Evaluation of bridge load capacity using proof-load tests

A proof-load test is often necessary to accurately measure the field behavior of a bridge structure. A new segmental steel bridge has been constructed over the Tisza River in Hungary. The bridge comprises of two independent steel box girders assembled by a welding system. Engineers performed proof load tests before opening the structure to evaluate its load-carrying capacity and deck deflection. This paper presents several aspects of the load testing and evaluation of the bridge structure under static and dynamic loads using a rating factor (RF) approach compared to a baseline finite element model. The load test results helped to calibrate the model and verify the method. The study reveals that the tested bridge has an elastic behavior, a high capacity, and adequate dynamic performance.


Introduction
Steel box girder bridges provide adaptable and space-saving support systems in urban areas.Prefabricated segments delivered to the site provide the initial elements of the structure.Fabricators then erect and assemble them in the field without requiring complex falsework and only a minimum of temporary support.The Hungarian national standard code requires load-carrying capacity investigations using static and dynamic load tests for spans greater than 100 m before opening for service [1].The primary objective of a proof load test is to provide direct evidence that a bridge can support its prescribed factored live loads without suffering any possible deficiencies after construction.To achieve this, dedicated sensors are typically installed temporarily to record measurement data, while in-situ dynamic load testing and short-term monitoring are carried out under service load [2].Some deficiencies, if left undetected, can cause damage or even a sudden collapse.Such collapses occurred while testing Serbia's steel truss bridge over the Morawa River, Switzerland's road bridge near Salez, and France's suspension bridge in Maurin [3].The deficiencies in a bridge during construction result from the premature yield of components whose specified properties do not meet design specifications immediately after the end of construction.Primarily, they are undetected defects caused by inappropriate design or assembly, so they appear without notice during the design and erection of the structure.They may reveal themselves during a comprehensive inspection or proof load testing.If they are detected, the contractor must initiate repair operations.If they do not affect the load-carrying capacity [4], reduced service may start while the contractor completes repair work.
As previously stated, a proof-load test produces load conditions that allow engineers to rate the bridge's performance and aid in detecting defects before going into service [2].The load tests also establish a more accurate load-carrying capacity based on the rating factor (RF) which indicates the actual capacity of the bridge structure under live loads.It can also help to estimate load distribution and impact factors [5].Essentially, it is an experimental evaluation of the actual behavior of the bridge to identify both observable and hidden defects that may restrict or reduce the bridge's serviceability.This study evaluates the load-carrying capacity for the new box girder bridge located over the Tisza River using load rating factors (RFs).A Finite Element (FE) model reproduces the load-displacement response of the entire superstructure.The FE model uses several static and dynamic load test combinations to evaluate the structure more accurately.The final section compares RFs, the FE model, and measured data.

Methodologies for load-carrying capacity evaluation of the bridge
Before opening to traffic, a visual inspection was conducted on the new bridge over the Tisza River.The inspection results indicated that the structure is in good condition, with no visible signs of deterioration on any of the assessed bridge elements.However, visual inspection makes it challenging to quantitatively evaluate the actual capacity of a bridge subjected to traffic loads.Due to the increase in traffic levels, the bridge damage, and the rating design code requirements.Accurate evaluation serves both present load-carrying requirements and provides a baseline for future condition-based maintenance.Therefore, field load tests conducted directly after the visual inspection, in November 2021, provided data to validate the FE-Model and evaluate the bridge's capacity.
The load rating procedure evaluates how much a bridge can safely carry when subjected to the weight of a specific vehicle, typically a truck.This is expressed as a rating factor (RF) [6], with RFs greater than one indicating that the bridge can safely support the loads being considered.

Proof load testing of the bridge
The proof load tests of the bridge are conducted near the end of construction according to Hungarian standards [7].At that time, engineers check the structure's load capacity before opening the bridge for service.During the proof load test of the bridge, instruments recorded deck deflections and fiber stress under static and dynamic loadings.The static load test had a negligible dynamic impact on the bridge and correctly represented actual loading.Test instruments measured mid-span deflections in all spans and stress conditions along the primary span (148m).Additional optical measurements verified the positions of foundations and support pillars.Trucks loaded the right-side deck for the static tests with 400 kN loads, shown in Figure 1

FE Structural Modeling
The bridge comprises two independent directional decks and seven spans made from steel orthotopic box plate girders.Its total length is 758m, with a central span of 148 m, and each deck is 14m wide.The spacing between interior diaphragms is 4m, and the primary material is welded S355 steel.Elastomeric bearings support the superstructure.The bridge report and project drawings provided input data for the FEM.The structural analysis software Midas Civil modeled the right side of the bridge, according to the details presented in [8].The numerical modeling phase assumed no cracking or defects existed since visual inspections verified the quality of construction. 3 The numerical model simulated static and dynamic loads by applying nodal loads.The static load consisted of nodal loads uniformly distributed according to the arrangement of the trucks, as shown in Figure 2. The dynamic load used time-dependent nodal loads that followed the progress of the moving trucks.Dynamic load application followed the speed of the trucks.

