Probability Distribution Sensitivity on the Thermo-Mechanical FEM of a Concrete Tunnel Exposed to Fire

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.