Probabilistic Risk Assessment of Life Safety for a Six-Storey Commercial Building with an Open Stair Interconnecting Four Storeys: A Case Study

Abstract

The gold standard for complying Performance Requirements is based on a Quantitative Probabilistic Risk Assessment method. This case study demonstrates the application of this approach to performance based design of a six-storey commercial building with an open stair interconnecting four storeys. Computational Fluid Dynamics based and zone fire as well as evacuation simulations are used to quantify consequences whilst detailed event trees underpinned by statistical data and analysis are utilised to calculate corresponding probabilities. Results are combined in a trade-off analysis tool which calculates the Expected Risk to Life (ERL) based on the trial design features included in each design option. The approach was used to determine a preferred design that achieves an acceptably low ERL and compliance with the Performance Requirements of the Building Code of Australia. The benchmark ERL was set as 1.36 deaths/1000 fires or a probability of death from a fire of 1.36 × 10⁻³ based on local statistical data. To obtain an optimum fire safety design (Alternative Solution) a layered approach was adopted in which fire safety systems were added until the risk to occupants in the building due to a fire is the same or less than the benchmark ERL. Eventually three sets of trial design were considered and in all cases the calculated ERL were roughly 22% lower than the benchmark. Eventually the trial design with the least number of fire safety systems was recommended as the Alternative Solution. The trade-off analysis shows the sprinklers and wall-wetting sprinklers in the office area resulted in a 20-fold difference in the building wide ERL, each.

Appendix: Quantified Design Fire

Design fires are expressed as t-squared fires where:

$$\dot{Q} = \alpha t^{2}$$

where $\dot{Q}$ heat release rate (kW), α = growth rate (kW/s²), t = time since ignition (s)

HRR is escalated over time according to the specified growth rate until sprinklers activate or until the peak HRR is reached. The HRR then remains constant until 80% of fuel has been consumed at which point the fire begins a t-squared decay until all available fuel has been combusted [65].

Sprinkler activation times have been calculated using FDS for design fires 1 and 2 (office fires), and using Alperts Correlation [66] for design fires 4 and 5 (retail fires) and 7 and 8 (carpark fires). To account for sprinkler efficacy in the scenarios where sprinklers activate, statistical data from Table 6.3 of HB-147 [57] was used to calculate the probability of two sub-scenarios (1) Only one sprinkler head is required to control the fire (sprinklers control fire early); and (2) Four sprinkler heads are required to control the fire (sprinklers control fire late). For Design Fires 1–6, 95th percentile fire growth rates were taken from Table 17 of Holborn et al. [58] according to occupancy type.

Peak HRR for Design Fires 1, 2, 4, 5, 7 and 8 are based on the assumption that HRR will remain constant once sprinklers have activated. Effectively it is assumed that sprinklers will control, but not suppress or extinguish the fire. Peak HRR for Design Fires 2 and 4 were taken from Table 10.3 of Staffannson [65]. Peak HRR and growth rates for design fires 7–9 were taken from C/VM2 [43]. HRRPUA was taken from Table 10.4 of Staffannson [65] based on fuel load type. The HRR versus time curves for each of the design fires is shown in Fig. 8.

Figure 8

HRR vs time curves for design fires

Fuel load density was taken from IFEG 2005 [22], Tables 3.4.1a and 3.4.1b based on the most applicable occupancy type and most conservative value between 3.4.1a and the 90% fractile value from 3.4.1b. Fuel load was based on the dominant fuel load in the affected area/floor for each scenario. Species yield and radiative fraction were taken from C/VM2 [43] which is based on a mix of materials. However, modern materials contain a significantly greater mix of polyurethane, in particular for a modern office opting for a larger breakout space with soft seating. This uncertainty was accounted for by picking the worst case scenario or what would be the pessimistic extremity of any range capturing uncertainty. Given the associated peak HRRs in the standard are in most cases higher than those prescribed above, the species yield and radiative fraction is considered conservative. Further, comparison with occupancy-specific recommended yields from Table 10.6 of Staffannson [65] shows that the values used above are conservative (see Table 11).

Table 11 Schematic Design Fires