fatigue of metallic bridges: the role of structural health ... · role of structural health...

Fatigue of metallic bridges: the

role of structural health

monitoring in assessment and

life prediction

Marios K Chryssanthopoulos

Growth of UK Transport Systems R

ou

te K

ilo

metr

es

(Bayliss, 2008)

1840 1848

Road

Rail

Pipeline

Water

(DoT/ORR/DECC, 2012)

Domestic goods moved by mode

• More than 15,000 metallic bridges on the network

• Most constructed between 1850 and 1900

• Wrought iron & early steel

• Riveted construction (built-up members)

• Lean structures, individually sized elements

• Mostly short-span (~ 10-15m)

• Not designed for fatigue

Metallic railway bridges

Age of UK Bridge Stock

0

10

20

30

40

50

60

70

80

90

100

1800 1840 1880 1920 1960 2000

Oxfordshire

Network Rail

Highways Agency

(Darby, 2001)

Perc

en

tag

e C

on

str

ucte

d

Metallic railway bridges

Wrought iron

Deterioration and Damage

Corrosion

Fatigue crack

Loss of rivet

Railway loading

Freight (1900-1940)

Freight (1940-1970)

Freight (contemporary)

(BBC, Network Rail)

Extreme Weather

Network complexity

Major Challenges

Ageing &

Deterioration

Inter-

dependency

MAINTENANCE

& RENEWAL

Are assets

safe?

If so, for how

long? At what cost? UNCERTAINTY

Short-span railway bridge

Railway bridge under cyclic load

Connection ranking

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

S7-S

5

S8-S

6

S3-S

5

S4-S

6

S6-S

8

S5-S

7

S7-S

9

S8-S

10

S3-S

1

S6-S

4

S4-S

2

S5-S

3

S2

S1

S10

S9

Tota

l fa

tigue d

am

age

Connection

Modified Class B Class WI Class D

Global-local modelling

0

1

2

3

4

Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Rivet 1 Rivet 2 Rivet 3 Rivet 4 Rivet 5 AngleFillet

Dl/ D

g

100 MPa 200 MPa

Global model damage

>1

00 y

rs

>1

00

yrs

>10

0 y

rs

>10

0 y

rs

>10

0 y

rs

>1

50

yrs

>1

50

yrs

>1

50

yrs

7 y

rs

12

yrs

81

yrs

30

yrs

84

yrs

39

yrs

73

yrs

73

yrs

Connection element ranking

Damage scenarios

Fatigue ranking

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

S7-S

5

S8-S

6

S3-S

5

S4-S

6

S6-S

8

S5-S

7

S7-S

9

S8-S

10

S3-S

1

S6-S

4

S4-S

2

S5-S

3

S2

S1

S10

S9

Tota

l fa

tigue d

am

age

Connection

Modified Class B Class WI Class D

Global Local

Identify most critical

connections in bridge

Identify most critical regions

in connection itself

Inspection

and SHM

0

1

2

3

4

Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Rivet 1 Rivet 2 Rivet 3 Rivet 4 Rivet 5 AngleFillet

Dl/ D

g

100 MPa 200 MPa

Global model damage

>1

00 y

rs

>10

0 y

rs

>10

0 y

rs

>10

0 y

rs

>10

0 y

rs

>15

0 y

rs

>1

50

yrs

>1

50

yrs

7 y

rs

12

yrs

81

yrs

30

yrs

84

yrs

39

yrs

73

yrs

73

yrs

Fatigue life:

challenges and opportunities

• Understand the past

• Establish the present

• Predict the future

Time Present

Accumulated damage

Fatigue

Damage Failure

Remaining life

Probabilistic fatigue analysis

• Loading Uncertainties

Dynamic amplification factor (DAF)

Annual train frequency (fti )

• Material Uncertainties

S-N curve (fatigue behaviour)

Damage index Δ in Miner’s sum (fatigue failure limit)

• Model Uncertainties Factor accounting for the differences between measured and

calculated stresses in metallic bridges

Railway loading

Historical

(1900-1970)

BS 5400

(1970- )

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

Stress range (MPa)

Nu

mb

er

of

ap

plied

cycle

s

Modified Class B

fatigue limit

Class WI

fatigue limit

Class D

fatigue limitMean = 5.79 MPa

CoV = 1.09

Weibull distribution parametersη=6.02 , β=1.0

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

8.0E+05

9.0E+05

1.0E+06

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

Stress range (MPa)

