Influence of concrete reduction on natural frequency.
80
90
100
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Frequency Reduction due to Concrete Elimination
Reduction to Natural Frequency (%)
10 9 8 7 6 5 4 3 2 1 0
0
10
20
30
40 50 60 Concrete Properties (%)
70
Fig. 11. Frequency reduction due to concrete elimination.
Fig. 12. Foundation stiffening alternatives.
80
90
100
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8. Results 8.1. Effect of individual foundation components Where piles were used, numerous iterations were carried out to eliminate the need for the RC and optimize the design once a comfort level with the modeling technique was reached. To acquire a sense of contribution of individual foundation components to the overall system frequency, the components stiffness was reduced to 10% of its original values. Table 2 illustrates the influence of reduction individual foundation components on the system natural frequency. As suggested by intuition, it was confirmed that the main stiffness contribution is provided by the pile system. With each reduction increment to the concrete properties, noticeable system frequency reductions were introduced; almost 9% reduction upon concrete elimination. Figs. 10 and 11 depict the influence of concrete reduction and elimination on the system natural frequency. 8.2. Optimization of foundation design The foundation system design was optimized through a parametric sensitivity-based approach, in which the radius of the pile group, grillage beams and piles sizes were varied to produce comparable alternatives. Various other stiffening techniques such as braces and plates stiffeners were also considered (Fig. 12). It was found that the radius of the pile group had a noticeable impact on the system frequency. A favorable radius was selected using a set of typical grillage beam and pile sizes. Fig. 13 illustrates the selection of such favorable pile group radius based on its impact on the system frequency at the Hooper Bay site. A series of further variations to the beam/pile sizes and different combinations yielded an optimized foundation design for each site. The optimized designs were achieved with enough separation (15%) between the natural and operational frequencies to prevent Influence of Pile Group Radius on Frequency
0.985
Natural Frequency (Hz)
0.980 0.975 0.970 0.965 0.960 0.955 0.950 0.945 0.940
3
4
5
6 Pile Group Radius (ft)
7
Fig. 13. Frequency variation due to pile group radius change.
8
9
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Table 3 Summary of design alternatives for Hooper Bay village. Foundation option
Natural frequency (Hz)
Difference Notes (%)
Existing foundation New foundation 1 New foundation 2
1.054 0.946 0.966
1.3 9.0 7.1
New foundation 3
0.979
5.9
New foundation 4
0.982
5.6
New foundation 5
0.983
5.5
New foundation 6
0.981
5.7
New foundation 7
0.978
6.0
New foundation 8 New foundation 9 New foundation 10
0.958 0.951 0.964
7.9 8.6 7.3
New foundation 11
0.947
8.9
New foundation 12 New foundation 13
0.948 1.019
8.8 2.0
New foundation 14
1.047
0.6
New foundation 15
1.050
0.9
New foundation 16
1.048
0.8
New foundation 17
1.042
0.2
New foundation 18
1.049
0.9
New foundation 19
1.042
0.1
New foundation 20
1.050
0.9
New foundation 21
1.041
0.1
New foundation 22
1.043
0.3
Current design, with 3000 of concrete and steel grillage Original model, removed concrete Original model, removed concrete, narrowed pile group radius from 8 to 7 ft Original model, removed concrete, narrowed pile group radius from 8 to 6 ft Original model, removed concrete, narrowed pile group radius from 8 to 5.5 ft Original model, removed concrete, narrowed pile group radius from 8 to 5 ft Original model, removed concrete, narrowed pile group radius from 8 to 4.5 ft Original model, removed concrete, narrowed pile group radius from 8 to 4 ft Original model, removed concrete, grouted piles Original model, removed concrete, welded piles to grillage beams Original model, removed concrete, added knee braces (HSS12 6 1/2, pinned) between piles and grillage beams Original model, removed concrete, added X-braces (HSS12 6 1/2, pinned) between piles Original model, removed concrete, added stiffeners to piles Original model, removed concrete, narrowed pile group radius from 8 to 5 ft, grouted piles, stiffened upper 12 ft of soil Original model, removed concrete, narrowed pile group radius from 8 to 6 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W36 170 Original model, removed concrete, narrowed pile group radius from 8 to 5 ft, grouted piles, stiffened upper 12 ft of soil, grillage beams W36 300 Original model, removed concrete, narrowed pile group radius from 8 to 6.5 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W36 170 Original model, removed concrete, narrowed pile group radius from 8 to 6.5 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W33 130 Original model, removed concrete, narrowed pile group radius from 8 to 7 ft, 2400 (t=0.75’’) open piles, stiffened upper 12 ft of soil, grillage beams W36 170 Original model, removed concrete, narrowed pile group radius from 8 to 7 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W33 130 Original model, removed concrete, narrowed pile group radius from 8 to 7.5 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W36 170 Original model, removed concrete, narrowed pile group radius from 8 to 7.5 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W33 130 Original model, removed concrete, pile group radius 8 ft, 2400 (t=0.7500 ) open piles, stiffened upper 12 ft of soil, grillage beams W36 135
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damage to the structural system. The optimization eliminated the need for any RC encasement to the steel foundation or grouting to the piles in many cases. Table 3 illustrates the comparison of the different considered designs for one of the Hooper Bay village locations. In most cases, an optimized foundation system design for a particular site was also found to be satisfactory for other locations. Thus, a small library of universally applicable standard designs was compiled in an effort to keep the fabrication cost low. Table 4 Table 4 Final design summary for Savoonga and Mekoryuk villages. Savoonga Tower height Turbine C.G. Turbineþblades mass Foundation beams Pile section Number of piles Point of fixity Modulus of horizontal subgrade reaction System natural frequency Recommended maximum rpmn
29 m 1.28 m (50 in) Above tower 7812 kg-mass (535.292 slugs) W36 170 24 in steel pipe, 3/4 in thick 6 18–11 ft below soil surface 19–319 kip/in 1.128 Hz 57 rpm
Mekoryuk Tower height Turbine C.G. Turbineþblades mass Foundation beams Pile section Number of piles Point of fixity Modulus of horizontal subgrade reaction System natural frequency Recommended maximum rpma
29 m 1.28 m (50 in) Above tower 7812 kg-mass (535.292 slugs) W36 170 24 in steel pipe, 3/4 in thick 6 30 ft Below soil surface 19–1070 kip/in 1.148 Hz 58 rpm
a
The recommended rpm incorporates a 15% safety factor.
