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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 1 Outline of presentation Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions Impedance of Bucket Foundations: Torsional, Horizontal and Rocking Motion Lars Andersen †, Lars Bo Ibsen † & Morten Albjerg Liingaard ‡ † Department of Civil Engineering, Aalborg University, Aalborg, Denmark ‡ DONG Energy A/S, Fredericia, Denmark

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 2 Motivation for the work A computationally efficient model of a foundation is required for the analysis of wind turbine response Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Motivation for the work Vacuum provides the necessary penetration force Bucket foundations are installed from a barge Can be used on shallow and medium water depth Prototype installed at Frederikshavn, Denmark A 3 MW wind turbine is installed on top 3 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Computational model Static and dynamic stiffness of a rigid footing – non-dimensional quantities 4 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Boundary elements for the subsoil Finite elements for the bucket foundation Boundary elements for the soil inside the bucket Computational model 5 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Computational model Formulation of a Finite-Element domain Formulation of a Boundary-Element domain Coupling in terms of nodal forces: Finite element assembly as usual Boundary elements are converted into macro finite elements 6 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional static stiffness of the bucket foundation Coupled Boundary-Element/Finite-Element model is based on time-harmonic response True static solution cannot be established with the present code The static response is approximated by the solution at a 0 = 0.01 Comparison with Finite-Element solution from ABAQUS 7 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional static stiffness of the bucket foundation 8 Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 9 Example results of the coupled Boundary Element/Finite Element model Torsional motion at the frequency 2 Hz Note: Poisson’s ratio = 0.4 ; H/D = 1 Torsion Horizontal Rocking Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 10 Example results of the coupled Boundary Element/Finite Element model Horizontal motion at the frequency 2 Hz Note: Poisson’s ratio = 0.4 ; H/D = 1 Torsion Horizontal Rocking Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 11 Example results of the coupled Boundary Element/Finite Element model Rocking motion at the frequency 2 Hz Note: Poisson’s ratio = 0.4 ; H/D = 1 Torsion Horizontal Rocking Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 12 Torsional stiffness not influenced by Poisson’s ratio (only S-waves) Like surface footing at low frequencies Smooth variation for H/D = 1/4 Very spiky for H/D > 1 Like infinite cylinder at high frequencies Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 13 Horizontal stiffness increases with increasing frequency Increase is stronger than for a surface footing for all values of Poisson’s ratio No obvious trend in change due to changing Poisson’s ratio BE/FE model of surface footing is very accurate compared to the reference solution by Veletsos and Wei (1971) Similar results for rocking Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 14 Coupling stiffness looks similar to horizontal stiffness BE/FE model fails to produce reliable results Alternative model based on half-space Green’s function Very accurate compared to the reference solution by Veletsos and Wei (1971) Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 15 Rocking term increases with an increase in H/D from H/D = 1/4 to H/D = 1 No additional increase from H/D = 1 to H/D = 2 Goes toward the solution for an infinite cylinder Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 16 Rocking term increases with an increase in H/D from H/D = 1/4 to H/D = 1 No additional increase from H/D = 1 to H/D = 2 Tips and dips coincide with those of the sliding stiffness Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Non-dimensional dynamic stiffness of the bucket foundation 17 Coupling term varies with H/D No clear pattern in location of tips and dips Very different from surface footing (alternative method) Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard 18 Conclusions Torsional stiffness: Independent of Poisson’s ratio and increasing almost linearly with increasing skirt length Significant peaks observed at a 0 ≈ 4, 7 and 10 as also observed for an infinite cylinder Static stiffness of BE/FE model within approximately 5% of the referece solution Horizontal sliding and rocking stiffnesses: Horizontal sliding stiffness does not increase very much with increasing skirt length Rocking stiffness increases more than linearly with increasing skirt length Slight increase with increasing Poisson’s ratio due to P-wave generation Tips and dips in the dynamic stiffness are not repeated with Δa 0 = π Significant coupling exists between horizontal sliding and rocking Static stiffness of BE/FE model within approximately 7% of the referece solution Coupling term is less accurate (the BE/FE model fails for a surface footing), and the coupling terms K HM and K MH do not match exactly (11% difference) High-frequency limit of non-dimensional dynamic stiffnesses presented in the paper Next step is to calibrate and implement lumped-parameter models in aeroelastic codes Motivation for the work Computational model Non-dimensional static stiffness of the bucket foundation Example results of the coupled BE/FE model Non-dimensional dynamic stiffness of the bucket foundation Conclusions

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ECT2008 ▪ Athens ▪ Greece ▪ 2–5 September 2008 ▪ Paper 189 ▪ L. Andersen, L.B. Ibsen & M.A. Liingaard Thank you for your attention Lars Andersen: 19

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