Nu

mb

er

of

ap

plied

cycle

s

Modified Class B

fatigue limit

Class WI

fatigue limit

Class D


CoV = 0.84


0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

Stress range (MPa)

Nu

mb

er

of

ap

plied

cycle

s

Modified Class B

fatigue limit

Class WI

fatigue limit Class D


CoV = 0.64


0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100

Stress range (MPa)

Nu

mb

er

of

ap

plied

cycle

s

Modified Class B

fatigue limit

Class WI

fatigue limit

Class D


CoV = 0.75


1900-1920

Probabilistic load spectra 1920-1940

1940-1970 1970-

Cumulative damage of connection S7-S5 (Class WI)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1900 1920 1940 1960 1980 2000 2020

Year

Cu

mu

lati

ve

Da

ma

ge

No DAF Byers EC1 Tobias & Foutch D23 Network Rail

21-31 yrs

120 yrs

No DAF

With DAF

Damage accumulation

0.000001

0.00001

0.0001

0.001

0.01

0.1

-50 0 50 100 150 200 250 300 350 400 450 500 550 600

Time after 2004 (years)

Pro

ba

bil

ity

of

fail

ure

Pf

Base Model Base model with mean DAF=1.20 Base Model with mean DAF=1.05

2.3% probability of failureMean = 412.8 years

CoV = 0.612

Mean = 891.3 years

CoV = 0.592

200 100 0

0.1

0.01

0.0001

300

0.001

0.00001

Fatigue life prediction

No. of Years after 2004

Annual P

robabili

ty o

f F

ailu

re

400 500

6,000 bridges = 100,000 connections

900

10

1

Load evolution

System analysis of connections

Main findings

• Inner stringer-to-cross-girder connections are fatigue critical.

• Significant increase in damage accumulation during the last decades.

• Load evolution has a considerable effect on fatigue life, especially when

associated with increased axle loads.

• System effects are beneficial but difficult to quantify in practice.

• Many connections approaching the end of their fatigue life → timely

management of repair/replacement is essential.

• High uncertainty in fatigue life predictions → importance of inspection and

structural health monitoring.

Bridge Monitoring

• Global monitoring

– Train loads and frequencies

– Dynamic amplification factor

– Model ‘bias’

• Local monitoring

– Hot spot stresses (S-N)

– Local strain distributions (connection failure)

– Cracks (fracture mechanics)

‘stock’ benefit

‘critical

asset’

benefit

Composite Patching

Fatigue crack growing from a

notch in the bottom flange

0 0.5 1 1.5 2

x 105

20

22

24

26

28

30

32

Number of cycle

Cra

ck length

[m

m]

BEAM2RP-BASIC

Crack#1

Crack#2

Crack#3

Crack#4

FEA prediciont UNPATCH

Composite patch delays

crack propagation rate

Composite Patching

Number of cycles

Cra

ck l

en

gth

(m

m)

Patch applied

-60

-55

-50

-45

-40

-35

1530 1535 1540 1545 1550 1555 1560

Wavelength, nm

Inte

ns

ity

, d

B

51,000

-60

-55

-50

-45

-40

-35

1530 1535 1540 1545 1550 1555 1560

Wavelength, nm

Inte

ns

ity

, d

B

40,000

-60

-55

-50

-45

-40

-35

1530 1535 1540 1545 1550 1555 1560

Wavelength, nm

Inte

ns

ity

, d

B

34,000

Incr

easi

ng C

ycl

es

• Use of Chirped Fibre Bragg Grating sensor to monitor disbond

• Successful applications: – composite-composite and

composite-metal bonded joints

– Detecting defects in poorly bonded joints

Monitoring Disbond in Composite Patches

#1#2

AB

#1

Web breathing

Crocetti, 2009

GFRP bonded stiffeners

- cure at room temp.

- 1 bar vacuum for 24h

Composite stiffeners

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

50

100

150

200

250

300

350

Axial strain [%]

Load [kN

]

A

B

Composite stiffeners

Before

stiffening

After

stiffening

Web buckling

Repair monitoring

• Metallic panel

– Deformation

– Cracking

• Bonded joint

– Workmanship

– Durability

– Disbond

– Temperature

– Humidity

– Wet-dry cycling

direct

indirect

4

3

The Great Belt Bridge (DK):

