Multifidelity Data Fusion for the Estimation of Static Stiffness of Suction Caisson Foundations in Layered Soil
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 150, Issue 8
Abstract
The static stiffness of suction caisson foundations is an important engineering factor for offshore wind foundation design. However, existing simplified design models are mainly developed for nonlayered soil conditions, and their accuracy for layered soil conditions is uncertain. This creates a challenge for designing these foundations in offshore wind farm sites, where layered soil conditions are commonplace. To address this, this paper proposes a multifidelity data fusion approach that combines information from different physics-based models of varying accuracy, data sparsity, and computational costs in order to improve the accuracy of stiffness estimations for layered soil conditions. The results indicate that the proposed approach is more accurate than both the simplified design model and a single-fidelity machine learning model, even with limited training data. The proposed method offers a promising data-efficient solution for fast and robust stiffness estimations, which could lead to more cost-effective offshore foundation designs.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The second author is funded by the Royal Academy of Engineering under the Research Fellowship scheme.
References
Achmus, M., C. T. Akdag, and K. Thieken. 2013. “Load-bearing behavior of suction bucket foundations in sand.” Appl. Ocean Res. 43 (Apr): 157–165. https://doi.org/10.1016/j.apor.2013.09.001.
Andersen, K. H., H. P. Jostad, and R. Dyvik. 2008. “Penetration resistance of offshore skirted foundations and anchors in dense sand.” J. Geotech. Geoenviron. Eng. 134 (1): 106–116. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:1(106).
Antoniou, M., R. Kourkoulis, F. Gelagoti, and I. Anastasopoulos. 2022. “Simplified method for performance-based seismic design of suction caissons supporting jacket offshore wind turbines.” Soil Dyn. Earthquake Eng. 155 (Apr): 107169. https://doi.org/10.1016/j.soildyn.2022.107169.
API (American Petroleum Institute). 2010. Recommended practice for planning, designing and constructing fixed offshore platforms. RP 2A-WSD. Washington, DC: API.
Bagheri, P., S. W. Son, and J. M. Kim. 2017. “Investigation of the load-bearing capacity of suction caissons used for offshore wind turbines.” Appl. Ocean Res. 67 (Apr): 148–161. https://doi.org/10.1016/j.apor.2017.07.002.
Barari, A., L. B. Ibsen, A. Taghavi Ghalesari, and K. A. Larsen. 2017. “Embedment effects on vertical bearing capacity of offshore bucket foundations on cohesionless soil.” Int. J. Geomech. 17 (4): 04016110. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000782.
Burd, H. J., et al. 2020. “Application of the PISA design model to monopiles embedded in layered soils.” Géotechnique 70 (11): 1–55. https://doi.org/10.1680/jgeot.20.PISA.009.
Byrne, B. W., et al. 2020. “PICASO: Cyclic lateral loading of offshore wind turbine monopiles.” In Proc., 4th Int. Symp. on Frontiers in Offshore Geotechnics (ISFOG 2021), Frontiers in Offshore Geotechnics IV. Hawthorne, NJ: Deep Foundations Institute.
Byrne, B. W., and G. T. Houlsby. 2003. “Foundations for offshore wind turbines.” Philos. Trans. A Math. Phys. Eng. Sci. 361 (1813): 2909–2930. https://doi.org/10.1098/rsta.2003.1286.
Dassault Systèmes. 2014. Abaqus user manual. Providence, RI: Simula.
Dey, S., S. Chakraborty, and S. Tesfamariam. 2021. “Multi-fidelity approach for uncertainty quantification of buried pipeline response undergoing fault rupture displacements in sand.” Comput. Geotech. 136 (Apr): 104197. https://doi.org/10.1016/j.compgeo.2021.104197.
Díaz, H., and C. G. Soares. 2020. “Review of the current status, technology and future trends of offshore wind farms.” Ocean Eng. 209 (Apr): 107381. https://doi.org/10.1016/j.oceaneng.2020.107381.
DNV (Det Norske Veritas). 2014. Design of offshore wind turbine structures. OS-J101. Oslo, Norway: DNV.
Doherty, J. P., G. T. Houlsby, and A. J. Deeks. 2005. “Stiffness of flexible caisson foundations embedded in nonhomogeneous elastic soil.” J. Geotech. Geoenviron. Eng. 131 (12): 1498–1508. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:12(1498).
Efthymiou, G., and G. Gazetas. 2018. “Elastic stiffnesses of a rigid suction caisson and its cylindrical sidewall shell.” J. Geotech. Geoenviron. Eng. 145 (2): 06018014. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002013.
