virtual engagement session for OSRC 2021 fixed offshore ...

virtual engagement session for OSRC 2021 fixed offshore structures

pre-meeting video 2 structural probability & statistics

pre-meeting background on…

- basic probability and statistics

- structural probability and statistics

- metocean probability and statistics

Human error in design &

construction is controlled by QA

and QC

RE

PR

ES

EN

TA

TIV

E C

AP

AC

ITY

= 1

47%

RE

PR

ES

EN

TA

TIV

E L

OA

D =

100%

Load or resistance as % of nominal load

Pro

bab

ility

de

nsit

y

load and resistance probability (API 1993) component level

Use of representative load

and resistance with partial

factors is a deterministic

recipe intended to result in

an acceptable probability of

collapse

1

0

1

0

Load or resistance as % of nominal load

metocean hazard curve & fragility curve - component level

RE

PR

ES

EN

TA

TIV

E C

AP

AC

ITY

= 1

47%

RE

PR

ES

EN

TA

TIV

E L

OA

D =

100%

𝑃𝑎𝑛𝑛𝑢𝑚 𝐿 > 𝑙 𝛼 𝑃 𝐿 > 𝑅 𝐿 = 𝑙, 𝛼

F(x) Fragility curve

Intensity Measure 𝐼𝑀 = 𝐿

1

0

H(x) Hazard curve

1E-2

1E-5

1E-4

1E-3

hazard curve & fragility curve –(annual probability of collapse)

𝐹 𝐿 = 𝑃 𝑐𝑜𝑙𝑙𝑎𝑝𝑠𝑒 𝐿 = 𝑙

𝐻 𝐿 = 𝑃(𝐿 > 𝑙)

𝑙


F(L) Fragility curve1

0

H(L) Hazard curve

1E-2

1E-5

1E-4

1E-3

hazard curve & fragility curve –(annual probability of collapse)

𝐹 𝐿 = 𝑃 collapse 𝐿 = 𝑙

𝐻 𝐿 = 𝑃(𝐿 > 𝑙)

𝑑𝐹 𝐿 = 1 if 𝐿 = 𝑙𝑐= 0 otherwise

𝐿 = 𝑙𝑐

𝑃(collapse) = න0

∞

𝐻 𝐿 .𝑑𝐹 𝐿 = 𝐻(𝑙𝑐)

𝐻(𝑙𝑐)



load profile randomness (for given base shear)

Stokes V regular wave

sampled unfocused steep/ breaking waves

P50 from sampled unfocused steep/ breaking waves

P10 P90 from sampled unfocused steep/ breaking waves

0MNm torsion

Sbs = 45 MN

30MNm torsion

Sbs = 45 MN Sbs = 45 MN0MNm torsion

WiD

WiJ

WiD

WiJ WiJ

1 32

platform collapse mechanisms due to AR of load

Metocean shear force (cumulative with depth) for 3 different wave shapes(all 3 have same base shear)

jacket shear force capacity

X = applied shear forceor shear force capacity

a fails

b

c

a

b fails

c no failurex = BS X



jacket shear force capacity

a fails

b failsc fails

b

c

a


x = BS X

collapse mechanisms for a given IM


a, b, c no failure


x = BS

a, b, c all cause failure

1

1

0

1E-2

1E-5

1E-4

1E-3

1.0 2.0 3.0

illustration of hazard curve & structure fragility curve


𝐻(𝐿) Hazard curve

𝐹(𝐿) Fragility curve

𝐼𝑀𝑅𝑃/𝐼𝑀100

Intensity Measure (linear scale)

𝐿/𝐿100


1

1

0


𝐹(𝐿) Fragility curve (AR)

1E-2

1E-4

1E-3

𝐼𝑀𝑅𝑃/𝐼𝑀100

Intensity Measure (linear scale)

1.0 2.0 3.0

illustration of hazard curve & structure fragility curve

𝐿/𝐿100


1E-5

𝐹(𝐿) Fragility curve(AR+EU )


1

0

1E-2

1E-5

1E-4

1E-3

𝑑𝐿

𝑑𝐹

𝐻(𝐿)



𝑑𝑃(collapse) = 𝐻(𝐿) . 𝑑𝐹 𝐿 = 𝐻 . 𝑑𝐹/𝑑𝐿 . 𝑑𝐿

annual probability of collapse



1

0

1E-2

1E-5

1E-4

1E-3



𝑃(collapse) = න

0

∞

𝐻(𝐿) . 𝑑𝐹 𝐿 = න

0

∞

𝐻 .𝑑𝐹

𝑑𝐿. 𝑑𝐿




𝑃 collapse = න

0

2𝜋

𝑃 collapse 𝛼 . 𝑑𝛼 = න

0

∞

𝐻(𝐿, 𝛼) . 𝑑𝐹 𝐿, 𝛼 𝑑𝛼


North

EDP- (inter-story drift) – bay drift(tilt) – total drift(tilt)

pancake leg collapse mechanism – GoM

pancake leg - collapse mechanism common in North Sea (not normally checked or designed for!)

