Reliability index after proof load testing: viaduct De Beek

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Proof load tests can be used for a field assessment of the bridge under study. This paper addresses the determination of the reliability index of an existing bridge by means of proof loading through the case study viaduct De Beek. The information of this bridge is used to determine the updated reliability index after proof load testing. A sensitivity study is carried out to identify the effect of the assumptions with regard to the coefficient of variation on the resistance and load effects. In the current practice of proof load testing with vehicles, it can typically only be demonstrated that a certain vehicle type can cross the bridge safely. The results in this paper provide a new insight on the updating of the reliability index after proof load testing. Consensus on the coefficients of variation that need to be used on the resistance and load effects, is still missing.

Ingénierie

Challenge the future
Delft
University of
Technology
Reliability index after proof load
testing: viaduct De Beek
Eva Lantsoght, Cor van der Veen, Dick Hordijk, Ane de Boer

2Reliability index after proof load testing: viaduct De Beek
Overview
• Introduction: load testing
• Reliability index after load
testing
• Viaduct De Beek
• Application of method to De
Beek
• Recommendations
• Summary and conclusions Testing of Ruytenschildt Bridge

3Reliability index after proof load testing: viaduct De Beek
Why load testing? (1)
Bridges from 60s and 70s
The Hague in 1959
Increased live loads
common heavy and long truck (600 kN)
End of service life + larger loads

4Reliability index after proof load testing: viaduct De Beek
Proof load testing of bridges
• Apply predetermined load to
bridge
• Information lacking
• Damage due to ASR, …
• Proof load testing
• Immediate approval of bridge
• Recalculate updated β

5Reliability index after proof load testing: viaduct De Beek
Reliability index after load testing
    1fb s RP F r f r dr


 
 fd R pP F s
 
    
1
1
1 p
fa s Rs
R p
P F r f r dr
F s
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6Reliability index after proof load testing: viaduct De Beek
Case study: viaduct De Beek
• RC slab bridge of 4 spans
• Insufficient flexural capacity
• Reduction of 2 lanes to 1
lane
• Proof load test at shear- and
flexure-critical position in
first span

7Reliability index after proof load testing: viaduct De Beek
Effect on reliability index
• g = R – S limit state function
• Before load test: β = 2.10
• After load test: β = 2.66
• Smaller than requirements:
RBK Usage β = 3.30
• But: choice of distribution
functions for existing bridges?

8Reliability index after proof load testing: viaduct De Beek
Sensitivity analysis (1)
COVR COVS Pfb βb Pfa βa
0.05 0.10 2×10-7 5.07 1.2×10-7 5.17
0.10 0.10 2.7×10-5 4.04 1×10-6 4.75
0.05 0.20 0.0022 2.84 0.0023 2.84
0.07 0.10 2.2×10-6 4.59 3.2×10-7 4.98

9Reliability index after proof load testing: viaduct De Beek
Sensitivity analysis (2)
• First analysis: based on
recommendations of JCSS
Not necessarily suitable for
existing bridges!
• Change values of COV: large
impact on β
• Recommended values for
existing bridges?
Recommendations of JCSS Model Code

10Reliability index after proof load testing: viaduct De Beek
Comparison to Unity Check
• For which values of COV are the results of probabilistic
method and Unity Check similar?
• See table: COV of R and S of 7%
• Further research needed for recommendations
mR COVR COVS Pfb βb
1.0 0.10 0.10 0.0098 2.34
1.0 0.05 0.10 0.0013 3.02
1.0 0.05 0.05 3×10-6 4.53
1.0 0.07 0.07 4.25×10-4 3.336

11Reliability index after proof load testing: viaduct De Beek
Summary and conclusions
• Proof load testing to approve existing
bridges
• Updating β after load testing
• Application of concepts to De Beek
• Using JCSS MC recommended
values: lower β than expected
• Value of COV to use?
• Sensitivity analysis: large effect of
COV
• First recommendation 7% COV on R
and S
Viaduct Zijlweg

12Reliability index after proof load testing: viaduct De Beek
Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec
+31(0)152787449

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Reliability index after proof load testing: viaduct De Beek

1. Challenge the future Delft University of Technology Reliability index after proof load testing: viaduct De Beek Eva Lantsoght, Cor van der Veen, Dick Hordijk, Ane de Boer

2. 2Reliability index after proof load testing: viaduct De Beek Overview • Introduction: load testing • Reliability index after load testing • Viaduct De Beek • Application of method to De Beek • Recommendations • Summary and conclusions Testing of Ruytenschildt Bridge

3. 3Reliability index after proof load testing: viaduct De Beek Why load testing? (1) Bridges from 60s and 70s The Hague in 1959 Increased live loads common heavy and long truck (600 kN) End of service life + larger loads

4. 4Reliability index after proof load testing: viaduct De Beek Proof load testing of bridges • Apply predetermined load to bridge • Information lacking • Damage due to ASR, … • Proof load testing • Immediate approval of bridge • Recalculate updated β

5. 5Reliability index after proof load testing: viaduct De Beek Reliability index after load testing     1fb s RP F r f r dr      fd R pP F s        1 1 1 p fa s Rs R p P F r f r dr F s     

6. 6Reliability index after proof load testing: viaduct De Beek Case study: viaduct De Beek • RC slab bridge of 4 spans • Insufficient flexural capacity • Reduction of 2 lanes to 1 lane • Proof load test at shear- and flexure-critical position in first span

7. 7Reliability index after proof load testing: viaduct De Beek Effect on reliability index • g = R – S limit state function • Before load test: β = 2.10 • After load test: β = 2.66 • Smaller than requirements: RBK Usage β = 3.30 • But: choice of distribution functions for existing bridges?

8. 8Reliability index after proof load testing: viaduct De Beek Sensitivity analysis (1) COVR COVS Pfb βb Pfa βa 0.05 0.10 2×10-7 5.07 1.2×10-7 5.17 0.10 0.10 2.7×10-5 4.04 1×10-6 4.75 0.05 0.20 0.0022 2.84 0.0023 2.84 0.07 0.10 2.2×10-6 4.59 3.2×10-7 4.98

9. 9Reliability index after proof load testing: viaduct De Beek Sensitivity analysis (2) • First analysis: based on recommendations of JCSS Not necessarily suitable for existing bridges! • Change values of COV: large impact on β • Recommended values for existing bridges? Recommendations of JCSS Model Code

10. 10Reliability index after proof load testing: viaduct De Beek Comparison to Unity Check • For which values of COV are the results of probabilistic method and Unity Check similar? • See table: COV of R and S of 7% • Further research needed for recommendations mR COVR COVS Pfb βb 1.0 0.10 0.10 0.0098 2.34 1.0 0.05 0.10 0.0013 3.02 1.0 0.05 0.05 3×10-6 4.53 1.0 0.07 0.07 4.25×10-4 3.336

11. 11Reliability index after proof load testing: viaduct De Beek Summary and conclusions • Proof load testing to approve existing bridges • Updating β after load testing • Application of concepts to De Beek • Using JCSS MC recommended values: lower β than expected • Value of COV to use? • Sensitivity analysis: large effect of COV • First recommendation 7% COV on R and S Viaduct Zijlweg

12. 12Reliability index after proof load testing: viaduct De Beek Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449

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