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virtual engagement session for OSRC 2021 fixed offshore structures session 2 performance-based design for metocean hazard

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Page 1: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

virtual engagement session for OSRC 2021 fixed offshore structures

session 2 performance-based design for metocean hazard

Page 2: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

motivation

(ideally) establish, agree & codify a reliability calculation, consistent for all hazards, that…

• quantifies operational risk v performance objectives;• sets mitigation strategies (inspection, maintenance, monitoring and evacuation);• communicates risk to stakeholders (regulators, corporations, insurance and workers);

1a) share recent R&D findings on extreme metocean loads for fixed offshore structures;1b) explain difference in the metocean hazard curve cf. historical methods.

2a) show that performance-based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment of fixed offshore structures for the seismic hazard, has an identical form for the metocean hazard;

2b) discuss any further work required to achieve industry consensus on adopting performance-based design/ assessment of fixed offshore structures for the metocean hazard.

Page 3: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

potential future design/ assessment approach for jackets subject to metocean hazard

based on19901-2 (2EQ) performance-based design

Page 4: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

OSRCs in 1995, 2012, 2014, 2016 & 2018 but no progress on codifying structural reliability for design / assessment for offshore structures….

except for seismic design of offshore structures (ISO 19901-2 and API 2EQ)

meanwhile, ASCE…

established and applied structural reliability (Performance-Based Design) for seismic design of every tall building in California since 2000.

published reliability targets for seismic design (life-safety, repair cost, facility’s availability)

there was a common factor… Allin Cornell

structural reliability (1995 to 2020)

Page 5: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

1995 OSRC - Denham UK

Issues for resolution

A couple of very important needs have been identified to bring some sense of order and consistency to the understanding and use of the values and/or approaches.

Reconcile basis for models in deriving reliability numbers

Reconciliation of the Shell model and other models is necessary before any confidence can be developed in moving from notional values to “true” values that would be consistent with actuarial data.

Establish basis and validation of COV values

For values to move beyond notional values, consistency and accuracy in the COV values must be developed.

5

Page 6: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

Allin Cornell’s approach – pragmatic engineering

notional (not actuarial) only useful for code calibration

any (absolute) result is possible depending on assumptions

complex maths (not suitable for designers)

no agreement on acceptable/ intolerable limits

for use in decision making…include epistemic uncertainty in hazard curve and aleatory randomness in fragility curve

define simple 10-step procedure with default inputs based on full solutions to real problems

formulate in 1-dimension (Intensity Measure) as a hazard curve & fragility curve

building owners & insurance companies require…

probability of - fatalities, repair cost and repair time

rather than being told “building conforms to design code”

PROBLEMS SOLUTIONS

Page 7: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

approach of one IOC to epistemic uncertainty…

Epistemic uncertainty shall be appropriately included in the study.

PSHA shall incorporate the views represented by the composite distribution of thescientific community as a whole, rather than any narrower specialized viewpoint owned bythe Contractor directly conducting the study.

Page 8: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

1) Hazard curve, Fragility curve, Aleatory Randomness (AR) & Epistemic Uncertainty (EU)

2) Why BS is the best scalar measure of metocean load but does not fully define the load AR

3) Deaggregation of hazard curve & fragility curve fitting

4) Recent application of 3) for jacket seismic design/assessment

5) Recent application of 3) for jacket metocean design/assessment

6) 19901-2 & 19902 codified version of 3) for seismic design

7) Possible codified version of 6) for metocean design

content

Page 9: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

PGD (rigid structure)

𝑆𝑆𝑑𝑑 𝑇𝑇 = spectral displacement

𝑆𝑆𝑑𝑑 𝑇𝑇

𝑆𝑆𝑎𝑎 𝑇𝑇 = spectral acceleration

max �̈�𝑥𝑟𝑟 rather than max 𝑥𝑥𝑟𝑟

pseudo spectral acceleration

= 2𝜋𝜋𝑇𝑇

2𝑆𝑆𝑑𝑑 𝑇𝑇

𝜁𝜁 = 5% 𝑡𝑡𝑡𝑡𝑡𝑡

𝜁𝜁

linear oscillator

Response spectrum𝑥𝑥𝑚𝑚𝑎𝑎𝑚𝑚 for 𝑇𝑇𝑖𝑖

𝑥𝑥𝑚𝑚𝑎𝑎𝑚𝑚

𝑇𝑇𝑖𝑖

𝑇𝑇

𝑇𝑇𝑖𝑖�̈�𝑥𝑔𝑔

�̈�𝑥𝑔𝑔𝑥𝑥𝑟𝑟

𝑥𝑥𝑟𝑟

seismic analogy - (pseudo) spectral acceleration

Page 10: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

Hazard curve creationa) identify earthquake sources.

