Collapse test and moment capacity of the Ruytenschildt reinforced concrete slab bridge

Abstract

A large number of existing reinforced concrete solid slab bridges in the Netherlands are found to be insufficient for shear upon assessment. However, research has shown additional sources of capacity in slab bridges, increasing their total capacity and possibly changing their failure mode. Previous testing was limited to half-scale slab specimens cast in the laboratory. To study the full structural behaviour of slab bridges, testing to failure of a bridge is necessary. Research on load testing is carried out in order to develop load testing guidelines. In August 2014, a bridge was tested in two spans. The bridge was load tested, and additional cycles until yielding occurred in the reinforcement were added to the experiment. Though calculations with current design provisions showed that the bridge could fail in shear, the field test showed failure in flexure before shear. The unity check for flexure was determined. The experiment shows that the methods for rating of existing reinforced concrete slab bridges are conservative.

Keywords:

• Assessment
• bridge tests
• concrete slabs
• field tests
• flexural strength
• shear strength

1. Introduction

The major expansion of the Dutch road network occurred during the decades of reconstruction after the Second World War. Therefore, the majority of the existing bridges in the Netherlands date from prior to 1976. These bridges were designed for the live loads of that era, which are considerably lower than the current design live loads from the Eurocode NEN-EN 1991-2:2003 (CEN, 2003). At the same time, the shear capacity calculated according to the currently governing Eurocode 2 NEN-EN 1992-1-1:2005 (CEN, 2005) is lower than according to the previously used Dutch codes, such as the VBC 1977 (Stichting Commissie Voorschriften Beton, 1977). These code changes resulted in a large number of existing Dutch-reinforced concrete bridges to be found insufficient for shear (Lantsoght, van der Veen, de Boer, & Walraven, 2013). In total, about 600 reinforced concrete slab bridges are subject of discussion.

Over the past years, research at Delft University of Technology studied the behaviour and shear capacity of reinforced concrete slab bridges. Shear tests on slab specimens under concentrated loads close to supports (Lantsoght, van der Veen, de Boer, & Walraven, 2014; Lantsoght, van der Veen, & Walraven, 2013) resulted in the conclusions that the capacity of slabs under concentrated loads benefits significantly from the transverse load distribution capacity of slabs (Lantsoght, van der Veen, de Boer, & Walraven, 2016). These experiments led to recommendations with regard to the effective width in shear (Lantsoght, van der Veen, Walraven, & de Boer, 2016) and the distribution of the peak stresses in linear finite element models (Lantsoght, De Boer, & van der Veen, 2014; Lantsoght, de Boer, Van der Veen, & Walraven, 2013). A procedure for finding the capacity of cracked cross sections of slab bridges was also developed (Lantsoght, van der Veen, Walraven, & de Boer, 2016).

The past few years, Delft University of Technology also executed a number of load tests on slab bridges. Load tests can be interesting when the effect of material deterioration is unknown (such as for viaducts with alkali–silica reaction or corrosion effects (Pape & Melchers, 2010)), when the structural system raises concerns (e.g. when it is unknown how much movement can take place in bearings and joints reaching the end of their service life), or when insufficient information is available about the structure to carry out an assessment. The aim of the load tests executed by Delft University of Technology is to develop a guideline for proof loading of structures. This guideline (Koekkoek, Lantsoght, Yang, De Boer, & Hordijk, 2016) should encompass the methods for determining the proof load (based on a certain reliability level) and the stop criteria (criteria based on the field measurements that indicate when the experiment needs to be prematurely aborted because the structure signals distress).

In 2014, the opportunity arose to test the Ruytenschildt Bridge, owned by the province of Friesland and scheduled for demolition. Since the bridge needed replacement, it was possible to carry out a load test, and to load the bridge until failure. The focus of this paper will be the ultimate capacity and the flexural analysis of the Ruytenschildt Bridge. Since there are doubts about the shear capacity of existing reinforced concrete slab bridges, the critical loading position that was used in the experiments on the Ruytenschildt Bridge was the critical position for a shear failure. Extra attention was paid to a possible failure in shear since a shear failure is a brittle failure mode, which could result in a collapse of a structure without much warning behaviour of the structure.

2. Literature review

2.1. Load testing of bridges

Two distinct types of load tests exist, each with their different purpose. Diagnostic load tests (Farhey, 2005; Jauregui, Licon-Lozano, & Kulkarni, 2010; Moses, Lebet, & Bez, 1994; Olaszek, Lagoda, & Casas, 2014; Russo, Wipf, & Klaiber, 2000) use a low load and verify if the stiffness and behaviour of the bridge are as expected. Several countries, such as Italy (Veneziano, Galeota, & Giammatteo, 1984), Switzerland (Brühwiler, Vogel, Lang, & Luechinger, 2012) and France (Cochet et al., 2004), require a diagnostic load test upon opening of a bridge. Proof load tests (Cai & Shahawy, 2003; Casas & Gómez, 2013; Moses et al., 1994; Saraf, Sokolik, & Nowak, 1996) use a higher load and proof a certain capacity of a bridge. Ideally, this capacity can be linked to a probability of failure of the bridge, so that the result of the test and analysis is an estimate of the safety. Guidelines for carrying out load tests and when a test needs to be stopped because the structure indicates damage (the so-called ‘stop criteria’) are available in Germany (Deutscher Ausschuss für Stahlbeton, 2000) for the limit state of flexure. In the United States, a relatively old manual exists that links load tests to bridge rating (NCHRP, 1998) as well as a guideline for load testing of buildings (ACI Committee 437, 2013), which includes stop criteria for the limit state of flexure. Other available guidelines are from the United Kingdom (The Institution of Civil Engineers – National Steering Committee for the Load Testing of Bridges, 1998), from Ireland (NRA, 2014) and from France (Cochet et al., 2004).

