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Finite Element Model Updating-based Load Rating of Bridges with Incomplete As-Built Information
Mehrdad S. Dizaji, Devin K. Harris, Mohamad Alipour, Abdou Ndong, Osman Ozbulut, Abdollah Bagheri
TL;DR
The paper addresses bridge load-rating inference when available information is insufficient, and examines updating-based estimates alongside established rating methodologies. The updating approach produced estimates within 0% to -17% of the AASHTO standard, while averaging multiple load paths reduced discrepancies to 2-11% for four bridges.
Problem
When plans and structural details are insufficient to determine a bridge’s nominal capacity, other methods are needed to infer its remaining safe load-carrying capacity.
Method
The study compares updating-based load-rating estimates with LRFR and static live-load testing using multiple load paths and average load ratings.
Results
0% to -17%: the updating approach produced the most reasonable rating-factor estimates relative to the AASHTO standard; averaging multiple load paths reduced discrepancies to 2-11% for four bridges.
Takeaways & Limitations
Using multiple load paths and averaging the resulting load ratings reduces the discrepancy of estimates across the four bridges.
Takeaways & Limitations
Only four bridges were evaluated, and further testing and analysis are required to determine whether the results generalize to all bridges.
Abstract
from arXiv · showhide
Load rating is the engineering process of determining the safe load-carrying capacity of an existing bridge structure often through analysis of its load-bearing members and their cross sections. However, when structural drawings and details of the structure are missing or insufficient for such calculations, alternative solutions must be used to infer the capacity. This study proposes a rational and consistent engineering solution for capacity inference based on structural identification (St-Id). The proposed approach uses finite element model updating (FEMU) to estimate the unknown characteristics of structures for use in an analytical load rating, which requires the development of an initial model developed in ABAQUS that can be updated based on experimental test data. ABAQUS allowed for the development of an interface with MATLAB, which facilitated the integration of an automatic iterative parameter optimization algorithm. The optimization algorithm developed in this investigation incorporated the features of a genetic algorithm (GA) and a gradient-based scheme to iterate on the unknown parameters. The proposed approach was evaluated on four in-service highway bridges including two concrete slab and two T-beam structures in varying deterioration condition states, which had sufficient plans available but were treated as having varying degrees of unknown details. The results illustrated that the finite element (FE) model updating approach generated load ratings that were within 0-17% of the target load ratings while alleviating the main challenges of the existing alternatives.
1 Corresponding Author: Postdoctoral Research Associate, Engineering Systems and Environment, University of Virginia, U.S
The study proposes finite element model updating to infer bridge characteristics for analytical load rating when as-built information is incomplete. Across evaluated bridges, ratings were close to target values, and limited instrumentation was sufficient.
- 0-17% difference from target load ratings was achieved using the finite element model updating approach.
- Limited sensor instrumentation was sufficient for successful implementation of the developed methods.
- The study addresses bridge load rating using finite element modeling, structural identification, FEMU, and field testing.
1. Introduction
Incomplete bridge plans make conventional capacity calculations insufficient, motivating measurement-based and analytical alternatives. Prior approaches include field surveys, load testing, and finite element analyses, but their limitations support a more rational model-updating strategy.
- Missing plans and structural details can make conventional calculations insufficient for determining a bridge’s nominal capacity.
- Engineering judgment introduces variability and uncertainty because it is not typically based on measurements of physical phenomena.
- Proof testing can cause damage, is expensive, and cannot be extrapolated to future performance.
- Existing alternatives include structural characterization, field surveys, diagnostic testing, proof testing, nondestructive measurements, and finite element analysis.
- Field and experimental studies reported bridge capacities substantially higher than indicated by some AASHTO rating procedures.
- The study develops rational engineering approaches for bridges with limited as-built information using finite element model updating and vibration response characterization.
2. Proposed Methodology
The proposed methodology updates parameterized finite element models using experimental bridge responses to infer unknown structural properties for load rating. It combines static, dynamic, and hybrid sensing scenarios with iterative optimization.
- Structural identification updates a structural model from experimental observations, while FEMU refines an initial finite element model using test data.
- ABAQUS was interfaced with MATLAB to support automatic iterative parameter optimization.
- The optimization minimizes differences between numerical and experimental responses by iterating on uncertain parameters.
- The algorithm combines genetic-algorithm global search with a gradient-based scheme to reduce computational cost and localize solutions.
- Unknowns include reinforcing-steel area, concrete elastic modulus and compressive strength, and secondary boundary-restraint properties.
- FEMU Type: FEMU-S uses quasi-static measurements, FEMU-D uses vibration-derived natural frequencies, and FEMU-H combines static and dynamic data.
3. Characterization of VDOT Inventory of Bridges with Limited Information
The inventory analysis characterizes bridges with limited information and motivates evaluation of concrete slab and T-beam structures. Four representative bridges were selected across structural types and condition states, while available plans were deliberately excluded from the updating process.
- Approximately 7% of Virginia’s 12,925 in-service highway bridges, or 933 structures, lacked plans.
- Concrete slab, arch-deck, and T-beam bridges were identified as the primary design configurations in the inventory.
- Concrete slab and T-beam bridges together represented 63% of the population of bridges without plans.
- Four test bridges were selected, comprising two slab bridges and two T-beam bridges in good and fair condition states.
- The selected bridges included War Branch and Smacks Creek slab bridges, plus Flat Creek and Brattons Creek T-beam bridges.