then …

b) characterize the distribution of earthquake magnitudes from each source

c) characterize the distribution of source-to-site distances from each source

d) Predict the attenuation (including uncertainty) of ground motion intensity at “r” from each source

Aggregate the contribution to the hazard curve from each earthquake source using b), c) & d) to compute the annual rate of exceeding a given ground motion intensity

spec

tral

acc

eler

atio

n

rL

siterA

truncated Gutenberg-Richter

Mw

spectral acceleration (g)

seismic analogy – hazard curve

Page 11: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

𝐹𝐹(𝐿𝐿) Fragility curve1

0

1E-2

1E-5

1E-4

1E-3

𝐻𝐻(𝐿𝐿) Hazard curve

19901-2 (2EQ) seismic annual probability of collapse

Intensity Measure 𝐼𝐼𝐼𝐼 = 𝐿𝐿 (ie spectral acceleration)

𝛽𝛽 = 0.3

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐿𝐿 > 𝑅𝑅 = �𝐻𝐻𝐻𝐻𝐹𝐹 < 1/2500

performance objectives

1. performance level2. acceptable RP for exceeding PL

no platform collapse (or LQ slide)RP=2500yrs

no post event repairsRP≅100yrs

Page 12: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

platform collapse mechanisms due to AR of load

Jacket shear force capacitya fails

b failsc fails

bc

a

X = applied shear forceor shear force capacity

x = BS X

Page 13: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

platform collapse mechanisms due to AR of wave load (explicit in the fragility curve)

11E-2

1E-4

1E-3

0 40 80 120 160

fragility curve for small variability in shear v depth profiles

(collapse mechanismnot sensitive to load AR)

01E-5

Fragility curve for large variability in shear v depth profiles

(collapse mechanism sensitive to load AR)

Intensity Measure - base shear (MN)

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

Page 14: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

IM =Sa(T1) or PGA

orSbs(T1)

EDP =Inter-story drift ratio

= lateral deck displacement/ platform ht.

DM =Loss of production due to repair

orplatform collapse

DV =dollar lossesordowntimeorfatalities

performance-based design

Page 15: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

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

Page 16: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

11E-2

1E-4

1E-3

H(x) Hazard curve

01E-5

deaggregation of hazard curve

0 40 80 120 160

Intensity Measure - base shear (MN)

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

Page 17: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

deaggregation of hazard curve

includes WiJL from breaking waves on the conductors and vertical WiDL

1

2

3

Page 18: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

Sbs40 80 120

40 80 120

10 %

20 %

30 %

Deaggregation Weights 𝑊𝑊𝑊𝑊

45

EDP

= re

sidua

l tilt

(deg

)Fr

actio

n fa

iling

tilt c

riter

ion

Sbs

EDP limit=6deg

30MNm torsion

0MNm torsion

0MNm torsion

Sbs = 45 MN

Sbs = 45 MN

Sbs = 45 MN

1

2

3

fragility curve construction – multiple stripes analysis

Page 19: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

40 80 120

EDP

= re

sidua

l tilt

(deg

)Fr

actio

n fa

iling

tilt c

riter

ion

0.0

0.2

0.4

0.6

0.8

1.0

0 0.5 1 1.5 2 2.5 3

P(c|

Sa=x

)

