Application of Modified Bond Model to the capacity of Ruytenschildt Bridge

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The Ruytenschildt bridge in Friesland is a continuously supported concrete slab bridge, and was tested in two spans to failure in August 2014. The results of this experiment are valuable for the analysis of existing slab bridges and for analyzing the moment and shear capacity of reinforced concrete slabs and slab bridges. Earlier analyses found that a large number of existing slab bridges in The Netherlands rate as insufficient for shear. However, these analyses did not take into account the beneficial effect of transverse load redistribution. Therefore, the Modified Bond Model was developed. This model covers beam shear, punching shear and flexure for reinforced concrete slabs. The test results are now to compare to the predictions with the Modified Bond Model. Since the Modified Bond Model is independent of the failure mode, the maximum load that is found can be directly correlated to the maximum tandem load in the experiment. Comparing the test results on the bridge with the predictions based on the Modified Bond Model shows good correspondence. The results are also compared to a new proposal for vmin, the minimum shear stress at which shear failure takes place. For smaller value, a moment failure takes place. While the presented results only show a comparison between 2 tests on an existing bridge and the proposed Modified Bond Model, the results indicate that the Modified Bond Model can become a useful tool for design and analysis of reinforced concrete slabs based on the principles of the theory of plasticity.

Science

Challenge the future
Delft
University of
Technology
Application of Modified Bond Model
to capacity of Ruytenschildt Bridge
Eva Lantsoght, Cor van der Veen, Ane de Boer, Dick Hordijk

2
Overview
• Introduction to case
• Modified Bond Model
• Test results
• Comparison results and MBM
• Summary & Conclusions
Slab shear experiments, TU Delft

3
Proofloading
Case Ruytenschildt Bridge
• Proofloading to assess capacity of
existing bridge
• ASR affected bridges
• Insufficient information
• Study cracks and deformations for
applied loads
• Crack formation: acoustic emissions
measurements
• Control load process
• Ruytenschildt Bridge: testing to
failure

4
Proofloading Ruytenschildt Bridge
Existing bridge Partial demolition and building new bridge

5
Proofloading
Case Ruytenschildt Bridge

6
Bond Model (1)
• Alexander and Simmonds,
1990
• For slabs with
concentrated load in
middle

8
Modified Bond Model (1)
• Adapted for slabs with concentrated
load close to support
• Geometry is governing as in
experiments
• Determine factor that reduces capacity
of “radial” strip
• Maximum load: based on sum capacity
of 4 strips

9
Unequal loading of strips
• Static equilibrium
• v2,x reaches max before v1,x
'
1, 0.1667x c
a
v f d
L a



10
Loads close to free edge
Edge effect:
when length of strip is too small to develop loaded length lw

11
Cross-sections Ruytenschildt Bridge
• Testing in span 1 and span 2
• close to end support
• close to mid support
• Critical position for shear

12
Test results proofloading
Span 1
• Maximum load 3049 kN
• Maximum available load for span 1
• Flexural cracks
• No failure
• Order additional load for test 2!
• Prediction MBM: 2864 kN
• Tested/Predicted = 1.06
• Tested; not failure load
0
500
1000
1500
2000
2500
3000
3500
0 5000 10000 15000 20000 25000
Load(kN) time (s)

13
Test results proofloading
Span 2
• Maximum load 3991 kN
• Large flexural cracks
• Flexural failure
• yielding of reinforcement
• Settlement of bridge pier
with 1.5cm
• Elastic recovery to 8mm
• Prediction MBM: 3816 kN
• Tested/Predicted = 1.05
• Bent-up bars??
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 2000 4000 6000 8000 10000
Load(kN) Time(s)

14
Conclusions
• Ruytenschildt Bridge
• Testing to failure in 2 spans
• Measurements
• Modified Bond Model
• Plasticity-based model
• For analysis of capacity of slabs
• MBM shows good predictions of capacity
of bridge
• For limited number of field experiments