The stop criteria are necessary to identify the maximum load for a non-destructive field test. Loading beyond this point will cause irreversible damage. The first symptoms of damage in concrete bridges for flexure are identified based on strains in the concrete and reinforcement steel, as described by the German guideline (Deutscher Ausschuss für Stahlbeton, 2000). Moreover, to avoid damage in the tested bridge, cycles of loading are used. After every cycle, the residual deformation is studied. Both the German guideline and ACI 437-2 M.13 study residual deformations to analyse if further loading is safe. When acoustic emission sensors are used, these measurements can also be used to study the formation and growth of cracks in the bridge (Anay et al., 2016; Olaszek, Świt, & Casas, 2012; Yang & Hordijk, 2015). So far, it is possible to capture the first signs of damage for the limit state of flexure, and to stop loading with a safe margin prior to the formation of irreversible damage. For the limit state of shear, which is a brittle failure mode, stop criteria still need to be developed, and currently research on this topic is being carried out (Schacht, Bolle, Curbach, & Marx, 2016).

In the Netherlands, Delft University of Technology is developing a guideline for proof loading of structures. The goal of the guideline is to consider the limit states of shear and flexure, and to define stop criteria for these limit states that are suitable for both new and existing structures. The following viaducts have been proof loaded under heavy instrumentation for the development of the guideline: the viaduct Vlijmen-Oost (Fennis, van Hemert, Hordijk, & de Boer, 2014), the Halvemaans Bridge (Fennis & Hordijk, 2014) in Alkmaar, the viaduct Zijlweg (Koekkoek, Lantsoght, & Hordijk, 2015) and the viaduct De Beek (Koekkoek, Lantsoght, Yang, & Hordijk, 2016). The Ruytenschildt Bridge is the only bridge so far in this programme of bridge tests that has been tested to failure.

2.2. Previous experiments to failure

A limited number of bridge tests to failure are available in the literature, see Table 1. The majority of the tested bridges were slab bridges and flexural failure was the dominating failure mode. Another test to failure from the literature is the testing of the Thurloxton underpass (Cullington, Daly, & Hill, 1996). This test is not included in the table because saw cuts over 1-m width were used, preventing the slab from developing transverse load redistribution. Similarly, for the case of the Maumee River Bridge, a pre-stressed box beam from the structure was dismantled and tested isolated from the original structure (Allbright, Parekh, Miller, & Baseheart, 1995). For similar reasons, the tests of Halsey and Miller (1996) and Rogers, Wotherspoon, Scott, and Ingham (2012) are not included in Table 1. The model bridge tested in the laboratory by Roschke and Pruski (2000) might be of interest to the readers, but is not included in Table 1 because this experiment deals with a scale model of a post-tensioned slab bridge. Before testing the Reibersdorf Overpass Bridge (Siringoringo, Fujino, & Nagayama, 2013), damage was introduced by cutting one of the piers at the footing level, changing the structural behaviour, and therefore this test is not included in Table 1.

Table 1. Overview of past testing to failure on bridges.

Reference	Bridge name	Type of bridge	Failure mode
Haritos, Hira, Mendis, Heywood, and Giufre (2000)	Barr Creek	Slab bridge	Flexural failure
Azizinamini, Boothby, Shekar, and Barnhill (1994), Azizinamini, Shekar, Boothby, and Barnhill (1994)	Niobrara River	Slab bridge	Flexural failure
Aktan, Zwick, Miller, and Shahrooz (1992), Miller, Aktan, and Shahrooz (1994)	–	Slab bridge	Punching failure
Jorgenson and Larson (1976)	ND-18	Slab bridge	Flexural failure
Bagge et al. (2015), Bagge, Shu, Plos, and Elfgren (2015)	Kiruna	Pre-stressed girder bridge	Punching failure
Wang, Kang, Cai, and Li (2011)	East Meng Jiang Nu Bridge	Pre-stressed hollow core slab bridge	Flexural failure
Bergström, Täljsten, and Carolin (2009, Elfgren (2011), Puurula et al. (2014, 2015)	Örnsköldsvik Bridge	Through bridge	Shear failure*
Zhang et al. (2009, 2011, 2013)	Nanping bridge	Channel beam bridge	Flexural failure
Bakht and Jaeger (1992)	Stony Creek Bridge	Concrete deck on steel girders	Yielding of steel girder
Jiaquan et al. (2006)	Huning Expressway Bridge	Box girder bridge	Flexural failure

* The Örnsköldsvik Bridge was strengthened with CFRP reinforcement to avoid a bending failure and induce shear failure.

3. Description of bridge

3.1. Location and history

The Ruytenschildt Bridge, shown in Figure 1, is located in the national road N924, which connects the villages of Lemmer and Heerenveen in the province of Friesland (The Netherlands). The bridge is situated over a waterway connecting the Tjeuker Lake to the Vierhuister Canal. The year of construction of the bridge is 1962. In 2014, the bridge was demolished and rebuilt at a larger clearance, so that taller boats can pass the underlying waterway. The bridge carries two lanes (one lane in each direction) as well as a single bike lane.

Figure 1. Photograph of Ruytenschildt Bridge.

