2007d_4_service_live_design_(adv.pdf

Performance Based Durability Design and Performance Based Durability Design and Assessment for Concrete BridgesAssessment for Concrete Bridges

Ha-Won Song

Concrete Materials, Mechanics and EngineeringSchool of Civil and Environmental Engineering

Yonsei Univ., Seoul 120-749, KOREA

2007. 11. 21. Yonsei University

Seoul, KOREA

International Joint Seminar between Yonsei University and Tokyo Institute of Technologyon Recent Progress on Bridges and Concrete Technology

Concrete Materials, Mechanics & Engineering Lab., Yonsei Univ.

Outline

- Introduction

- Probability-Based Durability Design

- Utilization of PBD for Assessment

- Refined model for design and assessment

- Discussion

- Conclusion


Old/Current Codes: ACI, AASHTO, EC2,BS• Simple deemed-to-satisfy

rules (deterministic)• Experience based rules of

thumb• Poor environmental classification

Result No relation between performance and service life (implicit 50 years)

Performance-based design codes (a partial factor method, full probabilistic method)• Degradation models • Material parameters • Detailing of environmental actions• Statistical quantification (mean, standard deviation, distribution) • Choice of service life

Result Documented service life design, failure probability

Old/Current Codes: ACI, AASHTO, EC2,BSOld/Current Codes: ACI, AASHTO, EC2,BS•• Simple deemedSimple deemed--toto--satisfysatisfy

rulesrules (deterministic)(deterministic)•• Experience based rules ofExperience based rules of

thumbthumb•• Poor environmental classificationPoor environmental classification

Result Result No relation between performance and No relation between performance and sserviceervice life (implicit 50 years) life (implicit 50 years)

PerformancePerformance--based based design codes (a partial factor method, full probabilistic methoddesign codes (a partial factor method, full probabilistic method))•• Degradation models Degradation models •• Material parameters Material parameters •• Detailing of environmental actionsDetailing of environmental actions•• Statistical quantification (mean, standard deviation, distributiStatistical quantification (mean, standard deviation, distribution) on) •• Choice of service lifeChoice of service life

Result Result Documented service life design, failure probability Documented service life design, failure probability

Comparison of durability design codes


ISO 2394 on general principles on reliability of structures

-ISO/WD 13823 on general principles on the design of structures for durability

(TC98 SC2/WG10)

-Fib MC SLD – Model code for service life design

->ISO TC71 SC3 TF and WG

-ISO 13822 on assessment of existing structures (TC98 SC2/WG10)

->ISO TC71 SC7 WG2

*ISO/TC98: Bases for Design of Structures

Durability design and assessment for concrete structuresDurability design and assessment for concrete structures


Marine environment of Korea for Concrete structures-> chloride induced corrosion


SALTSALT

VoidsVoids

BarBarIndentationIndentation

Corrosion initiationCorrosion initiation


Measures:• High quality and impermeable

concrete

- low chloride diffusivity(material)

- sufficient concrete cover(design)

- no early-aged cracks(construction)

(Service life design w/ ILS ) Durabilty design

verification of service life

min. cover thickness Comax. diffusion coefficent Dcl

Durability measures for concrete structures


Durability degradation due to chloride induced corrosion-initiation limit state

Free Cl-High pH

coverprotection

corrosioninitiation

physicaldamage

damagelimit

Det

erio

ratio

n

t0=service life

Chloride ContaminationCarbonation

t1

loss of steel insideconcrete

Time

Chloride Threshold LevelHigh pH buffering

Local chloride build upand local pH reduction


Time

Transfer mechanism

Resistancemechanism (R)

Environmental Action

Damage ordisfigurement

mechanism (Slim)

Action effects (damage, Reduced resistance, etc)

ULS : R ≥ S? SLS : S ≤ Slim?

collapse malfunction

Durable Structure

Initiation limit state

Service lifets ≥ tD

Yes

texposure

tstart

ts

Mass transport analysis

Structure Environment(combination of

rain, de-icing salts etc)Boundary conditions

Corrosion of reinforcementConcrete crackDeterioration of concrete

Structural analysis

tS = tstart + texposure

Performance based concept for service life design( ISO/WD 13823 of TC98/SC2)