› - Inaugurated in 1998

- 1624m main span

- Orthotropic steel deck

- Concrete towers

- 3rd longest suspension bridge

- Instrumented with a SHMS

SHM of welded joints in

long-span bridges

Asset management context

4

4

- Short-span bridge

- Long-span bridge

- Tunnel

- Dam

- Offshore wind turbine

…

Structural type

Deterioration:

- Fatigue

- Corrosion

- Wear and tear

- Extreme events,…

Component:

- Welded joint, cable, expansion joint,

Component and deterioration mechanism

- Design verification

- Service-life prediction

- Abnormal behaviour identification

- Support to Operation & Maintenance

- Etc…

Asset Management

Objectives

- Inspection

- Repair

- Maintenance

- Life extension

- Traffic disruption

Asset Management

actions/decisions

- Type of sensor: SG, thermometers, traffic classification

- Number of sensors: 20

- Location of sensors: 3

- Data acquisition: permanent monitoring/periodic

- Performance indicator: SN fatigue loading, fatigue lives

- SHM approach:

- Data-based / model-based

- Global / local

- Tools:

- Regression models, tim-series models, MCS, FFT, SSI, Bayesian networks, SRM, etc,,,

SHM strategy and tools

› A local, data-based

approach

› Study of critical components

and relevant deterioration

mechanisms.

› "Damage" locations are

assumed a-priori.

4

5

Asset management objectives

›Performance prediction (prognostics) › AIM: Determination of remaining fatigue lives.

› Short-term monitoring campaigns. Long-term infrastructure management.

› Performance assessment (diagnostics) › AIM: Determine if the component is behaving as expected.

› Continuous monitoring data. Short-term infrastructure management.

data interpretation)

Development of SHM Strategy

4

6

Fatigue Performance Indicators

Crack Size

Ds3

Modal

Frequency …..

Monitored

parameters SHM

technologies

…… Strain

Traffic Temperature

Camera

strain / temp. sensors

….

Methods and tools:

› Time-series models

› Regression models

› Statistical control charts

› Monte Carlo Simulation

SHM strategy

SHM system: location of sensors

4

7

Temp. section: T1,T2 Temp. section: T3,T4

E W

Strain section:

1624 m

Temperature section Temperature section

Focus: welded joints of the orthotropic deck

4

8

trough-to-deck weld

trough splice weld

SHM system: representative outcomes

4

9

06-May 13-May

5

10

15

20

25

30

35

40

45

Date

Hourly-a

vera

ged T

S9901

S9902

S9903

S9904

Pavement temperatures

09/09 09/16 09/23 09/30 10/07

100

101

102

103

104

Date

Vehic

les/h

Class 2

Class 3

Class 5

Vehicle classification

00:00 05:00 10:00 15:00 20:00-8

-6

-4

-2

0

2

4

6

8

10

12x 10

-5

Time [hour]

Str

ain

[-]

Strains

0 1 222

24

26

28

30

32

34

36

38

40

Time [seconds]

Str

ess [

MP

a]

2nd axle

1st axle

3rd axle4th axle5th axle

Data-based modelling

5

0

𝐷Δ𝑡(𝑡) = Δ𝜎𝑖3

𝑁𝑐

𝑖=1

› Performance indicator: Fatigue loading

› Characterization of the correlation patern among heavy traffic counts, pavement temperature and fatigue loading at welded joints.

› Time discretization

Daily count heavy vehicles

𝐷𝛥𝑡 𝑡

𝐵Δ𝑡(𝑡)= 𝜃𝑖−1

𝑝+1

𝑖=1

⋅ 𝑇Δ𝑡(𝑡)𝑖−1

Fatigue loading

Daily-averaged pavement temperature

Regression parameters

Model training

5

1

-10 -5 0 5 10 15 20 25 300.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

4

TDt

[ C]

DD

t / B

Dt

95% pred. band

95% conf. band

monitoring observation

regression line

01/05/11 08/05/11 15/05/11

2

4

6

8

10

12

14

x 106

time [day]

DD

t [MP

a3 ]SG2

95% pred. band

monitoring observation

model prediction

Model validation

5

2

5

3

Temperature modelling

› Autoregressive models of 1st order to model de-seasonalized daily-averaged

pavement temperatures Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan-10

0

10

20

30

40

T [

C]

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan-10

0

10

20

30

40

T [

C]

𝑇 𝑡 = 𝛼1 ⋅ 𝑠𝑖𝑛 𝛼2 ⋅ 𝑡 + 𝛼3 +𝑚𝑇

𝑇𝑡∗ =𝑇Δ𝑡(𝑡) − 𝑇 𝑡𝜎𝑇,𝑡

𝑇𝑡∗ = 𝜑𝑇,1 ⋅ 𝑇𝑡−1

∗ + 𝜖𝑇,𝑡

5

4

𝐵𝑡∗ =𝐵Δ𝑡(𝑡) − 𝜇𝐵,𝑡𝜎𝐵,𝑡

Traffic modelling

› De-seasonalization of heavy traffic daily counts

› Regression models to account for day-of-the-week and holiday effects

› Autoregressive models fitted to the residuals of the regression models.

