calculating a bridge assessment dynamic ratio using a bridge weigh-in-motion system jason dowling...

Calculating a Bridge Assessment Dynamic Ratio Using a Bridge Weigh-In-Motion system

Jason Dowling

Young Researchers Seminar 2009Torino, Italy, 3 to 5 June 2009

Overview

1. Bridge Weigh-In-Motion

2. Model Description

3. Assessment Dynamic Ratio

4. Theoretical Simulations - New Algorithm

5. Conclusions

Calculating a Bridge ADR Using a B-WIM system

Jason Dowling

Instrumented Bridges....

Bridge Weigh-In-Motion


Jason Dowling

Moses Algorithm (1979)



Jason Dowling

Typical ‘Measured’ Response, Mme...


0 5 10 15 20 25 30 35 40-2

0

2

4

6

8

10

12

14

16x 10

5

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)


Jason Dowling



Jason Dowling

0 5 10 15 20 25 30 35-1

0

1

2

3

4

5

6

7

8

9

10Influence Line Ordinates

Distance (m)

Influ

ence

Lin

e O

rdin

ate x

Mth...

Moses Algorithm (1979)

Matrix solution technique:



Jason Dowling

Truck Model...

Model Description


Jason Dowling

Road ‘Carpet’ Profile

Model Description


Jason Dowling

Statistical Data - GVW & Velocity - Axle Spacing & Axle Weights

Model Description


Jason Dowling

Definition:

associated with a return period

i.e. not a single event.

Assessment Dynamic Ratio (ADR)


Jason Dowling

Source: SAMARIS (2006)

Trends in ADR


Jason Dowling

Source: OBrien et. al (2009)

Trends in ADR


Jason Dowling

0 1 2 3 4 51

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

No. of trucks (× 106)

AD

R

0 500 1000 1500 2000 2500

2.3

2.4

2.5

2.6

2.7

2.8

2.9

No. of Days

Max

imum

Ben

ding

Mom

ent

(Nm

× 1

06 )

ADR

Max Dynamic

Max Static

10 years...

(500,000trucks/year)

25m BridgeClass ‘A’

Theoretical Simulations - ADR


Jason Dowling

0 1 2 3 4 51

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08


AD

R

0 500 1000 1500 2000 2500

2.3

2.4

2.5

2.6

2.7

2.8

2.9

No. of Days

Max

imum

Ben

ding

Mom

ent

(Nm

× 1

06 )

ADR

Inferred ADR

Max Dynamic

Max Static

Max Inferred Static

10 years...

(500,000trucks/year)




Jason Dowling

50 years




Jason Dowling

0 0.5 1 1.5 2 2.51

1.02

1.04

1.06

1.08

1.1


AD

R

2,500 5,000 7,500 10000 12500

1.8

2

2.2

2.4

2.6

2.8

3

No. of Days

Max

imum

Ben

ding

Mom

ent

(Nm

× 1

06 )

ADR

Max Dynamic

Max Static

50 years




Jason Dowling

0 0.5 1 1.5 2 2.51

1.02

1.04

1.06

1.08

1.1


AD

R

2,500 5,000 7,500 10000 12500

1.8

2

2.2

2.4

2.6

2.8

3

No. of Days

Max

imum

Ben

ding

Mom

ent

(Nm

× 1

06 )

ADR

Inferred ADR

Max Dynamic

Max Static

Max Inferred Static

SimulationVariability...

Five 10 yearsimulations



Jason Dowling

0 500 1000 1500 2000 25001.02

1.025

1.03

1.035

1.04

1.045

1.05

1.055

1.06

1.065

No of Trucks

AD

R

Tendency to under-weigh Steer Axle...

Theoretical Simulations - Errors...


Jason Dowling

0 10 20 30 40 50 60 70 80 90 1000.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Truck

Err

orAxle 1

Axle 2

Cause of under-estimation of ADR...

Theoretical Simulations - Errors...


Jason Dowling

0 10 20 30 40 50 60 70 80 90 1000.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Truck

Max

imum

Sta

tic E

rror

Dynamic Response - Time & Freq. Domains

Theoretical Simulations - New Algorithm


Jason Dowling

0 0.5 1 1.5-1

0

1

2

3

4

5

6

7

8

9

Time (s)

Ben

ding

Mom

ent

(Nm

× 1

05 )

Time Domain

0 5 10 15 200

1

2

3

4

5

6Frequency Domain

Frequency (Hz)

Am

plitu

de (

× 1

05 )

10 Responses represented in the Freq. Domain



Jason Dowling

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12Frequency Domain

Frequency (Hz)

Am

plitu

de (

× 1

05 )

Filtered Response - Time & Freq Domains



Jason Dowling

0 0.5 1 1.5-1

0

1

2

3

4

5

6

7

8

Time (s)

Ben

ding

Mom

ent

(Nm

× 1

05 )

Time Domain

0 5 10 15 200

1

2

3

4

5

6x 10

5 Frequency Domain

Frequency (Hz)

Am

plitu

de (

× 1

05 )

Incorporating filtering of dynamic signal...



Jason Dowling

0 4 8 12 16 200

1

2

3

4

5

6x 10

5

Frequency (Hz)

Am

plitu

de (

× 1

05 )Original Signal

Filtered Signal

‘Measured’ Influence Line



Jason Dowling

0 5 10 15 20 250

1

2

3

4

5

6

7

Bridge Length (m)

Influ

ence

Ord

inat

e

Filtered Measured

Ideal



Jason Dowling

x

New Mth...

Static BM using New Approach



Jason Dowling

0 5 10 15 20 25 30 35 40-1

0

1

2

3

4

5

6

7

8

9


Ben

ding

Mom

ent

(Nm

×

105 )

Total

Correct StaticInferred Static- New Method

Inferred Static- Classic Alg

Example 1:

10 years...



Jason Dowling

0 1 2 3 4 51

1.01

1.02

1.03

1.04

1.05

1.06

1.07


AD

R

ADR - Exact

ADR - New Algorithm

ADR - Classic Algorithm

Example 2:

10 years...



Jason Dowling

0 1 2 3 4 51

1.01

1.02

1.03

1.04

1.05

1.06

1.07


AD

R

ADR - Exact

ADR - New Algorithm

ADR - Classic Algorithm

Max Static BM Errors using New Approach...



Jason Dowling

0 10 20 30 40 50 60 70 80 90 1000.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Truck

Max

imum

Sta

tic E

rror

New Algorithm

Classic Algorithm

Worst Case...

Worst Case: Max Static BM Error...



Jason Dowling

0 5 10 15 20 25 30 35 40-0.5

0

0.5

1

1.5

2

2.5


Ben

ding

Mom

ent

(Nm

× 1

06 )

Total

Static - ExactStatic - New Alg

Static - Old Alg

Worst Case: Max Static BM Error...



Jason Dowling

0 5 10 15 20 25 30 35 40-0.5

0

0.5

1

1.5

2

2.5


Ben

ding

Mom

ent

(Nm

× 1

06 )

Total


Static - Old Alg

15 17 19 21 23 252

2.1

2.2

2.3

2.4


Ben

ding

Mom

ent

(Nm

× 1

06 )

Total


Static - Old Alg

In Summary:

General ADR trends in keeping with recent findings...

The Classic Moses Algorithm over-estimates Maximum Static Strain...

Incorporating Filtering of the dynamic signal improves predictions...

Conclusions


Jason Dowling

My Thanks to the 6th European Framework Project ARCHES for funding my work.

Thank you for listening.


Jason Dowling

calculating a bridge assessment dynamic ratio using a bridge weigh-in-motion system jason dowling...

Documents