Static loading results
During the static test, the vertical displacements along the box plate girders were measured at mid-span to evaluate the behavior of the continuous superstructure.The trucks reproduced loading in two traffic lanes near mid-span, above the support pillars (reverse moment), and along alternating lanes on several spans (torsion).
The vertical displacement results from the static tests and the calibrated model appear in Figure 3.The graphs show close agreement between the modeled and measured displacements, and the bridge's structural behavior showed no anomalies.The load distribution factor (DF) of the bridge is an essential parameter for structure behavior and load rating, which can be calculated using displacement responses all over the bridge [9].Equation (1) defines the distribution factor: Where i and j are the girder number, and δ is the displacement of the girders.The distributions of displacements across the box girders appear in Table 1 for three load cases.According to the previous formula, we chose the highest distribution factors: Table 1 shows that the distribution factors had the highest values when only one traffic lane was loaded.Indeed, it is better to adopt the two-lane and the side-by-side loading scenarios because the loads will be distributed here into all supporting plate-web girders since the deck slab is a wide plate.

Dynamic loading results
In the dynamic test, two trucks with 400 kN and 5 axles passed above the bridge at 10, 30, 50, 70, and 90 km/h.Figure 4 shows the variation of vertical displacement for a speed of 30 km/h, recorded at the mid-spans of Span 1 and 2. Once the bridge is loaded the graph begins with sagging displacements and progresses to a large peak under the front wheel of the trucks.When the truck gets to the following span, hogging displacements begin.As the truck continues, deflections rapidly decrease.The impact factors were also determined during the dynamic test.These factors are affected by the span's free length, the type of bridge elements, the material properties, boundary conditions, the nature of loading, and the type of response [8].Vertical displacements at the mid-spans provided the basis for computing the impact factor.The ratio of maximum dynamic displacements (δ dyn,max) at different speeds to the maximum pseudo-static displacement (δ stat,max) of 10 km/h speed at the same points appears in Equation 2.
Figure 6 summarizes the results showing that the impact factors generally rise with speed and achieve a value of 1.21 in the field test and 0.98 in the FE model, for speeds up to 90 km/h.The maximum values compare well to the recommended maximum permitted value of 1.7 by EUROCODE 1 [10].The reference values agree with the loading test results.

Evaluation of the load-carrying capacity
The loading tests achieved their primary objective by obtaining a reliable estimation of the bridge capacity.Load rating factors helped to evaluate the load capacity of the bridge.The factors usually represent the proportion of live load capacity and live load demand shown in Equation 3, based on the stress design formula [5]: Here: RF, equals load rating factor; σall, admissible stress of the structural material based on design code and test; σDL, stress under dead load; σLL, stress under live load, and finally δ, impact factor presented in Figure 6.
The stresses induced by truck loads in both field tests and simulations were utilized to calculate the corresponding RF, according to Equation (3).Table 2 shows that the bridge has enough capacity and the RF produced from the FE model tends to be more conservative.The standard load-carrying capacities determined using the FE model exceed the load-carrying capacities based on the measurement data, especially for higher speeds.Higher capacity means the FE model exhibits more stiffness than the measured structure.The difference may originate from many factors, such as different material stiffness in the field or differences in component cross-sections not considered during the analysis of new bridge.

Conclusion
The calibrated FE model results capture the bridge's actual state after comparing it to the proof test data.Vertical displacement analysis yields impact factors within the design limits of a structure behaving elastically.Based on these findings, the bridge structure is functioning as designed and can be open to traffic action.FE model rating factors indicate that the bridge structure may have greater strength than that predicted by proof testing.Some of the FE model assessments do not precisely agree with measured behavior.The model overestimates the rating factors for higher speeds compared to the proof load assessment, so it may sometimes not provide exact information relating to a structure's 'as built' behavior.
The proof-load tests verified the actual behavior of the bridge structure for safe serviceability.Thus, the collected data during the load testing will provide information for future monitoring and help to detect any loss of capacity or service capability.
(a).For dynamic load tests, two trucks side-by-side drove the length of the bridge at uniform speeds from 10 to 90 kph.The positions of the trucks appear in Figure 1(b).

Figure 2 .
Figure 2. FE model with static loads (pink lines) on the bridge deck (top view of the 3 rd span).

Figure 4 .
Figure 4. Dynamic response of the bridge for the first two spans at a speed of 30 km/h.

Figure 5
Figure 5 from the FE model shows the variation of vertical acceleration at mid-span 1 under a moving load speed of 90 km/h.The red, green, and blue lines indicate the location of the moving load as it crosses Span 1, 2, and 3.The Figure shows significant vibration as the truck traverses Span 1.The vibration attenuates as the truck moves on to Spans 2 and 3.All dynamic load analyses revealed such characteristics, illustrating a practical result from moving loads.

Figure 5 .
Figure 5. Vertical acceleration for the first span at a speed of 90 km/h.

Figure 6 .
Figure 6.Impact factors as a function of truck speed.

Table 2 .
Bridge rating factors as a function of truck speed.