Service life design and evaluation of Busan Geoje Fixed Link Bridge (2006-2010) in Korea:

LOT 2

LOT 3

US$1.5 billion project!-Marine environment

(Chloride induced corrosion)-1st Seabed structure

(Performance based durability design, 100 years)

LOT 1Cable Stayed Bridge Cable Stayed Bridge

Submergedtunnel


65.320.0670-Tunnel inside

65.315.3-0.19Atmospheric

82.615.3-0.51Splash

10015.3-0.51Submerged

Relative humidity (%)

Temperature (℃ )

CO2 concentration (ppm)

Chloride concentration

(mol/ℓ)Type of zones

Environmental conditions

Marine environmental condition of bridges and submerged tunnel in Busan-Geoje Fixed Link

Alkali aggregate reaction,Chemical decomposition of hydrated cement

Freeze-thaw damageTemperature gradientsHumidity gradients

Abrasion and Chemical Attack

Reinforcing steel corrosion

Con

cret

eR

ein

forc

ing

stee

l

Submergedzone

Concrete at atmospheric zone

Concrete atsplash and tidal zone

Low tide

High tide


Steps1. Selection of limit state Chloride Threshold Level (CTL)

CTL ;=the content of chloride ions at the depth of the embedded steel in concrete when chloride-induced corrosion starts

2. Selection of degradation model e.g. Fick’s law3. Quantification of stochastic variables and analysis

Selection of cement type, binder (SCM) typew/b-ratio, concrete mix

– Determination of diffusion coefficient

– Selection of relevant values ofother model parameters

4. Repeated probabilistic analysis until acceptable failure probability

Performance based SLD method-a probabilistic method


Corrosion initiates when,Corrosion initiates when,

( ) crCtcC ≥,Where,

c: concrete cover, t: timeCcr: Critical chloride concentration

(Chloride Threshold Level: CTL)

Where,c: concrete cover, t: timeCcr: Critical chloride concentration

(Chloride Threshold Level: CTL)

environment

low corrosionrisk electro-lytic process impeded

not carbonated concrete

carbonated concrete

high corrosionrisk

low corrosionrisk lack ofoxygen

~0.6 %

100 % r.hconstant

50 % r.hconstant

85 % r.hchanging

good quality

bad quality Crit. Cl-/Cement

Selection of limit state: CTL


00

a Dc

ke

kt

tD

n

⎟⎠⎞

⎜⎝⎛

= 00

a Dc

ke

kt

tD

n

⎟⎠⎞

⎜⎝⎛

=(( ))||||||

⎠⎠

⎞⎞

⎜⎜⎜⎜⎜⎜

⎝⎝

⎛⎛

⎥⎥⎥⎥

⎦⎦

⎤⎤

⎢⎢⎢⎢

⎣⎣

⎡⎡−−==

aaDDtt22xxerferf11ssCCttx,x,CC

Design target and quantification of stochastic variables

– Design life: 100 years.

– Nominal end of service life: corrosion initiation

– Level of Reliability: 90% (β = 1.3)

Bridge at splash zoneBridge at splash zone

ParameterParameter DimensionDimension Distr.Distr.--TypeTypexxcc Concrete coverConcrete cover mmmm 7575 88 Log normalLog normalDD00 Chloride migration Chloride migration coefcoef.. 1010--12 12 mm22/s/s 6.56.5 1.31.3

NormalNormal

DeterministicDeterministic

NormalNormalNormalNormal

Log normalLog normal

GammaGamma

0.600.60

0.40.4

0.920.92

1.01.0

4.04.0

0.07670.0767yearsyears

0.060.06

0.080.08

0.150.15

0.30.3

1.21.2

--

wt.wt.--%/binder%/binder

--

--

--

wt.wt.--%/binder%/binder

CCcrcr Critical chloride contentCritical chloride content

n Time factorn Time factor

kkee Factor, environmentFactor, environment

kkcc Factor, executionFactor, execution

CCss Chloride content at surfaceChloride content at surface

ttoo Reference timeReference time

μμ σσ

GammaGamma


0

1

2

3

4

5

0 20 40 60 80 100

Time [years]

