PO.ID DESIGN FORMULAE ON CONCRETE CAPACITY OF P...
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P-Wd-2-23 DESIGN FORMULAE ON CONCRETE CAPACITY OF WIND TURBINES PEDESTAL BASED ON THE NON-LINEAR FEM ANALYSIS Takehiko Sano 1 and Takeshi Ishihara 2 1 JDC CORPORATION Tokyo Head office Civil Engineering Technical Group, Tokyo, 107-8467 Japan [email protected] 2 Department of Civil Engineering, School of Engineering, The University of Tokyo, Tokyo, 113-8656 Japan [email protected] The concrete capacities of wind turbine pedestals are investigated using the non-linear FEM analysis. It is observed that the type of failure mode of concrete pedestal is due to bending moment. The design formula is proposed considering the effects of compressive strength of concrete, embed- ded depth of the anchor bolt and pedestal size. Keywords: Wind turbine pedestals, design formulae on concrete capacity, non-linear FEM analysis PO.ID GRAND RENEWABLE ENERGY 2014 Conference and Exhibition July 27(Sunday) ‒ August 1 (Friday), 2014 Tokyo Big Sight, Tokyo, Japan INTRODUCTION FEM ANALYSIS RESULTS DESIGN FORMULA FOR WIND TURBINES PEDESTAL Japan has more than 1,870 wind turbine generator systems as of March 2011 with a capacity of more than 2.56 million kW [1]. On the other hand, there were reported incidents wherein wind turbine support structures and foundations failed as shown in Fig.1 [2]. These incidents were mainly caused by extreme winds, topographical conditions and natural environ- ment unique to Japan. Hence, it is important that the structural analysis for the pullout failure of the anchor bolts is appropriately designed. In Interna- tional standard IEC61400, wind turbine foundations design method is not regulated. For example, foundation designer refer to US Building Code [3], ACI 318M-02 Requirements for Structure Concrete Appendix D‒Anchoring to Concrete for the purpose of anchor bolts design. Based on the research of Morgan [4], design formulae are both out of scale and with a very differ- ent geometry compared to that of the typical embedded tower anchorage. In this study, concrete pedestal design formula is proposed to consider the effects of compressive strength of concrete, embedded depth of the anchor bolt and pedestal size. The concrete pedestal design formula is based on the 33 cases of non-linear FEM analysis. Locations：Okinawa area Locations：Okinawa area Locations：Eastern Japan area Locations：Eastern Japan area it is important that the structural analysis for the pullout failure of the anchor bolts is appropriately designed. FEM ANALYSIS In order to propose concrete pedestal design formulae, non-linear FEM analysis COM3d was used in this study. COM3d is based on non-linear FEM analysis for Reinforced Concrete structure which developed concrete labo- ratory in the University of Tokyo [5]. Constitutive Equations The analytical model for concrete prior to cracking is constructed based on Maekawa and Okamura elasto- plastic and fracture model (1983) [5]. The equivalent stress - equivalent strain relation is formulated with the initial elastic modulus, the fracture parameter and the equivalent plastic strain (Fig2.a). Un-cracked concrete is used only by modifying the fracture param- eter as a function of the strain perpendicular to the crack plane (Fig2.b). Tension stiffening model was used as models the relation between the average stress and average strain if the concrete (Fig2.c). The shear stress in terms was expressed solely of the ratio of shear displacement to crack width, regardless the width of the crack (Fig2.d). 