Probabilistic-Based Approach for Evaluating the Thermal Response of Concrete Slabs under Fire Loading

Performance-based design for fire safety has been introduced in several international design frameworks. The fire models and simulations include various assumptions and simplifications, and the current fire resistance evaluation is based on deterministic approaches, leading to uncertainties in the performance of the structural members exposed to fire. An alternative is the application of probabilistic methodologies to assess the fire resistance of the structural members. The authors present the application of an efficient probabilistic methodology to perform a sensitivity analysis to identify the critical variables of a thermal model of a structural element exposed to characteristic fire loading. Furthermore, the methodology determines the reliability of the structural element. The methodology combines the elementary effects method with variance-based methods to rank the influence of the governing variables of the thermal and fire models on the thermal performance of a reinforced concrete slab and to determine their uncertainty contribution to the time-dependent thermal response. Furthermore, the Monte Carlo method is applied to calculate the probability of failure and the reliability index of the structural member exposed to fire loading. The critical governing variables from the fire model are the firefighting measures index, which accounts for firefighting measures used in the compartment ($FFMi$), characteristic fuel load density ($q_{f,k}$), compartment opening factor ($O$), and the ratio of the compartment’s floor area to total area ($A_f/A_t$). The critical governing variables from the thermal model are the coefficient of convection ($h$), concrete specific heat ($c_c$), concrete density ($d_c$), and concrete conductivity ($k_c$). As one moves away from the exposed surface, $h$, $q_{f,k}$, and $A_f/A_t$ are not as influential in the thermal response. Also observed is that the uncertainty of $FFMi$, $O$, $c_c$, and $h$ are the primary sources of the thermal response’s uncertainty. Considering the variability of the input variables, a low-reliability index is determined for buildings with no basic firefighting measures, and adding intervention measures, sprinkler systems, and detection systems will increase the reliability index by 53%, 85%, and 89%, respectively.