1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

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