0.2 0.4 0.6 0.8 0.5 1 1.5 2 Shear stress / Shear strength Shear displacement / Crack width β = δ / ω Ψ = β 2 / (1+β 2 ) 0 Ψ = τ st / f st 0 1 0.05 0.1 Equivalent Stress Equivalent strain ε t σ t 0 σ t = f t (ε tu / ε t ) C f t = 0.23f' c 2/3 ε tu 0.0 1.0 0.0% 0.5% Fracture parameter reducing factor Tensile strain perpendicular to cracks ω ε t 0.6 0.1% 1 0.5 1 1.5 Equivalent stress Equivalent strain σ' max ε' max ε' p E 0 ･K 0 E 0 =2 ε' σ' 0 Fig. 2. Constitutive Equations: (a) Equivalent stress-strain relationship, (b) Reduction in fracture parameter, (c) Tension stiffening model for envelope and (d) Simplified shear transfer model for one crack. Anchor bolt （Line element) Tower （ elastic model） Base plate , Anchor plate (elastic model) Concrete element BOND element Z X Y z y z x z y z y z x FEM mesh Boundary condition Classi- fication a/d r/d 0.33 0.66 1.0 TYPE 1 1 . 0 5models 3models 7models TYPE 2 1 . 5 4 2models 2models 6models TYPE 3 2 . 0 4models 4models C L d r/d=1.0 a/d=0.33 a=380mm d=1150mm r=1150mm a=410mm d=1260mm r=1260mm a=660mm d=2000mm r=2000mm Anchor bolt Tower Pedstal C L a/d=0.33 Tpwer d r/d=1.54 a=380mm d=1150mm r=1770mm a=410mm d=1260mm r=1935mm Anchor bolt Pedstal C L Tower d r/d=1.54 a=690mm d=1150mm r=1770mm a=755mm d=1260mm r=1935mm Anchor bolt Pedstal a/d=0.6 C L Tower d r/d=1.54 a=1150mm d=1150mm r=1770mm a=1260mm d=1260mm r=1935mm Anchor bolt a/d=1.0 Pedstal C L d r/d=2.0 a=380mm d=1150mm r=2300mm a=410mm d=1260mm r=2520mm a/d=0.33 Towe Pedstal Anchor bolt C L d r/d=2.0 a=1150mm d=1150mm r=2300mm a=1260mm d=1260mm r=2520mm Tower Pedstal Anchor bolt a/d=1.0 C L d a= 690mm d=1150mm r=1150mm a= 755mm d=1260mm r=1260mm a=1200mm d=2000mm r=2000mm Anchor bolt Tower a/d=0.6 Pedstal C L d a=1150mm d=1150mm r=1150mm a=1260mm d=1260mm r=1260mm a=2000mm d=2000mm r=2000mm Anchor bolt Tower a/d=1.0 Pedstal Total : 33cases Finite Element Model and Analytical method The pedestal and tower are modeled using 3-dimensional solid elements having 8 nodes and the anchor bolts are modeled using truss element. The displacement load (3mm/step) which is applied on the tower top is ana- lyzed with the use of incremental displacement method. For the conver- gence, modified Newton-Raphson method is used. 3D finite element half- model and boundary condition as shown in Fig.3. In numerical model, from the Table1 to Table 3, Material property is used. Definition of control parameters Fig.4 shows the definition of control parameters. The control parameters are concrete compressive strength FC, dimension ratio a/d, and embedded Tower Anchor bolts Base Plate M Anchor Plat e Pedestal Footing 0 10000 20000 30000 40000 50000 0 0.0002 0.0004 0.0006 0.0008 0.001 18N/mm2 24N/mm2 30N/mm2 40N/mm2 50N/mm2 Bending Moment (kN･m) Rotational angle (rad) r/d=1.0 a/d=1.0 N/mm 2 N/mm 2 N/mm 2 N/mm 2 N/mm 2 29step 30step 34step 0 20000 40000 60000 80000 100000 0 0.0005 0.001 0.0015 0.002 r/d=1.00 r/d=1.54 r/d=2.00 Bending Moment (kN･m) Rotational angle (rad) a/d=1.0 F c =30N/mm 2 29step 30step 34step 0 20000 40000 60000 80000 100000 0 0.0005 0.001 0.0015 0.002 a/d=0.33 a/d=0.60 a/d=1.00 Bending Moment (kN･m) Rotational angle (rad) r/d=1.54 F c =30N/mm 2 a M=26190kN･m (29step) b M=20455kN･m (30step) c M=10647kN･m (34step) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 4.0 4.5 5.0 5.5 6.0 6.5 7.0 a/d=1.00,r/d=1.00 a/d=1.00,r/d=1.54 a/d=1.00,r/d=2.00 a/d=0.33,r/d=1.00 a/d=0.33,r/d=2.00 P c (F c ，a/d，r/d)/P c (F c =30，a/d，r/d) Concrete compressive strength (N/mm 2 ) c F 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 βad r/d=1.00 r/d=1.54 r/d=2.00 Pc(F c =30,a/d,r/d) / Pc(F c =30,a/d=1.0,r/d) Pedstal dimension ratio a/d a/d=1.0 F c =30N/mm 2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.0 1.2 1.4 1.6 1.8 2.0 βrd d=2000mm d=1260mm d=1150mm Pc(F c =30,a/d,r/d) / Pc(F c =30,a/d=1.0,r/d=1.0) Embedded depth ratio r/d a/d=1.0 r/d=1.0 F c =30N/mm 2 0 40000 80000 120000 160000 0 40000 80000 120000 160000 r/d=1.00 r/d=1.54 r/d=2.00 Bending Moment (Design fomulae) (kN･m) Bending Moment (FEM analysis results) (kN･m) Where, Pc is per unit length along the circumference including anchor bolts (N/mm), F c is design value of concrete compressive