3.2. Geometry

The superstructure of the Ruytenschildt Bridge was a continuous reinforced concrete solid slab bridge of five spans. At the supports, cross-beams were cast integrally onto the piers. The bridge had a skew angle of 18^o. Drawings of the cross section, top view and side view are given in Figure 2. In Figure 2a, the stages of demolition are indicated on the cross section. As at least one motor lane and one bicycle lane were needed throughout the replacement of the bridge, the contractor and owner opted for a staged demolition process. The hatched part of the cross section in Figure 2a was isolated from the rest of the structure with a saw cut. The width of this part was 7.37 m. The remaining part of the bridge was used to carry one lane of traffic. The bike traffic was deviated over a floating pontoon. While the traffic used one lane, the Ruytenschildt Bridge was tested in spans 1 and 2 (see Figure 2(c)). As can be seen in Figure 2(b), the thickness of the bridge deck slab was 550 mm.

Figure 2. Overview of geometry of Ruytenschildt Bridge: (a) Cross section showing the stages of demolition. The hatched area was tested to failure; (b) Side view; (c) Top view.

Note: Units: [mm].

Figure 3 depicts a plan view and cross section of the reinforcement layout. An overview of the available reinforcement is given in Table 2. In span 1, two layers of φ = 22 mm with a spacing of 270 mm and one layer of ϕ = 19 mm with a spacing of 270 mm are available, so that A_s = 3866 mm²/m in span 1. In span 2, two layers of ϕ = 22 mm with a spacing of 270 mm and one layer of ϕ = 16 mm with a spacing of 270 mm are available, so that A_s = 3650 mm²/m in span 1. Over support 2, four layers of ϕ = 22 mm with a spacing of 270 mm are available, so that A_s = 5632 mm²/m over support 2. The mentioned layers are in the width direction, reducing the spacing between the bars but not changing the effective depth of the cross section.

Figure 3. Reinforcement drawing of Ruytenschildt Bridge, showing spans 1, 2 and half of span 3: (a) Plan view; (b) cross section. The structure is symmetric.

Note: Units: [mm].

Table 2. Available reinforcement.

Reinforcement	Span 1		Span 2
	Support 1	Span 1	Support 2	Span 2
Longitudinal, bottom	ϕ19–270	ϕ19–270	ϕ19–270	ϕ16–270
		2 × ϕ22–270		2 × ϕ22–270
	ϕ22–270
Longitudinal, top	ϕ22–270	ϕ10–130	4 × ϕ22–270	ϕ12–130
	ϕ12–130	ϕ19–270		ϕ22–270

3.3. Material properties

The concrete compressive strength was derived based on the results of 62 cores. The average cube compressive strength, recalculated from the core samples, was f_cm = 40 MPa with a characteristic value of f_ck = 25 MPa (Lantsoght, 2015). Further analysis of the cores, however, indicated that the surface treatment needed improvement. Currently, a level cut or epoxy glue can be used to create a level surface for the test. Experiments showed that even with a level cut, the surface tends not to have the correct properties. In the lab, a calibration factor was derived to correct for this discrepancy by comparing the compressive strength of cores with a level cut to the compressive strength of cores with an epoxy glue to create an even surface for testing. The cores with the surface treatment with epoxy glue were taken from the beams that were sawn out of the bridge and taken to the laboratory for additional testing. The corrected value of the average cube compressive strength was f_cm = 63 MPa (Yang, 2015), which converts to a cylinder compressive strength f_{cm, cyl} = 52 MPa. The asphalt layer was present on the cores and was measured as 51 mm on average.

The type of reinforcement steel in the Ruytenschildt Bridge was the old Dutch type QR 24. This reinforcement steel has a characteristic yield strength f_yk of 240 MPa. Tests on samples taken from the bridge resulted in a yield strength f_y = 352 MPa and an ultimate strength f_u = 435 MPa for the ϕ 12-mm bars and f_y = 309 MPa and f_u = 360 MPa for the ϕ 22-mm bars.

4. Prediction of capacity

4.1. Shear capacity

Average material parameters and expressions for the average cross sectional capacity are used to estimate the capacity in the bridge test. For this analysis, the shear capacity is calculated according to NEN-EN 1992-1-1:2005 (CEN, 2005). For members without shear reinforcement and without pre-stressing, the average shear capacity can be determined as (with f_cm in [MPa] and d_l in [mm]):

According to the Eurocode procedures, the value of v_min may be chosen nationally, and is recommended as (for average values, with f_cm in [MPa]):

in [MPa]

To calibrate the formula for finding average values, a statistical analysis (König & Fischer, 1995) showed that a factor of 0.15 can be used (Lantsoght, 2013). The effective width in shear for slabs (Lantsoght, de Boer, van der Veen, & Walraven, 2015) is determined based on a 45° load spreading from the far side of the axle to the face of the support for straight slabs. However, for skewed slabs, different interpretations of this recommendation are possible: b_str, the effective width for a straight slab, b_skew with horizontal load spreading under 45° from the far side of the wheel print to the face of the support and b_para based on a load spreading parallel to the straight case. Figure 4 shows these different options, as well as the critical position for shear at 2.5 d_l (Lantsoght, van der Veen, de Boer et al., 2013; Rijkswaterstaat, 2013b). For both spans, the face-to-face distance between the first axle of the load testing tandem and the support was taken as 2.5 d_l. This position is considered the critical loading position for shear in straight slabs, and was identified as such based on experiments on slabs under concentrated loads failing in shear (Lantsoght, van der Veen, de Boer et al., 2013).

