1 Introduction
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Compare a conventional risk-based design approach and the CFO approach, highlighting their differences and the potential advantages of the latter.
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Discuss the limitations of current (probabilistic) risk-based design methods for designing structures subject to fire and show how they can be addressed through integration with the CFO approach.
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Present an illustrative example regarding the fire-safety design of a bridge structure to compare the two approaches and discuss possible outcomes.
2 Considered Approaches
2.1 Risk-based Design Approach
2.2 Consequence-Oriented Fire Intensity Optimisation (CFO) Approach
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It treats fire scenarios as design variables: first, it calculates the scenario maximising consequences; next, it identifies design updates that, exploiting fire-structure coupling effects, optimise the balance between increasing structural member capacity and diminishing fire intensity (“fire-intensity optimisation”).
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It is “consequence-oriented,” expressing risk in terms of (maximum) consequences rather than distribution statistics of the considered consequence metric of interest or annual exceedance rates.
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It employs uncertainty propagation techniques to examine the impact of selected random inputs on the computed maximum consequences.
3 Limitations of Conventional Risk Assessment Procedures for Fire Safety Design
3.1 Fire-Scenario and Intensity Treatment
3.2 Fire Intensity Measure
3.3 Probabilistic Fire Hazard Analysis
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A “severe fire” cannot always denote a post-flashover (fully developed) fire. Indeed, a localised fire can also be “severe” and “endanger structural stability” in buildings where flashover conditions are not met. Furthermore, travelling fires in large, open-plan compartments are now a recognised phenomenon that can result in more challenging heating conditions with respect to flashover fires (e.g., [47, 48]).
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Because buildings falling in the same category may exhibit significant differences in \({\textbf{X}}\) and \({\textbf{X}}_{strat}\), an occupancy category is inadequate to determine whether a “structurally significant fire” would occur. This argument is supported by the terms entering flashover criteria [49], including area and height of window opening (ventilation factor), compartment area and heat transfer coefficients.
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Occurrence rates based on Eqs. 6 and 7 are calibrated on fire statistics from past events. For example, Sleich et al. [45] referred to incidents reported in different countries between 1983 and 1997. However, these statistics contain limited information on building and fire safety strategy features. Thus, a large open space office with a high ceiling would have the same “severe fire” occurrence rate as an old building with small rooms and limited compartmentation measures, which is clearly not the case. Consistent with this discussion, several authors highlighted the limited availability of fire data to characterise the random variables (e.g., rate of fire occurrence, fire growth rate, room geometry, number of occupants, time-temperature curve parameters) required for risk assessment (e.g., [10, 22, 23]) and pointed out concerns about their reliability (e.g., [18]).
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The built environment is continuously evolving. Consequently, innovative structural configurations and systems (as tall/special buildings, long-span bridges or tunnels often are) may exhibit unpredicted failure modes with unknown failure statistics [50]. This is also due to construction and civil engineering innovations usually happening faster than the evolution of fundamental fire science required to assess safety [51]. Therefore, the significance of fire statistics in computing the annual rate of “severe fire” is limited for risk calculation. Along similar lines, Hopkin et al. [12] explained that risk assessment for atypical or innovative buildings could not rely on a sufficient number of fire event observations.
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Due to the dependency on \({\textbf{X}}\) and \({\textbf{X}}_{strat}\) and the fire-structure coupling effect, Torero [51] discussed that each fire scenario is unique. Therefore, it should not be assigned a probability of occurrence. Similarly, Borg et al. [17] claimed the need for engineers to establish building-specific design fires.
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Akin to the discussion on building fires, the vehicle industry continuously evolves towards sustainable transportation and electric vehicles, which can increase fire occurrence and result in unpredicted fire scenarios. For example, battery fires are becoming an increasing threat [52]. Furthermore, changes in traffic composition (percentage of heavy goods vehicles and tankers), dictated by changing needs of communities, also affect bridge and tunnel fire occurrence rates. Accordingly, an increasing trend in bridge fires has been observed in recent years (e.g., [6, 53, 54]).
3.4 Fire Fragility Models
3.5 Risk Calculation
3.6 Towards an Integrated Approach
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The CFO approach can provide a range of solutions that meet the performance objectives for maximum consequences. In such cases, multi-criteria decision-making techniques [60] can be used to rank design configurations based on the importance of the selected consequence metrics (according to stakeholders’ preferences).
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Some risk-based consequence metrics such as the expected annual loss are well-understood by stakeholders and can provide valuable support for decision-making.
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As highlighted in Sects. 3.2 and 3.4, it is possible to conduct a risk-based assessment when all the fire-scenario component properties listed in Sect. 2.1 are fixed. For example, such properties can be obtained through the CFO approach, thereby bounding maximum consequences to a tolerable or acceptable level.