strength (N/mm 2 ), Dc is effective horizontal projected length of concrete cone failure (mm), βad is correction factor for dimension ratio, βrd is correction factor for em- bedded depth ratio, βn is correction factor for initial axial force, βd is cor- rection factor for scale effect, r is radius of tower (m), and d is embedded depth of anchor bolt (m). In Fig.5, bending moment peaks at the FEM result in case of r/d=1.0, a/d=1.0, Fc=18 to 50 N/mm 2 shows difference of condition due to concrete compressive strength. The pedestal strength is also increased with the increase of the con- crete compressive strength. It is presupposed that pedestal strength is in proportion to concrete strength.Fig.6 indicates that the maximum strength becomes larger as from tower edge to pedestal edge distance is larger. In Fig.7, the section modulus of the tower and pedestal connection is increased, maximum bending moment is increased. Fig.9 shows the effect of concrete compressive strength. In the figure, verti- cal axis shows the Maximum bending moment at each FEM results divided by the bending moment capacity at Fc=30N/mm 2 . It is observed that the moment capacity is directly proportional to the square root of concrete compressive strength F c . Fig.10shows the effect of dimension ratio a/d. The figure indicates that the bending moment capacity is increased with an increase in the pedestal dimension ratio. Fig.11 shows the effect of em- bedded depth ratio r/d. In the figure, it can be observed that it is necessary that the anchor bolts are embedded deep into the pedestal. The results are better the deeper the embedment. Fig.12 shows the comparison between FEM analysis results at Maximum bending moment and design formulae. Based on the abovementioned circumstances, the design formula for con- crete capacity of wind turbine pedestal based on the non-linear FEM analy- sis can be expressed as: In these circumstances, the design formulae on concrete capacity of wind turbines pedestal based on the non-linear FEM analysis expressed as follows. CONCLUSION ACKNOWLEDGMENT REFERENCES In this study, concrete pedestal design formulae are proposed to consider the effects of compressive strength of concrete, embedded depth of the anchor bolts and pedestal size based on the non-linear FEM analysis. From the study, main findings are summarized as follows: (1) It is found that the type of failure mode of concrete pedestal is due to bending moment. (2) The concrete capacity of wind turbines pedestal should be consider the effects of compressive strength of concrete, in addition, embedded depth of the anchor bolt and pedestal size. This study was conducted as part of the activities of the task committee on the wind-resistant design of wind turbines of the Japan Society of Civil En- gineers. The proposed design formulae were adopted from guidelines for the design of wind turbine support structures and foundations. The authors wish to express their deepest gratitude to the concerned parties for their assistance during this study. [1] Agency for Natural Resources and Energy, Annual Report on Energy 2013 (Energy White Paper 2013), pp.128-130[in Japanese]. [2] Ishihara T, (ed.). Guidelines for design of wind turbine support struc- tures and foundations, Japan Society of Civil Engineers, 2010[in Japanese]. [3] Building Code Requirements for Structural Concrete (ACI 318M-02) and Commentary (ACI 318RM-02) [4] Kirk Morgan,Eric Ntambakwa:Wind turbine Foundation Behavior and Design Considerations:AWEA WIND- POWER Conference,Houston,June 2008 [5] Maekawa, K., Okamura, H. and Pimanmas, A.: Nonlinear Mechanics of Reinforced Concrete, SPON PRESS, 2003. [6] Standard specifications for concrete structures 2012, Design, Japan So- ciety of Civil Engineers[in Japanese]. Fig.1. Example of concrete cone failure at the pedestal a b c d Compressive Stiffness (N/mm 2 ) Tensile