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Fire Technology

, Volume 55, Issue 4, pp 1319–1347 | Cite as

A Monte Carlo-Based Probabilistic Barrier Failure Model for Arbitrary Fire Environment

  • Xiao LiEmail author
  • Xia Zhang
  • George Hadjisophocleous
Article

Abstract

Failure of building assemblies is a combined results of both heat attack and the mechanical response of the assembly components. The latter could change the integrity of a fire barrier and the pattern of heat transfer. The prediction of failure becomes more complicated when it comes to non-standard fires where real-world experiments are limited. 2-D or 3-D numerical models may provide useful results but their sophistication of use still drives the needs for simple models that offer quick results. A probabilistic barrier failure model is developed to simulate the dynamic process of barrier failure and reflect its stochastic nature. The model comprises a deterministic heat transfer and component response submodel that calculates one-dimensional heat transfer and component responses in fire such as the fall-off of gypsum boards. Further, a Monte Carlo-based probabilistic barrier failure model is created by sampling the influential factors that affect the failure of components. The fire barriers applied in the model include light timber frame and light steel frame assemblies as well as cross laminated timber assembly, but the model is open to other assemblies where data are available. The model results are validated against five room fire tests with good agreements, and an example calculation demonstrates that in a real fire the failure of fire barriers may occur earlier or later than that in the standard fire.

Keywords

Barrier failure Fire resistance Monte Carlo Heat transfer Fire test 

List of symbols

∆x

Width of control volume (m)

ε

Emissivity

εls

Emissivity of left surface

εrs

Emissivity of right surface

εc

Emissivity in cavity

σ

Stefan–Boltzmann constant

ρi

Density at control volume i (kg/m3)

ρJ,left

Densities in left half of grid (J)

ρJ,right

Densities in right half of grid (J)

ci

Specific heat at control volume i (J/kg·K)

cJ,left

Specific heats of left half of grid (J)

cJ,right

Specific heats of right half of grid (J)

h

Convective heat transfer coefficient at ambient surface (W/m2·K)

hc

Convective heat transfer coefficient in void cavity

hf

Convective heat transfer coefficient at fire side

ki,l

Interface conductivity (W/m·K) at left face of control volume i

ki,r

Interface conductivity (W/m·K) at right face of control volume i

kl

Interface conductivities on left face of grid (J)

kr

Interface conductivity at right face of grid (J)

\( T_{i}^{m} \)

Temperature in node i at time step m (K)

Tls

Temperature on left surface of void cavity (K)

Trs

Temperature on right surface of void cavity (K)

Tfail,gyp,fire

Failure temperature of fire-exposed gypsum board (°C)

Tfail,assemly

Failure temperature of unexposed component (°C)

Tfail,steelstud

Deflection temperature of steel stud in LSF assembly (°C)

Notes

Acknowledgements

The authors would like to thank Natural Sciences and Engineering Research Council of Canada (NSERC), FPInnovations and all other sponsors of NEWBuildS (NSERC strategic research Network for Engineered Wood-based Building Systems, www.newbuildscanada.ca) network for their funding support of this work.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vortex Fire Consulting IncTorontoCanada
  2. 2.WSPOttawaCanada
  3. 3.Department of Civil and Environmental EngineeringCarleton UniversityOttawaCanada

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