Uncertainty management for the probabilistic simulation of the thermal resistance of fire barriers

Abstract

Due to the inadequate availability of engineering tools, the conventional test-based method, currently, regulates the design of fire barriers. This thesis aims to provide a supporting simulation-based approach. The objective is to develop numerical models and a simulation framework for the prediction of fire barrier thermal resistance under uncertain fire load and material conditions. The main challenges are the complexity of the thermal behaviour of fibrous barriers to be simulated, the high computational cost of the stochastic simulations accounting for the input uncertainties, and the propagation of model uncertainty to the output distribution. To predict the thermal behaviour of the stone wool, I present a multiphysics model of a fibrous layer, capable of tracking the heat transfer, chemical decomposition and oxygen transfer. As an alternative, I use heat conduction -based model with reaction kinetics coupled to the stone wool's organic content. The results show that the exothermic oxidation of the stone wool's organic matter is responsible for the observed peaks in the cold-side surface temperatures, but the amount of released energy and the height of these temperature peaks are limited by the unavailability of oxygen in stone wools with high organic content. To reduce the computational burden of the probabilistic fire barrier resistance evaluation, I present the use of the Response Surface Method (RSM) and Gaussian Process (GP) regression. The results show that the simple polynomial-based RSM approximation fails when the heat transfer is affected by exothermic reactions. Fortunately, this is in contrast with GP, where the kernel combination made the approximation possible even for such a case. Alongside, I studied the propagation of modelling uncertainty to the predicted output distributions using various examples: compartment fire experiment, stone wool thermal resistance test, a chain of two models, and meta-model based analysis. I propose a simple method of eliminating the propagated modelling uncertainty from the stochastically simulated output distribution. The results show that the proposed method effectively corrects the outputs if the uncertainty correction metric well represents the model uncertainty of the investigated stochastic analysis scenario. The illustrated examples mostly use normal or uniform input distributions, but the method is not bound to any distribution type.