Stiffness (N/mm 2 ) Shear Stiffness (N/mm 2 ) 100000 0.01 10700 Compressive strength c F (N/mm 2 ) Tensile strength t f (N/mm 2 ) Modulus of elasticity c E (N/mm 2 ) Poisson’s ratio ν 18 1.580 22000 0.17 24 1.914 25000 30 2.221 28000 40 2.690 31000 50 3.122 33000 Number Diameter (mm) Elastic modulus (N/mm 2 ) Yield strength (N/mm 2 ) Effective area (mm 2 ) 2×64 36 200000 900 816.7 Table1. Concrete material property of the wind turbine pedestal. [6] Table 2. Material property of joint element Table 3. Specification of Anchor bolt Anchor bolt Base plate Concrete Anchor plate Bond element Table 4. Analysis case 0.48 c ad rd d n c c P FD β β ββ = c D a b = + ( ) 2 0.4 1.0 1.0 ad ad β = − − + ( ) 0.33 1.0 ad ≤ ≤ ( ) 2 0.5 2.0 0.5 rd rd β = − + 1 d d β = ( ) 1.5 d β ≤ 1.0 n β = ( ) 1.0 2.0 rd ≤ ≤ Fig. 5. Effect of concrete compressive strength at pedestal Fig. 6. Effect of dimension ratio at pedestal Fig. 7. Effect of embedded depth ratio at pedestal Fig. 8. FEM analysis results. Upper: Principal strain at baseplate Lower: Deformation (magnified 200 times) Fig. 9. Effect of concrete compressive strength Fig. 10. Effect of dimension ratio a/d Fig. 11. Effect of embedded depth ratio r/d. Fig. 12. Comparison of FEM analysis results and design formulae. r/d : Effect of embedded depth ratio a/d : Effect of pedestal dimension ratio Fig.3. 3D finite element half-model and boundary condition. a a r d Fc Fig. 4. Definition of control parameters a : Effective horizontal projected length of cone failure r : Radius of tower d : Embedded depth of anchor bolts Fc : Design value of concrete compresive strength
Transcript of PO.ID DESIGN FORMULAE ON CONCRETE CAPACITY OF P...
P-Wd-2-23
DESIGN FORMULAE ON CONCRETE CAPACITY OFWIND TURBINES PEDESTAL BASED ON THE NON-LINEAR FEM ANALYSIS
Takehiko Sano1 and Takeshi Ishihara21JDC CORPORATION Tokyo Head office Civil Engineering Technical Group, Tokyo, 107-8467 Japan
[email protected] of Civil Engineering, School of Engineering, The University of Tokyo, Tokyo, 113-8656 Japan
The concrete capacities of wind turbine pedestals are investigated using the non-linear FEM analysis. It is observed that the type of failure mode of concrete pedestal is due to bending moment. The design formula is proposed considering the effects of compressive strength of concrete, embed-ded depth of the anchor bolt and pedestal size.
Keywords: Wind turbine pedestals, design formulae on concrete capacity, non-linear FEM analysis
PO.ID
GRAND RENEWABLE ENERGY 2014 Conference and ExhibitionJuly 27(Sunday) ‒ August 1 (Friday), 2014 Tokyo Big Sight, Tokyo, Japan
INTRODUCTION FEM ANALYSIS RESULTS
DESIGN FORMULA FOR WIND TURBINES PEDESTAL
Japan has more than 1,870 wind turbine generator systems as of March 2011 with a capacity of more than 2.56 million kW [1]. On the other hand, there were reported incidents wherein wind turbine support structures and foundations failed as shown in Fig.1 [2]. These incidents were mainly caused by extreme winds, topographical conditions and natural environ-ment unique to Japan. Hence, it is important that the structural analysis for the pullout failure of the anchor bolts is appropriately designed. In Interna-tional standard IEC61400, wind turbine foundations design method is not regulated. For example, foundation designer refer to US Building Code [3], ACI 318M-02 Requirements for Structure Concrete Appendix D‒Anchoring to Concrete for the purpose of anchor bolts design. Based on the research of Morgan [4], design formulae are both out of scale and with a very differ-ent geometry compared to that of the typical embedded tower anchorage. In this study, concrete pedestal design formula is proposed to consider the effects of compressive strength of concrete, embedded depth of the anchor bolt and pedestal size. The concrete pedestal design formula is based on the 33 cases of non-linear FEM analysis.
