P 1195- Risk and Reliability in Geotechnical Engineering

8/10/2019 P 1195- Risk and Reliability in Geotechnical Engineering

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72

=roceedings: .Fourth International Conference on Case Histories in Geotechnical Engineering St. Louis, Missouri

March 9-12, 1998.

RISK AND RELIABILITY IN GEOTECHNICAL ENGINEERING

zanne Lacasse and Farrokh Nadim

rwegian Geotechnical Institutelo. Norway

STRACT

Paper No. SO

tistics. reliability analyses and risk estimates can he very useful decision-making tools in geotechnical problems. Yet the methoe used in practice. The offshore and mining industry arc at the forefront for the usc of these approaches, having encouraged their sponsored research that has enabled the methods to he well-documented and of proven usefulness in the study of alternativ

ign and decision-making in face of uncertainties. The paper presents a few case studies in diiTerent areas of geotechnical enginediscusses the results that would have hccn nhtained without the use nf the risk approach. Special emphasis is given to dams a

shore structures, hoth piled and shallow foundations. The authors take a look at the reasons why the methods arc not used to a greatent in praclice and make rec ommendations as to when and how one should uses such methods.

YWORDS

k, reliability, um:crtainty, foundations, failure, dams offshore foundations. soil parameters, probabilistic analysis

TRODUCTION

s invited paper presents the role or reliability- and risk-basedroaches in solving geotechnical design problems. It discusses

sting geotechnical applications, available reliability tools amlhcncfits of nsk and reliahility estimates when used in con

ction with deterministic analyses. Case studies with damign, piled and shallow foundations. earthquake analysis. slopebility, rock mechanics and mining engineering, arc presentedexamples of the application uf such line of thought.

iability analyses arc needed because geotechnics IS not anct science. Predictions of foundation behaviour cannot hede with certainty due to spatial variation of soil and loadperties. limited site exploration. limited c.:alculation models,

uncertainties in the soil parameters. Reliability-based analyenable: one to map and evaluate the uncertainties that enter informulation of a geotechnical prohlcm. If a deterministic

del for the analysis of a geotechnical problem exists. a p r o ~istit: analysis model can always be easily established with thels i.wailablc today. That one finds difficult the quantifying of

uncertainties is not a good reason to avoid defming theertainties or cstahlishing their significance in design.

s increasingly important lOday to adopt rational, consistent,documentable design approaches that inform of and

account for the uncertamtics in the analysis parameters. reliability analyses can provide the designer with insightinherent risk level of a design.

TI c paper aims at establishing that reliability-based approacharc a necessary and useful complement to the conven(detenninistic) analyses: they are not a replacement, but addition to conventional analyses that provides importainformation on the effects of uncertainty on the response.

RISK. RELIABILITY AND STATISTICS

I t is fair to say that other areas of civil engineermg, sucstructural and hydrodynamics analysis, lie ahead of geotec

practice in the area of reliability. Geotechnical engineers learning and gaining benefits From the experience of thested fields: mathematical solutions to complex approximationiteration problems already exist. the significance of differliability aspects have already heen estahlished, advancesresearch in reliahility engineering and the advent of popersonal computers bring the exploitation of the available\vithin everyone\ reach, the language barrier between problists and geotechnical engineers is decreasing. The mengineer will also cxpniencc increasing demands for multidplinary expertise.


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k analysis is about prediction events that have not yetpened. Usually the analysis is broken down into its constint parts. No matter what type of analysis technique is adop. the actual comroncnts to be n l y ~ c dwill he the same as

a deterministic (conventional) analysis. Such analyseswever do not eliminate the risk of an


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he equilibrium function describing for example failure isfined hy a "limit state function" which has the same form ase deterministic equation. The probability of 1 ~ 1 i l u r ci.e. wheree load can exceed the r c s i ~ t a n c eis calculated. Instead of aoint estimate of factor or safety, the distribution or thesistance is compared with the distribution nf the load_ Theobability of failure is the probability that the distributionsnibing the load and the distribution describing the resistancetersect.

nalysis tools

s long as there exists a dctenninistic model to analyse aotechnical problem, a probabilistic analysis can always hetablished using the tools described in the next section. Theseols arc ready-made software that are easily linked with theftware describing the deterministic geotechnical solution. Probilistic analyses provide the following results:

Probability of failure (probability of non-performance)Reliabili ty index, or where is the most probable responserelative to failureSensitivity of result to any change in parameters

ne prohahili.stic analysis will give the same insight as a largeumber of parametric analyses with all of the uncertainrameters that arc part or the formulated solution. As input. theer must supply I) the equation defining failure and 2 ) theean and distribution function (often normal or lognormal) forch parameter in the analys1s. Except for distribution function.e required input is the same as for deterministic analyses.

he following methods can he used to quantify the effect ofncertainties in a geotechnical response:

ORM: First-Order Reliability Method. Probably the hestactical method today, it approximates the limit state function

y a lirst-order function. The method works well over a widenge of probabilities and is simple to implement when one has

explicit limit state formulation. FORM c c o u n t ~for theobability distribution of all uncertain variables.

ORM: Second-Qrder Reliability Method As FORM, but themit state function is approximated hy a second-order function.he results of the SORM analyses have for all geotechnicaloblems modelled so far given probabilities of failure very

ose to the values obtained with f-ORM.

ORM+: SORM with ;-;ampline: around solution point. ImprovedORM, with a search around the solution for an even more

tical point. The results of the SORM+ analyses have also beenund to be dose to the results obtained with FORM.

OSM: First-Order Second Moment apProximation. The mostasible approach for complex rormulations where the perforance mechanism cannot be formulated explicitly. The POSMproximates mean and variance but cannot account for the

probability distribution of the uncertain variables. The smethod is used, for example, for the probabilistic analyfinite element models.

Monte-Carlo simulation (MCS). Repeated simulation of psolution with randomly selected values of variables. The mapplies to all problems hut can require a large numbersimulations. t can be made more efficient with Latin Hypercusampling (LHS), which is a Monte-Carlo simulation optimby "organised" sampling. It reduces considerably the numbsimulations required for a reliable distribution of the respo

Bayesian updating. Bayesian updating is a method topredicted behav1our with observations, for example updatingfactor of safety or settlement prediction on basis of pore pand settlement records: updating of pile capacity on basisdriving records and/or instrumentation results; updatingbearing capacity on basis of preload test.

