Probabilistic CFD and Evacuation Simulation for Life Safety Assessment

1. Probabilistic CFD andEvacuation Simulation forLife SafetyAssessment Cornelius Albrecht & D. HosseriBMB FireProtection Engineering DivisionTechnische Universität Braunschweig

2. Introduction & Motivation • Conventional empirical safety concept: • ASET/RSET > Arbitrary safety factor (usually chosen 2.0-3.0) • Is that overly safe? • Or even too optimistic? • Does it provide the same safety level as “deemed-to-satisfy” (prescriptive) codes? • How do fire protection barriers (sprinklers etc.) influence the safety level? • Are they worth their investment? • Client: Is my life safetydesign really cost-benefit optimized?

3. Introduction • Risk-informed design: • Risk = Sum of Probabilities x Consequences • What are the consequences if it fails? • What is the probability of failure of my life safety design? • Consequences: • People are “delayed” in their egress (visibility/optical density, walking speed) • People are severely harmed and/or incapacitated which can ultimately lead to death (toxic smoke, heat) • Quantification of the consequences in monetary terms? • Life quality index, ALARP, mortality rates, lost-life-years? • Data is missing almost entirely and ethically questionable! • Thus comparative design: How does my solution perform compared to the “deemed-to-satisfy” prescriptive code solution? • Probabilistic reliability analysis!

4. Introduction • Reliability analysis life safety design • State function: z(x) = tASET – tRSET • Failure domain: Ωf≡z(x) ≤ 0 • “Design” point : z(x) = 0 • x is a vector of uncertain parameters, i.e. • Pre-movement time • Walking speed • Number of occupants • Max. heat release rate • Time to 1 MW tg or α, respectively • Soot and/or CO yield • etc. • tASET: complex and “expensive” numerical fire simulation (CFD) • tRSET: (more or less) complex evacuation simulation + additional Δt‘s

5. Reliabilityanalysis • Commonly used reliability algorithms • Classic FORM: not applicable to implicit state functions • Monte Carlo: required number of simulations simply not possible with CFD • Classic least square RSM: only coarse global approximation, results not accurate enough or overfitting • Fast and accurate response surface algorithm: • Preceding sensitivity analysis: reduces dimensionality (filters irrelevant par’ms) • Interpolating Moving Least Squares (IMLS): fast and locally accurate surrogate • Adaptive Importance Sampling to solve reliability problem using the surrogate • This allows for reliability analysis using complex numerical tools with • reasonable accuracy and • in a reasonable time (several 10 runs instead of several 1000, independent evaluation allows for crude parallelization on HP/HT clusters) • More information on the methodology in the paper!

6. Applicationexample • 240 m² small-medium size assembly building • Analysis with probabilistic FDS and FDS+evac • Visibility (optical density 0.1/m, low pass filter to stabilize numerical results) • FED (1.0 with lump sum of irritant gases of 0.3 as they cannot be simulated) • Stochastic modeling based on the literature (partly educated guess) • Two scenarios loosely based on NFPA 101 (which actually requires no t²) • Fire in the bar area: t² with linear incubation phase • Ultra-fast fire on the dance floor: t² • Fire protection barrier analyzed: automatic detection & alarm system • Modeling: Warning/Premovement times are reduced from 180s to 90s on average – this is an assumption! • Failure probability: 10% (BS7974) to “work as designed on demand” From: Madrzykowski (1996)

7. Sensitivityanalysis • Simple: linear or rank correlation and t-test or stepwise regression • What parameters are important? Which are not? Which can we omit to reduce dimensionality and thus numerical costs for the reliability analysis?

8. Reliabilityanalysis • “Per hostile fire” – failure probabilities without detection system • For reference period “1 year” • Fire occurrence 0.02 per year (simplified from BS7974) • Manual intervention at fire start (~50%) Calculatedpfs per hostilefire

9. Impact of a Detection & Alarm System • Re-running the model with reduced warning/premovement times • Additional sub-event tree to model potential failure of the system • Correlation effects are modeled within the scenarios, thus simple multiplication in horizontal direction is possible • Vertically it is a “random walk” through the system, thus summation of the probabilities denotes an upper bound of the system failure probability

10. Impact of a Detection & Alarm System • Results “per hostile fire” WITH and WITHOUT Detection & Alarm System • Results “per hostile fire” considering the previous event tree and 10% failure • Visibility: 0.9 x 0.2142 + 0.1 x 0.6819 = 0.2610 • FED: 0.9 x 0.0174 + 0.1 x 0.0540 = 0.0211 • Results per annum • Visibility: 0.0013 per annum (compare to 0.0034) • FED: 0.000105 per annum (compare to 0.0003)

11. Impact of a Detection & Alarm System • Absolute values have to be treated with care due to all the assumptions • Not comparable to structural reliability requirements • Thresholds, parameters, models, scenarios etc. are highly influential on the calculated probabilities and thus only those based on the same parameter set are comparable! • We call them “operational” probabilities and they usually are conservative • But: comparative design is possible: • Visibility: Increase of safety of a factor 2.6 for the bar fire • FED: 2.85 for the bar fire • That already includes the 10% probability of failure • As the costs of the systems are approx. known, similar analyses with other systems (sprinklers, smoke extraction) can yield the cost-benefit-optimal solution for the particular problem.

12. Conclusions & Outlook • Quantitative, risk-informed design using highly complex numerical tools becomes possible with the RSM approach presented! • Unfortunately, accurate data, scenarios, and models are still missing, but engineer tend to be conservative in their assumptions • Calculated probabilities are “operational” and likely to be conservative • Performing extensive calculations with various similar models for code-compliant buildings allows for the quantification of the currently acceptable safety levels based on the “deemed-to-satisfy” codes • The quantified values can then be used to validate non-code-compliant designs based on quantitative and thus objective comparison using numerical FPE tools • Effect of fire protection systems can be objectively considered and compared to find a cost-benefit optimized solution without (subjective) “gut feeling” • Future: Derivation of a semi-probabilistic safety concept (?)

13. Probabilistic CFD andEvacuation Simulation forLife SafetyAssessment Cornelius Albrecht & D. HosseriBMB FireProtection Engineering DivisionTechnische Universität Braunschweig