4. Instrumentation and Field Testing
Field testing combined live-load and vibration measurements to characterize bridge responses for model updating. Instrumentation and loading configurations were adapted to bridge geometry, with repeated truck crossings and ambient or impact excitation.
- Each bridge used static measurement sensors and vibration sensors, with instrumentation configured for the bridge geometry.The equipment included strain gauges, string potentiometers, tiltmeters, and accelerometers.
- Each crossing was repeated three times to support repeatability and reliability of the measurements.
- Live-load tests used known trucks traversing predetermined transverse positions at crawl, moderate, and near-posted-limit speeds.The reported speeds were approximately 3–5 mph, 25 mph, and 50 mph.
- Measured live-load responses were force-effect and load-path guided, with maximum deformation occurring at specific sensor locations.
- Vibration testing used ambient and impact-hammer excitation to identify bridge natural frequencies and compare the two excitation methods.Ambient excitation came from traffic, wind, and pedestrians; impact testing used selected excitation points and repeated impacts.
- Limited accelerators required sensor relocation between span halves during some early vibration tests.
5. Load Rating Results from Different Methodologies
The study compared conventional AASHTO LRFR ratings with ratings informed by diagnostic load testing. Diagnostic testing adjusted original rating factors upward, reflecting measured as-built response and performance relative to design approximations.
- AASHTO LRFR Load Rating: AASHTO LRFR was selected as the baseline analytical load-rating method.The method corresponds to the current AASHTO LRFD Bridge Design Specifications.
- AASHTO LRFR Load Rating: The baseline calculations used bridge structural and mechanical properties reported in the as-built plans.Properties included concrete density, elasticity modulus, compressive strength, reinforcing-steel yield strength, and reinforcement area.
- AASHTO Load Rating Through Diagnostic Load Testing: Diagnostic load testing adjusted the original rating factors, RFc, to higher test-informed values, RFT.
- AASHTO Load Rating Through Diagnostic Load Testing: The diagnostic-testing ratings were summarized for all evaluated bridges in Table 5.
- AASHTO Load Rating Through Diagnostic Load Testing: The results indicated potential improvement in load ratings from better understanding of as-built response and performance than design approximation.
6. Finite Element Model Updating based Load Rating
FEMU-based load rating estimated bridge parameters and updated finite element models using multiple loading paths. Comparisons with measurements showed that the proposed approach effectively fine-tuned the initial models across the evaluated bridges.
- Estimated parameters, calculated capacities, and load-rating factors were reported for each evaluated bridge in Tables 6–9.
- FEMU-S and FEMU-H results were presented for three loading configurations to illustrate the robustness of the approach.The configurations corresponded to Paths 1 through 3.
- Comparisons between updated-model results and measured data showed that the proposed FE updating approach fine-tuned the initial model effectively.The comparisons included updated and measured displacements and rotations for selected bridges.
7. Comparison and Discussion of Load Rating factors Using Different Methods
The FEMU-H method produced the most reasonable load-rating estimates among the evaluated approaches, with improved consistency across loading configurations. Across four bridges, the proposed methods provided rational estimates relative to the AASHTO LRFR baseline, while sensor-reduction scenarios achieved comparable updating results.
- Load-rating comparison: FEMU-S showed the largest differences from AASHTO LRFR, with overestimation on two bridges, underestimation on two, and truck-path dependence.Localized material distribution, boundary conditions, and reinforcement configurations were identified as possible associated factors.
- Load-rating comparison: FEMU-H produced rating-factor estimates with percent differences ranging from 0% to -17% relative to the AASHTO standard.Negative differences indicate lower estimates than AASHTO.
- Load-rating comparison: Using multiple load paths and averaged ratings reduced FEMU-H discrepancies to 2-11% for the four bridges.The hybrid method also showed reduced differences among loading configurations compared with the static-only counterpart.
- Load-rating comparison: FEMU-D performed better than FEMU-S but was less accurate and consistent than FEMU-H.FEMU-D used only dynamic measurements, whereas FEMU-H combined static and dynamic measurements.
- Testing configuration: Ambient vibration testing produced natural frequencies close to impact-hammer results for all four bridges and can reliably support testing with minimal operational effects.Ambient excitation does not require traffic control, while impact-hammer excitation requires at least partial traffic closure.
- Sensor sensitivity: Comparable updating results were achieved with a more limited sensor suite, and results did not clearly favor one reduced sensing configuration.The evaluated scenarios used midspan deflection or longitudinal strain together with accelerometer sensors.
8. Conclusions
The study presents a FEMU-based methodology for estimating bridge load ratings when structural details are insufficient, using static and vibration sensing to update models. Across four test bridges, the approach produced feasible and comparatively consistent rating estimates.
- The proposed methodology uses sensing data from live-load and/or vibration tests to iteratively estimate structural properties needed for load rating.Three optimization scenarios used static-only, vibration-only, or combined sensing data.
- Including measurements that capture both local static and global vibration characteristics enhanced the model-updating process.
- The FEMU-based method showed feasibility for estimating load ratings on four test bridges.
- 0% to -17% was the percent-difference range for rating factors estimated with the FEMU-H method.FEMU-H incorporated both static and dynamic measurements.
- 2-11% was the discrepancy range when multiple load paths and average load ratings were used for the four bridges.The study recommends repeating live-load tests with several load paths to obtain more robust rating estimates.
- Comparable results were achieved with a more limited sensor suite, suggesting that the updating process was not constrained by sensor configuration.Sensitivity analysis did not identify one sensing configuration as clearly more appropriate than the others.