Uncertainties in soil parameters

To obtain the statistics of soil parameters, traditional procedcan be used or stochastic interpolation (gcostatistics) canimplemented when a lot of data exist. The techniques prounbiased estimates of mean and variance.

t can he useful to establish data banks for different typeparameters or geographical locations, or to review the literatuand compare one's values to values used by others. Thecstimales can be hiased by the beliefs of the designeprohahilistic analysis wilL however, single out the importancethe hypotheses on the results.

Defining probability distribution function may often appear as

problem. However, most geological processes follow a normor lognormal law. One may choose to use a bounded unifordistribution if one expects all values within a range to be equalprobable.

In probabilistic analysis, a "model uncertainly" needsdefined by a mean or hias and a coefficient of varianormal distribution is often assurncti). Model uncertaintdifficult to assess. It should be evaluated on the ha.;;is ofture, comparisons of relevant model tests with determincalculations, expert opinions, if available and relevant castudies of "prototypes", if they exist. Model uncertainty

includcU in a reliability analysis in one or three ways: (1global factor on the limit state function, {2 as a factor oparameter of the analysis, or (3) a.s a factor on componentsanalysis, for example on skin friction in each layer anbeming in the case of axial capacity of a pile.

And yes, considerable reflection and engineering judgemehave tn be used to establish the values of the model uncerhut do not all geotechnical analyses require a dose oengineering judgement' Including model uncertainty is neless one step forward compared to ignoring the uncertainties th


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me for example from the calculation model or the way ofovering soil samples.

se were a Cw basics on the approaches to account for theertainties in a geotechnical problem. Lacasse and Nadim96b) presents several examples of uncertainties l lracterising soil properties, and Lacasse and LamhallerieY5) give examples of the statistical treatment of coneetration test results.

es studies arc now used to illustrate that reliability studiesvide useful additional information. Risk and reliabilitysiderations permit the engineer to be probably right),,

ereas with deterministic analyses alone, the engineer risks toexactly '-"Tlmp).

Low risk project

> In-situ testing

> Disturbed samples

Logging tests(CPT, SPT, DMT)

Index tests

Empirical correlations

CPT: Cone penetra tion t n tSPT: Standa rd penetrat ion testDMT: Dilatomt la teJ

Costs : low

Moderate risk project

> In-situ testing

> High quality samples

Logging tests

Specific in-situ testsFV. PLT, PMT)

Basic laboratory tests onselected samples

Site specific correlations

f V

PLT:PMT:

FiPIJ m n e testPlate load testPrcssuremeter test

Costs : mode ra te

CASE STUDIES

Soil invcstiuations

Soil investigations. in the way they are planned, represeform of risk-based decision.

In general, the complexity level of a soil charaderisatibased on the level of risk of a project.

Figure 2 illustrates this with three soil investigations, each dpending on the importance of the construction. (The figurnodiricd from an oral contribution by P.K. Robertson at14th CSMFE 1n Hamburg in September 1997).

High risk project

In-situ testing(Identify critical zones)

Detailed site evaluation

> Additional in-situ tests

> High quality samples(undisturbed)

Advan ced laboratory tes

. In-situ stresses. Relevant stress path

. C ard ul measuremeCosts : h jgh

Fig 2 Risk based soil invest('?ations

small to medium sized foundations:

a low risk project involves fc\V hazards and has limitedconsequences. Relevant experience exists to assist mdesign. Simple in situ and laboratory testing would beselected.

in a moderalc risk project, there i: . concern for somehazards and the consequences of non-performance arcmoderate. Limited experience exists to assist in design.Specific in situ tests and good quality soil samples arcrequired.

a high risk pro jec t involves frequent hazards, and moderate to high consequences. High quality in s

laboratory tests are required.

The decision-making process for selecting the appropriate soinvestigation methods is risk-based, albeit sub-consciouslyit involves consideration of consequcm:cs and costs.

Uncertainty analysis and procedures can help optimise sinvestigations. The uncertainty in a geotechnical calculatioften related to the possible presence of an anomalyexample boulders, sufl clay pockets or even drainage layProbability approaches can be used to establish the co


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ectiveness of additional site investigation to detect suchnomalies''. Figure 3 presents an example \Vhcre the procere developed hy Lang ( 9 ~ 0 \Vas used.

. _ ~

'> .- 'a _' ';JC>e.,

. c0 - ~

-o' o8_c

>o

1 . 0 - - - - - - - - - - - - - - - -

0.8

0.6

0.4

0.2

50 chance of detectionw first boring

/80% chance

L o - - - - 2 ~ ~ ~ 4 ~ ~ ~ 6 b = ~ ~ s - - - - ~ t o

Number of borings

1.0

0.8

0.6

0.4

0.2

00

p Probability of no drainage layer

(1-p) f(a)

Extent of drainage layer

Requirement for cost reduction

p' ~ 0.5p' ~ 0.8

p' = a priori probability ofno drainage layer at 55 m

2 4 6 8 10Number of borings not detecting

drainage layer

12

Fig 3 ost reducrion wirh lncrc>ased number ~ f b o r i n g s

to detect a dminap e layer

In this application, having no drainage layer present at a deo f 55 m \Vas dctnminant on the resulting lifetime settlemesettlement of less than 50 cm would mean a reduction in cIr the prohahility of no drainage layer at a depth of 55 less than 2'7r, the settlement would not exceed 50 emdrainage layer detel;tability for each horing or 50 %and distribution of drainage layer extent as shown on Fione would need 3 to 6 horings to enable the required creduction.

Dams

The concept of probabilistic risk analysis for dams wamarised hy Whitman (1984). Important contributionsfound in the proceedings of an international conference::-.a Cty of dams (edited by Scrafim, 1984). The statusassessment for dams was made by H0cg ( 1996) and extensively at an international workshop on risk-basedsafety evaluation in Trondheim, Norway (NNCOLD, 19

Vick (1997) summarised risk analysis practice in differ

cnuntnes, based on a survey of 11 countries (AusAustria, Canada, Prance, Germany, Holland, Norway, SwedeSwitzerland, United Kingdom and the United StatAmerica):

I) Risk analyses for dams focus on safety and reliabiliexisting dams. The analyses arc run to establish a diagor set priorities among possible failure modes, tosupport in decision-making on issues related to dam safmodifications, and. to a slightly less extent, to esbudgeting priorities.