Figure 4. Top view of the slab showing first axle, support line and the free edge to explain the different possible interpretations for the effective widths for a skewed slab: (a) b_str, the effective width as for a straight slab; (b) b_skew the effective width with a horizontal load spreading under 45^o from the far side of the wheel print to the face of the support; and (c) b_para the effective width based on a load spreading parallel to the straight case.

Different interpretations for the capacity of skewed slab bridges are possible as there is no consensus yet on how to determine the effect of the skew. In the Netherlands, for the assessment of skewed slab bridges, a set of skew factors is used that increase the load effects (Rijkswaterstaat, 2013a) depending on the skew angle of the bridge. These factors have been determined based on a parameter study with linear finite element models. A similar approach, but leading to different factors, is available from Canada (Theoret, Massicotte, & Conciatori, 2012) and similar studies have been carried out in the United States (Menassa, Mabsout, Tarhini, & Frederick, 2007). The number of experiments available in the literature is very limited (Cope & Rao, 1983; Cope, Rao, & Edwards, 1983; Cusens, 1987), and a first conclusion of these experiments is that the failure mode changes as the skew angle increases and the position of the wheel prints is kept unchanged. Until more experimental results are available, no definite answers can be given on the effect of the skew angle on the shear capacity of reinforced concrete slab bridges.

The results of the calculations are presented in Table 2 based on the maximum total tandem load, P_tot, at which shear failure is expected in the bridge test. Transverse load redistribution in slabs subjected to loads close to supports increases the shear strength in straight slabs by 1.466 (Lantsoght, 2012) as a characteristic value when compared to the Eurocode prediction. This factor was derived from a series of experiments on slabs in shear in which the majority of the parameters that influence the shear capacity, except the specimen height, were varied. The slabs that were used in these experiments had a height of 300 mm, and an effective depth d_l of 265 mm. P_{tot, slab} takes this multiplication factor into account. However, in skewed slabs, stress concentrations in the obtuse corner have a negative effect on the shear capacity (Cope et al., 1983). P_tot and P_{tot, slab} are thus the bounds between which the shear capacity is expected to lie. The value of the maximum load P_tot for which shear failure is expected is determined in the Quick Scan sheet (Vergoossen, Naaktgeboren, ‘t Hart, De Boer, & Van Vugt, 2013).

4.2. Flexural capacity

The flexural capacity is subdivided into the moment at cracking M_cr, yielding M_y and the ultimate M_u, based on a traditional beam analysis and the present reinforcement. The cracking moment M_cr is determined as:

with with f_cm in [MPa]

The moment capacity at yielding, M_y, is based on Thorenfeldt’s stress–strain diagram for concrete. The stress–strain diagram of Thorenfeldt for f_cm = 52 MPa is shown in Figure 5. A linear strain diagram over the depth of the cross-section is assumed, with ε_c the strain in the extreme compression fibre:

Figure 5. Thorenfeldt’s stress–strain diagram, applied to f_cm = 52 MPa.

The ultimate moment capacity, M_u, is based on a rectangular stress block diagram and can be determined as:

Table 2 contains the results of this analysis. These results are for the position of the load test, which is the critical position for shear. The critical position for shear was selected to investigate if there is a possibility for shear failure in existing reinforced concrete slab bridges. The corresponding maximum loads P_cr, P_y and P_u are based on a model of a five-span beam.

5. Testing of the bridge

5.1. Test set-up

The load used in the test on the Ruytenschildt Bridge had the geometry of the design tandem from live load model 1 from NEN-EN 1991-2:2003 (CEN, 2003): four wheel prints of 400-mm square with a transverse distance of 2 m and a longitudinal distance of 1.2 m. As the goal of the experiment was, amongst others, to verify if shear failure is possible (which is a brittle failure mode that could cause an unexpected collapse of a bridge with insufficient capacity), the face-to-face distance between the axle and the cross-beam at the support was 2.5 d_l, the critical position for shear (Lantsoght, van der Veen, de Boer et al., 2013; Rijkswaterstaat, 2013b). In the transverse direction, the critical position is in the obtuse corner (Cope, 1985) and as close to the edge as possible, which is the situation that creates the largest shear stress concentrations. The edge distance was 800 mm in span 1 and 600 mm in span 2. The edge distance was taken as small as possible.

One danger in testing a bridge to failure is the possibility that the entire loading set-up falls down when the bridge collapses. To avoid this possibility, the bridge was gradually loaded through a load spreader construction as shown in Figure 6: ballast blocks were placed on the load spreader over the support, and then hydraulic jacks gradually applied the load onto the slab at the loading position during the experiment. Unloading at the jacks would result when large deformations at failure occur.

Figure 6. Load spreader system for loading the Ruytenschildt Bridge: (a) Photograph; (b) principle of unloaded and loaded situation.

5.2. Instrumentation

The instrumentation on the Ruytenschildt Bridge was elaborate, and served the purpose to study both proof loading and testing to failure. The measurements followed the deformations in the longitudinal and transverse directions with linear variable differential transformers (LVDTs) and laser triangulation sensors, the strain on the bottom surface with LVDTs on steel bars of 1 m, the crack width with LVDTs and the activity in the cracks with acoustic emission measurements. The full plan of instrumentation, with the measurement range of the sensors, is shown in Figure 7, which also includes the position of the wheel prints during the experiments in span 1 and span 2. In this drawing, AE denotes the positions of the acoustic emission sensors. The positions of LVDTs 7 through 10 were determined in the field, where the largest existing cracks were selected for monitoring during the test. The acoustic emission sensors were used for research purposes, as the possibility is explored to use acoustic emission measurements as a stop criterion, especially for a brittle failure mode like shear. This topic is currently under research.