15
Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec
+31(0)152787449

In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge (reinforced with plain bars) in the Friesland province in the Netherlands was tested until failure. One of the goals of proof loading and testing this bridge to failure, was to study the failure mode of existing slab bridges. The combination of smaller shear capacities as prescribed by the Eurocode in combination with the heavier live load models, has raised concerns with regard to a number of existing slab bridges in the Netherlands. As the shear capacity of existing bridges is under study, the results of testing an actual slab bridge until failure are used to compare to the results of testing half-scale slab specimens in the laboratory, and the conclusions resulting from those experiments. In this paper, the results of the predictions based on the first order of approximation rating procedure from the Netherlands for shear, the Quick Scan method, as well as based on predictions of the failure mode and the average predicted capacity are compared to the experimental results. The predictions show a possibility of shear failure in the second span of the bridge. The experiment showed that both spans of the bridge failed in flexure. The observed failure mode is important, as some of the results indicate that the solid slab bridges, currently under discussion with regard to their shear capacity, fail in flexure in reality. Flexural failure is considered a ductile failure compared to the brittle failure mode in case of a shear failure.

Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

Eva Lantsoght

For the assessment of existing structures and the design of new structures, it is important to have a good understanding of the flow of forces, here applied to reinforced concrete solid slabs. Two analyti-cal methods are used: finite element models with 3D solid elements and a plasticity-based model that is suita-ble for hand calculations, the Modified Bond Model. The slabs that are modeled are half-scale models of rein-forced concrete solid slab bridges. As the Eurocode live load model prescribes more heavily loaded trucks in the first lane, the load model is asymmetric. For the finite element models, limited use is made of the redistri-bution capacity of the slab. For the Modified Bond Model, the influence of torsion and the edge effect need to be taken into account. The results of these studies improve the current state-of-the-art for analysis and design of reinforced concrete slabs.

Shear and moment capacity of the Ruytenschildt Bridge

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In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge, in Friesland, the Netherlands was tested until failure. One of the goals of the experiment is to analyze the failure mode of the slab bridge under a tandem of 4 wheel loads and to compare the capacity of the full bridge structure to the predicted results, to have an idea of the residual strength of existing bridges. The methods used are experi-mental (testing of the bridge to failure in two of its five spans) and analytical. The analytical work involved predicting the bending moment capacity, the shear capacity and the punching capacity of the bridge. In both spans, the bridge failed in flexure. The total capacity during the experiment was significantly higher than pre-dicted. The results indicate that the traditional rating procedures for shear are very conservative when applied to slab bridges that benefit from transverse load redistribution.

Bridging the gap between one way and two-way shear in slabs

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The shear capacity of slabs under concentrated loads is particularly of interest for bridge decks under concentrated live loads. Often, one-way shear will be analyzed by considering the slab as a wide beam (without taking advantage of the transverse load redistribution capacity of the slab) and two-way shear by considering the punching area around the load. Since experiments showed that the failure mode of slabs under concentrated loads is a combination of one-way and two-way shear as well as two-way flexure, a method was sought that bridges the gap between traditional one-way and two-way shear approaches. The proposed method is a plasticity-based method. This method is based on the Strip Model for concentric punching shear and takes the effects of the geometry into account for describing the ultimate capacity of a slab under a concentrated load. The model consists of “strips” that work with arching action (one-way shear) and slab “quadrants” that work in two-way shear. As such, the resulting Extended Strip Model is suitable for the design and assessment of elements that are in the transition zone between one-way and two-way shear.

Defining loading criteria for proof loading

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As the bridge stock in The Netherlands and Europe is ageing, various methods to analyse existing bridges are being studied. Proof loading of bridges is an option to study the capacity when crucial information about the structure is lacking. This information could be related to the material (for example, the effect of alkali-silica reaction on the structural capacity) as well as to the structural system (for example, the effect of restraints at the supports or transverse redistribution capacity). When it is decided to proof load a bridge, the question arises which maximum load should be attained during the experiment to approve the capacity of the bridge, and which criteria, based on the measurements during the test, would indicate that the proof loading needs to be aborted before reaching the maximum desired load (the so-called stop criteria). To define the required loading criteria, a review of the literature has been made, finite element models of existing viaducts have been made, and on these viaducts, proof loading tests have been carried out. These bridges were heavily instrumented, with a goal of learning as much as possible about the structural behaviour during proof loading. As a result of the analysis and experiments, recommendations are given for proof loading of bridges with respect to the required maximum load and the stop criteria. These recommendations are important, since they form the basis of a guideline for proof loading of existing concrete bridges that is under development in The Netherlands.

