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The structural fire resistance of buildings is often determined through the application of guidance documents or defined in prescriptive requirements. Probabilistic risk assessment (PRA) provides an alternative framework within which it is possible to assess the appropriate fire resistance in terms of time-equivalence. Typically, PRA studies require several building specific stochastic parameters as inputs and involve a multitude of calculation iterations to assess an output variable distribution (in an un-biased manner). However, it can be difficult to adopt PRA in design due to limitations with the current available engineering tools. This paper describes a library of a probabilistic functions written in Python that can be used to estimate the distribution of fire severities expected within an enclosure for a given scenario. The application of the Python library is illustrated by an exemplar 18 m tall office building design case, where the required structural fire resistance is computed based upon the (conditional) reliability targets underpinning BS 9999.
The required fire resistance of a given structure is most commonly specified based upon contemporary guidance documents. In the UK, this could be applying BS 99991 or other guidance documents2,3,4 depending on the building height, its use, etc. Such guidance provides a simple approach to determining the minimum required structural fire resistance. In BS 9999 the specific ventilation-dependant fire resistance period tables were derived from the time equivalence method, applied in a probabilistic framework based the works by Kirby et al5. However, limitations inherited from the studies underpinning the guidance in BS 9999 are often overlooked. For example, the corresponding background research5 notes that the recommendations for offices are only compatible with compartment sizes of up to 1,000 m² in floor area. In addition, the underlying fire models (i.e. the Eurocode parametric fire) are only readily applicable to fire compartment areas of up to 500 square metres6. These limitations mean that building specific analyses are often required to realise the rationalisation opportunities provided by BS 9999 when buildings sit outside the noted limitations.
Probabilistic risk assessment (PRA), as documented in PD 7974-7:2019, provides an alternative framework within which to assess the appropriate fire resistance (e.g. in terms of time-equivalence) for a spectrum of building specific fire scenarios, adopting stochastic variables for key fire development inputs. Such methods have been documented in the literature and employed by others5,8,9,10,11, and have been adopted on real world engineering projects12. Since PRA can be building specific and apply fundamental methods, the limitations within the prescriptive methods as stated previously can be addressed.
Monte Carlo simulation (MCS) is one method of conducting a PRA. A general MCS procedure is shown in Figure 1. The MCS intake stochastic parameters, each defined as a probability distribution based upon statistics of historical data. Then several (equal to desired number of simulations to run) sets of parameters are randomly generated using the prescribed probability distributions. Finally, a calculation is carried out for each input parameter set. In this work this is the time-equivalence calculation.
Nevertheless, it is difficult to adopt PRA in engineering projects due to limitations in the current available engineering tools. A building specific PRA involves relatively complex calculation procedures and given the available timeframe in the realm of real-world engineering design, conducting a building specific PRA using custom made tools can lead to difficulties for reviewers in the reproduction of results.