observed data

max liklihood fit

40 80 120 160 200 240

PED

P>lim

it𝑆𝑆 𝑏𝑏

𝑏𝑏=𝑥𝑥

Sbs40 80 120Sbs

fragility curve construction – MLM

Page 20: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

0.0

0.2

0.4

0.6

0.8

1.0

observeddata

PED

P>lim

it𝑆𝑆 𝑏𝑏

𝑏𝑏=𝑥𝑥

SbsMSA – Multiple Stripes Analysis

Logistic regression

fragility curve construction – 2 x 3 options

IDA - Incremental Dynamic Analysis Bayesian inference

Logistic regression exampleMaximum Likelihood Method

2x30 THA

1000 THA

Page 21: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

fragility curve fitting available at 18mins into the following video…

https://www.youtube.com/watch?v=Q8e0_d81a40&feature=youtu.be

fragility curve fitting spreadsheet (as shown in above video) can be downloaded …

http://femap58.atcouncil.org/supporting-materials

fragility curve by Bayesian inference – Gokkaya, Baker & Deierlein (2015)…

https://pdfs.semanticscholar.org/303a/50379f4a2d77dd1e1f53cd2aa303236c659b.pdf

fragility curve fitting

Page 22: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

1

0

Posterior predictive Fragility curveEpistemic Uncertainty (EU)andAleatory Randomness (AR)

1E-2

1E-4

1E-3

IMRP /IM100 Intensity Measure (linear scale)

2.0 3.01E-5

Posterior predictive Hazard curveAleatory Randomness (AR)andEpistemic Uncertainty (EU)

AR & EU on fragility curve

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

1.0

Page 23: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

30,000 MCS for LOAD & RESISTANCE

LOAD - 20 time histories- TH scaled (15 times) by IDA

RESISTANCE- 100 draws of 4 random variables above

using Latin Hypercube Sampling

2017 example of seismic fragility curve

Page 24: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

topsides mass yield strength

damping Youngs modulus

Sensitivity of Fragility curve to EU

3 Fragility curves for P2.5, P50 & P97.5 values of sensitivity variable together with P50 value of remaining 3 variables

seismic fragility curve – dispersion β= 44%

0 1 20

0.25

0.5

0.75

11

0

F x( )

2.50 x

Prob

abili

ty o

f Col

laps

e

Sa (T1,5%) (g)

Mean Fragility

100 Fragility curves – each based on samples of 4 variables using LHS

Each curve is fitted to 15 magnitudes of 20 THA(ie IDA with up to 300 points)

Page 25: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

2019 example of metocean fragility curve

Platform North direction – MSA stripe 2 (with approx 15MN WiD)

resulting fragility curve(for 1 direction)

fitted using logistic regression

22 24 26 28 30 32 34

Fbs

Page 26: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

2019 example of metocean fragility curve

The Fragility curve for the platform has been calculated by a contractor using USFOS based upon random, irregular, nonlinear, wave time history data.

The metocean wave time history data received from metocean consultant was reduced to the following cases for USFOS THA by …

For each direction – 3 sets of base shears

For each base shears – 10 realisations of metocean time history loading (WiJ + WiD)

Failure modes revealed were …

1. foundation failure due to pile push-in

2. Deck leg tearing due to high plastic strain at plastic hinge

Page 27: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

design for seismic hazard to ISO 19901-2 and ISO 19902

Page 28: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

design for seismic hazard to ISO

Page 29: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

ISO 19902

Select 7 sets of accelerograms that have

design for seismic hazard to ISO

Page 30: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

ISO 19901-2 requirement for seismic design of fixed offshore structures is based on a 1996 paper by Allin Cornell http://www.iitk.ac.in/nicee/wcee/article/11_2122.PDF

The method was proposed by Cornell (and adopted by ISO 19901-2) for design of jacket structures to resist seismic loading. It also EXACTLY applies to metocean loading.

The data in the paper was based on non-linear THA of jacket structures by one of Cornell’s PhD students (Paolo Bazzurro) in 1993.. https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9445%281994%29120%3A11%283345%29

ISO 19901-2 design/ assessment for seismic hazard, developed 24 years ago, can be adopted for design / assessment for metocean hazard.

background – design for seismic hazard to ISO

Page 31: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

0.0001

0.001

0.01

0.1

1

10

100

Ann

ual p

roba

bilit

y of

exc

eeda

nce

of s

pect

ral a

ccel

erat

ion

define the slope of the hazard curve as -1/log(aR) approximate aR at Poccur asslope =-1/log(aR) =(log(P1)-log(P2))/(log (Sa1)-log(Sa2))-1/log(aR) =-1/log (Sa1/Sa2) as P1/P2=0.1

background – design for seismic hazard to ISO

Approximate hazard curve by straight line on log-log plot

19901-2, Figure 5 (log x axis)

