PROBABILISTIC VERIFICATION FRICTION BASED MP SEAFASTENING WWW.TWD.NL

PROBABILISTIC VERIFICATION FRICTION BASED MP SEAFASTENING

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.

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.

This 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.

1. INTRODUCTION

WWW.TWD.NLWWW.TWD.NLPROBABILISTIC VERIFICATION FRICTION BASED MP SEAFASTENING

2. CALCULATION METHOD

4. PROBABILISTIC ASSESSMENT

3. MEASUREMENTS

Monopile stability can be verified with a relatively straightforward hand calculation based on the schematic

presented in Figure 1 and Ref. 7. Design accelerations (ax, ay, αz) are applied to determine the support

reactions at the coated and uncoated interface of the monopile, often at starboard (STBD) and portside

(PS) (FZ,STBD and FZ,PS). The sum of the support reactions multiplied by their respective coefficients of friction

(μSTBD and μSTBD) 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.

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.

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.

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

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)

PS STBD

COATED UNCOATED

FZ,PS

FZ,STBD

Fμ,PS = FZ,PS μPS Fμ,STBD = FZ,STBD μSTBD

Y

Z

ay

azαx

Fμ,STBD + Fμ,PS

CoG

M ayUC =

MASS (M)

5

X

Z

5FZ

FZ

FN1

FN2 FN3

FN4

FN1 FN2

α α

cos α

FzPF =

FN1 + FN2 + FN3 + FN4PF =

FZ

REALISTIC CASE, PF ≈ 1.3 CONSERVATIVE CASE, PF ≈ 1.065

PAD SAMPLEPAD SAMPLE

MP STEEL SAMPLE

PUSH FORCE

PULL FORCE

2 3

WWW.TWD.NLWWW.TWD.NLPROBABILISTIC VERIFICATION FRICTION BASED MP SEAFASTENING

6. REFERENCES

5. CONCLUSION

References can be made available upon request.

1. DNVGL-ST-N001, Marine operations and marine warranty (Edition 2019)

2. A0917951-001 Verification of friction test setup and probabilistic friction verfication

3. Anonymized but representative input data of a MP seafastening project

4. Measurements on friction between MP steel (coated/uncoated) poly-urethane material (08-05-2020)

5. DNV Classification Notes No. 30.6 Structural reliability analysis of marine structures

6. ISO2394 - General principles on reliability for structures

7. TWD-NL-2019-367-C-001, Deterministic friction verification of MP seafastening

8. TWD-NL-2020-367-M-02-REV-0, Friction test procedure

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.

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 10⁶ 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%).

VARIABILITY ASSESSMENT COEFFICIENT OF FRICTION

MEASUREMENT CAMPAIGN

VARIABILITY ASSESSMENT

BOOTSTRAP ANALYSIS

DIRECT RELIABILITY ANALYSIS OFVERIFICATION OF MP STABILITY

MP SEAFASTENING INPUT DATA (GEOMETRY, ACCELERATIONS, SUPPORT CONDITIONS ETC.)

ANALYTIC CALCULATION METHOD FOR MP STABILTIY (SECTION 2)

20 40 60

Number [-]

0.2

0.35

0.5

Coefficient of friction [-]

Measurements

Sample values

Sample mean: 0.37 [-]

0.35 0.5

Coefficient of friction [-]

0

10

20

30

Histogram

[-]

Input for analysis:

Size sample set: 60

Boostrap size: 8

Bootstraps: 100000

Bootstrap analysis

Sample mean: 0.37 [-]

95% interval: 0.34 - 0.4 [-]

Samples

Bootstrap samples

-1.0 0.0 1.0 2.0

Unit quantiles [-]

0.2

0.35

0.5

Param

eter quantiles [-]

Errors calculated:

Normal: 0.28

Uniform: 0.29

Exponential: 0.57

Lognormal: 0.8

QQ analysis

Sample values

Linear fit (error = 0.28)

0.35 0.5

Coefficient of friction [-]

0

2

4

6

8

10

PD

F [-]

Parameters:

1: 0.37

2: 0.04

Probability density function

Fitted distribution

Empirical histogram

0.35 0.5

Coefficient of friction [-]

0.0

0.2

0.4

0.6

0.8

1.0

CD

F [-]

95% confidence interval:

Lower: 0.29

Upper: 0.45

Cumulative density function

Empirical distribution

Fitted distribution

Contact details:

Made by: Joost Remmers

Date: 2020-05-21

Contact: mail@joostremmers.nl

References

1. TWD-NL-2020-367 TWD Research Measurements (performed on 08-05-2020)

2. ISO2394 - General principles on reliability for structures

STBD: Uncoated MP steel - LUCTEC87

o

- Wet conditions - 3MPa

This datasheet assesses the best fitting distribution for the measured variation in the coefficient of friction. Measurements are scaled for wet conditions and time effect with a factor of 0.88.

20 40 60

Number [-]

0.2

0.35

0.5

Coefficient of friction [-]

Measurements

Sample values

Sample mean: 0.37 [-]

0.35 0.5

Coefficient of friction [-]

0

10

20

30

Histogram

[-]

Input for analysis:

Size sample set: 60

Boostrap size: 8

Bootstraps: 100000

Bootstrap analysis

Sample mean: 0.37 [-]

95% interval: 0.34 - 0.4 [-]

Samples

Bootstrap samples

-1.0 0.0 1.0 2.0

Unit quantiles [-]

0.2

0.35

0.5

Param

eter quantiles [-]

Errors calculated:

Normal: 0.28

Uniform: 0.29

Exponential: 0.57

Lognormal: 0.8

QQ analysis

Sample values

Linear fit (error = 0.28)

0.35 0.5

Coefficient of friction [-]

0

2

4

6

8

10

PD

F [-]

Parameters:

1: 0.37

2: 0.04

Probability density function

Fitted distribution

Empirical histogram

0.35 0.5

Coefficient of friction [-]

0.0

0.2

0.4

0.6

0.8

1.0

CD

F [-]

95% confidence interval:

Lower: 0.29

Upper: 0.45

Cumulative density function

Empirical distribution

Fitted distribution

Contact details:

Made by: Joost Remmers

Date: 2020-05-21

Contact: mail@joostremmers.nl

References

1. TWD-NL-2020-367 TWD Research Measurements (performed on 08-05-2020)

2. ISO2394 - General principles on reliability for structures

STBD: Uncoated MP steel - LUCTEC87

o

- Wet conditions - 3MPa

This datasheet assesses the best fitting distribution for the measured variation in the coefficient of friction. Measurements are scaled for wet conditions and time effect with a factor of 0.88.

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 4, Probabilistic assessment of friction

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

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

4 5

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