2) The analysis tools used are in order of frequency qtive methods, event trees, B a y ~ : s i a napproaches witabilistic charac.:tcrlsation of judgement, and relapproaches with probabilistic characterisation of parum:ertainty.

3) The results of the analyses arc generally done on a cacase basis with no formal criteria, although nearlythe countries used


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e consists of six steps (sec H'1cg, 1996 or Vick and StcwarL96 for more details):

Darn site inspection, including review of documents.

Failure mode screening, defining all failure modes, eliminating those that physically not possible.

Construction of event tree, listing failure sequences

(events), and the interrelationshipamong

evenh.

Probability assessment of reach event, often bast.:d on subjective beliefs, sometimes on observations and experience.

Evaluation ofn:sults: the failure proba bility for an outcomeis evaluated from the product of the probability or e.achevent occurring: along any one branch of the event tree; therealism in whether a given combination of events (failuremode) has higher probability of failure than another is alsoconsidered.

Iteration: with the results of the tlrst analysis, identifyunlikely failure modes and the dam s vulnerability andstrengths and include failure modes that were overlooked.This iteration can he repeated, as needed.

P e t e ~tool nu'llber of fataiolocs

Fig . J Exampll of


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me component events were treated statistically, for examplee 100-yr. and 1000-yr. flood were hased on h1stonc data, ande earthquake frequency and response spectrum were basctl

the Norwegian database for earthquakt:s. The events reprent the expected r e ~ p o n s cof the dam following an initiatingent.

he calculation with an event tree for each or the loading casesn event tree was huilt for each or the llood, earthquake and

rmal loadings) resulted in the following annual probabilitiesfailure:

LoadingFloodEarthquake

Annual rnlhahilitv of failure1 2 X 10 6

I I X 5

Normal (internal erosion) S S X 1

e total annual probability of failure for all modes is the sumthe three components, or 5.6 x 10 1 _ The results represent a

ative order of magnitude for the different scenarios. Theyould not he interpreted to he an accurate probability.

practice, the results of the analysis proved even more usefulhen done on several dams and compared, as was done inhansen ct al. ( 1996).

fshore structures

e Norwegian offshore industry has heen at the l'ort:front inplying reliability-based analysis to assist in decision-making.is, associated to the fact that all types of foundations arcry costly and often hcavliy i n ~ t r u m e n t e dhas contributed toe documentation of case studies where reliability conceptsve been used.

e offshore structure case study selected for this paperesents the LictcrministJC and probabilistic analyses of anfshore pile foundation at two times in its lifetime:

I In 1975, before platform installation, when limitedinformation and lirnitctl methods of interpretation ofthe soil datu were available

2) In 1993, after a n:inh.:rpn:talion of the available datausing: the geotechnical improvements attained in theinterim additional and more advanced laboratorytests, a re-analysis of the loads, and an analysis of theinstallation records

e re-analysis in 1993 was prompted because the environntal loads had been revised, the structure had been hit by a

ip by accident. and the operators hoped to increase the loadsdeck. The structure is a steel jacket installed in II 0 m of

ater in the North Sea in 1976. The jacket rests on four pileoups, one at each corner. Each pile group consists of sixes (Fig. 6). The piles in the groups are 60 diamct(.;r

bulars, with wall thickness of 3 and 2.5 .

CJeotechnical investinations. The soil profile consists ofstiff tn hard clay layers, with thinner layers of very densin bct\.vet:n. In 1975, two soil borings were done at thelocation. The two borings indicated somewhat comparable soprofiles, although the hori.wn and the thickness of thlayers differed. Based on the information obtained from tborings, the soil charactcrislics in Fig. 7 were derived from tstandard strength index types of tests in common use time: t n r v ~ m c ,pocket penetrometer, unconfined compress

test, unconsolidated undrained ( UU) test), and an interpretion of the results based on the judgement and experiethe geotechnical consultant at the time. The friction anthe dense sand was based on the results of consodrained triaxial compression tests on recompacted specimenThe friction angle for the specimens compacted to the highdensity possible was measured as 38-40 degrees.

The profiles selected in 1975 showed a wide variation in soil parameters, with considerably higher shear strength belo20 m if one believed the one boring:. The positionsecond sand layer differed for the two borings. No advanc

laboratory tests enabled one to estimate more approvalues for the soil parameters. There is no doubt that samdisturbance must have contributed to the scatlcr in the results

- ---

s m

~ C o n d u c t o r s

o o o o o o o o o o o o

o o o o o o o o o o o

o o o o o o o o o o o

Borir:g8 2

---

Fif< 6 Offshore srmcf/lre Pile foundation layout

During pile installation. records were made of the blowduring driving. The individual blow counts for the piles in B I arc given in Fig. R No instrumentation of the operation was done. The installed pile lengths were betw36 and 45 m The pile driving records were evaluated bconsuhan t in 1993 and used to adjust the soil stratigraphy (F


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In 1993, new samples were also taken and more advancedngth tests were run, including consolidated undrainedxial com pres ...ion tc.-.ts.