Page 32: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

4E-4 max 0.5

1

0

F(x) Fragility curvesfor different designs (strengths)all have β = 0.3 (which is based on Bazzurro’s PhD)

1E-2

1E-4

1E-3

𝑥𝑥 = IMRP /IM100 Intensity Measure (linear scale)

2.0 3.0

H(x) mean Hazard curve

𝑥𝑥1E-5

𝑥𝑥 = 𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝑥𝑥 = 𝑆𝑆𝑆𝑆4𝐴𝐴−4

Cc

1.0

background – design for seismic hazard to ISO

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

Page 33: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

• 𝑃𝑃𝑐𝑐 = ∫0∞𝐻𝐻. 𝑑𝑑𝑑𝑑

𝑑𝑑𝑚𝑚𝐻𝐻𝑥𝑥

• 𝑙𝑙𝑙𝑙𝑙𝑙𝐻𝐻 = −𝑚𝑚. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

• 𝐻𝐻 = 𝑙𝑙. 𝑥𝑥−𝑚𝑚

• 𝑑𝑑𝑑𝑑𝑑𝑑𝑚𝑚

= 1𝑚𝑚𝑥𝑥 2𝜋𝜋

𝑒𝑒−𝑙𝑙𝑙𝑙𝑙𝑙−𝜇𝜇𝛽𝛽√2

2

• 𝜇𝜇 = 𝜇𝜇𝑎𝑎𝑎𝑎𝑙𝑙 = mean of 𝑙𝑙𝑙𝑙𝑙𝑙

• 𝛽𝛽 = 𝜎𝜎𝑎𝑎𝑎𝑎𝑙𝑙 = SD of 𝑙𝑙𝑙𝑙𝑙𝑙=dispersion

• 𝑃𝑃𝑐𝑐 = ∫0∞ 𝑙𝑙𝑥𝑥−𝑚𝑚 1

𝑚𝑚𝑥𝑥 2𝜋𝜋𝑒𝑒−

𝑙𝑙𝑙𝑙𝑙𝑙−𝜇𝜇𝛽𝛽√2

2

𝐻𝐻𝑥𝑥

𝑃𝑃𝑐𝑐 = 𝑙𝑙 𝑒𝑒𝜇𝜇 −𝑚𝑚𝑒𝑒12𝑚𝑚

2𝑥𝑥2

𝜃𝜃 = 𝑒𝑒𝜇𝜇 = median

𝑃𝑃𝑐𝑐 = 𝑙𝑙𝜃𝜃−𝑚𝑚𝑒𝑒12𝑚𝑚

2𝑥𝑥2

𝜃𝜃−𝑚𝑚 = 𝑃𝑃𝑐𝑐𝑐𝑐𝑒𝑒−

12𝑚𝑚

2𝑥𝑥2

𝜃𝜃 =𝑃𝑃𝑐𝑐𝑙𝑙

−1𝑚𝑚𝑒𝑒12𝑚𝑚𝑥𝑥2

𝜃𝜃 =𝑙𝑙

4 × 10−4

1𝑚𝑚 𝑒𝑒

12𝑚𝑚𝑥𝑥2

𝜃𝜃 = 𝑥𝑥4𝐴𝐴−4 × 𝑒𝑒12𝑚𝑚𝑥𝑥2

𝜃𝜃 = 𝑥𝑥4𝐴𝐴−4 × 𝐶𝐶𝐶𝐶

background – design for seismic hazard to ISO

Page 34: virtual engagement session for OSRC 2021 fixed offshore … · 2021. 1. 6. · 2a) show that performance -based design, as used in ISO 19901-2 and API RP 2EQ for design/ assessment

4E-4 max 0.5

7/7

6/7

5/7

4/7 Pcollapse=1-4/7 = 0.42

3/7

2/7

1/7

0/7 THA passes 1

0

F(x) Fragility curvesfor different designs (strengths)all have β = 0.3 (which was based on Bazzurro’s PhD)