Rel

iabi

lity

inde

x

Dcl=3.5x10-12 m2/sInterrelation chloride diffusion coefficient Dcl-- age factor 　 - reliability 　

2.31.91.14 x10-12

2.52.11.33.5 x10-12

2.72.31.53 x10-12

3.33.02.22 x10-1275

　(m2/s)(mm)

　 = 0.6

　 = 0.5

　 = 0.4

Max. DCl-Cover

Designed value for bridges at splash zone


Bridge

Below-3.5

Above-3.5

Level

756.5x10-12Submerged

75Splash

503.5x10-12

Atmospheric

cover

(mm)

Max. Dcl-

(m2/s)

Exposure zone

Sub-merged(outside)

756.0x10-12

Atmos-pheric(inside)

cover

(mm)

Max. Dcl-

(m2/s)

Exposure zone

Tunnel

durability designed parameters


6.0×10-127565.320.0670-CarbonatedImmersedTunnel inside

6.5×10-125065.315.3-0.19Atmospheric

3.5×10-127582.615.3-0.51Splash

3.5×10-127510015.3-0.51SubmergedCableStayedbridge

Dcl(m2/s)

Cover Depth(mm)

R.H(%)

Temp(℃)

CO2Concentraion

(ppm)

Surface chloride concentration

(mol/l)Zone

Service life designEnvironmental conditions

Structures

Specific gravity- coarse aggregate : 2.64 - sand : 2.58- cement : 3.16 - slag : 2.89- fly ash : 2.19 - silica fume : 2.21Air content : 4.0 %

102076576-1521521420.375t4

102077838-1701701420.375t3

102075180-1601601400.350t2

102076440-1801801400.350t1Immersed

Tunnel(t)

102078272-1431431430.375b4

102076576-1521521420.375b3

1020797-11.41841841420.375b2

SP : 0.65~2.0%AE : 0.014~0.023%

102075180-1601601400.350b1Bridge

Structures(b)

FASFSLAGOPCAdmixtureG

(kg/m3)S

(kg/m3)Binder (kg/ m3)W

(kg/m3)W/BArea

Mix proportions of concrete


Japanese spec. (JSCE, 2002)Korean spec. (MOCT, 2004)

Deterministic partial factor method for durability design

id

isd CtD

xerfCCC +⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅−⋅−=

21)(

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅−⋅=

tDxerfCC

dscld 2

1γ

0.1lim

≤CC d

iγlimCC KdP φγ ≤

Safety Factor : 3.1=K

P

φγ

Safety Factor : 3.1=⋅ cli γγ

clγ : Factor with consideration to the variation in the Cd value, in general, 1.3 is acceptable

Clim=CTL(= 1.2 kg/m3 of total chloride)

pγ

kφ: Environmental factor for chloride attack

: Durability reduction factor for chloride attack

Revised to (2007)- 0.4 % of binder


Durability evaluation

⎟⎠

⎞⎜⎝

⎛ −⋅=Dt

xerfCtxC cS 2

1),(

Clim=1.2 kg/m3Chloride threshold level

Concrete Standard Specification on Durability (2004)

Constant D, Cs

Chloride transport equation

0

30

60

90

120

150

0 50 100 150 200 250 300

Cover depth (mm)

Cor

rosio

n in

itiat

ion

time

(yea

rs)

Demanded cover depth260mm unrealistic coverfor 100 years service life

Need to revised for Clim, D, Cs, etc.

