design life and reliability-based design concept for long-span cable...

대한토목학회정기학술대회, 2012. 10. 26., 전남대학교

Design Life and Reliability-based Design Concept for Long-Span Cable-Supported Bridge

Hae Sung Lee (Seoul Nat’l Univ., Korea)Inyeol Paik (Gachon Univ., Korea)Seung Han Lee (Seoul Nat’l Univ., Korea)

2

CONTENTS

CONTENTS

I

II

III Safety level of design load combination

Determination of target reliability

Introduction

IV Conclusion

3

I

II



Introduction

IV Conclusion

4

Introduction

The safety concept of the long-span cable-supported bridge(LSCSB)design is discussed.

The safety factors in the proposing code are determined afterconducting probabilistic study.

The statistical properties for the loads and the resistances are based onthe domestic field data as well as the relevant references.

The safety level of the design load combinations for the ultimate limitstate and the accidental event limit state are under examination and abrief result is shown in this presentation.

Depending on the importance of the structural components, the relativesafety levels of the current design are presented.

To appreciate the behavior of the cable-supported bridge sufficiently,the geometrical nonlinearity of the cable member should be considered.

5

I

II



Introduction

IV Conclusion

6

Determination of Target Reliability (1)

Importance of Structure - 200-year Design Life

Design guidelines for ordinary bridges, such as Eurocode and AASHTO LRFD,use 75~100 years as design life of bridge, and select 3.5~3.7 to the targetreliability.

To guarantee the equivalent reliability level for 200-year design life, 1-yearprobability of failure needs to be halved. It means that the importance of bridgeshould be doubled in terms of annual probability of failure, just due to theincrease of design life from 100 years to 200 years.

Table 1 : 1-year Probability of Failure to Guarantee the Same Reliability Level for Design Life

Based on 1-year time PeriodBased on Design Life

100-year Design Life 200-year Design Life

Target Reliability

Probability of Failure

RatioTarget

Reliability Probability of Failure

Target Reliability


4.75 1.00×10-6 1 3.72 10-4 3.54 2.00×10-4

4.89 5.00×10-7 1 / 2 3.89 5.00×10-5 3.72 10-4

7


Importance of Structure - Construction costs of bridge

When viewed simply in terms of the amount of costs in constructing thestructures, the probability of failure of the long-span cable-supported bridgeshould be lower than that of the ordinary bridge.

The construction costs per unit slab section of long-span cable-supportedbridges are around four times those of the ordinary bridge. Even afterconsidering the increase in construction costs for the sub-structure of the multi-ordinary bridges covering the same bridge span, the probability of failure of thelong-span cable-supported bridges should be between one third and a quarterof that of the ordinary bridge.

Table 2 : Average Construction Costs per Unit Slab Section(1m2) of Ordinary Bridges [unit : 103 KRW]

Type of

Bridge

Ordinary Bridge Cable-supported Bridge

PSC Beam

Steel Girder

Composite Girder Rahmen

Suspension Bridge Cable-stayed Bridge

Ulsan Bridge

(1,150m)

Yi Sun-Sin Bridge

(1,545m)

HandolBridge (500m)

BukhangBridge (540m)

Costs 1,685 2,307 2,636 2,702 11,380 10,570 8,070 8,590

8


Importance of Structure - Recovery costs of bridge

Assuming a situation when the long-span cable-supported bridge collapses,the recovery costs concerning the damage to human lives, economic and sociallosses are expected to be much larger than those of the ordinary bridges.

To reflect the impact of the recovery costs in the importance of bridge,a detailed risk analysis concerning the damage to human lives, economic andsocial losses is required.

In current study, however, as the risk analysis has not been sufficientlyconsidered, we could not reflect the information of the recovery cost to theimportance of bridge. At present stage of research, only the design life and theconstruction costs would be considered in the importance of bridge fordetermination of target reliability.

Through the collaborative research with experts in the field of risk analysis inthe remaining 2nd Step research period, it might be necessary to find ways howto perform the risk analysis and how to reflect the result on the importance ofbridge for determination of target reliability.