Undrained shear strength s (kPa}

'" ' 5J(I 700

"

"

g_"

"

;o

4

: '=9 kN/m'

5 Iy'=g kN/m

Boccg 81 Y . : ~ : : ; bI : ,.._O'I:lg 2

f===O=l=J ~ _ ,/ ' - + . - ~ , - , , - N - i m - j=-

. ~ ~ u u' ' _

1 ~--

I

(f>'o:40'(Boring 81

1 < > < ~ t0 ' -9 kN/rr

o;p -40' i

Boring 82) I .. 1 . '"-10,kN,illf'

I I _ : ~ N i m l

Fig. 7 O f j ~ l w r estructure Soil profile for /1. 75 analy.;es

Blowcount (blows 0.25 m) Blowrount (biOVIs/0.25m)

40 BO 120 160 ?00 40 BO 1?0 160 200

' ' '0

~ lI I

J_ ~ ~I

T- - -

+

_ l _ l ~

I ' 10-J---R.tc. l - 1-- 1 +-110

- - III

h Stopped- change follower

I

- - -r- l - .- f - ~

"I L -

- rr- I I

~ II I I~ ~ ' '' ' I -?'d ' I

ZL i I I

30

35

40

Fig. H j j ~ h o r e.\HIIcture- Pile drivinJ? records. leg A5

The result of this educated adju stmen t on the hasispile dnving. and a re-evaluation of the borings and labotest results using normalised soil characteristics, new ssamples and the running of more advanced lahnratory (direct simple shear tests, consolidated undrained triaxial tesled to the adjusted soil shear strengths in the stiff to firmshown in Fig. I0, where a much narrower rangestrengths is suggested. The full curve represents pessimvalues. the dotted line the hest estimate values. No r etion of the friction angle in sand was done, although ideathis should have het.:n done.

Analysis. The deterministic analyses were done with the ARP2A recommended practice in usc at the time of the aThe design requirement at hoth times in the platform liwas a factor of safety of 1.50 under extreme loading anunder operation loading. The axial pile capacitysummation o f the skin friction on the pile shaft andhearing on the pile tip.

The probabilistic analyses were done with first-order reliabilmethod (FORM), where the deterministic axial pile capacmodel was formulated in terms of random variableslayer. In this paper, only the results of the analysiscapacity of most loaded pile arc considered.

Geotechnical parameters in model. Table I gives the tainties associated with the soil parameters in two of thimportant soil layers. The coefficients of variation uncertainties m the laboratory test results. posmeasurement errors, spatial variability and the uncertainty degradation due to cyclic loading. Cyclic degradatioimportant for an overconsolidatcd clay subjected to a faihigh ratio of cyclic loading. The effect of cyclic loadingpected to be minor for the dense sand. Very little dataavailable for the different soil parameters. The mecoefficients of variation were obtained as follows:

SuhmergNl unit weight, y : No measurements were avaiThe mean value and coefficient of variation were basexperience acquired for similar soils where many measuments have been taken. For sLiiT clays. the mean submunit weight is 8.5 to 9.0 kN/m 3 (as stiffness increases); fdense sand, the mean submerged unit weight is nonnkN/nr'. A coefficient of variation of 5o c: is a common valscatter in submerged unit weight.

Depth,::.: The layer thickness can vary. Since only two borarc available. the values used in the analysis arc unThe mean layer thickness is hascd on the measured vfrom the site investigations. The coefficient of variaIW l is based on engineering judgement. The positiothickness of Layer 7 were quite uncertain in 1975. Freason the coefficient of variation was increased for this from 10 to 20%.


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..

-- i 1 ....

'- .

~ ...-

FiK. 9 O f f ~ h o r estructure- Stmti;;:raphy inj"crredfrom piledriving and re-analysis of soil data

Itw

Undramed shear strength, s, (i1'::- P ' N J ~ '

1 5- r== - - ~ - = -r = = = _:__ _= - - - : - ~..= :._: __::( = ~ ~ - = - f - . = = - - = - - - -

' II

V _.,. I~ f"-t-t,' ~ Prcf:le

~ " " ' - ' )- ' - - - - -

4 ~ kN:m'

I5I

9 k N t m

' I

'I

I Y ~ " ' ~ 6 ~ N ~ '-----r----- - - - - - ~ - - - ~-----

~ ~ - - - - ~ - - - - ~ - - - - ~ - - - - ~ - - - - ~ - - - - ~ ~ ~ ~

J :

' . ;:.;.'----- -- ~ I . ' 8kNim' 145 .l.s, from c o ~ s o . : d a t e dunc alned L - + + - - - + - - - t ' - ' '- ' ' ' ,-r_: ~ _ a x i a lcompression lels. I / 1,J __ - r - - ~ - - : :Fig. 10 O j j ~ / w r estructrtre- Soil profihfor /993 analyses

ndrained shc>ar strength in stUf clay, s 1 : fn 1975, the undraid shear strength was based on punctual measurements fromdex strength tests, known to give a relatively poor estimatethe undrained shear strength. The data points are shown in

fig. 7. which explain the high coefficient of variation. In the undrained shear strength profile was based on:

(I) results of consolidated-undrained triaxial compresstests at effective stresses relevant for the in situ valu

(2) a recalculation of the soil shear strength basednormalised strength ratio for similar clays within tsame geographical area and with similar geologic

history.

This led to new soil strength profiles in 1993 and Coefficof variation of 10 or lYk.

Friction angles. 'and 0 and coefficient of earth presxurin very dense sand: Very little information was availablethe very dense sand layers. A friction angle, 1 , of 40soil friction angle 0 of 35) is typical for a very dense sand.1975 there was little known about this angle and tcoefficient of variation was set to I Yk In 1993, consideresearch contributed to reducing this coefficient of variat

about 5'lo. Lacasse and Goulois ( 19X9) collate d the opinio n40 international experts who suggested that the uncertainabout the mean is quite small. For the coefficient ofpressure. K. values arc undocumented. but basedengineering judgement, experience and the resultsLacasse and Goulois (1989) study.

Pile C(lpacily parameter in day, a: The prediction of thcapacity of a pile in clay is done with the rriction parametetimes the undrained shear strength. The mean value ison the API RP2 A guide.line. The coefficient of variatbased on engineering judgement and the experience gath

for piles in stiff clay.

