Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Cornelius Albrecht & D. Hosser iBMB Fire Protection Engineering Division Technische Universität Braunschweig Probabilistic CFD and Evacuation Simulation for Life Safety Assessment

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 2 Introduction & Motivation  Conventional empirical safety concept:  ASET/RSET > Arbitrary safety factor (usually chosen )  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 safety design really cost-benefit optimized?

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 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!

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 4 Introduction  Reliability analysis life safety design  State function: z(x) = t ASET – t RSET  Failure domain: Ω f ≡ 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 t g or α, respectively  Soot and/or CO yield  etc.  t ASET : complex and “expensive” numerical fire simulation (CFD)  t RSET : (more or less) complex evacuation simulation + additional Δt‘s

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 5 Reliability analysis  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!

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 6 Application example  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)

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 7 Sensitivity analysis  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?

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 8 Reliability analysis  “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%) Calculated p f s per hostile fire

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 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

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 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 x =  FED:0.9 x x =  Results per annum  Visibility: per annum (compare to )  FED: per annum (compare to )

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 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.

Fire & Evacuation Modeling Technical Conference | Baltimore, August 2011 | Cornelius Albrecht | Page 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 (?)

Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Cornelius Albrecht & D. Hosser iBMB Fire Protection Engineering Division Technische Universität Braunschweig Probabilistic CFD and Evacuation Simulation for Life Safety Assessment