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


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.


Barrier failure Fire resistance Monte Carlo Heat transfer Fire test 

List of symbols


Width of control volume (m)




Emissivity of left surface


Emissivity of right surface


Emissivity in cavity


Stefan–Boltzmann constant


Density at control volume i (kg/m3)


Densities in left half of grid (J)


Densities in right half of grid (J)


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


Specific heats of left half of grid (J)


Specific heats of right half of grid (J)


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


Convective heat transfer coefficient in void cavity


Convective heat transfer coefficient at fire side


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


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


Interface conductivities on left face of grid (J)


Interface conductivity at right face of grid (J)

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

Temperature in node i at time step m (K)


Temperature on left surface of void cavity (K)


Temperature on right surface of void cavity (K)


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


Failure temperature of unexposed component (°C)


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



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, network for their funding support of this work.


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Copyright information

© 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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