Pile capacity parameter in sand, fiim: The mean value ofspecified by the API RP2 A design guidelines. The dein the coefficient of variation of flim from 25 to 15% he1975 and 1993 reflects the understanding acquired over thyear on pile friction in sand and the results of the opinion pooling summarised in Lacasse and Goulois (1989)

TabLe 1 Examples o f uncertain )' in soil parameters inL a y t ~ r s5 7 and X- 1975 and 1993 analyses

Coefficient of variationLayer Variable 1975-analyses 1993-analyscs

5 y' 5 59(

z 10 rye 10%s, 25 15%a 10 rfc: 10%----------------------------------

7 y' 5 % 5z 20% 10%K l ' i % 10%ii 15 % 5%


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fhm 25 t/{, 15 N

y 5 (lr 50' '. I 0 7r, IOtyr NSu 25% 109(, LNa 10 r r I Y'Ir- LNN, 15 q, 150( N

otation:=submerged unit weight 7. =depth to hotlom or layer

=undrained shear strength a skin friction factorc =bearing capacity factor K= codTicicnt of earth pressure

=soil-pile friction= f-5 ' = friction angle (of sand)im=limiting skin friction( sand ) N LN=normal/lognormal PDPDF= probability distribution function

oads in model. The characteristic load used for deterministicundation design of I xed offshore structure on the Norwegianontinental Shelf is defined as the load with an annualccurrence probability of 19(_. (i.e. the maximum load assoated with the 100- year storm).

he extreme axial load on the most loaded pile is the sum of aermanent component resisting the submerged platform weightnd a transient (cyclic) component resisting the storm, currentnd wind-induced forces. The key parameters entering the loadlculations arc the environmental characteristics, the platformeight, and the model used for estimating the response of theatform to the environmental loads.

he main environmental parameters for the foundation loadsthe platform under consideration \verc the significant wave

eight (Hs) and the spectral peak period corresponding to thegnificant wave height (TpiHs)

ata on storm characlcristit.:s were gathered during almost twocades of platform operation. A H>O-ycar value for thegnificant wave height of 13.5-14.5m was expected for theea of the North Sea around the site, so a storm threshold ofs = 7m was used in the calculations. A total of 130 eventsceeding this threshold were observed during the time periodmmer 1975-summcr 1992. A truncated Weihull distributionas used for the significant wave height and a lognormalstribution (conditional on H,) was adopted for the spectralak period. To quantify the uncertainty in the significantave height for the 100-year event, the fitted /cibull modelrameters were treated as random variables (Haver and Gudeslad ( 1992).

he procedure used for estimating the foundation loads in thesign phase was deterministic. To make a comparison. simir types of distributions were assumed for the environmentalrameter s in 1975, hut the site specific data were not used inting the distribution parameters. Rather. the distributionsere chosen to be representative of the general area ofrthern North Sea, which meant that there was a larger

spersion in the parameters.

To obtain lhc unconditional distribution of the 1 00-ycarload on the most loaded pile (Leg A5), the probabilcxl'eeding a given load level was estimated using theand SORM approaches. The load level was varied andresults were plotted on the Gumbel scale as shown in FAs seen. a Gumbel distrihullon with mean of 20 MNcoefficient of variation of I0 provides a good fit extreme axial pile load based on the 1993 informatiowhereas with the information available in 1975, the same lohas a mean of 19 MN and a coefficient of variation of 1

4

>- 3

u.c:.,.c: 2'

Q)

'''cE

: I

Cl

020 21 22

1993Mean =20 MNcov = 10

'11975Mean= 19 MCOV = 15

23 24

Maximum axial load (MN)~ ~

Fig. I I Assumed distrih llion l4 the 100 yr extrone axiaon Pile P2 in Leg A5

In both situations, the significant wave height was tdominrmt random variable contributing ahout xockuncertainty in axial pile load. Model uncertainty was themost important parameter. The contrihulion of other rvariables such as the spectral peak period, submerged platweight, and wind characteristics was negligible. Thecomponent (due to design s.torm) represented about 40 the static component (due to submerged weight) represthe remaining 60o/r of the extreme axial load in 1975. In

the cyclic component represented about 35% of the raxial load. The reduction of uncertainty in the extremepile load reflects the change in knowledge with incresearch, almost two decades of site-specific wave data,the increased proportion of the gravity load on the totalload.

Model u n c ~ r t i l l J ~ ~ .in axial pile capacity calculation. Iprobabilistic pile capacity analysis. a variable describinguncertainty in side friction cak:ulation in each layer was usedAn independent model uncertainty variable in each larequired because the soil type can vary from one layer


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r and ditlcrent resistance mechanisms need then to be

sidered. In the bottom layer, two mmlel uncertaintyables should be com.iden:d. the first apply1ng to the sidetion calculation and the secoml to the end bearingulation. The duality of moUe uncertainty in the last layermportant because side friction and end hearing arc t\.\'0

erent resistance mechanisms \.Vhich arc moJelted hy

erent equation:-._ The model uncertainty variables weren as normally distributed.

a dense to very demc sand. the uncertainties Uuc theulation model can ht: vt:ry large, ami th..: bias is believed tow a lot i f conservat ism m the API RP2A method. The unainties arc hclicveJ to he far greater for piles m sand than

piles in clay. The model uncertainty values used in theyses were based on the study by Lacasse and Goulois

89) for sand. and on several NGI research projects for claye a ~ s eand Nadim, 1996a).

API RP2A I Y93) model for side J"riction is believed toict quite well the side friction in softer clays. The hias is

hahly 1.00 for hoth normally and overcomolidatcd clays

asse and Nadim, 19lJ6a). These values were evaluatedm back-calculations o f model tests and comparisuns of

ral methods of analyses. The c o c f l i e ~ e n tof variation wasn as 0.15 to rellect the lack of kno\vlcdgc for pile driven ins with high undrained :-.hear strength and high (unknown)c(msolidation ratio. >.

he other hand for ri les I l l . in the anparameters affect prohahility of failure, hut the"ie uncertado not intervene in the deterministic calculation o ffactor.

As for deterministic calculations, the essential componenrdiahi l i ty c ~ t i r n a t c sin g:cotcchnics arc (I) a clearstanding of the physical a:-.pects of the geotechnical hchato model and (2) the experience and engineering judge

that enter into all decis10ns at any level, whether for parasdcctiun. dunce of most realistic analys1s model, or decmaking on the viability of :1 concept. A" illustrated in th~ l u d y .the most important contribution of reliability concep

geotechnical engineering is increasing the engineer's awarenof thc exi..,l ng: unu:rtain ies and the1r consequences.