Locations：Okinawa area Locations：Okinawa area
Locations：Eastern Japan area
Locations：Eastern Japan area
it is important that the structural analysis for the pullout failure of the anchor bolts is appropriately designed.
FEM ANALYSISIn order to propose concrete pedestal design formulae, non-linear FEM analysis COM3d was used in this study. COM3d is based on non-linear FEM analysis for Reinforced Concrete structure which developed concrete labo-ratory in the University of Tokyo [5].
Constitutive EquationsThe analytical model for concrete prior to cracking is constructed based on Maekawa and Okamura elasto- plastic and fracture model (1983) [5]. The equivalent stress - equivalent strain relation is formulated with the initial elastic modulus, the fracture parameter and the equivalent plastic strain (Fig2.a). Un-cracked concrete is used only by modifying the fracture param-eter as a function of the strain perpendicular to the crack plane (Fig2.b). Tension stiffening model was used as models the relation between the average stress and average strain if the concrete (Fig2.c). The shear stress in terms was expressed solely of the ratio of shear displacement to crack width, regardless the width of the crack (Fig2.d).
0
0.2
0.4
0.6
0.8
0 0.5 1 1.5 2Shear
str
ess
/ S
hear
str
engt
h
Shear displacement / Crack width
β = δ / ω
Ψ = β2 / (1+β2)
0
Ψ = τst / fst
0
1
0 0.05 0.1
Equ
ival
ent
Str
ess
Equivalent strain
εt
σt
0
σt = ft (εtu / εt)C
ft = 0.23f'c2/3
εtu
0.0
1.0
0.0% 0.5%Fra
ctu
re p
aram
ete
r re
ducin
g fa
cto
r
Tensile strain perpendicular to cracks
ω
εt
0.6
0.1%0
1
0 0.5 1 1.5
Equ
ival
ent
stre
ss
Equivalent strain
σ'max
ε'maxε'p
E0･K0E0 =2ε'
σ'
0
Fig. 2. Constitutive Equations: (a) Equivalent stress-strain relationship, (b) Reduction in fracture parameter, (c) Tension stiffening model for envelope and (d) Simplified shear transfer model for one crack.
Anchor bolt （Line element)
Tower（elastic model） Base plate , Anchor plate (elastic model)
Concrete elementBOND element
Z
X
Y
z
y
z
x
z
y
z
y
z
x
FEM mesh Boundary condition
Classi-fication
a/dr/d 0.33 0.66 1.0
TYPE1 1.0
5models 3models 7models
TYPE2 1.54
2models 2models 6models
TYPE3 2.0
4models 4models
CLd
r/d=1.0
a/d=0.33
a=380mm d=1150mm r=1150mm
a=410mm d=1260mm r=1260mm
a=660mm d=2000mm r=2000mm
Anchor bolt
Tower
Pedstal
CL
a/d=0.33
Tpwer
d
r/d=1.54
a=380mm d=1150mm r=1770mm
a=410mm d=1260mm r=1935mm
Anchor bolt
Pedstal
CL
Tower
d
r/d=1.54
a=690mm d=1150mm r=1770mm
a=755mm d=1260mm r=1935mm
Anchor bolt
Pedstal
a/d=0.6
CL
Tower
d
r/d=1.54
a=1150mm d=1150mm r=1770mm
a=1260mm d=1260mm r=1935mm
Anchor bolt
a/d=1.0
Pedstal
CLd
r/d=2.0
a=380mm d=1150mm r=2300mm
a=410mm d=1260mm r=2520mm
a/d=0.33
Towe
Pedstal
Anchor bolt
CLd
r/d=2.0
a=1150mm d=1150mm r=2300mm
a=1260mm d=1260mm r=2520mm
Tower
Pedstal
Anchor bolt
a/d=1.0
CLd
a= 690mm d=1150mm r=1150mm
a= 755mm d=1260mm r=1260mm
a=1200mm d=2000mm r=2000mm
Anchor bolt
Tower
a/d=0.6
Pedstal
CLd
a=1150mm d=1150mm r=1150mm
a=1260mm d=1260mm r=1260mm
a=2000mm d=2000mm r=2000mm
Anchor bolt
Tower
a/d=1.0
Pedstal
Total : 33cases
Finite Element Model and Analytical methodThe pedestal and tower are modeled using 3-dimensional solid elements having 8 nodes and the anchor bolts are modeled using truss element. The displacement load (3mm/step) which is applied on the tower top is ana-lyzed with the use of incremental displacement method. For the conver-gence, modified Newton-Raphson method is used. 3D finite element half-model and boundary condition as shown in Fig.3. In numerical model, from the Table1 to Table 3, Material property is used.
