Influence of the Accuracy of a Bridge Weigh-In-Motion System on the

Determination of a Bridge Assessment Dynamic Ratio

Jason DowlingArturo GonzálezEugene O’Brien

Quick Overview

- Bridge Weigh-In-Motion

- Model Description

- Assessment Dynamic Ratio - Bridge Weigh-In-Motion Accuracy

Bridge Weigh-In-Motion systems use instrumented bridges to collect data on the truck fleet at a specific location.

- This concept was first proposed by Moses (1979)

- Strain transducers are attached to the soffit of a bridge

- Axle detectors are placed on the road surface - An algorithm is used to interpret the data

Bridge Weigh-In-Motion

source: WAVE (2001)

Moses Algorithm (1979) remains the most popular algorithm used in Bridge Weigh-In-Motion systems.

- Based on minimizing the sum of squares of differences between theory and measurements:

Lots of measurements are available during the truck crossing...

- This is utilised to smooth out the dynamic component.

Bridge Weigh-In-Motion

Typical ‘Measured’ Response

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

)

Bridge Weigh-In-Motion

Theoretical Response

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

Bridge Weigh-In-Motion

Matrix Solution Technique

Minimizing the Error function,

gives a system of simultaneous equations in Wi

Where {W} is a vector of the desired axle weights

Bridge Weigh-In-Motion

Truck Model

- 8 Degrees of Freedom

Model Description

Data Used for simulations of truck crossings...

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

Model Description

Data Used for simulations of truck crossings...

Carpet Profile

Model Description

Model Accuracy Classification

COST323 (2002) proposed a method of classification for Bridge Weigh-In-Motion systems

- The models classification under this method is ‘B+(7)’

- Most individual axle weights predicted within ± 7%

- Axle group weights & GVW predicted within ± 5%

Model Description

Assessment Dynamic Ratio (ADR) is defined as:

Recent work has discovered a tendency for ADR to decrease as Return Period, or Load Effect increases.

i.e. Not necessarily associated with a single loading event

Assessment Dynamic Ratio

Trends in ADR with Time...

source: Rattigan (2007)

Assessment Dynamic Ratio

Trends in ADR with Time...

source: SAMARIS (2006)

Assessment Dynamic Ratio

Trends in ADR with Time...

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6

x 105

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

No. of trucks

AD

R

0 20 40 60 80 100 120 140 160 180

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

x 106

No. of Days

Max

BM

ADR

Max Dynamic

Max Static

0 5 10 15 20 25-0.5

0

0.5

1

1.5

2

2.5

3

3.5x 10

5

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)

Total

Correct StaticInferred Static

Assessment Dynamic Ratio

Inferred Static Response

0 5 10 15 20 25 30 35 40-2

0

2

4

6

8

10

12

14x 10

5

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)

Total

Correct StaticInferred Static

Bridge Weigh-In-Motion Accuracy

Inferred Static Response

0 5 10 15 20 25-0.5

0

0.5

1

1.5

2

2.5

3

3.5x 10

5

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)

Total

Correct StaticInferred Static

Bridge Weigh-In-Motion Accuracy

Inferred Static Response

12 14 16 18

2.2

2.4

2.6

2.8

3

3.2

x 105

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)

Total

Correct StaticInferred Static

Error in Maximum Static

0 5 10 15 20 25-0.5

0

0.5

1

1.5

2

2.5

3

3.5x 10

5

First Axle Distance (m)

Ben

ding

Mom

ent

(Nm

)

Total

Correct StaticInferred Static

Bridge Weigh-In-Motion Accuracy

Error in prediction of ADR

0 1 2 3 4 5 6 7 8

x 104

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

No. of Trucks

AD

R

Correct & Inferred

Exact

Inferred

Bridge Weigh-In-Motion Accuracy

In Summary:

Moses Algorithm tends to over estimate the maximum static response.

This leads to an underestimation of ADR

Future work will look at further understanding this inaccuracy

With a view to quantifying this or suggesting possible remediation measures...

My Thanks to the 6th European Framework Project ARCHES (Assessment and Rehabilitation of Central European Highway Structures) for funding my work.

Thank you for listening.