Esfeh, P. K., and A. M. Kaynia. 2020. “Earthquake response of monopiles and caissons for offshore wind turbines founded in liquefiable soil.” Soil Dyn. Earthquake Eng. 136 (Apr): 106213. https://doi.org/10.1016/j.soildyn.2020.106213.
Feldstein, A., D. Lazzara, N. Princen, and K. Willcox. 2020. “Multifidelity data fusion: Application to blended-wing-body multidisciplinary analysis under uncertainty.” AIAA J. 58 (2): 889–906. https://doi.org/10.2514/1.J058388.
Ferguson, A. L., and K. A. Brown. 2022. “Data-driven design and autonomous experimentation in soft and biological materials engineering.” Ann. Rev. Chem. Biomol. Eng. 13 (1): 25–44. https://doi.org/10.1146/annurev-chembioeng-092120-020803.
Foglia, A., G. Gottardi, L. Govoni, and L. B. Ibsen. 2015. “Modelling the drained response of bucket foundations for offshore wind turbines under general monotonic and cyclic loading.” Appl. Ocean Res. 52 (Feb): 80–91. https://doi.org/10.1016/j.apor.2015.04.005.
Gelagoti, F., I. Georgiou, R. Kourkoulis, and G. Gazetas. 2018. “Nonlinear lateral stiffness and bearing capacity of suction caissons for offshore wind-turbines.” Ocean Eng. 170 (Jun): 445–465. https://doi.org/10.1016/j.oceaneng.2018.10.020.
Gourvenec, S., and S. Barnett. 2011. “Undrained failure envelope for skirted foundations under general loading.” Géotechnique 61 (3): 263–270. https://doi.org/10.1680/geot.9.T.027.
Han, T., K. S. Ahmed, A. K. Gosain, A. B. Tepole, and T. Lee. 2022. “Multi-fidelity gaussian process surrogate modeling of pediatric tissue expansion.” J. Biomech. Eng. 144 (12): 121005. https://doi.org/10.1115/1.4055276.
He, B., J. Jiang, J. Cheng, J. Zheng, and D. Wang. 2021. “The capacities of tripod bucket foundation under uniaxial and combined loading.” Ocean Eng. 220 (Dec): 108400. https://doi.org/10.1016/j.oceaneng.2020.108400.
Houlsby, G. T., and B. W. Byrne. 2005a. “Design procedures for installation of suction caissons in clay and other materials.” Proc. Inst. Civ. Eng. Geotech. Eng. 158 (2): 75–82. https://doi.org/10.1680/geng.2005.158.2.75.
Houlsby, G. T., and B. W. Byrne. 2005b. “Design procedures for installation of suction caissons in sand.” Proc. Inst. Civ. Eng. Geotech. Eng. 158 (3): 135–144. https://doi.org/10.1680/geng.2005.158.3.135.
Hung, L. C., and S. Kim. 2014. “Evaluation of undrained bearing capacities of bucket foundations under combined loads.” Mar. Georesour. Geotechnol. 32 (1): 76–92. https://doi.org/10.1080/1064119X.2012.735346.
Jalbi, S., M. Shadlou, and S. Bhattacharya. 2018. “Impedance functions for rigid skirted caissons supporting offshore wind turbines.” Ocean Eng. 150 (Aug): 21–35. https://doi.org/10.1016/j.oceaneng.2017.12.040.
Kang, F., S. Han, R. Salgado, and J. Li. 2015. “System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling.” Comput. Geotech. 63 (Sep): 13–25. https://doi.org/10.1016/j.compgeo.2014.08.010.
Kennedy, M. C., and A. O’Hagan. 2000. “Predicting the output from a complex computer code when fast approximations are available.” Biometrika 87 (1): 1–13. https://doi.org/10.1093/biomet/87.1.1.
Kourkoulis, R. S., P. C. Lekkakis, F. M. Gelagoti, and A. M. Kaynia. 2014. “Suction caisson foundations for offshore wind turbines subjected to wave and earthquake loading: Effect of soil–foundation interface.” Géotechnique 64 (3): 171–185. https://doi.org/10.1680/geot.12.P.179.
Larsen, K. A., L. B. Ibsen, and A. Barari. 2013. “Modified expression for the failure criterion of bucket foundations subjected to combined loading.” Can. Geotech. J. 50 (12): 1250–1259. https://doi.org/10.1139/cgj-2012-0308.
Latini, C., and V. Zania. 2017. “Dynamic lateral response of suction caissons.” Soil Dyn. Earthquake Eng. 100 (Jan): 59–71. https://doi.org/10.1016/j.soildyn.2017.05.020.