Figure 7. Sensor plan and position of wheel prints: (a) span 1, (b) span 2.

Note: Ranges of the sensors are given, and distances have units [mm].

6. Results

6.1. Span 1

The loading scheme and the measurements of the laser covering the maximum displacement for both spans are shown in Figure 8. For the acoustic emissions measurements and to check for non-linear behaviour, typically three cycles were carried out to each load level. The values of the maximum loads in the field test are given in Table 3 for comparison. On span 1, failure did not take place. The maximum available load provided by the ordered ballast blocks was 3049 kN. Flexural distress was observed, but flexural failure did not take place.

Figure 8. Loading diagram and displacement measurements of the Ruytenschildt Bridge: (a) Span 1, force vs. time; (b) Span 2, force vs. time; (c) Span 1, displacement measured by laser 1 vs. time; and (d) Span 2, displacement measured by laser 3 vs. time.

Table 3. Calculated shear and moment capacity of tested spans.

Span	Span 1		Span 2
Shear capacity	Ptot [kN]	Ptot, slab [kN]	Ptot [kN]	Ptot, slab [kN]
bstr	3760	5512	4020	5893
bpara	3236	4744	3432	5031
bskew	4804	7043	5328	7811
Experiment	≥3049		≥3991
Flexural capacity	Span		Support	Span
Pcr (kN)	880		1432	1460
Py (kN)	2368		7720	3532
Pu (kN)	3102		9940	4496
Flexural capacity	Span moment		Support moment	Span moment
Mcr (kNm)	1816		1690	1592
My (kNm)	3925		5662	3717
Mu (kNm)	4964		7064	4705
Mtest (kNm)	4889		3306	4188

Notes: P_tot is the total predicted maximum load, and P_tot,slab is the increased load based on the magnification factor from experiments on straight slabs, with effective widths b_str, b_para and b_skew as shown in Figure 4. M_cr is the moment at cracking, M_y the moment at yielding and M_u the moment at the ultimate. The corresponding tandem loads are P_cr, P_y and P_u. The maximum moment in the experiment is M_test.

The calculated shear capacity was higher than the maximum load that was applied and shear distress was not observed. The maximum flexural capacity as calculated with the average material parameters was also higher. The Ruytenschildt Bridge is an integral bridge, which leads to a support moment over the end support. In practice, the rotational stiffness of the support is difficult to estimate, and the support was conservatively modelled as a hinge. As a result of the end moment, the span moment that occurs under a given loading will be smaller than calculated when assuming a hinged support.

6.2. Span 2

Since failure in span 1 could not be achieved, more counterweights were ordered for the next test on span 2. The deck was tested at its critical position for shear. For this test, the maximum load was 3991 kN, and flexural failure of the slab occurred. Moreover, the pier of support 2 underwent a settlement of 15 mm right after the application of the maximum load. The loading scheme and the displacement versus time are shown in Figure 8. In Figure 9, the load–displacement diagram is shown. It can be seen that non-linear behaviour starts to occur around 2050 kN. As a result of delayed recovery, the final residual settlement at the pier was 8 mm. The maximum applied load was smaller than the load necessary to achieve a shear failure according to most calculation methods from Table 2. The resulting moment was somewhere between the yielding and ultimate moment of the slab as calculated in Table 2, which corresponds to the observations in the experiment. Yielding of the steel caused large cracks and deformations, but the load was not applied until the point of actually causing collapse of the entire deck and breaking of the steel reinforcement or crushing of the concrete compression zone. An estimate of the shear capacity cannot be provided because there was no indication of shear distress or of shear failure.

Figure 9. Load–displacement diagram of the test in Span 2.

As failure was reached in the second span, the results and the measurements could be used to determine when the stop criteria from the German guideline and ACI 437.2 M-13 were exceeded, and how far from or close to the failure load the load was when the stop criterion was exceeded (Tersteeg, 2015). Using the German guideline, a proof load test would be stopped at 2050 kN, when non-linear behaviour was observed in the load–displacement diagram. The stop criterion for residual deflection was only exceeded at 3181 kN. Using ACI 437.2 M-13, the stop criterion of the permanency ratio, based on ratios of maximum and permanent deflections, is exceeded at 3191 kN, the residual deflection at 3696 kN and the deviation from linearity index (based on the tangent of the load–displacement diagram) at 3700 kN. The test would have been stopped at 2050 kN, when non-linear behaviour was observed in the load–displacement diagram. These observations confirm that for flexure, the stop criteria, and especially the use of instrumentation to follow the load–displacement diagram in real-time during the test, have indicated that the test needs to be stopped before reaching the failure load.

7. Analysis of bending moment capacity of Ruytenschildt Bridge

7.1. Description of finite element model and applied loads

To further analyse the moment capacity of the two tested spans of the Ruytenschildt Bridge, the Unity Checks for bending moment will be determined in more detail. The first step of the analysis is to construct a linear finite element model of the bridge. A linear finite element model of the slab with a width of 7.37 m and five spans of each 9 m was made in SCIA Engineer (Nemetschek Scia, 2016). The skew angle of 18° of the bridge is modelled. All supports are modelled as hinges, neglecting the restraint at the end supports caused by the bridge being an integral bridge.