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llow foundations

e studv I. The first case study calculates the limitingilibrium analysis or gravtty pbtform (offshore, but theroach is the same on land) installed on a uniform softstic clay. As for a deterministic analysis. the approach tooko account the different stress conditions along the potential

slip surface since the prohahdistic formulation is exactlsame as the d e t e r m i n i ~ t ione. The potential slip surfaces13) \verc analysed individually and as a system wpotential failure surface included.

L'.pw

//

1 / /B=3.88B=3.96 / /_______ /

3 ___ B=3.80 / /4::::. =: .:: .:: ::> : : B=4.02lip surface

1234

Ym for Yf =1.0)3.002.852.842.87

/

B =reliability index

Ym= material coefficient, Yt = load coefficient

Stress conditions along potential slip surfaceAndersen et al., 1988)

Spatial variability

Fig 3 Ro;u/rs t ~ p m h a h i l i s t i canalysis t l nning capacity o f shalimv foundation

tial variability, which can reduce the uncertainty in the soilperties such as undrained shear strength of the c : lay, wasuded Vanmarckc, 1977: 1984). The coefficient ofation of the extreme environmental loads was taken as 15the horiLtmlal load and moment were taken as perfectly

related. The uncertainty in the soil parameters at the softy site was very low hecausc of the exceptional homogeneityhe deposit.

reliahility analyses indicated the following:

The critical slip surface based on the highest probabilifailure was different from the critical slip surface ha the results of deterministic analyses. This is seen repeafor different soil profiles and illu tratcs well thatuncenainty in the analysis parameters plays an imporole on the margin of safety. The discrepancy is due different uncertainties in the tnaxial compression antriaxial extension strengths used in the equilibriumsJs.


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Based on the results of analyses of gravity structures onboth soft and stiff day, model uncertainty and momentwere very sigmficant uncertain variables. For the soft clay.this was partly due to the homogeneity of the site.

First-order, second-order and improved second-orderapproximations gave same probability of failure. Thesimpler first-order approximation is therefore sufficient.

Changing the probabili ty distribution of the soil parametersfrom normal to lognormal had only a modest effect on thecomputed probability of failure.

The reliability analysis induding all failure surfacesresulted in a probability of failure equal to that of the mustcritical failure surface_ (The same conclusion was true withdifferent failure modes). The most critical slip surfaceswere essentially perfectly correlated.

ase study 2. Probabilistic stability analyses were done us1nge mobilised friction angle>> approach (an effective stressprow.:h) and the available shear strength)-> approach (based

the undraincJ shear strength of the soil). The twoproaches define factor of safety with two differentrmulations:

the ratio between the undrained shear strength and theshear stress mobilised for equilibrium

the ratio between the tangent or the characteristic tiictionangle and the tangent of the friction angle being mobilisedat equilibrium.

oth analysis m e t h o d ~arc often allowed in code of practice.

allow foundations on tv. o soil types were considered: antractanl soi (loose sand, normally consolidated clay. pathE on Fig. 14) and a dilatant soil (dense sand, heavily overnsolidated clay, path DG on Fig. 14). The approach. uncertainties inction angle, cohesion, pore pressure parameter andbmerged unit weight were considered. For the the two analysis methods, a moJcl uncenainly

ctor would have to be included.

This case study Jocumcnls again how wrong an impressiosafety factor alone can give or the actual safety margin agafailure.

Shear stress

//

E

A

D, . . - - " " C

B

H

Effective normal str

Fi;;: 14 Effective stress paths for contractant and dilatant

Fable 3 Results o f stability anaf_yse s vvith f iO approachesNadim et al., /994

Soil

Contractant

Dilatant

Analysismethod

Mobilised friction angle

A vailablc shear strength

Mobilised friction angleAvailable shear strength

Eanhuuake response

Factorof l e t ~

1.9

1.4

1.41.5

Probof f

l . 7x

2.5

6 .7 x2.3

Figure 5 presents an application of the seismic reliabn l y ~ i sof a group of offshore platforms that answers

following question: given thai a strong earthquake with 10:mnual occurrence probability takes place at the Statfjord oifield, what arc the chances that oil production must be stoppedcompletely? The seJsmJc reliability was evaluatedconsidering the possible failure modes of the planetwork, the correlation between the failure modes, the seismireliability of each platform and the spatial variation oearthquake peak ground acceleration.

A typical gravity platform designed on the basis oNorwegian Petroleum Directorate guidelines has an implieprobahility of failure of 5 o r}under the 10-4/year earthquAnalyses were done with 5 % probability of failure for platform taken individually. The effect of increasing the faprohability of the Statfjord A platform to 10 was aconsidered_ As listed on Pig. 14, the reliability of the sywas much greater than the reliability of each platfAccounting for the spatial variation of the earthquake loaparameters reduced the probability of failure by a factabout 5 (Nadim and Gudmestad, 1994).


15/21


16/21

ste in ( 1996) concluded from three case s tudies that it isessary to include the uncertainties in the analyses tn order

fa


17/21

Judgement, as illustrated by the case studies in this paper,IS not cxdudcd from nsk anJ rcliahihty analyses:judgement can he formally included. ami one can evenexamine the dfc-.:ts of this additional uncertainty on theresults obtained.

tablishing acceptable risk levels

ablishing the basis for acceptable risk criteria is difficultd controversial. Sm:icty requires now. with increasing freency, that analyses he done to Jetcrrnine the kvel or riskposed on the public (as opposed to voluntary risks, likeving one's own car).

sk statistics for persons voluntarily or involuntarily involvedhazards range from I X ] f 5 death per year ror air travel. 3 X4 for road accidents to 2 x 10 -'for parachuting Californiansept to live in Parkfield or the San Francisco Peninsulaere there is a 90 X and 20 lr respectively probability of aor earthquake on the San Andreas Fault oc.;.;urring betweenr 9RR and 201K.

ure 17 presents a compilation of prohahilistit: risk forjects vs c.;.;onornit: and human losses resulting from Llilureich can he used as a guitleline (rnoJifled from Whitman,84 . Figure l R shows the risk criteria .;.;hart proposed byC. Hydro for dams, and Fig. 19 illustrates the risk evaluationdeline proposed hy USER (quoted by Whitman, \997 ).

ne of these represent ~ < o f f i c i a l risk criteria, they arc reallystarting point of a discussion which some day needs to be

alised.

proposed guidelines have in common Lhal they are essenly hascd on engineering judgement and experience, and

ggest somewhat similar bounds of acceptable and unaccepte levels of annual probability of occurrence. The engineers,ause of their understanding of both technical and safetyues, arc the ones who can and need to establish the.:ccptahlc risk:.->, based on the design standards and degree ofief in our methods.