Required cover depth for 100 service life for the bridge

Clim : 1.2kg/m3 0.4% binder weight


A modification by considering time dependent characteristics of chloride transport

Sea waterSea water

t = 1 year

t = 10 year

t = 30 year

t = 30 yeart = 10 year

t = 1 year

increase of CSwith time

decrease of Dwith time

chlo

ride

con

cent

ratio

n

depth

CS

diff

usio

n co

effic

ient

time

D

RC Structure

Considering time dependency of CS and D

durability evaluation assessment


Conventional chloride transport model

Chloride transport mechanisms :

- diffusion due to a concentration gradient- absorption due to a capillary action- migration in an electrical field- a pressure-induced flow- wick action

the primary mechanism

2

2

xCD

tC

∂∂

=∂∂

C(x,0) = 0 at t = 0, C(0,t) {= Cs (constant at x=0 )}=Co

⎟⎠

⎞⎜⎝

⎛ −=Dt

xerfCtxC2

1),( 0

∵ no applied electric field andstableness of the moisture condition

Fick’s diffusion law :

boundary conditions :

this model can not consider time dependency of CS and D

Conventional model

D = const.


Solutions with time dependent CS

Kassir & Ghosn2002Cs(t)= C0[1 - e-γt]

Cs(t)=k2t1/2

Uji et al. 1990Amey et al. 1998

Cs(t)=k1t

Crank 1983Cs=constant

ReferencesSolutionsCS functions

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

DtxerfCtxC S 2

1),(

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+= − Dtxe

Dtx

Dtxerfc

DtxtktxC 4/

2

1

2

2221),(

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= −

Dtxerfc

DtxetktxC Dtx

22),( 4/

2

2 π

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−= − )]([

21),(

2

2

40 izerfcdeRe

DtxerfCtxC zDt

x

Solving the Fick’s 2nd law

2

2

xCD

tC

∂∂

=∂∂


A general solution to Fick’s 2nd law for time-varying CS

∫ ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⋅

−= −

−ttD

xS de

ttC

DxtxC

0

)(42/3

2

)()(

2),( υ

υπυ

)(2 υω

−=

tDx

∫∞

−⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−=

Dtx

S deDxtCtxC

2

2

22

42),( ω

ωπω

2

2

xCD

tC

∂∂

=∂∂

A heat conduction solution in Solids by Carslaw and Jaeger (1959)

Fick’s diffusion law :

The solution can be used for any type of CS functions

A general solution for CS (t) :

D = const.

It is possible to consider any time dependent CS

assumption :


Proposed time dependent CS model (1)

CS(t)= α[ln(βt+1)]Proposed CS model :

0

5

10

15

0 5 10 15 20 25 30Time(years)

CS

(kg/

m3 )

Weyers et al.(1994)

0

5

10

15

0 5 10 15 20 25 30Time(years)

CS

(kg/

m3 )

Weyers et al.(1994)

계열2계열3계열4계열5

Cs(t)= k1tCs(t)= k2t1/2

Cs(t)= C0[1-e-γt]Cs(t)= α[ln(βt+1)]

ConductingRegression Analysis

withCs(t)= k1t

Cs(t)= k2t1/2

Cs(t)= C0[1-e-γt]

(where, α and β are constants)


Proposed time dependent CS model (2)

CS (t) = α [ln(β t+1)]

Shape factor β

CS values(at t=100 years)

Song et al (2006)0.99α= 1.37, β = 3.77Cs(t)= α[ln(βt+1)]

Kassir & Ghosn 20020.98C0= 5.34, γ= 0.25Cs(t)= C0[1-e-γt]

0.90k2= 1.56Cs(t)= k2t1/2Uji et al. 1990

0.35k1=0.44Cs(t)= k1t

Referencesregressionfactors (=R2)

Constants for modelsCS functions

3.77β

0.250.340.510.761.52αthisstudy

1.52.03.04.59.0CS (kg/m3)MOCTJSCE

10005002501000

distance from the sea (m)parameters

Results of regression analysis

Constants for time dependent CS model

Calculating α

Proposed CS model :

Very accurate model


Proposed time dependent D model

time, t

chlo

ride

diff

usio

n co

effic

ient

diffusion coefficient at time t, D(t)

∫ ⋅=t

m dDt

tD0

)(1)( ττ

S(tS(t))

the mean value of the chloride diffusion coefficient

∫ ⋅=t

dDtS0

)()( ττ

t0

the area under the curve D(t)

mR

R ttDtD ⎟⎠⎞

⎜⎝⎛=)(

m

RR t

tDtD ⎟⎟⎠

⎞⎜⎜⎝

⎛=

lim

)(

(t ≤ 30 years)