Reinforced concrete slab bridges are assessed for a combination of loads that include self-weight, superimposed loads, and distributed and concentrated live loads. The shear capacity of reinforced concrete slabs subjected to a combination of loads is thus an important topic for the assessment of existing bridges. Currently, a plastic model exists for the assessment of reinforced concrete solid slabs subjected to a concentrated load: the Extended Strip Model, based on the Strip Model for concentric punching shear. To apply this model to slabs subjected to a combination of loads, the model needs to be adapted based on theoretical principles. The results are then compared with the results from experiments on half-scale slab bridges subjected to a combination of a concentrated load close to the support and a line load. The result of this comparison is that the proposed method is suitable to find a safe estimate of the maximum concentrated load on the slab. The implication of this development is that an improved tool is available to estimate the maximum load of a truck that can be placed on a reinforced concrete bridge, thus improving the current assessment.

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Slabs subjected to concentrated loads close to supports, as occurring for truck loads on slab bridges, are less studied than beams in shear or slab-column connections in punching. To predict the shear capacity for this case, the Bond Model for concentric punching shear was studied initially. Modifications to this model resulted in the Modified Bond Model, which takes into account the enhanced capacity from the direct transfer of the load to the support, is able to deal with moment sign changes as occurring near continuous supports, and can take into account the reduction in capacity, resulting from the geometry when the load is placed close to the edge. The model is then compared to the results of experiments on slabs subjected to concentrated loads close to supports. As compared to the Eurocode and the ACI code, the Modified Bond Model leads to a significantly better prediction of the experimental results. The Modified Bond Model is one of the few models available to describe the shear capacity of slabs subjected to concentrated loads close to supports and can be used for design and assessment.

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As the bridge stock in The Netherlands and Europe is ageing, various methods to analyze existing bridges are being studied. Load testing of bridges is an option to study the capacity when crucial information about the structure is lacking. This information could be related to the material (for example, the effect of ASR on the capacity) as well as to the structural system (for example, the effect of restraints at the supports or transverse redistribution capacity). When it is decided to load test a bridge, the question arises which maximum load should be attained during the experiment to approve the capacity of the bridge, and which criteria, based on the measurements during the test, would indicate that the test needs to be aborted before reaching the maximum desired load (the “stop criteria”). A number of reinforced concrete slab bridges have been load tested over the course of the past few years. These load tests were pilot cases, in which the bridges were heavily equipped with sensors, to study the bridges’ behavior at critical positions for bending moment and shear. The test results were then extensively analyzed, and compared to the stop criteria available in the currently used codes and guidelines. As a result of the analysis and experiments, recommendations are given for proof loading of bridges. These recommendations are important, since they will form the basis of a guideline for proof loading of existing concrete bridges that is under development in The Netherlands.

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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.

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For an initial design or assessment of a reinforced concrete solid slab bridge, spreadsheet-based or hand calculations are typically used. The shear stress is compared to the shear capacity as prescribed by the code. The distributed loads result in a uniform shear stress at the support. Concentrated loads are less straightforward to take into account. It is known that transverse load redistribution occurs in slabs. To explore the topic of transverse load redistribution, experiments on elements subjected to a concentrated load close to the support were carried out. These elements had an increasing width, starting at 0.5 m and increasing with steps of 0.5 m up to 2.5 m, so that the effect of transverse load redistribution could be studied. The threshold effective width resulting from the experiments was then compared to load spreading methods, in order to give recommendations for the practical use with concentrated loads. It was found that the load spreading method as used in French practice is to be preferred. As compared to load spreading methods that were used previously, the French load spreading method results in smaller shear stresses at the support. This result allows for more economic designs and provides a better assessment tool.

