Demonstrating adequate safety for a concrete column exposed to fire, using probabilistic methods

Abstract

Demonstrating adequate safety for exceptional designs and new design applications requires an explicit evaluation of the safety level, considering the uncertainties associated with the design. The recently published PD 7974-7:2019 provides five routes to demonstrating adequate safety through probabilistic methods but does not include worked examples. The case study in this paper presents three state-of-the-art approaches for demonstrating achievement of an absolute safety target (acceptance concept 'AC3' in PD 7974-7:2019) for a concrete column in an office building with stringent reliability requirements. The case study shows how fragility curves listed by, for example, industry organizations can support probabilistic approaches and a more comprehensive understanding of design performance.

Generalized fragility curves for concrete columns exposed to fire through surrogate modelling

“…The high-fidelity model is a finite element model in SAFIR [17], which involves a computational cost to solve the nonlinear thermalstructural computation. The probabilistic studies have been presented in [18] and incorporated in [19]. The cross-section of the considered column is 500 mm × 500 mm, reinforced with 12 bars of 20 mm diameter, which is shown in Figure 1(a).…”

“…Finally, the high-fidelity model is evaluated for each of these generated training and cross-validation sample points. In the present study, to allow comparison with the results by Van Coile et al [18], the surrogate model is trained to predict the maximum axial load bearing capacity of the column (Pmax) for a specified duration (240 min) of ISO 834 fire exposure. In order to achieve this, the numerically obtained fire resistance for the RC column is considered as input parameter for the surrogate model, while the axial load on the column is considered as response of the surrogate model.…”

“…To validate the proof-of-concept, the probability density function (PDF) and cumulative density function (CDF) for the considered RC column, developed based on the proposed framework is compared against that obtained by a traditional direct Monte Carlo approach. The validation is carried out for maximum axial load for the considered RC column exposed to 4 hours of ISO834 fire, as presented in [18]. Table 2 shows the uncertain model variables along with their probabilistic distributions [18,21] for the probabilistic evaluation.…”

“…The validation is carried out for maximum axial load for the considered RC column exposed to 4 hours of ISO834 fire, as presented in [18]. Table 2 shows the uncertain model variables along with their probabilistic distributions [18,21] for the probabilistic evaluation. A set of 10 4 LHS samples are developed for the considered stochastic variables.…”

A practical tool for evaluating fire induced failure probability of steel columns designed based on U.S. prescriptive standards

“…Steel modulus of elasticity reduction factor F, = 1.1 × Model uncertainty for capacity KR: Lognormal distribution, mean of 1.0 and COV = 0.15 [8] Note: is the standard normal distribution and is the temperature in [°C].…”