Session description

This session considers the broad topic of fixed offshore foundation systems and includes papers addressing the primary elements of global or whole-structural-system analysis and assessment. A range of speakers will represent academia and industry with contributions covering different aspects of bottom-fixed support structures and foundations, their design, analysis and optimisation. Topics addressed will include hydrodynamic loads, soil-structure interaction and geotechnical issues, support structure dynamics and simulation technology, field testing and laboratory experiments as well as pile design.

Learning objectives

• Better understand soil-structure interaction mechanisms and analyse methods
• Appreciate how to analyse and assess structural dynamic behaviour
• Examine fatigue damage models applied to offshore wind foundations
• Recognise performance indicators for the whole-structure
• Identify methods to objectively assess optimum foundation configuration

Angel Diez MS-ENERTECH , Spain
Co-authors:
Angel Diez (1) ^{F P} Jesus Minguez (1) Iñigo Moreno (1)
(1) MS-ENERTECH , Burgos, Spain

Fatigue verification in wind turbines foundation applying Markov matrices to a FEM model

Introduction

Fatigue is one of the critical and most important parameters that affect the design of the structural elements of a wind turbine, and particularly the design of foundations.
Wind turbines are subjected to a much higher number of load cycles than the common civil structures and also its variability is much greater. This leads to a complex analysis of the structural fatigue.


Approach

Three methods for testing fatigue phenomena are used in a foundation model: the equivalent load method, the rain flow spectrum method and finally the Markov matrix method. The first two ones are currently the most used. But the method which best fits the real loads applied to the structural element is the Markov matrix one. Therefore our foundation fatigue verifications are based on this third method, which is further presented within this paper.
Markov matrix application
Using Markov matrix involves analyzing a large number of load cases applied to the model (more than 1000). This makes necessary the use of tools and procedures which are able to automate the process. This way we have developed our own FEM calculation tools based on:
• initial analytical regression
• checking analytical results which fit with the real situation
• calculation of the whole load cases of Markov matrix with an automatic tool developed by us for this specific analysis
In this paper a real case of the Markov Matrix application to a wind turbine foundation is shown.
The foundation analized is modeled using a shell finite element type. This element has 8 nodes.

Figure 1FE model
The sign convection for the efforts considered for the Shell element are presented in the next figure:
Figure 2 Sign convectio
Also a triangular shell element has been used formed by the combination of a triangular element for plane stress, and a triangular element for plates.
The thickness corresponding to the center of the element is assigned to each element according to the geometry planes. The thickness and height of the pedestal is not considered.


Main body of abstract

Study of loads application
The first stage of the model analysis is the study of the loads application to the foundation transmitted by the tower of the wind turbine.

Local axis 'x' of the elements has radially direction, and the local axis 'y' of the elements has counterclockwise circumferential direction.
The loads transmitted by the wind turbine tower to the foundation are introduced into the model as a system of equivalent forces in diameter where the connecting bolts are located.

Figure 3 Load application

Soil characteristics
To take into account the deformability of the soil the value of the ballast modulus considered is:
Kz = 50 MN / m².
When the calculation of the structure is performed it is taken into account the possible separation of the foundation from the soil by eliminating the springs in the nodes with vertical ascending motion.
Fatigue Verification
The fatigue verification is performed by implementing in the model all the load cases of the Markov matrix. . The forces transmitted by the wind turbine to the foundation are introduced into the model as a group of load states. Then the safety factor of the fatigue life with the Miner´s rule is obtained, which is based on the fatigue life linked to the fatigue SN curves of the material to be analyzed. These curves are included in the international standards.

Stress Checking
To check the stress the equivalent bending moments are obtained using the method of Wood Armer. To obtain the stress in the concrete and in the reinforcement corresponding with the equivalent moments the next hypotheses have been considered:
• Concrete is in compression with linear relationship between stress and strain
• Tensile in concrete is not considered.
• Steel has a linear relationship between stress and strain
• Compatibility between steel and concrete strains
To take into account the increase of the shear stresses in the steel reinforcement in cracked sections the expressions of paragraph 6.2.3 of Eurocode 2 Part 1-1 are applied.
This increase must be considered only a distance from the support with a value of the height of the section. In this case we consider that the section is coincident with the radius where are the bolts which connect the tower to the foundation are allocated.

Concrete and steel reinforcement bending verification
To check the fatigue of concrete and steel reinforcement, the formulation in the Eurocode 2 has been used

Figure 4 Fatigue damage coefficient for radial concrete top face

Steel reinforcement shear verification
To check the steel reinforcement shear the formulation used is the same as bending verification. It is also taken into account the reduction coefficient for the reinforcement bending ς, having been adopted for all the reinforcement bars corresponding to the most unfavorable position.

The fatigue safety factors obtained applying the Markov matrix are compared with those values obtained in the rainflow load spectrum and in the equivalent load method.
The results show that for sensitive materials to the stress level variation (such as concrete) rainflow method provides higher peak values than the Markov matrix method and therefore provides more conservative and less real results.


Conclusion

In this paper three methods are presented to check the fatigue phenomena in a foundation model: the equivalent load method, the rain flow spectrum method and finally the Markov matrix method. The first two ones are currently the most used. But the method which best fits the real loads applied to the structural element is the Markov matrix one
Using Markov matrix involves analyzing a large number of load cases applied to the model (more than 1000). This makes necessary the use of tools and procedures which are able to automate the process.
A Markov matrix procedure for the fatigue verification within wind turbine foundations has been developed by automatizing the analysis with a FEM tool which reduces calculation time.
The fatigue verification is performed by implementing in the model all the load cases of the Markov matrix.
Then, the three methods previously listed in the introduction have been used for fatigue verification in a wind turbine foundation using a FEM tool.
The fatigue safety factors obtained applying the Markov matrix are compared with those values obtained in the rainflow load spectrum and in the equivalent load method.
The results show that for sensitive materials to the stress level variation (such as concrete) rainflow method provides higher peak values than the Markov matrix method and therefore provides more conservative and less real results.
And finally it is shown that the use of Markov matrix method generates more real and accurate results.
Therefore a more realistic approach to the problem of fatigue in the wind turbine is achieved.


Learning objectives
A Markov matrix procedure for the fatigue verification within wind turbine foundations has been developed by automatizing the analysis with a FEM tool which reduces calculation time.


References
[1] "EN 61400-1 2005: Wind turbine generator systems - Part 1: Safety requirements.", European Standard, (2005)
[2] "Eurocode 2: ENV1992-1-1 Design of concrete structures. Part 1-1: General Rules and Rules for Buildings", European Committee for Standardization, (2004)
[3] “Guidelines for Design of Wind Turbines” Det Norske Veritas (DNV) (2002)
[4] "Model Code 2010 ", Comité Euro-International du Béton CEB, (2010)
[5] "Rules and Guidelines: IV-1 Guideline for the Certification of Wind Turbines", Germanischer Lloyd (GL), (2010)