Definition of control parametersFig.4 shows the definition of control parameters. The control parameters are concrete compressive strength FC, dimension ratio a/d, and embedded
Tower
Anchor bolts
Base Plate
M
Anchor Plate Pedestal
Footing
0
10000
20000
30000
40000
50000
0 0.0002 0.0004 0.0006 0.0008 0.001
18N/mm224N/mm230N/mm240N/mm250N/mm2
Bendin
g M
om
ent
(kN
･m)
Rotational angle (rad)
r/d=1.0a/d=1.0
N/mm2
N/mm2
N/mm2
N/mm2
N/mm2
29step
30step
34step
0
20000
40000
60000
80000
100000
0 0.0005 0.001 0.0015 0.002
r/d=1.00r/d=1.54r/d=2.00
Bendin
g M
om
ent
(kN
･m)
Rotational angle (rad)
a/d=1.0
Fc=30N/mm2
29step
30step
34step0
20000
40000
60000
80000
100000
0 0.0005 0.001 0.0015 0.002
a/d=0.33a/d=0.60a/d=1.00
Bendin
g M
om
ent
(kN
･m)
Rotational angle (rad)
r/d=1.54
Fc=30N/mm2
a
M=26190kN･m
(29step)
b
M=20455kN･m
(30step)
c
M=10647kN･m
(34step)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
4.0 4.5 5.0 5.5 6.0 6.5 7.0
a/d=1.00,r/d=1.00
a/d=1.00,r/d=1.54
a/d=1.00,r/d=2.00
a/d=0.33,r/d=1.00
a/d=0.33,r/d=2.00
Pc(Fc，
a/d，
r/d)
/
Pc(Fc=30，
a/d，
r/d)
Concrete compressive strength (N/mm2)cF
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
βadr/d=1.00r/d=1.54r/d=2.00
Pc(Fc=30,a/d,r/d)
/
Pc(Fc=30,a/d=1.0,r/d)
Pedstal dimension ratio a/d
a/d=1.0
Fc=30N/mm2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.0 1.2 1.4 1.6 1.8 2.0
βrdd=2000mmd=1260mmd=1150mm
Pc(Fc=30,a/d,r/d) / Pc(Fc=30,a/d=1.0,r/d=1.0)
Embedded depth ratio r/d
a/d=1.0r/d=1.0
Fc=30N/mm2
0
40000
80000
120000
160000
0 40000 80000 120000 160000
r/d=1.00r/d=1.54r/d=2.00
Bending Moment (Design fomulae) (kN･m)
Bending Moment (FEM analysis results) (kN･m)
Where, Pc is per unit length along the circumference including anchor bolts (N/mm), Fc is design value of concrete compressive strength (N/mm2), Dc is effective horizontal projected length of concrete cone failure (mm), βad is correction factor for dimension ratio, βrd is correction factor for em-bedded depth ratio, βn is correction factor for initial axial force, βd is cor-rection factor for scale effect, r is radius of tower (m), and d is embedded depth of anchor bolt (m).
In Fig.5, bending moment peaks at the FEM result in case of r/d=1.0, a/d=1.0, Fc=18 to 50 N/mm2 shows difference of condition due to concrete compressive strength. The pedestal strength is also increased with the increase of the con-crete compressive strength. It is presupposed that pedestal strength is in proportion to concrete strength.Fig.6 indicates that the maximum strength becomes larger as from tower edge to pedestal edge distance is larger. In Fig.7, the section modulus of the tower and pedestal connection is increased, maximum bending moment is increased.