4 Illustrative Example
4.1 Case Study Description
Parameter | Symbol | Units | Distributon* |
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Fire scenario (only for risk-based) | |||
Peak HRR | \(hrr_{max}\) | kW | Weibull (5256, 2.03) [67] |
Time to peak | \(t_{max}\) | min | Weibull (31.3, 2.12) [67] |
Energy released | ER | MJ | Weibull (5233, 3.23) [67] |
Fuel bed location | \(\alpha _{bed}\) | − | Uniform (0.035, 0.965) |
Tandem system location | \(\alpha _{ts}\) | − | Uniform (0.028, 0.972) |
Steel material (risk-based and CFO) | |||
Yield stress | \(\sigma _y\) | MPa | Lognormal (281, 0.07) [68] |
Elastic modulus | E | GPa | Lognormal (210, 0.03) [68] |
Density | \(\rho\) | \(kg/m^3\) | Normal (7850, 0.01) [68] |
4.2 Thermomechanical Response Calculation
4.2.1 Heat Transfer and Thermal Analysis
4.2.2 Structural Response and Consequence Analysis
4.3 Results and Discussion
4.3.1 Fire Scenarios and Consequence Metrics
Variable | Design A | Design B | |||
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Symbol | Units | Risk-based | CFO | Risk-based | CFO |
\(X_H\) | – | 1.00 | 1.00 | 1.05 | 1.05 |
\(X_{Hgir}\) | – | 1.00 | 1.00 | 1.20 | 1.20 |
\(X_{wf}\) | – | 1.00 | 1.00 | 1.15 | 1.15 |
\(\alpha _{bed}\) | – | Random | 0.654 | Random | 0.734 |
\(\alpha _{hrr_{max}}\) | – | Random | 1.580 | Random | 1.272 |
\(\alpha _{tmax}\) | – | Random | 0.608 | Random | 0.612 |
\(\alpha _{ts}\) | – | Random | 0.631 | Random | 0.696 |
\(t_{c}\) | min | Random | 11.47* | Random | 20.23* |
\(Pr[\overline{t}_{c}<20 min]\) | – | 0.043 | – | \(1.29\times 10^{-5}\) | – |
\(\lambda \left( \overline{t}_{c}<20 min\right)\) | 1/year | \(2.90\times 10^{-3}\) | – | \(8.79\times 10^{-7}\) | – |
\(Pr[\overline{t}_{c,MC}<20 min]\) | – | – | 1.000 | – | 0.026 |
\(CoV(\overline{t}_{c,MC}|collapse)\) | – | – | 0.040 | – | 0.021 |
\(C_I\) | $ | 930,118 | 1,041,378 |
4.3.2 Uncertainty Effect
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Optimised design: By explicitly treating fire scenarios as design variables, the design tolerability is achieved through an optimised trade-off between enhanced structural capacity and reduced fire intensity.
5 Conclusions
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The fire phenomenon is strongly coupled with the structure wherein it develops, enabling an ad-hoc design variable selection to decrease fire intensity (to an extreme where the fire intensity tends to zero). In this sense, the fire intensity becomes an additional design variable (analysis output). This coupling also results in fire scenarios maximising fire impact being specific to each structure. However, most risk-based design approaches consider fire hazard scenario features (first ignited object and its location, fire propagation, fire protection features and characteristics of the studied structure) as additional uncertainty sources (i.e., variables with uncertainties) and set them as analysis inputs.
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The CFO approach, on the other hand, implements a different strategy. It considers fire protection and structure characteristics as design variables and, for a given combination of these features, determines the ignition source and propagation characteristics maximising consequences. The approach then uses MCS to investigate the impact of selected uncertainty sources on the estimated maximum consequence. This process is iterated until design variables are found that reduce fire intensity and ensure that maximum consequences meet the performance objectives. In this way, the design update takes advantage of the fire-structure coupling effect while considering the uncertainty’s impact.
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Limitations were identified in conventional fire risk analysis procedures when used for design purposes. These limitations exist in various analysis steps, including how fire scenarios and intensity are treated, identifying appropriate fire intensity measures, defining models for the annual rate of intensity measure exceedance/scenario occurrence (hazard curves), developing fire fragility models, and carrying out risk calculations. Despite these limitations, it was highlighted that risk-based consequence metrics provide valuable support in ranking design configurations obtained through the CFO approach based on stakeholder preferences. Therefore, the CFO and risk-based approaches can be integrated in the context of multi-criteria decision-making.
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The two approaches were compared through the fire safety design of a simplified case study bridge. The initial design configuration could meet performance objectives in terms of the chosen scalar risk metric. Still, it exceeded a maximum consequence threshold in the low-probability, high-consequence region. The design was therefore updated through CFO approach-informed decisions that simultaneously reduced fire intensity (altering the clearance and the section factor) and enhanced the cross-sectional capacity (modifying the girder’s depth and flange width). When considering the entire risk curve, the risk-based method yielded similar conclusions about the initial design’s compliance. Nonetheless, it faced limitations in finding solutions bounding maximum consequences during design updates.