9


Target Reliability

The target reliability based on design life and the corresponding 1-yearprobability of failure by considering the importance of bridge are as follows:

Table 3 : Target reliability for Design Life by Classification of Bridge

Class Structure

Based on 1-year time PeriodTarget Reliability

Based on Design Life

Target Reliability


Ratio 100 year 200 year

1 Ordinary Bridge (100 year) 4.75 1.00×10-6 1 3.72 3.54

(Ref.) Ordinary Bridge (200 year) 4.89 5.00×10-7 1 / 2 3.89 3.72

(Ref.) Long-Span Cable-Supported Bridge (100 year) 4.98 3.16×10-7 1 / 3.16 4.00 3.83

2 Long-Span Cable-Supported Bridge (200 year) 5.11 1.58×10-7 1 / 6.32 4.16 4.00

(Ref.)Nuclear Power ReactorsMajor Dams and Barriers

Strategic Defence Structures5.20 1.00×10-7 1 / 10 4.26 4.11

10

Variable Design Life for Structural Components (1)

Replaceable components

Relatively easy for replacement. The performance and design life of these components can be determined from life-cycle cost aspect.

Repairable components

Permanent components

Cable band HangerExpansion joint Painting Pavement

11



Hardly replaceable but feasible for repair/rehabilitation to an acceptable level of damage.



AnchorageConcrete PylonSteel girder

12



Sustainable to the lifetime of bridge with minimal level of repair.



Splay SaddleMain cable Pile foundation Pylon Saddle

13


Design Concept

Lower reliability index could be applied for replaceable components.

Replacement periods needs determined based on life cycle cost analysis.

Feasible details of structural components should be considered for easyreplacement




Performance of element

repair/rehabilitation

replacement

Service lifetime

Time

Design life: 20~50 years

Design life: 75~100 years

Design life: 200 years

200year

replacement

Required performance

repair/rehabilitation

replacement replacement



14


Target Reliability for Variable Structural Components

The target reliability in design life and the corresponding 1-year probability offailure by considering the relative importance of variable structural componentsare as follows:

Table 4 : Target reliability for Design Life by Classification of Structural Components

Class Structural Component

Based on 1-year time Period

Target Reliability Based on Design Life

Target Reliability


20 year

30 year

50 year

100 year

200 year

(Ref.) Ordinary Bridge (100 year) 4.75 1.00×10-6 4.11 4.01 3.89 3.72 3.54

1

Replaceable Components (20 year) 4.66 1.58×10-6 4.00 3.90 3.78 3.60 3.42



2Repairable Components

5.11 1.58×10-7 4.52 4.43 4.32 4.16 4.00Permanent Components

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Example for Design Life of Replaceable Components

Design Life of 20 years

- Pavement

- Steel surface treatment


- Mechanical devices

- Bridge bearings

- Expansion joints

- Secondary steel structures


- Concrete cover in splash zone

- Hanger cables and Main cable wraps (for Suspension Bridge)

- Stay cables system (for Cable-stayed Bridge)

16

Target Reliability for Cable Components (1)

Target Reliability for Cable Components

To determine the target reliability for cable component, a different approach isconducted due to the highly empirical nature of the current levels of safetyfactors for the cables. Thus the reliability assessment for cable element of thebridge should be preceded.

The reliability indices are 13.25~13.70 in main cable of suspension bridge and9.41~9.50 in stay cable of cable-stayed bridge by the reliability assessmentcorresponding to design safety factors 2.5 and 2.2, respectively.

Considering the decrease in variability due to the increase in main span lengthand the secondary stresses of main cable, it is reasonable that the targetreliability for main cable of suspension bridge could be determined around 12,corresponding to design safety factor of 2.2.

Considering the decrease in variability due to the increase in main span lengthand the possibility of replacement, it is reasonable that the target reliability forstay cable of cable-stayed bridge and hanger rope of suspension bridge could bedetermined around 8.5, corresponding to design safety factor of 2.0.

17


Reliability Assessment for Cable Elements

Because the cable-supported bridge shows the geometrical nonlinearbehavior, the traditional reliability analysis method, which is applied to theordinary bridge or the linear system, cannot appreciate the behavior of thecable-supported bridge sufficiently.

Table 5 summarizes the reliability analysis method for the cable-supportedbridge.