Fig.9 shows the effect of concrete compressive strength. In the figure, verti-cal axis shows the Maximum bending moment at each FEM results divided by the bending moment capacity at Fc=30N/mm2. It is observed that the moment capacity is directly proportional to the square root of concrete compressive strength Fc. Fig.10shows the effect of dimension ratio a/d. The figure indicates that the bending moment capacity is increased with an increase in the pedestal dimension ratio. Fig.11 shows the effect of em-bedded depth ratio r/d. In the figure, it can be observed that it is necessary that the anchor bolts are embedded deep into the pedestal. The results are better the deeper the embedment. Fig.12 shows the comparison between FEM analysis results at Maximum bending moment and design formulae. Based on the abovementioned circumstances, the design formula for con-crete capacity of wind turbine pedestal based on the non-linear FEM analy-sis can be expressed as: In these circumstances, the design formulae on concrete capacity of wind turbines pedestal based on the non-linear FEM analysis expressed as follows.
CONCLUSION
ACKNOWLEDGMENT
REFERENCES
In this study, concrete pedestal design formulae are proposed to consider the effects of compressive strength of concrete, embedded depth of the anchor bolts and pedestal size based on the non-linear FEM analysis. From the study, main findings are summarized as follows:
(1) It is found that the type of failure mode of concrete pedestal is due to bending moment.(2) The concrete capacity of wind turbines pedestal should be consider the effects of compressive strength of concrete, in addition, embedded depth of the anchor bolt and pedestal size.
This study was conducted as part of the activities of the task committee on the wind-resistant design of wind turbines of the Japan Society of Civil En-gineers. The proposed design formulae were adopted from guidelines for the design of wind turbine support structures and foundations. The authors wish to express their deepest gratitude to the concerned parties for their assistance during this study.
[1] Agency for Natural Resources and Energy, Annual Report on Energy 2013 (Energy White Paper 2013), pp.128-130[in Japanese].[2] Ishihara T, (ed.). Guidelines for design of wind turbine support struc-tures and foundations, Japan Society of Civil Engineers, 2010[in Japanese]. [3] Building Code Requirements for Structural Concrete (ACI 318M-02) and Commentary (ACI 318RM-02)[4] Kirk Morgan,Eric Ntambakwa:Wind turbine Foundation Behavior and Design Considerations:AWEA WIND- POWER Conference,Houston,June 2008[5] Maekawa, K., Okamura, H. and Pimanmas, A.: Nonlinear Mechanics of Reinforced Concrete, SPON PRESS, 2003.[6] Standard specifications for concrete structures 2012, Design, Japan So-ciety of Civil Engineers[in Japanese].
Fig.1. Example of concrete cone failure at the pedestal
a b c d
Compressive Stiffness (N/mm2)
Tensile Stiffness (N/mm2)
Shear Stiffness (N/mm2)
100000 0.01 10700 Compressive strength cF
(N/mm2)
Tensile strength tf (N/mm2)
Modulus of elasticity cE (N/mm2)
Poisson’s ratio ν
18 1.580 22000
0.17 24 1.914 25000 30 2.221 28000 40 2.690 31000 50 3.122 33000
Number Diameter (mm)
Elastic modulus (N/mm2)
Yield strength (N/mm2)
Effective area
(mm2) 2×64 36 200000 900 816.7
Table1. Concrete material property of the wind turbine pedestal. [6]
Table 2. Material property of joint element
Table 3. Specification of Anchor bolt
Anchor bolt
Base plate
Concrete
Anchor plate
Bond element
Table 4. Analysis case
0.48c ad rd d n c cP F Dβ β β β= cD a b= +
( )20.4 1.0 1.0ad a dβ = − − + ( )0.33 1.0a d≤ ≤
( )20.5 2.0 0.5rd r dβ = − +
1d dβ = ( )1.5dβ ≤
1.0nβ =
( )1.0 2.0r d≤ ≤
Fig. 5. Effect of concrete compressivestrength at pedestal
Fig. 6. Effect of dimension ratio at pedestal Fig. 7. Effect of embedded depth ratio at pedestal
Fig. 8. FEM analysis results. Upper: Principal strain at baseplateLower: Deformation (magnified 200 times)
Fig. 9. Effect of concrete compressive strength Fig. 10. Effect of dimension ratio a/d Fig. 11. Effect of embedded depth ratio r/d.
Fig. 12. Comparison of FEM analysis results and design formulae.
r/d : Effect of embedded depth ratio a/d : Effect of pedestal dimension ratio
Fig.3. 3D finite element half-model and boundary condition.
a a
r
d
Fc
Fig. 4. Definition of control parameters
a : Effective horizontal projected length of cone failurer : Radius of towerd : Embedded depth of anchor boltsFc : Design value of concrete compresive strength