Le Gratiet, L., and J. Garnier. 2014. “Recursive co-kriging model for design of computer experiments with multiple levels of fidelity.” Int. J. Uncertainty Quant. 4 (5): 365–386. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2014006914.
Liu, H., Y. S. Ong, and J. Cai. 2018. “A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design.” Struct. Multidiscip. Optim. 57 (1): 393–416. https://doi.org/10.1007/s00158-017-1739-8.
Liu, M., M. Yang, and H. Wang. 2014. “Bearing behavior of wide-shallow bucket foundation for offshore wind turbines in drained silty sand.” Ocean Eng. 82 (Jun): 169–179. https://doi.org/10.1016/j.oceaneng.2014.02.034.
Liu, T., Y. Zhang, and Q. Meng. 2023. “Numerical investigation and design of suction caisson for on-bottom pipelines under combined VHMT loading in normal consolidated clay.” Ocean Eng. 274 (Sep): 113997. https://doi.org/10.1016/j.oceaneng.2023.113997.
Liu, X., W. Zhao, and D. Wan. 2022. “Multi-fidelity Co-Kriging surrogate model for ship hull form optimization.” Ocean Eng. 243 (Aug): 110239. https://doi.org/10.1016/j.oceaneng.2021.110239.
Meng, X., H. Babaee, and G. E. Karniadakis. 2021. “Multi-fidelity Bayesian neural networks: Algorithms and applications.” J. Comput. Phys. 438 (Jul): 110361. https://doi.org/10.1016/j.jcp.2021.110361.
Meng, X., and G. E. Karniadakis. 2020. “A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems.” J. Comput. Phys. 401 (Apr): 109020. https://doi.org/10.1016/j.jcp.2019.109020.
Mentani, A., L. Govoni, F. Bourrier, and R. Zabatta. 2023. “Metamodelling of the load-displacement response of offshore piles in sand.” Comput. Geotech. 159 (Mar): 105490. https://doi.org/10.1016/j.compgeo.2023.105490.
Minga, E., and H. J. Burd. 2019. Validation of PLAXIS MoDeTo based on the Cowden Till PISA field tests. Oxford, UK: Oxford Univ.
Minisci, E., M. Vasile, and H. Liqiang. 2011. “Robust multi-fidelity design of a micro re-entry unmanned space vehicle.” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 225 (11): 1195–1209. https://doi.org/10.1177/0954410011410124.
Nielsen, S. D. 2019. “Finite element modeling of the tensile capacity of suction caissons in cohesionless soil.” Appl. Ocean Res. 90 (May): 101866. https://doi.org/10.1016/j.apor.2019.101866.
Pawar, S., O. San, P. Vedula, A. Rasheed, and T. Kvamsdal. 2022. “Multi-fidelity information fusion with concatenated neural networks.” Sci. Rep. 12 (1): 5900. https://doi.org/10.1038/s41598-022-09938-8.
Peherstorfer, B., K. Willcox, and M. Gunzburger. 2018. “Survey of multifidelity methods in uncertainty propagation, inference, and optimization.” SIAM Rev. 60 (3): 550–591. https://doi.org/10.1137/16M1082469.
Perdikaris, P., M. Raissi, A. Damianou, N. D. Lawrence, and G. E. Karniadakis. 2017. “Nonlinear information fusion algorithms for data-efficient multi-fidelity modeling.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 473 (2198): 20160751. https://doi.org/10.1098/rspa.2016.0751.
Poulos, H. G. 1979. “Settlement of single piles in nonhomogeneous soil.” J. Geotech. Eng. Div. ASCE 105 (5): 627–641. https://doi.org/10.1061/AJGEB6.0000799.
Raissi, M., P. Perdikaris, and G. E. Karniadakis. 2017. “Machine learning of linear differential equations using Gaussian processes.” J. Comput. Phys. 348 (Jul): 683–693. https://doi.org/10.1016/j.jcp.2017.07.050.
Rasmussen, C. E., and C. K. Williams. 2006. Vol. 1 of Gaussian processes for machine learning, 159. Cambridge, MA: MIT Press.
Samui, P., S. Das, and D. Kim. 2011. “Uplift capacity of suction caisson in clay using multivariate adaptive regression spline.” Ocean Eng. 38 (17–18): 2123–2127. https://doi.org/10.1016/j.oceaneng.2011.09.036.
Senders, M., and M. F. Randolph. 2009. “CPT-based method for the installation of suction caissons in sand.” J. Geotech. Geoenviron. Eng. 135 (1): 14–25. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:1(14).
Shen, Q., F. Vahdatikhaki, H. Voordijk, J. van der Gucht, and L. van der Meer. 2022. “Metamodel-based generative design of wind turbine foundations.” Autom. Constr. 138 (Jan): 104233. https://doi.org/10.1016/j.autcon.2022.104233.