1E-2

1E-4

1E-3

2.0 3.0

H(x) mean Hazard curve

1.0 𝐿𝐿𝐿𝐿100

1E-5Cc

𝑥𝑥 = 𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 = 𝜃𝜃𝑥𝑥 = 𝑆𝑆𝑆𝑆4𝐴𝐴−4 𝐴𝐴𝐴𝐴100

=Intensity Measure

background – design for seismic hazard to ISO

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

19901-24 passes from 7 THAs

ASCE 7-1610 passes from 11 THAs11 passes from 11 THAs

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ISO 19902

elastic design for seismic hazard to ISO

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elastic design for seismic hazard to ISO

𝐶𝐶𝑟𝑟 = 𝐶𝐶𝑏𝑏𝑟𝑟 × 𝐶𝐶𝑑𝑑𝑟𝑟

𝐶𝐶𝑏𝑏𝑟𝑟 = �∆𝑢𝑢∆𝐸𝐸𝐸𝐸𝐸𝐸 strengthening part of deformation curve

𝐶𝐶𝑑𝑑𝑟𝑟 = 1 + 𝐴𝐴𝑑𝑑𝑑𝑑𝑢𝑢∆𝑢𝑢

degrading part of deformation curve

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background – elastic design for seismic hazard to ISO

5E-3 max

0.5

1

0

Fragility curve“collapse” (LSR)

1E-2

1E-4

1E-3

2.0 3.01.0

𝑥𝑥 = 𝑆𝑆𝑆𝑆4𝐴𝐴−4

4E-4 max

Cc1E-5

Fragility curve“repair” (BR)

Cr

𝑥𝑥 = 𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 𝑥𝑥 = 𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 = 𝜃𝜃

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅𝑐𝑐𝑐𝑐𝑎𝑎𝑎𝑎𝑎𝑎𝑐𝑐𝑏𝑏𝑐𝑐 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

𝑃𝑃 𝐿𝐿 > 𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐𝑎𝑎𝑖𝑖𝑟𝑟 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

𝐿𝐿𝐿𝐿100 𝐴𝐴

𝐴𝐴100=Intensity Measure

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5E-3 max

1

0

1E-2

1E-4

1E-3

2.0 3.01.0 𝑥𝑥 = 𝑆𝑆𝑆𝑆𝑎𝑎𝑐𝑐𝑚𝑚

1E-5

Fragility curve“repair” (BR)

𝑥𝑥 = 𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴

𝐹𝐹 1.1𝐺𝐺 + 1.1𝑄𝑄 + 0.9𝐸𝐸(𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴) <𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐𝛾𝛾𝑅𝑅

𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 < 𝐸𝐸−11

0.9𝐹𝐹−1

𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐𝛾𝛾𝑅𝑅

− 𝐹𝐹(1.1𝐺𝐺 + 1.1𝑄𝑄)

𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 < 𝑆𝑆𝑆𝑆𝑎𝑎𝑐𝑐𝑚𝑚

background – elastic design for seismic hazard to ISO

𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚 𝐿𝐿 > 𝑙𝑙 𝛼𝛼 𝑃𝑃 𝐿𝐿 > 𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐𝑎𝑎𝑖𝑖𝑟𝑟 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

𝐿𝐿𝐿𝐿100 𝐴𝐴

𝐴𝐴100=Intensity Measure

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0.2 0.4 0.6 0.81 10 4−×

1 10 3−×

0.01

0

0.2

0.4

0.6

0.8

H x( )F x( )

fac_HdF x( )

xSa_Pf 0.5524:= Sa_ALE 0.628:= Pf

0

xH x( )x

F x( )dd

⋅⌠⌡

d 4 10 4−×=:=

H Sa_Pf( ) 3.999 10 4−×= F Sa_ALE( ) 0.501=

CcSa_ALESa_Pf

1.137=:=1H Sa_Pf( ) 2501=

1H Sa_ALE( ) 3600=

X axis = (Sa)

Y axis = P(X>x)

Y axis = P(X<x)

Cc1/3600=3E-4

1/2500=4E-4

4.0

2500

0.5

background – design for seismic hazard to ISO

Figure 5 ISO 19901-2

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hazard curvea) is structure specific and location specific;b) accurately defined by recent R&D;c) could be approximated (for WiJ only) by structure type and

location (eg as illustrated opposite from NS1200 ph2).