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Proof loading of existing bridges is an interesting option when insufficient information about a bridge is available. To safely carry out a proof loading test, high loads are placed on the bridge. To avoid permanent damage to the structure, a controlled loading protocol needs to be described, and the measurements need to be closely monitored to identify the onset of distress. The criteria from existing codes and guidelines to evaluate the measurements, called stop criteria, are not universally applicable. To develop recommendations for proof loading of reinforced concrete solid slab bridges, beam experiments were analysed. The beams were heavily instrumented to evaluate the existing stop criteria, and possibly develop new stop criteria. The result of these experiments is the development of a standard loading protocol for the proof loading of reinforced concrete slab bridges. Recommendations for the use of the stop criteria are also formulated. These insights are used to develop a new guideline for the proof loading of reinforced concrete slab bridges in the Netherlands.

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As a result of the heavier live load models and more conservative shear approaches prescribed by the recently implemented Eurocodes, a large number of existing reinforced concrete solid slab bridges in the Netherlands were found to be shear-critical. The beneficial effect of the transverse load redistribution in slabs under concentrated loads is not taken into account. To quantify this effect, a comprehensive number of experiments was carried out. These results are used to formulate recommendations for the assessment practice for the case of solid slab bridges. The recommendations focus on the effective width over which the axle load can be distributed and its lower bound, the beneficial effect of transverse load redistribution and the influence of the yield strength of the reinforcement on the lower bound of the shear capacity. These recommendations are implemented in the “Quick Scan” method, leading to a significant reduction of the shear stresses.

Applying Experimental Results to the Shear Assessment Method for Solid Slab B...

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The combination of increased live loads and a more conservative shear capacity in the recently implemented Eurocodes, resulted in a large number of existing solid slab bridges in the Netherlands being shear-critical upon assessment. However, an enhancement of the shear capacity can occur in slabs under concentrated wheel loads due to transverse load redistribution. To quantify this effect, a comprehensive series of experiments on slabs and slabs strips under a concentrated load near to the support and under a combination of a concentrated and a line load was carried out. The experiments show the difference in behaviour for slabs, carrying the load in a two-dimensional way, as compared to beams in shear. The results from the laboratory research are used to develop recommendations, that are easily used in combination with the codes. These recommendations are implemented in a spreadsheet-based first-level assessment tool, the Quick Scan method. The assessment with this tool of selected cases of existing solid slab bridges shows that applying the experimental results into the assessment practice leads to an improved selection ability of the Quick Scan method.

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Proof loading of existing bridges is an option to study the capacity when crucial information about the structure is lacking. To define the loading criteria for proof load testing, a review of the literature has been made, finite element models of existing viaducts have been made, and on these viaducts, proof loading tests have been carried out. These bridges were heavily instrumented, to learn as much as possible about the structural behaviour during proof loading. Additional laboratory experiments have been used to develop controlled loading protocols, and to identify which stop criteria can be used for which case. As a result of the analysis and experiments, recommendations are given for proof loading of bridges with respect to the required maximum load and the stop criteria. These recommendations have resulted in a guideline for proof loading of existing reinforced concrete slab bridges for The Netherlands.

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Proof load testing can be a suitable method to show that a bridge can carry the required loads from the code without distress. This paper addresses the preparation, execution, and analysis of a proof load test on a four-span reinforced concrete solid slab bridge, viaduct de Beek. The bridge has one lane in each direction, but was restricted to a single lane, since an assessment showed that the capacity is not sufficient to allow both lanes. For this proof load test, the bridge was heavily equipped with sensors, so that early signs of distress can be seen. The difficulty in this test was that, for safety reasons, only the first span could be tested, but that the lowest ratings were found in the second span. A direct approval of the viaduct by proof loading was thus not possible, and an analysis was necessary after the field test. The result of this analysis is that only by allowing 6.7% of plastic redistribution in the second span, sufficient capacity can be demonstrated.