Table 5 : Evaluation of Reliability Indices for Cable Elements (Nonlinear Analysis)

- Limit State Function

- Sensitivity of Response Function

wDC , wDW , wVL Component wcable Component

- Sensitivity of Limit State Function Cu

Afg

=∂∂

wu

uT

w)u(T

w ∂∂

∂∂

−=∂

∂−=

∂∂g

),,,()( VLcableDWDCu wwwwTfRg −=

wP

wuK

wuK

wF

wuK

∂∂

=∂∂

+∂∂

=∂∂

+∂∂ ∑∑

e

eet

CFe

ec

F )(

( )wPKK

wu

∂∂

+=∂∂ −1t

CF

0=∂∂

+∂∂ ∑

e

ec

F wF

wuK

( ) ( )

+

∂∂

∂∂

−−+=

∂∂ − e

cable

ecable

e

ec

ec

CFcable

L

w

ww 0

T1 1000000

0φ

φ

kkKKu

18


Reliability Assessment for Main Cable of Suspension BridgesCorresponding to Design Safety Factors

(a) Yi Sun-Sin Bridge (Suspension Br.) (b) New Millennium Bridge (Suspension Br.)

Fig. 1: Reliability Indices of 2 Suspension Bridges by Nonlinear Analysis

10

12

14

16

0 500 1000 1500 2000

Reilia

bility

inde

x

10

12

14

16

0 500 1000 1500

Relia

bility

inde

x

βmin=14.03Real Resistance

S.F.=2.5

S.F.=2.2

S.F.=2.0

βmin=13.25

βmin=11.90

βmin=10.72

βmin=13.72

βmin=13.70

βmin=12.33

βmin=11.13

19


Reliability Assessment for Stay Cable of Cable-stayed BridgesCorresponding to Design Safety Factors

(a) Hwayang Bridge (Cable Stayed Br.) (b) Mokpo Bridge (Cable Stayed Br.)

Fig. 2: Reliability Indices of 2 Cable-stayed Bridges by Nonlinear Analysis

S.F.=2.2S.F.=2.0S.F.=1.8

βmin=9.54βmin=8.32βmin=7.00

βmin=9.41βmin=8.20βmin=6.90

βmin=9.92 βmin=14.79

Real Resistance

20

Target Reliability in General

Target Reliability for Variable Structural Components

The target reliability in design life and the corresponding 1-year probability offailure of variable structural components are as follows:

Table 6 : Target reliability for Design Life

Structural Component

Based on 1-year time Period

Target Reliability Based on Design Life

Target Reliability


20 year

30 year

50 year

100 year

200 year

ReplaceableComponent

Stay cable and Hanger Rope 9.09 4.74×10-20 8.76 8.72 8.66 8.58 8.50

Other Components (20 year) 4.66 1.58×10-6 4.00 3.90 3.78 3.60 3.42



Repairable&

Permanent Component

Main Cable 12.43 8.88×10-36 12.19 12.16 12.11 12.06 12.00

Other Components 5.11 1.58×10-7 4.52 4.43 4.32 4.16 4.00

21

I

II



Introduction

IV Conclusion

22

Safety Factor Format

Safety factor format The safety factor format for the design of the LSCSBs adopts similar concepts

to the recently issued domestic bridge design code , KBDC-LSD (2012)

The design resistance for the concrete member is obtained by applying the

material resistance factors φk to the characteristic values of the material

strength Xk .

The design resistances of other members are obtained by applying the

member resistance factor φ to the nominal member strength Rn .

rimpii RQ φγ ≤∑

}{ kkr XRR φ=

kr RR φ=

23

Load Combinations & Load Factors (1)

Load Combinations

The load combinations and the resistance factors for the proposed design

manual for the LSCSB are based on those of the KBDC-LSD (2012).

The load combination for live load is 1.25D1 + 1.5D2 + 1.8(L+I) in which D1 is

the dead load, D2 is the weight of the wearing surface, L is the live load and I is

the impact.

The wind load combination is 1.25D1 + 1.5D2 + 1.4W in which W is the wind

load.

The earthquake load combination is 1.0D + 1.0EQ with EQ denotes the

earthquake load.

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Load Combinations & Load Factors (2)

Load Combinations & Load Factors

Table 7 : Load Combination

Limit States

Permanent Loads

Variable LoadsAccidental Loads

Live Wind/Wave Others

DC DW L+I WS WL WP FR WA CR/SH TU TG SD EO PS1 EQ IC CT CV PS2

Ultimate I γD

1.8 - - - 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 - - - - - -

Ultimate II γD

1.4 - - - 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 - - - - - -

Ultimate III γD

- γWS

- 1.0 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 - - - - - -

Ultimate IV γD

- 1.0 - 1.4 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 - - - - - -

Ultimate V γD

1.4 0.4 1.0 - 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 - - - - - -

Ultimate VI γD

1.5 - - - 1.0 1.0 0.5/1.2 0.5/1.2 γTGγ

SE1.0 1.0 - - - - -

Accidental I γD

γEQ

- - - - 1.0 - - - - - - 1.0 - - - -

Accidental II γD

0.50 - - - - 1.0 - - - - - - - γIC

- - -

Accidental III γD

0.50 - - - - 1.0 - - - - - - - - 1.0 - -

Accidental IV γD

0.50 γCV

γCV

γCV

- 1.0 - - - - - - - - - 1.0 -

Accidental V γD

0.75 - - - - 1.0 - - - - - - - - - - 1.0

25

Resistance Factors (1)

Member & Material resistance factors

For the steel and cable members, the member resistance factors are defined

and the material resistance factors are set to unity.