VANTAGES 01' RELIABILITY METHODS

at is not generally recognised is that the concepts and theroaches may he usct.l for diffcn.:nt purposes and at differentels, for example (modified from Ht;eg, 1996):

during design, to place the main design efforts where theuncertainties and the consequences of these on design andcosts arc g r c ~ t c s t ;

during operation of major or critical engineered facilities,to enahle the engineer to have at hand a number of actionscenanos depending: on the observed response of thestructure;

--

0iS2eo._

u;cc

wowI

C o ~ : ~51 0 ~ ~

LIVES LOST 10 100 1000 OSTin USD 1M 10M 100M 18

CONSEQUENCE OF FAILURE

Fig. 17 Pru JaiJi isric ri.\kfor r r ~ j e l f svs economic andl o s s ~ S(modified from Whitman, 1984 ).

- - - - 1 - 1 -

I -1&2 - - - - - - - - - - - f - - - - - - - - - - - 1

1 8

UNSAFE

1 - - - - ' 5

- 1 6 - - 1 4 - - - -

0,1 10 100 100J

Potential number of fatalities

Fig. JX Risk criteria chart proposed b:v B.C. Hydro(Vick and Stnmrt , 1996)


18/21

analysis t:an he umsidcred ao ; an approach to establish anostic. Thl.: procedure. or some of its steps, provides aework for the wstcmatK usc of etH inccring jud emcnt in

sion-making, when uncertainties arc present. In geotechniengineering:. uncertainties will always be present hecausehe nature of the material we arc dealing vvith and the fact

there will never be nough della that \Viii remove all uncerty.

systematic approach is also a means of documcntin" thatdifferent critical aspects of a problem have been consideredre and how in the anctlysis engineering Judgement has been. Such documentation is essential today vvhen qualityrance and quality control should be at the basis o f ourk whether it is rcqum:d by the client or not). t is the dutythe engineering profession to present and explain thertainties involved, and the t:onventional safely factor doeso that.

In a rcliahility approach, assumptions can he clearly separand criteria for conservatism can be placed where they bThe approach will indicate h1gh probabilities of failure,\vill have a sohcnng dfcct, because not all our designhcen optimum. h is no use to hide behind a safety factor probably wrong, because it docs not account properly foruncertaimics. nature has a way to catch with this ~ ~

head-in the-sand attitude.

One of the important benerits of an rcliahility-bascd anlies in carrying out the analysis. h i ~aspect could evento he more important than the actual result of the analysibrings to light the most important issues in a design.

Reliability methods also brings together the professionals

different engineering speciality areas and creates a diwhid1 has long hecn needed. Examples of this havepresented by Lacasse and Nadim 1994) and Heg (1996

Estimated numberof

lives lostif

failure occurred0 1 1 10 100

1.00E 7

CD Low Consequence Level

Risk outsidegenerally

acceptable limits

Risk withingenerally

acceptable limits

1000

-economic consideration generally govern, con:--.idcr alternative means for life-loss reduction< l Risk generally acceptedQ:l Marginally acxeptable risk

@ Risk outside generally act:cptable limitsHigh ConSClJUCncc Level- usc best availahle methods, multiph.: defence design, and maximum loading conditions

Fig [4 Rlsk e\ a{uariott gttidditte propm;ed l1y USBR qtwted 6v \VItitrncm, 1997)


19/21

geotechnical structure can usually be made safer hy spendg more money. The real challenge. however, is to improvee reliability of the structure without spenJing rnme money.

do his, it is important to adapt the level of complexity ofe analysis to the prohkm that needs to be solved and thedltional expense that c : an he saved.

COMMENDA riONS

single risk analysis format is nut universally applicable to allues in geotechnical engineering. There lies one of the strongints of the appmach. Methods and procedures can he variedcording to the type of the problem, failure modes and theture and uncertainty of the conventional {detcrrninJstic)alysis, the purpose of the analysis and the needs the analysismeant to fill. Differences in methods can he associated withferences in response, umsequenccs or safety issues.

e analyses should be robust: they should \Vithstand criti-:ismd scrutiny. They should he crcdihlc, defensible. transparentd error proof. This requires good documentation.

sk and reliability based analyses arc established hut they areally only prototypes. Much \vork still needs to be done. Theproaches shoulJ not be oversold, but there is no doubt in thethor s mind that the approach can provide additional inforation to the designer. which otherwise stays hidden in theterministic analysis. The more critic.:al this information is toe design, the more important it is to include them in thealysis with the ~ l p p r o p r i t cdegree of' allcntion such that thensequence connected to cac.:h critical aspect is included ine analysis.

sk and rdiahility hascd methods, while not a substitute fore conventional Jctcrrninistic design analyses, offer a systeatic and quantitative way of accounting for uncertainties. Theproach is most cffcc.:livc when used lD organise and quantifye uncertainties in engineering design and to help makingcisions. They can he helpful for a wide range of problems,pecially when there is not enough experience available. Thiscommendation was also reached hy the committee onreliability methods for risk mitigation in geotechnicalgineering)> (NRC 1995

ere arc some types nf rroblems where doing reliability

sed evaluations will not give adequate assistance: when thecertainties arc very large. \vhen the mechanisms or theoblem arc not well understood. or \vhen the parameters ofalysis model arc not well dc.fined.

th rcspcd to future implementations, they shouldncentrate on the practical application of reliability models toke advantage of the added knowledge the methods can givee designer in particular and profession in general. Fault treesuld be used more often tu look into the possible outcome ofdesign, t has the advantage of being easy to undcr


20/21

T h e n ~is also the need to develop methods to check theresults of the reliability-based analyses.