Skau, K. S., G. Grimstad, A. M. Page, G. R. Eiksund, and H. P. Jostad. 2018. “A macro-element for integrated time domain analyses representing bucket foundations for offshore wind turbines.” Mar. Struct. 59 (Feb): 158–178. https://doi.org/10.1016/j.marstruc.2018.01.011.
Skau, K. S., H. P. Jostad, G. Eiksund, and H. P. Sturm. 2019. “Modelling of soil-structure-interaction for flexible caissons for offshore wind turbines.” Ocean Eng. 171 (Jan): 273–285. https://doi.org/10.1016/j.oceaneng.2018.10.035.
Soubra, A. H., T. Al-Bittar, J. Thajeel, and A. Ahmed. 2019. “Probabilistic analysis of strip footings resting on spatially varying soils using kriging metamodeling and importance sampling.” Comput. Geotech. 114 (Apr): 103107. https://doi.org/10.1016/j.compgeo.2019.103107.
Sturm, H. 2017. “Design aspects of suction caissons for offshore wind turbine foundations.” In Proc., Technical Committee 209 Workshop at the 19th Int. Conf. on Soil Mechanics and Geotechnical Engineering, Seoul, South Korea. London: International Society for Soil Mechanics and Geotechnical Engineering.
Suryasentana, S., B. Byrne, and H. Burd. 2019. “Automated optimization of suction caisson foundations using a computationally efficient elastoplastic Winkler model.” Coastal Struct. 2019 (Jun): 932–941. https://doi.org/10.18451/978-3-939230-64-9_093.
Suryasentana, S. K., H. J. Burd, B. W. Byrne, and A. Shonberg. 2020a. “A systematic framework for formulating convex failure envelopes in multiple loading dimensions.” Géotechnique 70 (4): 343–353. https://doi.org/10.1680/jgeot.18.P.251.
Suryasentana, S. K., H. J. Burd, B. W. Byrne, and A. Shonberg. 2021. “Automated procedure to derive convex failure envelope formulations for circular surface foundations under six degrees of freedom loading.” Comput. Geotech. 137 (Apr): 104174. https://doi.org/10.1016/j.compgeo.2021.104174.
Suryasentana, S. K., H. J. Burd, B. W. Byrne, and A. Shonberg. 2022. “A Winkler model for suction caisson foundations in homogeneous and non-homogeneous linear elastic soil.” Géotechnique 72 (5): 407–423. https://doi.org/10.1680/jgeot.19.P.172.
Suryasentana, S. K., H. J. Burd, B. W. Byrne, and A. Shonberg. 2023a. “Modulus weighting method for stiffness estimations of suction caissons in layered soils.” Géotech. Lett. 13 (2): 1–8. https://doi.org/10.1680/jgele.23.00007.
Suryasentana, S. K., H. J. Burd, B. W. Byrne, and A. Shonberg. 2023b. “Small-strain, non-linear elastic Winkler model for uniaxial loading of suction caisson foundations.” Géotech. Lett. 13 (4): 170–181. https://doi.org/10.1680/jgele.23.00043.
Suryasentana, S. K., B. W. Byrne, H. J. Burd, and A. Shonberg. 2017. “Simplified model for the stiffness of suction caisson foundations under 6DoF loading.” In Proc., SUT OSIG 8th Int. Conf. London: Society for Underwater Technology.
Suryasentana, S. K., B. W. Byrne, H. J. Burd, and A. Shonberg. 2018. “An elastoplastic 1D Winkler model for suction caisson foundations under combined loading.” In Numerical methods in geotechnical engineering IX, 973–980. Boca Raton, FL: CRC Press.
Suryasentana, S. K., H. P. Dunne, C. M. Martin, H. J. Burd, B. W. Byrne, and A. Shonberg. 2020b. “Assessment of numerical procedures for determining shallow foundation failure envelopes.” Géotechnique 70 (1): 60–70. https://doi.org/10.1680/jgeot.18.P.055.
Suryasentana, S. K., and B. M. Lehane. 2014a. “Numerical derivation of CPT-based p–y curves for piles in sand.” Géotechnique 64 (3): 186–194. https://doi.org/10.1680/geot.13.P.026.
Suryasentana, S. K., and B. M. Lehane. 2014b. “Verification of numerically derived CPT based p-y curves for piles in sand.” In Proc., 3rd Int. Symp. on Cone Penetration Testing, 3–29. Boca Raton, FL: CRC Press.