Fig. 14. Steel tower support.
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summarizes the final design for two of the tower locations and demonstrates how one optimized design was found to be adequate at an another location with different geotechnical conditions. Fig. 14 below shows the optimized all-steel tower support foundation in its final state just before field installation. 9. Conclusions Detailed 3D finite-element models of the tower–foundation–soil systems revealed differences in natural frequencies when SSI was considered. When piles were used as foundations, the optimized designs were achieved through numerous iterations of varying pile size and pile group radius. After considering different loading conditions, the foundation system design was controlled by the natural frequency of the soil–foundation– structure system rather than by strength or serviceability. The use of all-steel foundations lowered the natural frequency of the system. This had to be reflected into lower operational velocities. Accounting for the foundation flexibility, using SSI yielded a more realistic estimate of the natural frequency. Had a fixed-base-tower assumption been adopted, under-designed systems would have been built. References [1] M. Al Satari, S. Hussain, Vibration-based wind turbine tower foundation design utilizing soil–foundation– structure interaction, in: Proceedings of The Third International Conference on Modeling, Simulation and Applied Optimization (ICMSAO’09), Sharjah, UAE 2009. [2] International Electrotechnical Commission 61400-01, Wind Turbine Generator Systems—Part 1: Design requirements, 2005. [3] Bonnett Danny, Wind turbine foundations loading, dynamics and design, Structural Engineer 83 (3) (February 1, 2005) 41–45. [4] Gill, Alistair; Fraser, Ramsay, Challenges in the design of an offshore wind turbine foundation for arctic conditions, in: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering—OMAE, v 4, pp. 507–515, 2002. [5] Fei, Chaoyang; Wang, Nan; Zhou, Bo; Chen, Changzheng, Dynamic performance investigation for large-scale wind turbine tower, in: Proceedings of the Eighth International Conference on Electrical Machines and Systems (ICEMS), v 2, (2005) pp. 996–999. [6] M.B. Zaaijer, Foundation modeling to assess dynamic behavior of offshore wind turbines, Applied Ocean Research 28 (1) (February 2006) 45–57. [7] Xu, Yan; Sun, Wenlei; Zhou, Jianping, Static and dynamic analysis of wind turbine tower structure, Advanced Materials Research, v 33-37 PART 2, 2008 pp. 1169-1174, Advances in Fracture and Materials Behavior—Selected, peer reviewed papers of the Seventh International Conference on Fracture and Strength of Solids (FEOFS2007). [8] American Society of Civil Engineers (ASCE), ASCE 7-05: Minimum Design Loads for Buildings and Other Structures, Reston, Virginia, 2005. [9] International Code Council (ICC), in: International Building Code, 2009 edition, Falls Church, Virginia, 2009. [10] E. Simiu, R. Scanlan, in: Wind Effects on Structures: Fundamentals and Applications to Design, third edition, John Wiley & Sons, New York, 1996. [11] J. Mander, S. Chen, K. Shah, A. Madan, Investigation of light pole base integrity report, research project funded by the Erie County Department of Public Works, Erie County, New York, 1992. [12] B. Taranath, in: Steel, Concrete, & Composite Design of Tall Buildings, second edition, McGraw-Hill, New York, 1997 pp 123–124. [13] A. Chopra, in: Dynamics of Structures: Theory and Applications to Earthquake Engineering, first edition, Prentice Hall, Upper Saddle River, New Jersey, 1995.
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[14] S. Teachavorasinskun, P. Thongchim, P. Lukkunaprasit, Shear modulus and damping of soft Bangkok Clays, Canadian Geotechnical Journal v 39 (2002) 1201–1208. [15] R. Cook, D. Malkus, M. Plesha, in: Concepts and Applications of Finite Element Analysis, John Wiley & Sons, New York, 1989 pp 553–582. [16] Golder Associates, Inc., Geotechnical Reports, Anchorage, Alaska, 2005.