In this model, first, the Eurocode loading is applied. The applied loading is the self-weight, the layer of asphalt of 51 mm and with a weight of 23 kN/m³, and the live load from Load Model 1 from NEN-EN 1991-2:2003 (CEN, 2003). The distributed load of the live load model is 9 kN/m² in the first lane and 2.5 kN/m² in the second lane. Since the saw cut reduced the number of lanes to less than 3, the α_qi factors for determining the distributed lane load for bridges with multiple lanes from Load Model 1 are taken as 1. Two lanes fit the geometry, so that two design tandems are applied. The tandem in the first lane is 300 kN per axle and in the second lane 200 kN. The wheel print is 400 mm × 400 mm, with a transverse distance of 2 m and a distance between axles of 1.2 m. With this model, the most unfavourable position of the design tandems is sought. For flexure, the most unfavourable position results in the largest moment. The load combinations are determined by NEN 8700:2011 (Code Committee 351001, 2011). The analysis is carried out at the safety level ‘Reconstruction’, which corresponds with a reliability index β = 3.3 and a reference period of 30 years (Koekkoek, Yang, Fennis, & Hordijk, 2015). The load factor on the self-weight and permanent loads is 1.15 and on the live loads 1.3. For the first and second spans, the positions of the design tandem for which the largest moments are found, as well as these moments, are given in Table 4.

Table 4. Calculated moments at position x causing largest moment with the Eurocode loads, and calculated moments for maximum load on proof load tandem.

	EC load		Proof load
	Span 1	Span 2	Span 1	Span 2
x (m)	4.63	14.50	3.39	12.46
mx (kNm/m)	417.87	325.16	803.26	810.08
mxy (kNm/m)	−20.62	−5.28	−16.36	−4.19
mux^+ (kNm/m)	438.49	330.44	819.62	814.27

m_x is the bending moment, m_xy the torsional moment and m_ux⁺ the moment based on Wood and Armer’s combination of bending and torsional moments (Wood, 1968).

In a next step, the proof load is applied to the finite element model. For this case, the distributed lane load and the permanent load of the asphalt, which was removed before the test, are omitted. The position is as used in the experiment, closer to the support to study a possible shear failure. The x-coordinate in the finite element model of the tandem was 3.39 m for the first span as a result of the skew. A total proof load of 3049 kN or of 762.25 kN per wheel print was applied for the first span. For the second span, a total proof load of 3991 kN or of 997.75 kN per wheel print was applied. The resulting moments for these positions and loads are given in Table 4. Figure 10 shows the moments m_x caused by the proof load tandem in span 1.

Figure 10. Results of finite element model for bending moment in the longitudinal direction m_x with maximum load in the experiment in Span 1.

7.2. Plastic analysis

A plastic analysis of the first span was carried out with a beam model in MASTAN2 (Ziemian & McGuire, 2015). The load on the axles is increased until the yield moment is achieved in the span, after which a hinge is inserted where the yield moment is reached. Then, the method aims at increasing the load further until the yield moment (hogging moment) of the cross section at continuous support is achieved. If plastic redistribution cannot take place, a moment larger than the yield moment occurs over the support, which means the development of a mechanism and collapse.

An axle load of 1184 kN is necessary to reach the yield moment in the span of 3925 kNm at the location of the second axle. Note that the same load was applied on both axles, so that the total load of the tandem is the double of the presented axle loads. If a hinge is then inserted at the location of the second axle, the moment over the continuous support becomes 13,780 kNm. M_y at the support equals 5662 kNm, see Table 3, and no redistribution after the development of the plastic hinge can take place. A mechanism forms instead of a stable configuration. The maximum axle load in the test was 1524.5 kN. This analysis shows that the axle load to obtain yielding was 1184 kN. However, the effect of the integral bridge and the moment at the end support were not taken into account for this analysis because there is no estimate of the restraint at the end support. Estimating the effect of the restrain would have been possible if span 1 would have been tested to failure, so that the restraint could have been derived from the observed moment diagram in the test.

In span 2, M_y was 3717 kNm, see Table 3, which corresponds to an axle load of 1766 kN. If a hinge is inserted at the second axle, the moment over the continuous support becomes 8013 kNm, which is larger than the capacity of 5662 kNm. A mechanism develops, as happened in the first span, and no further redistribution is possible after achieving yield at the location of the second axle. The maximum axle load in the test was 1995.5 kN. The calculated axle load to achieve yield was 1766 kN based on a beam model.

Based on the observed cracking, a more refined analysis can be carried out for the second span. In this refined analysis, the beam model is replaced by a slab model. An overview of the major cracks is shown in Figure 11. Table 5 then summarises the resulting yielding moments for the present reinforcement, where the plastic moment M_plastic is determined as the product of the length of the crack and the yield moment of the present reinforcement. Indications for yielding were observed in the experiment based on the non-linearity of the load–displacement curve at a total load of 2050 kN on the tandem. This load corresponds with two axles of 1025 kN or a wheel load (four wheels) of 512.5 kN.

Figure 11. Cracks in span 2 after experiment, bottom side of bridge deck: (a) sketch of cracks; (b) damage to the pier; and (c) photograph of cracks on bottom of bridge slab.

Table 5. Observed cracks (see Figure 11) and determined yield moments m_yield as the yield moment for the provided reinforcement per unit length, and M_plastic the total yield moment of the crack, i.e. the product of the length and m_yield.

