Scientific advances and innovation

The deterministic computation of wind turbine foundations requires a three-dimensional (3D) analysis since these structures are subjected to complex loading (due to waves, wind, etc.) thus leading to very time-consuming computational models. This presents a great obstacle to the use of conventional probabilistic methods as Monte Carlo Simulation (MCS) methodology. On the other hand, taking into account the 3D soil spatial variability within a probabilistic analysis significantly increases the number of calls to the deterministic code. The objective of this project is to provide for these complex 3D offshore geotechnical structures, a reliable and efficient methodology for the propagation of uncertainty. Our aim is to determine the Probability Density Function (PDF) of the system response and the failure probability against a prescribed threshold within a reasonable computation time. Indeed, the existing probabilistic approaches do not allow one to rigorously compute the failure probability due to the use of a small number of simulations thus leading to a large value of the coefficient of variation on this failure probability.


Expected technical and economic impact

The analysis and design of offshore structures are generally performed using deterministic approaches. These approaches do not allow one to take into account the soil spatial variability and the variability of the loading. The object of the present project is the rigorous analysis of offshore structures taking into account the effect of these two variabilities. The study focuses on the probabilistic analysis of wind turbines foundations. The methods and tools developed within this project will be transfered to to practical geotechnical engineers, working in the area of offshore structures.

Key project milestones

  • October 2016 - Begining of the project
  • October 2017 - Developpement of deterministic approaches for wind turbines foundations
  • October 2018 - Developpement of probabilistic approaches
  • October 2019 - End of the project (Theisis defense and publications in international journals


Development of numerical tools for the analysis of wind turbine foundations that may be used by practical geotechnical engineers working in the area of offshore structures.



The work of this project involves two main items: (i) Development of efficient three-dimensional mechanical models for offshore wind turbine foundations subjected to axial and lateral loadings and (ii) Development of probabilistic models in order to calculate the probability of failure of offshore geotechnical structures taking into account the three-dimensional soil spatial variability.


Adopted methodologies:

– For the development of mechanical models, two offshore geotechnical structures were modelled using Abaqus finite elements software: (i) Large diameter monopile foundation and (ii) Bucket foundation. Two types of modelling were considered in the mechanical model: A wished in place model and a more sophisticated model taking into account the installation process (using the coupled Eulerian-Lagrangian approach implemented in Abaqus software).


– For the probabilistic analyses, three efficient probabilistic methods based on the Kriging metamodeling technique were developed in this work: GSAS, AK-MCSd and AK-MCSm. GSAS approach is recommended for the case where very time consuming mechanical models are involved in the analysis. Otherwise, AK-MCSd approach may be recommended. Finally, for the case where distributed (or parallel) computing facilities are available, AK-MCSm may be used for the analysis.


The main results of the different simulations are as follows:

  • For the determination of the ultimate vertical bearing capacity, there was an agreement between the numerical results provided by Abaqus and those obtained using the API. The contribution of the shaft and the base to the total resistance of the monopile has been determined. The results showed a major contribution of 60-80% for the shaft and a contribution of 20-40% for the base. Also, it was noticed that shaft failure occurs in a first place. It has been shown that the soil inside the monopile does not undergo slipping with respect to the internal interface of this monopile during the loading process. The bearing capacity of the monopile can thus be calculated as the sum of the shaft resistance and the base resistance (soil + annulus). This is in agreement with the recommendations of the API.
  • The deterministic results of the large diameter monopile subjected to lateral loading have shown that the monopile undergoes a rotational rigid movement about a rotation point located at about the bottom third of the monopile embedded length. The results related to the monopile installation process in sand have shown that soil plugging phenomenon increases with the decrease of monopile diameter and the increase in sand density. Furthermore, the plugging phenomenon was shown to be more significant for jacked piles as compared to driven piles. Finally, the degree of soil plugging was found to be higher for smaller penetration depths.

    The three probabilistic methods were shown to present high efficiency (in terms of computational effort) with respect to the conventional Monte Carlo probabilistic approach and the classical Kriging-based probabilistic methods. It has been shown that the effect of the 1-D vertical spatial variability on the failure probability is significant as long as the vertical autocorrelation distance is lower than the length of the monopile. Furthermore, it has been shown that the effect of the horizontal spatial variability in the loading direction is significant as long as the horizontal autocorrelation distance is lower than  where D is the monopile diameter. This value of 2.5D represents the distance adjacent to the monopile, below which significant soil displacements were obtained. In the case of a 3-D soil variability, the use of a classical random field discretisation method (e.g. EOLE) induces a memory problem. In order to address this issue, the Turning Band Method TBM was proposed. This method was shown to be very efficient for the discretisation of a three-dimensional random field with very small autocorrelation distances (i.e. for the case of a very heterogeneous soil medium). This method will be used in the future in order to perform a probabilistic analysis taking into account the soil spatial variability in the three dimensions.

Publications and papers published

  • El Haj A-K., Soubra A-H., Al-Bittar T. «Probabilistic analysis of a strip footing resting on a spatially varying soil using Kriging and global sensitivity analysis», 19th working conference of the IFIP Working Group 7.5 on Reliability and Optimization of Structural Systems, ETH Zurich, Switzerland, June 26-29, 2018.
  • El Haj A-K., Soubra A-H., Fajoui J., Al-Bittar T. «Probabilistic model of an offshore monopile foundation taking into account the soil spatial variability», Proceedings of the 54th ESReDA Seminar, Nantes, France, April 25-26, 2018.
  • El Haj A-K., Soubra A-H., Fajoui J. «Probabilistic analysis of an offshore monopile foundation taking into account the soil spatial variability». Computers and Geotechnics, February 2019
  • Abdul-Hamid Soubra, “Numerical modelling of offshore anchors for floating structures “, French-American Innovation Day (FAID), March 18 & 19th 2019
  • El Haj A-K., Soubra A-H., «Probabilistic analysis of an offshore monopile foundation using Kriging with multipoint enrichment ».  13th international Conference on Applications of Statistics and Probability in Civil Engineering-ICAPS13, May 26-30, 2019