Suryasentana, S. K., and B. M. Lehane. 2016. “Updated CPT-based p–y formulation for laterally loaded piles in cohesionless soil under static loading.” Géotechnique 66 (6): 445–453. https://doi.org/10.1680/jgeot.14.P.156.
Suryasentana, S. K., and P. W. Mayne. 2022. “Simplified method for the lateral, rotational, and torsional static stiffness of circular footings on a nonhomogeneous elastic half-space based on a work-equivalent framework.” J. Geotech. Geoenviron. Eng. 148 (2): 04021182. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002731.
Thieken, K., M. Achmus, and C. Schröder. 2014. “On the behavior of suction buckets in sand under tensile loads.” Comput. Geotech. 60 (Apr): 88–100. https://doi.org/10.1016/j.compgeo.2014.04.004.
Ukritchon, B., and S. Keawsawasvong. 2016. “Undrained pullout capacity of cylindrical suction caissons by finite element limit analysis.” Comput. Geotech. 80 (Jun): 301–311. https://doi.org/10.1016/j.compgeo.2016.08.019.
van de Berg, D., T. Savage, P. Petsagkourakis, D. Zhang, N. Shah, and E. A. del Rio-Chanona. 2022. “Data-driven optimization for process systems engineering applications.” Chem. Eng. Sci. 248 (Jul): 117135. https://doi.org/10.1016/j.ces.2021.117135.
Vulpe, C. 2015. “Design method for the undrained capacity of skirted circular foundations under combined loading: Effect of deformable soil plug.” Géotechnique 65 (8): 669–683. https://doi.org/10.1680/geot.14.P.200.
Wang, H., and X. Cheng. 2016. “Undrained bearing capacity of suction caissons for offshore wind turbine foundations by numerical limit analysis.” Mar. Georesour. Geotechnol. 34 (3): 252–264. https://doi.org/10.1080/1064119X.2015.1004766.
Wang, Q., and P. Owens. 2022. “Reliability-based design optimisation of geotechnical systems using a decoupled approach based on adaptive metamodels.” Georisk: Assess. Manage. Risk Eng. Syst. Geohazards 16 (3): 470–488. https://doi.org/10.1080/17499518.2021.1884884.
Wang, X., L. Yu, Q. Yang, and X. Tang. 2022. “The drained tension capacity of suction buckets in sand under vertical uplift loading.” Ocean Eng. 266 (Aug): 113169. https://doi.org/10.1016/j.oceaneng.2022.113169.
Wu, Y., Q. Yang, D. Li, and Y. Zhang. 2022. “Limit equilibrium solutions to anti-overturning bearing capacity of suction caissons in uniform and linearly increasing strength clays.” Can. Geotech. J. 59 (2): 304–313. https://doi.org/10.1139/cgj-2020-0557.
Yang, X., X. Zeng, and X. Wang. 2018. “Lateral-moment loading capacity and bearing behavior of suction bucket foundations for offshore wind turbines in sand.” Int. J. Geomech. 18 (11): 04018152. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001279.
Yin, X., H. Wang, F. Pisanò, K. Gavin, A. Askarinejad, and H. Zhou. 2023. “Deep learning-based design model for suction caissons on clay.” Ocean Eng. 286 (May): 115542. https://doi.org/10.1016/j.oceaneng.2023.115542.
Yin, Z. Y., J. C. Teng, Z. Li, and Y. Y. Zheng. 2020. “Modelling of suction bucket foundation in clay: From finite element analyses to macro-elements.” Ocean Eng. 210 (Sep): 107577. https://doi.org/10.1016/j.oceaneng.2020.107577.
Zhang, P., Z. Y. Yin, Y. F. Jin, J. Yang, and B. Sheil. 2022. “Physics-informed multifidelity residual neural networks for hydromechanical modeling of granular soils and foundation considering internal erosion.” J. Eng. Mech. 148 (4): 04022015. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002094.
Zhu, F. Y., B. Bienen, C. O’Loughlin, M. J. Cassidy, and N. Morgan. 2019. “Suction caisson foundations for offshore wind energy: Cyclic response in sand and sand over clay.” Géotechnique 69 (10): 924–931. https://doi.org/10.1680/jgeot.17.P.273.
Zhu, F. Y., C. D. O’Loughlin, B. Bienen, M. J. Cassidy, and N. Morgan. 2018. “The response of suction caissons to long-term lateral cyclic loading in single-layer and layered seabeds.” Géotechnique 68 (8): 729–741. https://doi.org/10.1680/jgeot.17.P.129.
Information & Authors
Information
Published In
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Mar 31, 2023
Accepted: Mar 22, 2024
Published online: Jun 6, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 6, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.