Nr.	Direction	Length [m]	myield [kNm/m]	Mplastic [kNm]
1	EW	3.47	504.6	1832
2	NS	2.35	95.5	224
3	NS	3.63	95.5	331

The SCIA Engineer (Nemetschek Scia, 2016) model, presented in the previous paragraph, is used for this refined analysis and a cut along crack 1 from Table 5 is made, see Figure 12. In a next step, the percentage of the load carried by 3.47 m (the crack length) is determined. The length of the crack is considered the length of the plastic hinge, as the observed cracking is an indication of the occurrence of yielding during the experiment. The percentage of load carried over the cracked distance of 3.47 m is determined based on the moment diagram along the cut. The analysis shows that 77.4% of the moment is carried by the part of the crack and that 22.6% is carried by the part of the section that is still linear elastic. The plastic hinge develops over a length of 3.47 m, so that 3.90 m remains linear elastic. In other words, the uncracked part of the width of the slab is considered to still be linear elastic at a total tandem load of 2050 kN. The total moment, integrated over the full width of the slab, in the cross section caused by the wheel loads of 512.5 kN is 2271 kNm. The linear elastic part of the moment is calculated as:

Figure 12. Moment diagram in y-direction at the location of the studied crack.

In this linear elastic part, the moment can increase until reaching the yield moment of the cross section, determined previously, so that:

The moment that can be achieved to reach yielding over the full width, including the linear elastic part, is ξ = 2614 kNm. This moment corresponds to an axle load of 1188 kN or a total load of 2376 kN based on a beam model in MASTAN2. This maximum value of the total load will be used to determine the Unity Check for bending moment.

7.3. Required proof load to reach maximum moment Eurocode loading

In this paragraph, it will be explained which value of the load applied on the tandem would result in the same maximum sectional moment as Eurocode live load model 1. In the first span, the maximum sagging moment for span 1 was found when the design tandems of the Eurocode live load model 1 were placed at 4.63 m from the support. In this part of the analysis, the proof load tandem (replacing live load model 1 from the Eurocode) is applied in the finite element model at this position (4.63 m), and the distributed lane load (which is part of live load model 1) and the asphalt layer, which was removed prior to the test, are removed to represent the testing conditions. The maximum load on the proof tandem to achieve the same highest moment as with the Eurocode loading is now sought. Note that the tandem for this analysis is placed farther into the span than what was used during the test. To achieve a design moment m_ux⁺  = 438.49 kNm/m, a total load on the proof load tandem of 1240 kN needs to be applied. This load is considerably lower than the maximum load that was achieved in the experiment of 3049 kN.

In the second span, the x-coordinate of the position was 14.50 m, or 5.50 m from support 2. To achieve the design moment m_ux⁺  = 330.44 kNm/m which results from applying the Eurocode loading (live load model 1), a total load on the proof load tandem of 1088 kN needs to be applied. This value is again significantly lower than the maximum load that was achieved in the experiment of 3991 kN. To proof sufficient capacity in a proof load test for the safety level of ‘Reconstruction’, the maximum value to be applied on the proof load tandem would be 1088 kN, and then the loading would be stopped. In this experiment, the load was increased beyond this value because the Ruytenschildt Bridge was tested until failure.

7.4. Unity Checks

With the previous calculations, the Unity Check for bending moment is determined. The Unity Check for bending moment is the moment caused by the applied loading divided by the bending moment capacity of the cross section. If the Unity Check value is lower than or equal to unity, sufficient capacity has been proven for the considered cross section. The moment caused by the applied loading can be determined in two ways:

(1)	The moment caused by the proof load at a distance of 2.5 dl from the support.
(2)	The moment caused by the Eurocode loading (live load model 1) at the position that causes the largest bending moment (4.63 m from support 1 and 5.50 from support 2, for both spans, respectively).

The capacity can also be determined in two ways:

(1)	From the bending moment capacity from Table 2.
(2)	From the refinement based on the formation of the plastic hinge over a part of the width of the slab. This method is only possible for span 2, where the measured cracks led to the refinement.

The values of the capacity side and the loading side are given here as the total load on the proof load tandem, so that the refinement based on the plastic redistribution after the formation of the crack in span 2 can be taken into account. An overview of the calculated loads and resulting Unity Checks is given in Table 6. The results indicated with ‘Unity Check’ are based on the load corresponding to the maximum moment caused by the Eurocode loading, divided by the minimum capacity from the considered span given in Table 6. The result indicated with ‘Unity Check with proof load’ is based on the applied load in the test. The calculated Unity Checks in Table 6 show that the bridge would rate sufficient for bending moment capacity in an assessment (UC < 1), and that during the experiment, a significant larger capacity is found (UC > 1) as a result of transverse redistribution and, for span 2, plastic redistribution. The methods for rating bridges are thus conservative.

Table 6. Overview of calculated loads and capacities, and resulting Unity checks. The presented values are recalculated axle loads to achieve the same result, given in [kN].

Load				Capacity
Equivalent		In test		Moment capacity		Mechanism
Span 1	Span 2	Span 1	Span 2	Span 1	Span 2	Span 1	Span 2	Refine Span 2
1240	1088	3049	3991	2368	3532	2368	3532	2376
Unity check		Unity check with proof load
Span 1	Span 2	Span 1		Span 2
0.524	0.458	1.288		1.680

The reader should keep in mind that the bridge was tested to failure at the critical position for shear. Regardless of this position, flexural failure was governing over shear failure for span 2, in which failure was achieved. When the moment caused by the proof load is used for the Unity Check, then it needs to be considered that the load to reach a flexural failure is higher than the load necessary to achieve failure when the tandem would be placed at the critical position for flexure (4.63 m from support 1 for span 1 and 5.50 m from support 2 for span 2).