(t > 30 years)

mR

m tt

mDtD ⎟

⎠⎞

⎜⎝⎛

−= lim

1)(

m

RRm t

tt

tmmm

DtD ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡ +−

−=

lim

lim)1(1

)(

(t ≤ 30 years)

(t > 30 years)

Time dependent D model :

∫ ⋅=⋅=t

m dDt

tSt

tD0

)(1)(1)( ττ


Chloride threshold level (Clim)

Chloride threshold level (Clim) can be presented :

a ratio of chlorides to hydroxyl ionsfree chloride content (% by weight of cement or kg/m3)total chloride content (% by weight of cement or kg/m3)

takes into account the inhibiting effect of cement.represents the total aggressive potential of chloride ions.

0.3~0.6 kg/m3 in the acceleration test for a concrete specimen1.2~2.4 kg/m3 in exposure experiment under the actual environment

the lowest limit value for concrete structures(corresponds to 0.4 % by weight of cement

for the concrete containing a cement content of 300 kg/m3)

∴ 0.4 % by weight of cement as a Clim is more reasonable

JSCE(2002) and MOCT (2004) specified the Clim value :


Refined model considering time dependency

∫∞

−⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−=

Dtx

S deDxtCtxC

2

2

22

42),( ω

ωπω

Time dependent D model :

A general solution to the Fick’s 2nd law :

mRR

m tt

mDtD ⎟

⎠⎞

⎜⎝⎛

−=

1)(

m

RRm t

tt

tmmm

DtD ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡ +−

−=

lim

lim)1(1

)(

(t ≤ 30 years)

(t > 30 years)

CS(t)= α[ln(βt+1)]Time dependent CS model :

Clim : 0.4 % by weight of cement


)()0)(()0)(( lim, t

dtF N

tCCnNtgnP β−Φ=

<−=

<=

Limit state function )()()()( lim tCCtStRtg d−=−=

Time

S(t)

Pf

Distribution of R(t)R,S

Distribution of S(t)

R(t)

Service life density

Mean service life

Target Probabilityof Failure Pf

Probability of failure

Fully probabilistic assessment of existing structures (1)



Sampling from properties of variables

SAMPLES(N: the number of simulation)

VARIABLE

m(N)DR(N)Clim(N)Xc(N)Cs(N)

m(2)DR(2)Clim(2)Xc(2)Cs(2)

m(1)DR(1)Clim(1)Xc(1)Cs(1)

:::::

:::::

mDRClimXcCs

-DR : (u,σ)

m : (u,σ)Clim : (u,σ)

xc : (u,σ)Cs : (u,σ)Property(u: Meanσ: Standard dev.)

Estimating statistical properties of input parameter



VARIABLE

m(N)DR(N)Clim(N)xc(N)Cs(N)

m(2)DR(2)Clim(2)xc(2)Cs(2)


::::::::::

mDRClimxcCs


durability failure at t !!0),(lim <− txCC c

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅−=

tDxerfCtxC c

s 21),(

m

R ttDtD ⎟⎠⎞

⎜⎝⎛= 0)(previous

model



VARIABLE

m(N)DR(N)Clim(N)xc(N)Cs(N)



::::::::::

mDRClimxcCs

∫∞

−⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−=

Dtx

S deDxtCtxC

2

2

22

42),( ω

ωπω

mRR

m tt

mDtD ⎟

⎠⎞

⎜⎝⎛

−=

1)(


durability failure at t !!0),(lim <− txCC c


0

5

10

15

20

25

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Diffusion coefficient (m2/s × 10-12)

Num

ber o

f Tes

ts

0

2

4

6

8

10

95 100 105 110 115 120 125 130cover depth (mm)

Num

ber o

f Tes

ts

Histogram of cover depth measured Histogram of diffusion coefficients

Inspection for exiting structures- measured values of D and cover thickness of the immersed tunnels

unit: [m2/s ×10-12] unit: [mm]

N(3.77, 0.92) N(110.7, 9.5)