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For the assessment of reinforced concrete slab bridges in the Netherlands, the shear stress resulting from the dead loads and live loads is determined in a spreadsheet or from a finite element model. In a spreadsheet-based approach, an assumption for the distribution of the loads from the wheel prints is necessary. When finite element methods are used, it is necessary to determine over which length (a multiple of the effective depth) the peak shear stress can be distributed for comparison to the design shear capacity. To recommend a load-spreading method, experiments were executed on slab strips of increasing widths. The shear capacity did not increase with the increasing width upon passing a threshold. This threshold is compared to different load spreading methods, indicating that a distribution from the far side of the wheel print is to be preferred. This recommendation is also supported by the results of a statistical analysis and the stress distribution in nonlinear finite element models. To find the distribution width in a finite element method, a numerical model is compared to an experiment on a slab subjected to a concentrated load in which the support consists of a line of 7 bearings equipped with load cells measuring the reaction forces. These measurements were compared to the stress profile at the support from the model, showing that the peak can be distributed over 4 times the effective depth. These recommendations for the effective width and distribution width are research-based tools that replace the previously used rules of thumb resulting from engineering judgement.

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Application of Modified Bond Model to the capacity of Ruytenschildt Bridge

1. Challenge the future Delft University of Technology Application of Modified Bond Model to capacity of Ruytenschildt Bridge Eva Lantsoght, Cor van der Veen, Ane de Boer, Dick Hordijk

2. 2 Overview • Introduction to case • Modified Bond Model • Test results • Comparison results and MBM • Summary & Conclusions Slab shear experiments, TU Delft

3. 3 Proofloading Case Ruytenschildt Bridge • Proofloading to assess capacity of existing bridge • ASR affected bridges • Insufficient information • Study cracks and deformations for applied loads • Crack formation: acoustic emissions measurements • Control load process • Ruytenschildt Bridge: testing to failure

4. 4 Proofloading Ruytenschildt Bridge Existing bridge Partial demolition and building new bridge

5. 5 Proofloading Case Ruytenschildt Bridge

6. 6 Bond Model (1) • Alexander and Simmonds, 1990 • For slabs with concentrated load in middle

7. 7 Bond Model (2)

8. 8 Modified Bond Model (1) • Adapted for slabs with concentrated load close to support • Geometry is governing as in experiments • Determine factor that reduces capacity of “radial” strip • Maximum load: based on sum capacity of 4 strips

9. 9 Unequal loading of strips • Static equilibrium • v2,x reaches max before v1,x ' 1, 0.1667x c a v f d L a  

10. 10 Loads close to free edge Edge effect: when length of strip is too small to develop loaded length lw

11. 11 Cross-sections Ruytenschildt Bridge • Testing in span 1 and span 2 • close to end support • close to mid support • Critical position for shear

12. 12 Test results proofloading Span 1 • Maximum load 3049 kN • Maximum available load for span 1 • Flexural cracks • No failure • Order additional load for test 2! • Prediction MBM: 2864 kN • Tested/Predicted = 1.06 • Tested; not failure load 0 500 1000 1500 2000 2500 3000 3500 0 5000 10000 15000 20000 25000 Load(kN) time (s)

13. 13 Test results proofloading Span 2 • Maximum load 3991 kN • Large flexural cracks • Flexural failure • yielding of reinforcement • Settlement of bridge pier with 1.5cm • Elastic recovery to 8mm • Prediction MBM: 3816 kN • Tested/Predicted = 1.05 • Bent-up bars?? 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 2000 4000 6000 8000 10000 Load(kN) Time(s)

14. 14 Conclusions • Ruytenschildt Bridge • Testing to failure in 2 spans • Measurements • Modified Bond Model • Plasticity-based model • For analysis of capacity of slabs • MBM shows good predictions of capacity of bridge • For limited number of field experiments

15. 15 Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449

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