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Cornelius Albrecht & D. HosseriBMB Fire Protection Engineering DivisionTechnische 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 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?

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) = 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

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 pfs 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 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)

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. HosseriBMB Fire Protection Engineering DivisionTechnische Universität Braunschweig

Probabilistic CFD and Evacuation Simulation for Life Safety Assessment