0

20

40

60

80

100

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Diffusion coefficient (m2/s ×10-12)N

umbe

r of T

ests

0

5

10

15

20

25

30

1.5 2.0 2.5 3.0 3.5 4.0Diffusion coefficient (m2/s ×10-12)

Num

ber o

f Tes

ts

Histogram of diffusion coefficient measured in atmospheric and submerged zone

Histogram of diffusion coefficients in splash zone

- Measured values of diffusion coefficient for the pier and pylon

unit: [m2/s ×10-12] unit: [m2/s ×10-12]

N(2.84, 0.53) N(5.16, 0.86)


a=N(0.36, 0.11)b=N(3.77, 0.38)N(3.0, 0.9)N(3.0, 0.9)N(3.0, 0.9)% of binder

Piers & PylonsPiers & PylonsImmersed tunnelPiers & Pylons

N(0.4, 0.04)

N(0.36, 0.07)

N(5.16, 0.86)

N(75.0, 7.5)

CS=const.

Submerged zone

N(0.4, 0.04)

N(0.54, 0.11)

N(3.77, 0.92)

N(110.7, 9.5)

CS=const.

N(0.4, 0.04)

N(0.36, 0.07)

N(2.84, 0.53)

N(75.0, 7.5)

CS=const.

Splash zone

chloride threshold

level

aging factor

diffusion coefficient

cover depth

surface chloride

concentration

Atmospheric zone

N(0.4, 0.04)% of binderClim

N(0.36, 0.07)-m

N(5.16, 0.86)m2/s ×10-12D

N(75.0, 7.5)mmxc

CS(t)=a[ln(bt+1)]CS types

CS

UnitsVariables

Input parameters to assess the service life of the structure


0

20

40

60

80

100

100 200 300 400 500

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-4

-2

0

2

4

Rel

iabi

lity

Inde

x

PFβ

submerged zoneimmersed tunnel

Assessment results by standard specification- the immersed tunnel in submerged zone

Targetprobability of failure

10 %

Targetreliability index

1.3


- the bridge structure

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ submerged zone

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ splash zone

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ atmospheric zone The bridge structures designed for 100 years

of service life in marine environment, which are under construction,does not satisfy target service life (=100 years)

(one reason is that Clim value used in spec.e.g. In a design stage

submerged zone : 1.8 %splash zone : 0.6 %atmospheric zone : 0.8 % )


0

10

20

30

40

0 100 200 300 400Time (years)

Prob

abili

ty o

f Fai

lure

(%)

COV=9%COV=18%COV=27%COV=36%

mean value = 110 mm

COV: coefficient of variance

service life- 220 years- 184 years- 143 years- 99 years

Possible assessment (same mean value, but different deviation):Influence of concrete cover scatter due to construction quality on the service life

Targetprobability of failure

10 %


Comparison of assessment method

considerationN/AconsiderationAge factor

0.4 (%, binder)1.2 (kg/m3)0.4 (%, binder)Clim

time dep.time indep.time dep.D

time dep.(in atmospheric zone)

time indep.time dep.

(in atmospheric zone)CS

time dep. of CStime indep. of CS and Dtime dep. of CSFick’s law

deterministic modeldeterministic modelprobabilistic modelanalysis

Revised Spec.Standard spec.Probability analysis


a=N(0.36, 0.11)b=N(3.77, 0.38)N(3.0, 0.9)N(3.0, 0.9)N(3.0, 0.9)% of binder


N(0.4, 0.04)

N(0.36, 0.07)

N(5.16, 0.86)

N(75.0, 7.5)

CS=const.

Submerged zone

N(0.4, 0.04)

N(0.54, 0.11)

N(3.77, 0.92)

N(110.7, 9.5)

CS=const.

N(0.4, 0.04)

N(0.36, 0.07)

N(2.84, 0.53)

N(75.0, 7.5)

CS=const.

