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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 systemJason Dowling
Instrumented Bridges....
Bridge Weigh-In-Motion
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Moses Algorithm (1979)
Bridge Weigh-In-Motion
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Typical ‘Measured’ Response, Mme...
Bridge Weigh-In-Motion
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
)
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Bridge Weigh-In-Motion
Calculating a Bridge ADR Using a B-WIM systemJason 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:
Bridge Weigh-In-Motion
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Truck Model...
Model Description
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Road ‘Carpet’ Profile
Model Description
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Statistical Data - GVW & Velocity - Axle Spacing & Axle Weights
Model Description
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Definition:
associated with a return period
i.e. not a single event.
Assessment Dynamic Ratio (ADR)
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Source: SAMARIS (2006)
Trends in ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
Source: OBrien et. al (2009)
Trends in ADR
Calculating a Bridge ADR Using a B-WIM systemJason 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 DynamicMax Static
10 years...
(500,000trucks/year)
25m BridgeClass ‘A’
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason 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 )
ADRInferred ADR
Max DynamicMax StaticMax Inferred Static
10 years...
(500,000trucks/year)
25m BridgeClass ‘A’
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
50 years
25m BridgeClass ‘A’
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 0.5 1 1.5 2 2.51
1.02
1.04
1.06
1.08
1.1
No. of trucks (× 107)
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 DynamicMax Static
50 years
25m BridgeClass ‘A’
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 0.5 1 1.5 2 2.51
1.02
1.04
1.06
1.08
1.1
No. of trucks (× 107)
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 )
ADRInferred ADR
Max DynamicMax StaticMax Inferred Static
SimulationVariability...
Five 10 yearsimulations
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason 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...
Calculating a Bridge ADR Using a B-WIM systemJason 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
Erro
rAxle 1Axle 2
Cause of under-estimation of ADR...
Theoretical Simulations - Errors...
Calculating a Bridge ADR Using a B-WIM systemJason 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
Calculating a Bridge ADR Using a B-WIM systemJason 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 (×
105 )
10 Responses represented in the Freq. Domain
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12Frequency Domain
Frequency (Hz)
Am
plitu
de (×
105 )
Filtered Response - Time & Freq Domains
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason 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 (×
105 )
Incorporating filtering of dynamic signal...
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 4 8 12 16 200
1
2
3
4
5
6x 10
5
Frequency (Hz)
Am
plitu
de (×
105 )
Original SignalFiltered Signal
‘Measured’ Influence Line
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 5 10 15 20 250
1
2
3
4
5
6
7
Bridge Length (m)
Influ
ence
Ord
inat
e
Filtered MeasuredIdeal
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
x
New Mth...
Static BM using New Approach
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 5 10 15 20 25 30 35 40-1
0
1
2
3
4
5
6
7
8
9
First Axle Distance (m)
Ben
ding
Mom
ent (
Nm
× 1
05 )TotalCorrect StaticInferred Static- New MethodInferred Static- Classic Alg
Example 1:
10 years...
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 1 2 3 4 51
1.01
1.02
1.03
1.04
1.05
1.06
1.07
No. of trucks (× 106)
AD
R
ADR - ExactADR - New AlgorithmADR - Classic Algorithm
Example 2:
10 years...
Theoretical Simulations - ADR
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 1 2 3 4 51
1.01
1.02
1.03
1.04
1.05
1.06
1.07
No. of trucks (× 106)
AD
R
ADR - ExactADR - New AlgorithmADR - Classic Algorithm
Max Static BM Errors using New Approach...
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason 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 AlgorithmClassic Algorithm
Worst Case...
Worst Case: Max Static BM Error...
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 5 10 15 20 25 30 35 40-0.5
0
0.5
1
1.5
2
2.5
First Axle Distance (m)
Ben
ding
Mom
ent (
Nm
× 1
06 )TotalStatic - ExactStatic - New AlgStatic - Old Alg
Worst Case: Max Static BM Error...
Theoretical Simulations - New Algorithm
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
0 5 10 15 20 25 30 35 40-0.5
0
0.5
1
1.5
2
2.5
First Axle Distance (m)
Ben
ding
Mom
ent (
Nm
× 1
06 )
TotalStatic - ExactStatic - New AlgStatic - Old Alg
15 17 19 21 23 252
2.1
2.2
2.3
2.4
First Axle Distance (m)
Ben
ding
Mom
ent (
Nm
× 1
06 )
TotalStatic - ExactStatic - New AlgStatic - 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
Calculating a Bridge ADR Using a B-WIM systemJason Dowling
My Thanks to the 6th European Framework Project ARCHES for funding my work.
Thank you for listening.
Calculating a Bridge ADR Using a B-WIM systemJason Dowling