For the concrete members, the material resistance factors are defined and the

member resistance factors are set to unity.

Table 8 : Resistance Factors for the Ultimate Limit State

Type Member Resistance Factor f Material Resistance Factor fk

Steel

Flexure 1.00

1.00Shear 1.00

Compression 0.90

CableMain cable for Suspension Br. 0.58~0.68

1.00Stay Cable and Hanger Rope 0.67~0.73

Concrete 1.00Concrete 0.65

Rebar or PS tendon 0.95

26

Resistance Factors (2)

Table 9 : Structural Importance Factor

Structure TypeOrdinary Bridge Long-Span Cable-Supported Bridge

Target ReliabilityImportance Factor, 𝜙𝜙imp

Target ReliabilityImportance Factor, 𝜙𝜙imp

Steel Girder3.72

1.04.0

0.95

RC Pylon 1.0 0.85

Importance factors

The target reliability level for the steel girder and the concrete pylon is 4.0

which is larger than 3.72 of ordinary bridge members.

The importance factors are selected in order to achieve the corresponding

target reliability level of the major structural component for the LSCSB.

The importance factor of 0.95 for the steel girder and 0.85 for the concrete

pylon ensure the reliability index above 4.0, if the member and material

resistance factor are set up by target reliability of 3.72.

27

Statistical Properties (1)

Statistical properties of design parameters The statistical characteristics for the material strength are obtained by

collecting the material test data from domestic construction sites and steel

manufacturing companies.

The goodness-of-fit tests such as the Chi-square test and the Anderson-

Darling test are performed in order to find the proper distribution type for the

data. Most data satisfy the normal distribution and lognormal distribution.

Concrete CDF Rebar CDF Goodness-of-fit test for cable

28


Statistical properties of member strength The strength and the statistical properties of RC pylon section are calculated

by writing a computer program. Typical shapes of the pylon section can be

analyzed.

Fig. 3: Input and Output of PM Diagram and Statistical Characteristics for RC Pylon

29


Typical shapes of RC pylon

Solid sections : rectangular, circle, track, octagon

Hollow sections : rectangular, circle, track, octagon

30

I

II



Introduction

IV Conclusion

31

Conclusion

The ongoing research project for the development of the design manualof the long-span cable-supported bridge is presented.

The target safety level is increased considering the importance of thestructure and the design safety factors are calibrated by the reliabilityanalysis.

The reliability levels of the major members of the cable-supportedbridge are obtained by applying to the actual cable-supported bridgesand the corresponding safety factors to fulfill the required reliabilitycould be decided.

Because the reliability level of the cable component designed by thecurrent safety factor is very high compared with that of other maincomponents, there are some demands to lower the target reliability ofthe cable.

32

References

Gulvanessian, H., Calgaro, J.-A. and Holicky, M., Designers’ Guide To EN 1990, Eurocode: Basis of

structural Design, Thomas Telford, London, 2002.

AASHTO, LRFD Bridge Design Specifications, American Association of State Highway and

Transportation Officials, 5th ed., Washington, D.C., 2010.

MLTM, Highway Bridge Design Code (Limit State Design Method), Korea Ministry of Land,

Transportation and Maritime Affairs, Seoul, 2012.

FIB (2010), Model Code 2010 Volume 1, International Federation for Structural Concrete, pp. 75-102.

Paik, I., Shim, C., Chung, Y. and Sang, H., “Statistical Properties of Material Strength of Concrete, Re-

Bar and Strand Used in Domestic Construction Site”, Journal of the Korea Concrete Institute, Vol. 23, No.

4, 2011, pp. 421-430.

Nowak, A. S., Calibration of LRFD Bridge Design Code, NCHRP Report 368, Transportation Research

Board, Washington DC, 1999.

design life and reliability-based design concept for long-span cable...

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