takes years of experience to make a good geotechnical engier. The same is true for all branches of engineering andthematics. To a.;.;hicvc good results. one needs to assembleecialists, and exchange knowledge, vocabulary and experice. so that they can communicate and understand each other,e significance o f a parameter and the ways their respectiveputs arc to be used in the analysis.

e existing terminology could be improved to facilitatemmunication between the geotechnical practising engineerd the one used to statistics and probability concepts. Thisuld easily he done, it just needs that one person decides to

it.

liability approache:-., if they arc to hccorne more widelycepted, will need to be based on well-recognised convennal (deterministic) approaches, and v.'ill have to ensure thatcertainty can be built into them.

is hoped that the examples gi \en and the discussion madell help convince the reader that risk and reliabilityproaches have the potential for wider applications inotechnical engineering. and that the implementation of thecthmls should benefit the profession, hoth the cnnsultant ande client.

concluding, one should not always have recourse to reliaity analyses. hut the authors find that the approach fits inll with what R.B. Peck taught us hack in 1902:

Indeed the conventional procedures now used to calculatehearing capacity. settlement. or factor of safety of a slopeare valid and justified only to the extent that they have hccnverified hy experience. The science of soil mechanicsmerely provides devices fur interpolating among thespecific experiences of many precedents in order to solvecurrent problems which arc recogni.t.ed to fall within thelimits o f previous experiences. ln addition, however. soilmechanics provitlcs the means hy which we can go beyondthe limits o f our own experience to that of others. It pointsthe way to new solutions or old problems. or to the solutionof previously unsolved problems. In this respect. soil mechanics is a means of extrapolating our experience. orcourse, .such extrapolation involves a mea..,urc of uncertainty until the pertinent experience becomes available.>>

KNOWLEDGEMENT

e authors thank oil companies. contractors and consultants,Norwegian and British authorities, and the Research

uncil of Norway for sponsoring research and developmentrk in this area. Elf Produc:tion Norway, Elf Aquitaine Protion. Health and Safety Executive (L/K). Mobil Research

d Development, N S Norske Shell. Shell Research BY

(KSEPL), Norweg-ian Petroleum Directorate and Statoicially arc responsible for supporting the recent researchStatoil, Shell Research BY. and Del norske Veritas A./Sgreatly with multi-disciplinary dialogues on problemgeotechnicians cnuld not solve.

The authors '1-vish to also acknowledge the many colleagN(il who have provided the data to prepare the caseand done the analyses. This paper is basedcontributions, often ddcrministic, of many colleagues\Vhosc co-operation, skill and dedication is much appreci

RE 'ERENCES

Andersen, K.H. R Laurit.t.scn. R. Dyvik and P.M. Aas,,cyclic Bearing Capacity Analysis for Gravity PlaCalculation Procedure, Verification by Model TestsApplication for the Gullfaks C Platform. Proc BOSS'88Trondheim. Norway. V J, pp. 311-325.

API f1993]. Recommended Practice for Planning, Desand Constructing Fixed Offshore Platfmms - Load andtance Factor Design. API RP2A-WSD. American PetroleumInstitute. 20th edition. Dallas, Texas, Sept. 1993.

Christain, .J.T. f J 9961. Reliability methods for stabiexisting slopes.)> >. ASCE Geotechnical Special PublicatioNo. 5R. Uncertainty in the Geologic Environment;Theory to Practice. Proc. Uncertainties '911, Vol. 1 p418.

Crudcn, D. and R. Fell [1997].


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cg. K [ 1996]. Performance evaluation, safety assessmentd risk analysis for dams.>> Hydropower and Dams. lssuc Six,v 1996. R p.

eg. K. and R.P. Murarka {1974]. . Journal of the Geotechnicalgineering Division, ASCE. Vol. 100, No. GT3, pp. 349-6.

ansen. P.M., S.G. Vick and C. Rikartscn r19971. Risklyses of three Norwegian rockfill darns. Proceedings

ernational Conference on Hydropower (HYDROPO\VER), June 1997, Trondhcim. Norway. pp. 431-442.

casse, S. and A. Goulois [ 1989]. ('Uncertainty in API Paraters for Predictions of Axial Capacity of Driven Pile in

nd. 21st OTC Houston, Texas. USA. Paper 600 I pp. 353-8.

casse, S. and J.-Y.N. Lamhallcric [1995]. Statistical Treatnt of Cone Penetration lesting. lnlern. Symp. on Conenetration testing CPT '95, Link0ping, Sweden. Vol. 2.

369-377.

casse, S. and F. Nadim [ 1994]. . 2Xth OTC Houston. Texas,A, Proc. pp. 369-.lSO (Paper 7996).

casse, S. and F. Nadim l1996h]. dJm:crlainties in Characsing Soil Properties},_ J\SCE Geotechnical Special Publiion No. 58, Uncertainty in the Geologic Environment; Fromeory to Practice. Proc. Uncertainties '96, Vol. 1, pp. 49-75.

w, B.K. and W.H. Tang [1997]. :-. Geotechniquc, Vol. 12. No. I.

Reagan. R.T. and F. Mosteller and C. Youtz [. Structural Safety, V 4, pp.l51-163.

Vanmarcke. E.H. {1977 j. }, In Risk-Based Dam Safety EvaluatioProc. Int. Workshop, Trondheim. Norway. Sept. 1997.

Vick, S. and S tewart [ 1996]. Risk Analysis in DamPractice >_ ASCE Geotechnical Special Publication No. Uncertainty in the Geologic Environment; Prom TheoryPractice. Proc. of Uncertainties '96, Vol. I, pp. 586-603.

Vick, S. [1996]. Personal communication. NGI, Jan 1996.

Whitman, R.V. [ 1984]. Evaluating Calculated Risk Geotechnical Engineering. Journal of Geotechnical enging. ASCE. Col. 10. No.2, pp. 145-188.

Whitman, R.V. [1996]. Organizing and evaluating uncertainin g e o t e ~ . . : h n i c a lengieering. ASCE Geotechnical Spe

Publication No. 58, Uncertainty in the Geologic Environmhorn Theory to Practice. Proc. Uncertainties '96, Vol. I, p1-28.

Whitman, R.V. [ 1997].

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P 1195- Risk and Reliability in Geotechnical Engineering

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