EDP- (interstory drift) – bay drift(tilt) – total drift(tilt)

❑ portal frame

❑ non-linear jacket material

❑ braced frame

❑ non-linear jacket material

❑ plasticity very localised in members

❑ reqd. for local buckling and tearing

❑ not reqd. for deck displacement

❑ non-linear soil material (P-y and T-z)

❑ non-linear pile material

❑ P-D amplification

❑ P-d amplification for member buckling

PP

D

risk matrixleg D/t=100

LOADS – steps 10 to 14Steps

Step 12Reduce collapse load if failure mode is pancake leg.Calculate Pcollapse

Step 13Determine IRPA and TRIF given Pcollapse

Safety Engineer

Structural Engineer

Step 11Determine collapse load - USFOS time history analysis (THA) (dynamic pushover)

Structural Engineer

Step 10Deaggregate hazard curve at RP to give (unfocused) wave and WiDL

Metocean & Engineer

Structural Engineer

Safety and structural Engineer

Step 14Demonstrate L-S risk and B-R is tolerable & ALARP (or apply mitigation measures)

8 9 10 11 12 13 14 15

7 8 9 10 11 12 13 14

6 7 8 9 10 11 12 13

5 6 7 8 9 10 11 12

4 5 6 7 8 9 10 11

3 4 5 6 7 8 9 10

2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

Exce

ed

en

ce F

req

ue

ncy

Seismic hazard curve

similar shaped hazard curves for all other hazardsIM= kinetic energy

IM= spectral acceleration

H(x) = P(IM>x)

H(x) = P(IM>x)

Maximum Credible collision energy

Maximum Credible earthquake (Sa)

hazard curves for other hazardsVessel collision hazard curve

epistemic uncertainty - hazard curve (seismic)

xx

similar approach now being used for epistemic uncertainty in long term metocean models

1

0

F(x) Fragility curveEpistemic Uncertainty (EU)

1E-2

1E-4

1E-3

IMRP /IM100 Intensity Measure (linear scale)

2.0 3.0

H(x) Hazard curveAleatory Randomness (AR)andEpistemic Uncertainty (EU)

1E-5

1.0

epistemic uncertainty - hazard curve


hazard & fragility for seismic & metocean

0 1 2 3 4 5 61 10

4−

1 103−

0.01

0

0.2

0.4

0.6

0.8

H x( )

F x( )

HdF x( )

x

Sa_Pf 0.5524= Sa_ALE 0.628=

Pf

0

xH x( )x

F x( )d

d

d 4 104−

==Sa_Pf

x100

3.107=

Sa_ALE

x100

3.532=

RPf1

Pf

2500==

HSa_Pf

x100

3.999 104−

= FSa_ALE

x100

0.501=

1

HSa_Pf

x100

2501=1

HSa_ALE

x100

3600=

Cc

Sa_ALE

Sa_Pf

1.137==

0 1 2 3 4 5 61 10

4−

1 103−

0.01

0

0.2

0.4

0.6

0.8

H x( )

F x( )

HdF x( )

x

Sbs_Pf 1.65= Sbs_P50 1.85=Pf

0

xH x( )x

F x( )d

d

d 6.503 105−

==

RPf1

Pf

15378==

H Sbs_Pf( ) 1.308 104−

= F Sbs_P50( ) 0.5=

1

H Sbs_Pf( )7645=

1

H Sbs_P50( )26949= Cc

Sbs_P50

Sbs_Pf

1.121==

hazard & fragility for seismic & metocean

0 1 2 3 4 5 61 10

4−

1 103−

0.01

0

0.2

0.4

0.6

0.8

H x( )

F x( )

HdF x( )

x

Sbs_Pf 1.85= Sbs_P50 2.3=Pf

0

xH x( )x

F x( )d

d

d 1.804 104−

==

RPf1

Pf

5542==

H Sbs_Pf( ) 3.391 104−

= F Sbs_P50( ) 0.5=

1

H Sbs_Pf( )2949=

1

H Sbs_P50( )12661= Cc

Sbs_P50

Sbs_Pf

1.243==

0 1 2 3 4 5 61 10

4−

1 103−

0.01

0

0.2

0.4

0.6

0.8

H x( )

F x( )

HdF x( )

x

Sa_Pf 0.5524= Sa_ALE 0.628=

Pf

0

xH x( )x

F x( )d

d

d 4 104−

==Sa_Pf

x100

3.107=

Sa_ALE

x100

3.532=

RPf1

Pf

2500==

HSa_Pf

x100

3.999 104−

= FSa_ALE

x100

0.501=

1

HSa_Pf

x100

2501=1

HSa_ALE

x100

3600=

Cc

Sa_ALE

Sa_Pf

1.137==

Questions

Dr Ramsay Fraser

Engineering Technical Authority – offshore structures

I&E - engineering

Mobile: +44(0) 7803260300

TEAMS: +44(0)1224 934836

[email protected]

mailto:[email protected]

virtual engagement session for OSRC 2021 fixed offshore ...

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