further work required on hazard curvea) complete verification & validation of recent R&D for

extreme metocean load;b) calculate Hazard curves for a wide range of platform

shapes and locations in order to determine simple approximations for the hazard curve by platform type/ location.

potential design for metocean hazard to ISO

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fragility curve:a) is structure specific and location specific;b) accurately defined by THA & Bayesian inferencec) could be approximated (for WiJ only) by structure type and location

(if a database of fragility curves are created).

further work required on metocean fragility curve:a) investigate use of Bayesian inference to determine the

(posterior predictive) fragility curve.b) calculate fragility curves (by NLTHA) for a wide range of platform

shapes and locations (WiJ only) in order to determine simple approximations for the dispersion by platform type/ location.

c) calculate table of Cc factors (based on above)d) calculate table of Cr factors (based on above)

potential design for metocean hazard to ISO

𝑃𝑃 𝐿𝐿 > 𝑅𝑅𝑐𝑐𝑐𝑐𝑎𝑎𝑎𝑎𝑎𝑎𝑐𝑐𝑏𝑏𝑐𝑐 𝐿𝐿 = 𝑙𝑙,𝛼𝛼

𝐿𝐿𝐿𝐿100

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design recipea) write a design recipe for metocean hazard (similar to that in

19901-2 and 19902 for seismic hazard).b) agree the target (and limiting?) performance objective.

further work required on design recipe a) determine a suitable number of THA to be

performed and the pass/ fail ratio.b) determine the partial factors for the elastic

design code-check.

𝐹𝐹 1.1𝐺𝐺 + 1.1𝑄𝑄 + 0.9𝐸𝐸(𝑆𝑆𝑏𝑏𝑏𝑏 𝐴𝐴𝐴𝐴𝐴𝐴) <𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐𝛾𝛾𝑅𝑅

𝐹𝐹 1.3𝐺𝐺 + 1.3𝑄𝑄 + 1.0𝐸𝐸(𝑆𝑆𝑏𝑏𝑏𝑏 𝐴𝐴𝐴𝐴𝐴𝐴) < 𝑅𝑅𝑟𝑟𝑐𝑐𝑐𝑐

potential design for metocean hazard to ISO

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data for 119 wavelets to be Read from .txt file

When Type=Spect & SpecType=Readthis is dummy data and is not used

When SpecType=Readthese fields are replaced byFilename Spec <filename>NB SpecType=Read is not described in the Nov 2019 USFOS manual

If N_ini=0then X1 f1 to XN_ini fN_ini are not provided

USFOS data to create irregular wave time history

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n height period direction phaseexample content of .txt file where

n = wavelet numberheight = wavelet height (m)period = wavelet period (s) direction = wavelet direction (deg)phase = wavelet phase (deg)

USFOS data to create irregular wave time history

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USFOS uses Wheeler stretching and so“stretches” the solid grey (linear) curvevertically to give the solid black curve.

The velocity profile can be changed fromthe black curve to the red curve (NB theLOADS JIP curve also lies on the red curve)by using the USFOS input record Wave KRF

For the black & red curves shown theWave_KRF factor will be

>1 for Z > -7m <1 for Z< -7m

where Z=0 is the still water elevation

USFOS data to create irregular wave time history

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example data to factor kinematics as a function of depth

USFOS data to create irregular wave time history

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These results were produced by using the WAVEDATA andWAVE_KRF commands (as described above) for a large jacketstructure.The loading was plotted from the USFOS calculated base shear.The dynamic amplification was produced by plotting the reactionsfrom an USFOS time history analysis.

focused wave

example results from USFOS irregular wave time history

unfocused wave

DAF=1.2

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Energy Institute - guidance on the application of performance-based design/ assessment

− regulatory background

− performance-based design (history, future and basis)

− performance-based design applied by codes

− non-linear structural analysis

− review of latest research on wave loading

− establishing good practice (understanding impact of latest methods)

− mitigation of life-safety & environmental risk associated with metocean hazards

− example application based on a North Sea platform

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discussion points from panellists

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Questions

Dr Ramsay Fraser

Engineering Technical Authority – offshore structures

I&E - engineering

Mobile: +44(0) 7803260300

TEAMS: +44(0)1224 934836

[email protected]