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A probabilistic finite elements analysis (FEA) of a tunnel lining subject to fire is presented. 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.

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.

A probabilistic approach for finite element analysis (FEA) for tunnel linings exposed to the nominal fire is presented. The probabilistic FEA accounted for the uncertainties distributions tied to the conductivity and specific heat as well as of the compressive strength, tensile strength, Young’s modulus, and ultimate strain in compression. To get an understanding on the influence of different probability density functions on the distribution of maximum displacements of the tunnel lining, a sensitivity analysis was performed. Four sets of FEAs were carried out with different probability distributions of the conductivity, the specific heat, and the compressive strength of the concrete, respectively. An experimental design based on a Latin Hypercube Sampling algorithm was performed to define the input parameters which describe each analysis case. A reliability analysis was executed considering a limit state function based on the temperature-dependent ultimate strain. The results show that, depending on the distribution adopted, the standard deviation of the maximum displacements can vary up to 47,4% of the minimum standard deviation. The large standard deviation is associated with the possibility of a greater displacement and, hence, to a structure more vulnerable to fire.

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.