**Summary**

This article presents a probabilistic analysis of the fixation verification of a monopile during transport. It shows that workability and cost of seafastening design can be improved while maintaining the highest safety standards. This is all done with TWD’s dedicated static friction measurement set-up, existing design and safety standards and calculation methods. Both the friction measurement procedure as well as the probabilistic verification method are approved by DNVGL.

**1 Introduction **

Seafastening large diameter monopiles (MPs) on heavy lift installation vessels becomes an ever-increasing challenge. One of the main design challenges is verification of monopile fixation on the friction-based interface at its supports. The offshore wind industry moves into new territories where more severe environmental conditions occur. Finding solutions for the fixation verification of a seafastened monopile becomes a design challenge of increased interest.

The article elaborates on a method of probabilistic verification of the fixation of MPs developed by TWD. It combines a verified tailor-made static friction test set-up (Ref. 2), calculation methods according to industry standards (Ref. 7) and advanced insights in the variability of the coefficient of friction at the interfaces (Ref. 4). Both input, calculation method as well as outcomes and a case study are presented.** **

**2 Calculation method**

Monopile stability can be verified with a relatively straightforward hand calculation based on the schematic presented in Figure 1 and Ref. 7. Design accelerations (a_{x}, a_{y, }α_{z}) are applied to determine the support reactions at the coated and uncoated interface of the monopile, often at starboard (STBD) and portside (PS) (F_{Z,STBD }and F_{Z,PS}). The sum of the support reactions multiplied by their respective coefficients of friction (μ_{STBD }and μ_{STBD}) is the total resistance against sliding. A straightforward unity check is the outcome of this analysis (see Ref. 7 for an example). TWD uses additional finite element modelling to improve this model with incorporation of the effect of the shape of the support and global pile deformation.

*Figure 1, Representation of the conventional deterministic verification of monopile stability based on friction*

**3 Measurements**

Contrary to widely held belief, friction is a system behavior and not a material characteristic. Therefore, it is important to perform verification measurements of the coefficients of friction used in design. This is particularly the case for interfaces with rubber and polyurethane as their friction depends on a number of parameters. TWD developed a DNVGL verified static friction measurement set-up (Ref. 8). It simulates an actual design case and measures static and dynamic friction between monopile steel (coated and uncoated) and the support material considered (Figure 2).

The coefficient of friction is subsequently determined from the output of the measurements performed. Often the peak of static friction is easily observed in the output data (see Figure 3). Over the course of a year TWD performed over 200 tests to investigate material behavior and optimize the method of testing.

**4 Probabilistic assessment**

Current standards do provide guidelines for testing on friction, material factors to incorporate and selecting governing upper- and lower bounds (Ref. 1). Although these guidelines are clear, it is apparent that they are generic and not aimed at a specific problem such as monopile seafastening. A probabilistic assessment was undertaken to verify the safety of this approach. Figure 2 shows the setup of the analysis.

*Figure 2, Friction test set-up and measurement (checked by DNVGL, Ref. 2)*

*Figure 3, Analysis of observed coefficient of friction from measurements obtained in one test (Ref. 4)*

** **

*Figure 4, Probabilistic assessment of friction*

Tests were performed for both the interface at the coated and uncoated part of a MP (see Section 2). By performing significantly more tests than necessary (as required by Ref. 1) the outliers are captured and a probability density function can be fitted through the observed data. Due to the amount of measurements the fit of this distribution is of high quality. Figure 5 shows the frictional behavior for one material at the uncoated steel of the monopile. By performing a bootstrap analysis insight is gained in the expected distribution of the variability of the coefficient of friction over the entire support at each side of the monopile.

*Figure 5, Probability density function of coefficient of friction uncoated steel and PU material*

At this point all information required to perform a direct reliability analysis is available.

The accelerations used are typical for future floating installation vessels in transit and survival conditions. Variability on sway, heave and roll acceleration, friction at STBD (non-coated interface) and friction at PS (coated interface) are implemented in this analysis. A standard deviation of 1% of the mean is applied on design accelerations to account for uncertainty in these estimates.

The strictest target safety level of 10^{-6} is selected as a benchmark for verification of stability (Ref. 5 & Ref. 6). In total 5 x 10^{6} independent calculations of the friction check are performed in a Monte Carlo analysis. For each of them random samples are retrieved from the distributions. Every time the unity check is calculated and stored. Figure 6 shows the outcome of all these individual checks. It is visible that the unity checks lower significantly with respect to the deterministic approach (the difference can be up to 20-50%).

*Figure 6, Direct reliability analysis of friction verification (including deterministic input, Ref. 7) (for input see Table 1)*

**5 Conclusion**

The stability of a seafastened MP with frictional supports can be verified based on a probabilistic analysis based on measured variability of the coefficient of friction. TWD proposes this method as an alternative to existing methodologies. This will help assuring accurate assessment of the actual limitations and lead to safer and more workable designs.

**6 References**

References can be made available upon request.

- DNVGL-ST-N001, Marine operations and marine warranty (Edition 2019)
- A0917951-001 Verification of friction test setup and probabilistic friction verfication
- Anonymized but representative input data of a MP seafastening project
- Measurements on friction between MP steel (coated/uncoated) poly-urethane material (08-05-2020)
- DNV Classification Notes No. 30.6 Structural reliability analysis of marine structures
- ISO2394 – General principles on reliability for structures
- TWD-NL-2019-367-C-001, Deterministic friction verification of MP seafastening
- TWD-NL-2020-367-M-02-REV-0, Friction test procedure

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