Splash zone

chloride threshold

level

aging factor

diffusion coefficient

cover depth

surface chloride

concentration

Atmospheric zone

N(0.4, 0.04)% of binderClim

N(0.36, 0.07)-m

N(5.16, 0.86)m2/s ×10-12D

N(75.0, 7.5)mmxc

CS(t)=a[ln(bt+1)]CS types

CS

UnitsVariables

Recall of Input parameters of existing structure


Assessment by probability analysis

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ

splash zonepiers and pylons

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ

atmospheric zonepiers and pylons

0

20

40

60

80

100

100 200 300 400 500

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-4

-2

0

2

4

Rel

iabi

lity

Inde

x

PFβ



220 years0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ

submerged zonepiers and pylons

22 years

48 years50 years


0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

Assessment by Standard specification (2004)




16 years


5 years

6 years9 years


0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100

Time (years)

Chl

orid

e co

nten

ts (%

, bin

der

Assessment by revised spec.




450 years


38 years

71 years84 years


Comparison of results by different assessment method

54 years66 years371 years29 years

Refinedmodel

(Clim=1.2kg/m3)(SF=1.3)

6 years9 years16 years5 yearsStandard

specification(2004)


38 years

22 years

Submerged zone

450 years

220 years

84 years

50 years

Splash zone Atmospheric zone

71 years

Refinedmodel

(Clim=0.4%)(SF=1.3)

48 yearsProbability analysis

(Pf=10%)

Current spec. << probability analysis (Pf=10%) < refined model <refined model (0.4%C)


Use of different Pf- Predicted service life by different probability of failure (1)

0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ


Service lifePF

52 years50%

44 years40%

36 years30%

29 years20%

22 years10%


0

20

40

60

80

100

100 200 300 400 500

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-4

-2

0

2

4

Rel

iabi

lity

Inde

x

PFβ



Service lifePF

556 years50%

468 years40%

380 years30%

300 years20%

220 years10%

- Predicted service life for different probability of failure (2)


0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ splash zone

piers and pylons

Service lifePF

108 years50%

92 years40%

78 years30%

64 years20%

50 years10%



0

20

40

60

80

100

0 20 40 60 80 100

Time (years)

Prob

abili

ty o

f Fai

lure

(%)

-5

-3

-1

1

3

5

Rel

iabi

lity

Inde

x

PFβ


Service lifePF

94 years50%

82 years40%

70 years30%

60 years20%

48 years10%



Different service life by different probability failure!same for SF ?

PF

0.5

0.4

0.3

0.2

0.1






22 years

Submerged zone

220 years 50 years


48 years


Yes, then how to select the safety factor for the spec.?- Probability of failure (reliability index) vs. safety factor

Probabilistic Analysis(Probabilistic assessment)

Deterministic Analysis(Standard specification)

Service Lifeof the target structure

Probability of failure(PF)

Safety factor(SF)

relationship between PF and SF

PF=function of time

SF=function of time


Predicted service life for different Safety Factors using Refined Spec.

Clim=1.2kg/m3

1.5 49 years61 years343 years26 years

SafetyFactor

1.4

1.3

1.2

1.1

1.0






36 years

Submerged zone

433 years 79 years


66 years


Predicted service life for different Safety Factors using Refined Spec.

Clim=0.4% of binder

1.5 63 years76 years411 years34 years

SafetyFactor

1.4

1.3

1.2

1.1

1.0






48 years

Submerged zone

539 years 102 years


88 years


Analysis Results of both Probabilistic and Deterministic methods

DeterministicMethod(Refined Spec.)

1.5 496134326

SafetyFactor

1.4

1.3

1.2

1.1

1.0

587038831

546637129

526335627

627440833


36

Submerged zone

433 79


66

ProbabilisticMethod

Prob.Failure

0.5

0.4

0.3

0.2

0.1

707838036

829246844

9410855652

606430029


22

Submerged zone

220 50


48

Clim=1.2kg/m3


Analysis Results of both Probabilistic and Deterministic methods

DeterministicMethod(Refined Spec.)

