Probabilistic models for thermal properties of concrete

Thermal conductivity and specific heat of concrete are highly influential parameters for the heat transfer into the material during fire exposure. Reviewing the available literature has shown that there is a large scatter in the data for these thermal parameters. To quantify that uncertainty, novel probabilistic models for thermal conductivity and specific heat of concrete at elevated temperatures are developed. Analysis of available experimental data indicates that a temperature-dependent Gamma distribution can be recommended for both thermal properties. Closed-form equations for the temperature-dependent mean and standard deviation are derived. Thus, for both the thermal conductivity and the specific heat, a continuous probability distribution as a function of temperature is obtained, which can be easily implemented in numerical simulations. Using the example of the probabilistic analysis of a simply supported concrete slab exposed to the standard fire, the models are compared with the commonly used deterministic representation of the thermal properties. It is shown that the calculated probabilities of failure using the deterministic models are an order of magnitude lower and therefore unconservative. This analysis suggests that accounting for the uncertainty in thermal properties for concrete slabs can have a significant effect on evaluating the safety and therefore should not be ignored in cases of high importance.