The Boyne Viaduct: structural health monitoring and probabilistic analysis

The Boyne Viaduct in Drogheda, Co Louth, is being appropriately assessed to ensure continuing safety in practice, and probabilistic methods have been combined with structural health monitoring to allow robust safety analysis, writes Roughan & O’Donovan's Lorcan Connolly.

Introduction

The Boyne viaduct lies on the main Dublin-Belfast railway line and consists of a series of masonry arch spans and three steel truss spans. This work focuses on the central steel span (Fig 1, main image), which was constructed around 1932. As the structure is now beyond its expected design life, it is essential that it is appropriately assessed to ensure continued safe use. This paper describes a probabilistic Ultimate Limit State (ULS) assessment of the structure which was carried out and used design an optimal Structural Health Monitoring (SHM) strategy. The implications of the SHM data are quantified in terms of the variation in the calculated reliability of the structure at both the Ultimate and Fatigue Limit State.

Probabilistic ULS assessment

A Finite Element (FE) model was built in a commercially available software package using as-built drawings. The model is shown in Fig. 2. The bridge (and model) consists of an 80m truss with 10 bays, all of which are 8m. The top chord of the truss has an arched profile. The riveted built-up sections are modelled as linear elastic beam elements. Cross-beams span between the node points of the truss. The ballasted track is supported on a steel deck plate over the rail bearers, which span between the cross beams. There is transverse wind bracing on the top of the structure and internal portal bracing. This was included in the model but is omitted from Fig. 2, along with the track, for clarity. [caption id="attachment_46361" align="alignright" width="300"]

Fig 2. FE model of the Boyne Viaduct central span[/caption] The bridge was assessed deterministically in accordance with the Design Manual for Roads and Bridges (DMRB). The critical limit states were shown to be stress failure of the rail-bearers, the cross-girders and the first truss diagonal. A probabilistic assessment was then carried out on these elements in order to evaluate their safety at the design point. This means that instead of applying deterministic characteristic values to the assessment parameters, all inputs were modelled as random variables. The probability distributions which describe the potential variation in these inputs to the assessment are required. The assessment can then be carried out by evaluating the performance function below:

g(x)=Load-Resistance (1)

Advanced statistical models may then be used to evaluate the probability of failure (P[g(x)<0]). The probability of failure allows the results to be considered in a risk-based approach. The safety can also be quantified in terms of the reliability index (β), which is dependent upon the failure probability. Higher reliability indices represent high levels of safety. The Joint Committee on Structural Safety (JCSS) publish guidance on minimum required reliability levels (Table 1). [caption id="attachment_46362" align="alignright" width="300"]

Table 1. Minimum Reliability Indices (βt) (JCSS)[/caption] The reliability indices computed by the First Order Reliability Method (FORM) were equal to 4.196, 4.714 and 5.510 for stress failure, for the rail-bearer, cross girder and truss diagonal, respectively. A value of βt = 4.2 is recommended by the JCSS as the most common design situation. As the reliability index calculated for the rail bearer was slightly below this value, it was deemed appropriate to analyse the structure further by use of an SHM system.

Structural health monitoring

The critical rail-bearers and cross beam were instrumented with stacked rectangular rosette strain gauges (Fig. 3a). Rosette strain gauges measure strain in three axes. This allows calculation of principal stress, which can be compared to results from FE modelling. Triaxial Accelerometers were also installed on the bridge in order to assist in a dynamic analysis (Fig. 3b). All sensors were hardwired to a data logger and power supply located at the south pier of the structure. The system was in place from October 2015 to January 2016 and recorded 36 days of measurement, constituting 724 train-passage events.

By comparing the measured stress signals at the rail-bearers and cross girders (due to the passage of a train) to those generated by the FE model, it was found that the FE model was over-estimating the stress. Refinements were then made to the FE model, which resulted in a much better agreement in the measurement. (Fig. 4). The performance of this model calibration allowed a reduction in the model uncertainty associated with the probabilistic assessment. Recalculation of the reliability indices at this stage yielded values of 6.495, 6.612 and 5.378 for the rail bearers, cross girder and truss diagonal, respectively.

Dynamic amplification can have a significant impact on the safety assessment. Traditionally, Dynamic amplification of stress has been computed as the ratio between the characteristic total (static + dynamic) stress and the characteristic static stress. In this assessment, the Assessment Dynamic Ratio (ADR) was calculated from direct measurement. This dynamic ratio considers the actual dynamic amplification which should be applied to the characteristic load event.

Extreme value modelling of both the static and dynamic stresses

A low-pass filter was constructed and used to filter the dynamic stress amplification from the measured data. This allowed extreme value modelling of both the static and dynamic stresses in order to calculate dynamic amplification of stress which should be applied to the DMRB assessment (Fig. 5). Although the DMRB suggested a dynamic amplification of stress as high as 42 per cent for these members, the results indicated that the amplification of stress was actually of the order of one per cent in this case. This is to be expected, as speed restrictions to trains passing the bridge currently limit the stress to a near static value. [caption id="attachment_46365" align="alignright" width="300"]

Fig. 5. Extrapolation of characteristic static / dynamic stresses and calculation of dynamic allowance[/caption] This method of calculating the site-specific dynamic amplification of stress from measurement can be applied to any structure in which conservative codified dynamic assumptions restrict the load carrying capacity of the bridge. The implications of direct calculation of dynamic amplification on the probabilistic assessment were also considered by stochastic modelling of the dynamic amplification due to each train passage event. The results showed that the final ULS reliability indices were 7.133, 7.547 and 5.378 for the rail bearer, cross girder and truss diagonal, respectively.

Probabilistic fatigue assessment

Based on the monitoring data, a measurement-based probabilistic fatigue assessment of the structure was performed at the monitored locations. The performance function considered for probabilistic fatigue assessment is given by:

Where nEi is the number of cycles associated with stress range i and NRi is the endurance (in cycles) related to a specific detail category under consideration, at stress range i. Dcrit is defined here as the critical cumulative damage for the detail under consideration and is modeled as a lognormal distributed variable with mean and standard deviation equal to 1.0 and 0.3, respectively, as recommended by JCSS. A probabilistic S-N curve was used to obtain a distribution of NRi at a given stress range. By fitting distributions to the stress range histograms from one month of data, it was possible to extend the assessment over several years. [caption id="attachment_46367" align="alignright" width="300"]

Fig. 6. Evolution of reliability for fatigue at monitored locations.[/caption] It was shown that the rail bearers were the most fatigue-critical section monitored. However, very high levels of reliability were calculated for the locations assessed. The results are shown in Fig. 6. The vertical dashed line indicates the current age of the bridge.

Conclusions

The application of SHM and probabilistic methods to bridge assessment has been demonstrated. The application of these techniques can show bridge structures to have sufficient levels of safety, even after failure of more traditional conservative assessment techniques. As a vast percentage of Europe’s bridges are currently beyond their intended design life, it is essential that these robust methods are applied to quantify safety levels on a site-specific basis. Moreover, the installation of long-term SHM solutions to provide advanced warning of failures can be combined with these systems to allow increased safety on a continuing basis, prohibiting unnecessary repair/replacement. The research leading to these results was part of the DESTination RAIL project, a project funded by the EU Horizon 2020 Programme under call H2020-MG-2014 Mobility for Growth. Grant agreement no: 636285. The authors also gratefully acknowledge Iarnród Éireann for allowing the research associated with the Boyne Viaduct. Author: Lorcan Connolly is a research engineer with Roughan & O’Donovan Innovative Solutions. He is a chartered engineer with more than five years of experience in bridge safety assessment.