Reliabilty Project

8/3/2019 Reliabilty Project

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Course Project PresentationCourse Project Presentationonon

Factors of Safety and Reliability inFactors of Safety and Reliability inGeotechnical EngineeringGeotechnical Engineering

Presented byPresented by

Kamal Kant JainKamal Kant Jain


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IntroductionIntroductionBasic Tools of Reliability AnalysisBasic Tools of Reliability Analysis

Geotechnical Applications of ProbabilisticGeotechnical Applications of Probabilistic

Methods and Reliability AnalysisMethods and Reliability AnalysisExample:Example: Retaining Wall StabilityRetaining Wall Stability

ConclusionsConclusions

Outline of presentationOutline of presentation


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Factors of safety in Geotechnical EngineeringFactors of safety in Geotechnical Engineering

Based on experienceBased on experience

Dont depend on degree of uncertainty involvedDont depend on degree of uncertainty involved

Present status of use of Reliability theory inPresent status of use of Reliability theory inGeotechnical EngineeringGeotechnical EngineeringInvolves terms and concepts that are not much familiar toInvolves terms and concepts that are not much familiar to

most of the geotechnical engineersmost of the geotechnical engineers

Perception that it would require more data time, and effortPerception that it would require more data time, and effort

Is not used extensivelyIs not used extensively


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1) Normal Variables

M R Q!

M R Q! Q Q Q

2 2 2

2M R Q R QRQ

! VW W W W W

2) Lognormal Variables

Reliability Index1

1

QF !

WProbability of failure fP ! *F

= CDF of Standard Normal Variate*

/

ln ln ln

F R Q

F R Q

!

!

2

ln ln

1ln

2F F F

Q ! Q W

2 2

ln ln(1 )FF V! W

Direct Reliability Analysis


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Distributions other than normal or lognormal

arise often in practice like

Gamma distribution

Extreme Type distributions

Poisson


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Monte Carlo Simulation

1 2 3

1 2 3

( , , ... )

, , ...

n

n

i

ifM fx x x x

x x x x are uncorrelated random variables with

known distribution type, then we generate a large

numberofrandom data points for each ofx using

tables and spreadsheets

!

and determine parameters of

M us ingdata obtained


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Event Trees

Describe logical interactions among a complex set of events,

conditions, physical parameters and states

Start with an initiating event and consider no logical difference

between an event and a condition

Proceed with set of exhaustive and exclusive events that could

follow and each event is associated with conditional probability

Proceed along each path to evaluate the next outcomes, and

so on and so forth

At the end of the any stage of tree, the probability of each

outcome is simply the product of the conditional probabilities of

preceding events and conditions


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Geotechnical Applications of

Probabilistic Methods

Studies of Safety of Dams, Dikes, andEmbankments

Probabilistic Seismic Hazard Analysis

Limit State Design or Load and ResistanceFactor

Nuclear Waste Repositories

Mining

Analysis of Retaining Wall Stability


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FIG. 1 : Cantilever Retaining Wall with Silty Sand Backfill

(Source

:J. Michael Duncan. (2000), Factors of Safety andReliability in Geotechnical Engineering)

Example: Retaining Wall StabilityExample: Retaining Wall Stability

Cantilever

retaining wall

Compacted silty

sand backfill

Concrete footing

built on a layerof silty sand

Backfill drained

to prevent build

up of waterpressure behind

the wall


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Factor of Safety (FoS) against SlidingFactor of Safety (FoS) against Sliding

tanss

W

EF

H

!

W= Weight of wall and backfill over the heel of the wall (lb/ft or kN/m)

tanH = Tangent of friction angle between base of wall and sand

E= Earth pressure force on vertical plane through heel of wall (lb/ft or kN/m)


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HCV= Highest conceivable value of the parameter

LCV= Lowest conceivable value of the parameter

Steps involved in estimation ofFoSSteps involved in estimation ofFoS

Estimate the standard deviations of the

quantities involved In equation

1) Computation from data :

2

i

= 1

x x

NW

2) Computation from published values :

V=

Coefficient of variation

( )*( )V xW !

3) Computation from three sigma rule :( - )

6

HCV LCVW !


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Estimation of the standard deviation and theEstimation of the standard deviation and the

coefficient of variation of the factor of safetycoefficient of variation of the factor of safety

22 2 2

31 2 4

2 2 2 2F

F

F

MLV

F F F F

FV

W

W

(( ( ( !

!

;F F Fiii ( !

4) Graphical three sigma rule may also be used for

estimation of standard deviation

/

iF !Where Factor of safety calculated with the value of the

ith parameter increased / decreased by one

standard deviation from its best estimate value


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FMLV = Most likely value of factor of safety, computed using

best estimate values for all of the parameters.

Finding probability of failure and the reliability

of the factor of safety

Assuming that factor of safety follows a lognormal distribution :

2

ln 2

ln1

ln(1 )

MLVF

V

VF

!

lnF = lognormal reliability index

V= coefficient of variation of

factor of safetyFMLV = most likely value of

factor of safety


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ConclusionsConclusions


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Thank you

Reliabilty Project

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