virtual engagement session for osrc 2021 fixed offshore
TRANSCRIPT
virtual engagement session for OSRC 2021 fixed offshore structures
pre-meeting video 2 structural probability & statistics
pre-meeting background onβ¦
- 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%
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
F(x) Fragility curve
Intensity Measure πΌπ = πΏ
1
0
H(x) Hazard curve
1E-2
1E-5
1E-4
1E-3
hazard curve & fragility curve β(annual probability of collapse)
πΉ πΏ = π πππππππ π πΏ = π
π» πΏ = π(πΏ > π)
π
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
F(L) Fragility curve1
0
H(L) Hazard curve
1E-2
1E-5
1E-4
1E-3
hazard curve & fragility curve β(annual probability of collapse)
πΉ πΏ = π collapse πΏ = π
π» πΏ = π(πΏ > π)
ππΉ πΏ = 1 if πΏ = ππ= 0 otherwise
πΏ = ππ
π(collapse) = ΰΆ±0
β
π» πΏ .ππΉ πΏ = π»(ππ)
π»(ππ)
Intensity Measure πΌπ = πΏ
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
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
platform collapse mechanisms due to AR of load
platform collapse mechanisms due to AR of load
jacket shear force capacity
a fails
b failsc fails
b
c
a
X = applied shear forceor shear force capacity
x = BS X
collapse mechanisms for a given IM
platform collapse mechanisms due to AR of load
a, b, c no failure
X = applied shear forceor shear force capacity
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
πΉ πΏ = π collapse πΏ = π
π»(πΏ) Hazard curve
πΉ(πΏ) Fragility curve
πΌππ π/πΌπ100
Intensity Measure (linear scale)
πΏ/πΏ100
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
1
1
0
π»(πΏ) Hazard curve
πΉ(πΏ) Fragility curve (AR)
1E-2
1E-4
1E-3
πΌππ π/πΌπ100
Intensity Measure (linear scale)
1.0 2.0 3.0
illustration of hazard curve & structure fragility curve
πΏ/πΏ100
πΉ πΏ = π collapse πΏ = π
1E-5
πΉ(πΏ) Fragility curve(AR+EU )
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
1
0
1E-2
1E-5
1E-4
1E-3
ππΏ
ππΉ
π»(πΏ)
π»(πΏ) Hazard curve
πΉ(πΏ) Fragility curve
ππ(collapse) = π»(πΏ) . ππΉ πΏ = π» . ππΉ/ππΏ . ππΏ
annual probability of collapse
Intensity Measure πΌπ = πΏ
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
1
0
1E-2
1E-5
1E-4
1E-3
π»(πΏ) Hazard curve
πΉ(πΏ) Fragility curve
π(collapse) = ΰΆ±
0
β
π»(πΏ) . ππΉ πΏ = ΰΆ±
0
β
π» .ππΉ
ππΏ. ππΏ
annual probability of collapse
Intensity Measure πΌπ = πΏ
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
π collapse = ΰΆ±
0
2π
π collapse πΌ . ππΌ = ΰΆ±
0
β
π»(πΏ, πΌ) . ππΉ πΏ, πΌ ππΌ
annual probability of collapse
North
EDP- (inter-story drift) β bay drift(tilt) β total drift(tilt)
pancake leg collapse mechanism β GoM
pancake leg - collapse mechanism common in North Sea (not normally checked or designed for!)
EDP- (interstory drift) β bay drift(tilt) β total drift(tilt)
β portal frame
β non-linear jacket material
β braced frame
β non-linear jacket material
β plasticity very localised in members
β reqd. for local buckling and tearing
β not reqd. for deck displacement
β non-linear soil material (P-y and T-z)
β non-linear pile material
β P-D amplification
β P-d amplification for member buckling
PP
D
risk matrixleg D/t=100
LOADS β 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
πππππ’π πΏ > π πΌ π πΏ > π πΏ = π, πΌ
hazard & fragility for seismic & metocean
0 1 2 3 4 5 61 10
4β
1 103β
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 104β
==Sa_Pf
x100
3.107=
Sa_ALE
x100
3.532=
RPf1
Pf
2500==
HSa_Pf
x100
3.999 104β
= 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
4β
1 103β
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 105β
==
RPf1
Pf
15378==
H Sbs_Pf( ) 1.308 104β
= 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
4β
1 103β
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 104β
==
RPf1
Pf
5542==
H Sbs_Pf( ) 3.391 104β
= 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
4β
1 103β
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 104β
==Sa_Pf
x100
3.107=
Sa_ALE
x100
3.532=
RPf1
Pf
2500==
HSa_Pf
x100
3.999 104β
= 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 β offshore structures
I&E - engineering
Mobile: +44(0) 7803260300
TEAMS: +44(0)1224 934836