1.5 637641134

SafetyFactor

1.4

1.3

1.2

1.1

1.0

768947441

718445038

677942936

819550344


48

Submerged zone

539 102


88

ProbabilisticMethod

Prob.Failure

0.5

0.4

0.3

0.2

0.1

707838036

829246844

9410855652

606430029


22

Submerged zone

220 50


48

Clim=0.4% of binder


0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor

Probability failureSafety factor

0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400 500 600Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


Predicted service life for Probability of failure and Safety factor(Clim=1.2kg/m3)






Predicted service life for Probability of failure and Safety factor(Clim=0.4% of binder)

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400 500 600Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor


0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120Time (years)

Prob

abili

ty fa

ilure

1.0

1.1

1.2

1.3

1.4

1.5

Safe

ty fa

ctor







0.4% of binder

1.2kg/m3

Clim

SF=-3.35PF+1.85Pier & PylonAtmospheric zone

SF=-3.97PF+2.18Pier & PylonSplash zone

SF=-4.82PF+2.67Tunnel

SF=-3.75PF+2.06Pier & PylonSubmerged zone

Relationship equationsStructuresZone

SF=-2.32PF+2.02Pier & PylonAtmospheric zone

SF: Safety factor, PF: Probability of Failure

SF=-2.75PF+2.25Pier & PylonSplash zone

SF=-3.39PF+2.58Tunnel

SF=-2.71PF+2.19Pier & PylonSubmerged zone

Relationship between Probability of failure and Safety factor


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6


Safe

ty fa

ctor

Submerged, Pier & PylonSubmerged, TunnelSplash, Pier & PylonAtmospheric, Pier & Pylon


Regression CurveSF=-3.97·PF+2.19

Clim=1.2kg/m3


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0

Reliabiilty index

Safe

ty fa

ctor


Relationship between Reliability index and Safety factor

Regression CurveSF=-0.07β3-0.24β2+1.67β+0.19

Clim=1.2kg/m3


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6


Safe

ty fa

ctor



Regression CurveSF=-2.79·PF+2.26

Clim=0.4% of binder


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0

Reliabiilty index

Safe

ty fa

ctor


Relationship between Reliability index and Safety factor

Regression CurveSF=-0.05β3-0.17β2+1.18β+0.86

Clim=0.4% of binder


Correlation among Safety factor, Probability of failure and Reliability index

0.400.45

Deterministic analysis

Probabilistic analysis

0.200.50

0.600.40

0.800.35

1.000.30

1.200.25

1.400.20

1.590.15

1.790.10

1.990.05

SFPF

1.971.6



2.021.8

1.871.4

1.741.2

1.561.0

1.340.8

1.100.6

0.820.4

0.520.2

0.200

SFβ

Clim=1.2kg/m3


Correlation among Safety factor, Probability of failure and Reliability index

1.000.45



0.860.50

1.140.40

1.300.35

1.420.30

1.560.25

1.700.20

1.840.15

1.980.10

2.120.05

SFPF

2.111.6



2.141.8

2.041.4

1.941.2

1.821.0

1.670.8

1.490.6

1.300.4

1.090.2

0.860

SFβ

Clim=0.4% of binder

The safety factor of 1.3 corresponds to a probability of failure of 35%


Conclusion

1. It was found that the standard specification, which does not take the time dependency into account, underestimates service life ofconcrete structures exposed to the marine environment. It can beimproved by use of time dependent chloride transport model, the so-called refined model.

2. Fully probabilistic analysis was used to assess remaining service life of a concrete structure considering time dependent characteristics using an informative data on the cover depth and diffusion coefficient of existing structures. It was also found that service life of marine structures is significantly affected by the variation in cover depth, i.e., quality of construction.

3. Safety factor for a partial factor method for durability design can be well related to reliability index or probability of failure of structures of fully probabilistic design. Choice of reliability index should be consistent with selection of the safety factor in the specification, vice versa.


Thank you for kind attention !

“Deemed-to-satisfy” and “ Avoidance of deterioration” method will be applicable for engineering practice.

“ Full probabilistic method” will rarely be applied on new projects. “ Full probabilistic method” can be used when assessing existing structures.

Assessment of existing RC structures

“ Partial factor method” will be applicable when calibrated.

Durability design of new RC structures

Concluding remark

2007d_4_service_live_design_(adv.pdf

Documents