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This paper presents a probabilistic methodology based on the thermo-mechanical finite elements analysis to investigate the impact of the variability of the thermal properties of the concrete in the fire safety of structures. This is meant to evaluate if characteristic values or safety factors for the conductivity and specific heat are required during the semi-probabilistic structural fire safety assessment. To illustrate the use of the proposed methodology, this work includes a case-study with a tunnel lining which considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and the temperatures described by the standard temperature-time curve. Two failure criteria are considered: one was the maximum temperature of 300 °C at the reinforcement and the other based on the temperature-dependent strength as provided in the Eurocode EN 1992-1-2. Several finite element analyses are performed. The design of experiments is executed by a Correlation Latin Hypercube Sampling. The calculated probability of failure has different values depending on the adopted failure criteria. A sensitivity analysis using the Spearman's rank correlation coefficient was carried out and demonstrates that the uncertainty related to the specific heat has the greatest impact on the results.

Fire safety structural analyses contain uncertainties related to the mechanical aspects, such as compressive strength and tensile strength, and the thermal aspects, such as conductivity, specific heat and fire loads. The uncertainties related to the mechanical aspects are explicitly considered by the applicable standards. However, the uncertainties related to the conductivity and specific heat are implicitly considered by the standards, while the uncertainties related to the fire loads are only considered in the German National Annex of the Eurocode 1991-1-2. Nevertheless, considering the severe nature of tunnel fires, these uncertainties must be incorporated into the design. The complexity of the stresses in a tunnel lining in fire can be determined by a probabilistic thermo-mechanical analysis as proposed in the methodology presented in this work. The methodology presented here to investigate the influence of thermal parameters on the fire safety of concrete structures in tunnels is based on the thermo-mechanical finite element analysis. The methodology includes the design of experiments executed by a Correlation Latin Hypercube Sampling. This work includes three case studies to illustrate the use of the proposed methodology. The second and the third studies contain reliability analyses to evaluate the probabilities of failure. The first case study uses an analytical thermo-mechanical analysis based on the 500 °C isotherm method. It considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and the temperatures described by the standard temperature-time curve. The results demonstrate the importance of incorporating the characteristic values of conductivity and specific heat in the semi-probabilistic structural fire design. The probability of failure is Pf = 3.1 × 10−3. The second case study is a probabilistic thermo-mechanical analysis of tunnels using the standard temperature-time curve. It considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and temperature. The probability of failure is Pf = 0.06. The third case study is a probabilistic thermo-mechanical analysis of the tunnel using natural fire calculated with CFast. It considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and the fire load. The probability of failure is Pf = 0.08. Although the natural fire in the third study results in higher temperatures than the standard fire in the second study, the difference between the failure probabilities of both case studies is smaller than expected. The reason for the small difference is probably that the effects due to the higher temperatures are compensated by the decay phase of the natural fire. The reliability assessments of both the second and the third case study show that the investigated structures do not meet the reliability requirements derived from the EN 1990 standard. Therefore, the structures would either need to be redesigned or more protective methods would need to be provided, such as the thermal boards or sprinklers. The conductivity, specific heat, and fire load are the parameters that correlate to the results the most. For the tunnel structural fire design, the following safety factors are recommended based on this work: γfi = 1.76 for the conductivity, γfi = 0.31 for the specific heat, and γfi = 1.8 for the fire load. Given the range of results of the fire safety analyses, the inclusion of the uncertainties is demonstrated to be necessary. The choice of failure criterion has a significant influence on the probability of failure and is, therefore, a critical step in the safety analysis. For the tunnel fire, the model must be improved to accurately account for the fast heating rate and the cooling phase of tunnel fires.

Probabilistic thermo-Mechanical analysis of a concrete tunnel lining subject to fire The probability distributions of the parameters related to the thermal analysis was considered in order to study the variability of the results and to carry out a reliability analysis. This assessment considered as random variables the thermo-mechanical properties of the concrete, the maximum heat release rate (HRR), the duration of the period of maximum HRR, the convective coefficient, the emissivity at the surface exposed to the fire, the air velocity within the tunnel, and the initial fire radius. The temperature-time curve was described by a correlation. An experimental design based on a Latin Hypercube Sampling algorithm was performed to define the input parameters to each analysis case. The definition of a limit state function based on the punctual strain status has permitted to carry out a reliability analysis.

This paper presents a probabilistic methodology based on the thermo-mechanical finite elements analysis to investigate the impact of the variability of the thermal properties of the concrete in the fire safety of structures. This is meant to evaluate if characteristic values or safety factors for the conductivity and specific heat are required during the semi-probabilistic structural fire safety assessment. To illustrate the use of the proposed methodology, this work includes a case-study with a tunnel lining which considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and the temperatures described by the standard temperature-time curve. Two failure criteria are considered: one was the maximum temperature of 300 °C at the reinforcement and the other based on the temperature-dependent strength as provided in the Eurocode EN 1992-1-2. Several finite element analyses are performed. The design of experiments is executed by a Correlation Latin Hypercube Sampling. The calculated probability of failure has different values depending on the adopted failure criteria. A sensitivity analysis using the Spearman's rank correlation coefficient was carried out and demonstrates that the uncertainty related to the specific heat has the greatest impact on the results.