May 2008 Jun 2008 Jul 2008 Aug 2008

500

1000

1500

2000

2500

BD

t [veh./day]

Time

Observation

model prediction

𝐵𝑡∗ = 𝜆1 + λ2X2,𝑡 +⋅⋅⋅ +λ𝑘𝑋𝑘,𝑡 + ϵB,t

𝜖𝐵,𝑡 = 𝜑𝐵,𝑖 ⋅ 𝜖𝐵,𝑡−𝑖

𝑝

𝑖=1

+ 𝜈𝑡

Application 1: Fatigue life prediction

5

5

55 0 100 200 300 400 500 600 700 800 900 1000

0

2000

4000

6000

8000

10000

12000

Monte Carlo Simulation

t f [years

]

102

103

104

105

0.0005

0.005

0.05

0.25

0.5

0.75

0.95

0.995

0.9995

Data

Pro

bability

0 100 200 300 400 500 600 700 800-20

0

20

40

T24h [ C

]

0 100 200 300 400 500 600 700 8000

1000

2000

3000

4000

B24h [veh./h]

0 100 200 300 400 500 600 700 8000

2

4

6

8

10

12

14x 10

6

D24h [M

Pa3

]

Time [days]

0 100 200 300 400 500 600 700 800-20

0

20

40

T24h [ C

]

0 100 200 300 400 500 600 700 8000

1000

2000

3000

4000

B24h [veh./h]

0 100 200 300 400 500 600 700 8000

2

4

6

8

10

12

14x 10

6

D24h [M

Pa3

]

Time [days]

0 100 200 300 400 500 600 700 800-20

0

20

40

T24h [ C

]

0 100 200 300 400 500 600 700 8000

1000

2000

3000

4000

B24h [veh./h]

0 100 200 300 400 500 600 700 8000

2

4

6

8

10

12

14x 10

6

D24h [M

Pa3

]

Time [days]

Simulation of actions, i.e. traffic and temperature

(time-series models)

Simulation of fatigue loading

(regression models) Monte Carlo simulation: time to failure

realizations (S-N LSF)

0 50 100 1502

4

6

8

10

12

14

Time [years]

SG 1

SG 3

SG 4

SG 6

SG 7

SG 9

*=3.8

Fatigue life prediction

(reliability profile)

Application 1: Fatigue life prediction

5

6

› Assessment of the impact of different scenarios of pavement

temperatures (climate change) and heavy traffic intensities.

› Easy-to-understand output: fatigue lives [years]

› Tool for informing long-term infrastructure management decisions

(e.g. inspection scheduling).

Application 2: Performance assessment

5

7

04/29 05/06 05/13 05/20

-6

-4

-2

0

2

4

6

Norm

aliz

ed r

esid

uals

99 % LCL

99 %UCL

15/05/2012

› Detection of abnormal behaviour on

15/05/2012.

› Cause: Diversion of traffic due to

maintenance activities.

› Development of an algorithm for identifying abnormal behaviours based on statistical control charts of the regression models.

𝑍 ≃ 𝜃𝑖−1

𝑝+1

𝑖=1

⋅ 𝑇0𝑖−1 −𝐷Δ𝑡 𝑇0𝐵Δt 𝑚𝑜𝑛𝑖𝑡𝑜𝑟𝑒𝑑

⋅1

𝑠𝑡𝑜𝑡2

Concluding remarks

• SHM should be requirement-pull not technology-push

• SHM strategies depend on the Asset Management

objectives and constraints

• Key for exploitation of SHM in civil structures is the

chain from Data to Information to Knowledge

• Traffic light concept:

Healthy - Concern - Faulty

• Beware of Infobesity "As long as the centuries continue to

unfold, … one can predict that a time will

come when it will be almost as difficult to

learn anything from books as from the

direct study of the whole universe. Diderot,

"Encyclopédie" (1755)

fatigue of metallic bridges: the role of structural health ... · role of structural health...

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