8. Conclusions

The ageing bridge stock in the Netherlands has led to research on reinforced concrete slab bridges, as well as research on load testing for cases of bridges with material deterioration or when doubts about the structural system arise. In the Netherlands, there are especially concerns about the shear capacity of the existing reinforced concrete slab bridges because initial assessments showed high Unity Checks for the existing reinforced concrete slab bridges. Moreover, shear is a brittle failure mode, which is an additional cause for concerns.

For the Ruytenschildt Bridge, a load test was carried out, and then the load was further increased to achieve failure. Two spans of this bridge were tested in August 2014. The Ruytenschildt Bridge, opened in 1962, could be tested to failure since it was being replaced for functional reasons. This bridge has a skew angle of 18^o. The material parameters were determined from samples from the bridge. During the testing of the Ruytenschildt Bridge, a load spreader system was used to avoid major damage at collapse. The loading position was chosen as the critical loading position for shear to study the most unfavourable loading situation for shear. It was found in the experiments that failure only could be achieved in span 2. Flexural failure with a support settlement occurred in span 2. The maximum load was in between the axle load corresponding with the predicted yield and ultimate moment, so good correspondence with the test results was obtained for flexure.

To further analyse the safety of the bridge, the current rating procedures and the bending moment capacity of the Ruytenschildt Bridge, a study based on a linear elastic finite element model of the bridge was executed. The proof load level for flexure was determined, and it was concluded that the bridge would have been approved as having sufficient capacity in a proof load test. A finer plastic analysis was carried out, assuming a plastic hinge at the yielded parts in a beam model. This beam model did not allow for further plastic redistribution after the development of the first plastic hinge. A sharper study based on the linear elastic finite element model studying the bridge as a slab and using the observed yield lines from the test was then carried out. Finally, the Unity Checks for flexure for spans 1 and 2 were determined. These Unity Checks showed that the bridge would rate sufficient for flexure and that the tested cross sections have a larger capacity than predicted. The rating procedures are thus conservative.

Notation list
	=	The following symbols are used in this paper:
αqi	=	multiplication factors for live load model 1
β	=	reliability index
β1	=	parameter that determines average compressive stress in concrete
βult	=	parameter that gives relation between height of rectangular compressive stress block and depth of the compression zone
εc	=	strain in concrete fibre most in compression
εult	=	strain at crushing of the concrete
ε0	=	material parameter of the concrete
ξ	=	unknown
ρl	=	longitudinal reinforcement ratio
b	=	member width
bpara	=	effective width based on a load spreading parallel to the straight case
bskew	=	effective width with horizontal load spreading under 45o from the far side of the wheel print to the face of the support
bstr	=	effective width for a straight slab
bw	=	web width
cy	=	depth of the compression zone at yielding of the tension steel
cult	=	depth of the compression zone at the ultimate
dl	=	effective depth to the longitudinal reinforcement
d′	=	distance between fibre most in compression and centroid of compression steel
fck	=	characteristic cube compressive strength
fcm	=	average cube compressive strength
fcm, cyl	=	average cylinder compressive strength
fc, th	=	stress in the concrete using Thorenfeldt’s stress–strain diagram at yielding of the steel
fr	=	modulus of rupture of concrete
fs′	=	compressive stress in the compression steel at the ultimate
fu	=	average ultimate strength of steel
fy	=	average yield strength
fyk	=	characteristic yield strength
k	=	size effect factor
k2	=	factor for the centroid of the concrete compressive stress distribution
kth	=	parameter related to Thorenfeldt’s stress–strain diagram, indicating the relative position to the peak of the diagram
mux+	=	combined longitudinal moment
muy+	=	combined transverse moment
mx	=	longitudinal bending moment
mxy	=	torsional moment
my	=	transverse bending moment
myield	=	yield moment in kNm/m
nth	=	material parameter of concrete
vmin	=	lower bound of the shear capacity
x	=	position of x-coordinate of face of the tandem
ytension	=	distance between neutral axis and tension face
As	=	area of steel
As, comp	=	area of compression steel
Cc	=	resultant of concrete in compression
Cs	=	resultant of steel in compression
CR,c	=	calibration factor for the average value of the shear capacity
Ec	=	Young’s modulus of concrete
EW	=	east–west direction, longitudinal direction
Ig	=	moment of inertia of the gross (uncracked) section
LEpart	=	linear elastic part of moment
LEpartmax	=	increased moment to achieve the yield moment of the cross section
NS	=	north–south direction, transverse direction
Mcr	=	moment causing cracking of the cross section
Mplastic	=	yield moment multiplied with crack length
Mtest	=	maximum moment in cross section at experiment
Mu	=	moment causing crushing of the concrete in the cross section
My	=	moment causing yielding of the steel in the cross section
Pcr	=	tandem load corresponding to moment causing cracking of the cross section
Ptot	=	expected maximum tandem load for shear failure
Ptot, slab	=	expected maximum tandem load for shear failure taking into account the magnification factor for the shear capacity of slabs
Pu	=	tandem load corresponding to moment at the ultimate
Py	=	tandem load corresponding to moment at yielding
VR,c	=	average value of the shear capacity

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by Rijkswaterstaat, Ministry of Infrastructure and the Environment of the Netherlands; and the Province of Friesland.

Acknowledgements

The authors wish to express their gratitude and sincere appreciation to the Province of Friesland and the Dutch Ministry of Infrastructure and the Environment (Rijkswaterstaat) for financing this research work. The contributions and help of our colleagues A. Bosman, S. Fennis, P. van Hemert and Y. Yang, of the contractor de Boer en de Groot and of Mammoet, responsible for applying the load, are gratefully acknowledged.