Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la
première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Internal Report (National Research Council of Canada. Institute for Research in
Construction), 1999-08-01
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.
https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC : https://nrc-publications.canada.ca/eng/view/object/?id=ccb5ff62-254f-4689-bc9e-e98f43726479 https://publications-cnrc.canada.ca/fra/voir/objet/?id=ccb5ff62-254f-4689-bc9e-e98f43726479
NRC Publications Archive
Archives des publications du CNRC
For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.
https://doi.org/10.4224/20331362
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
FIERAsystem Theory Report: Life Hazard Model
*I
R
qa
7 I*I
Council Canada National Research de recherches Canada Conseil nationalnc..
731
c . 2
ZR-RC
FIERAsystem Theory Report= Life
Hazard
Model
D. Torvi, Ph.D., P-Eng., D. Raboud, Ph.D. and G. Hadjisophocleous,
Ph.D., P.Eng.
internal Report No. 781
FlERAsystem Theory Report: Life Hazard Model David Torvi, Ph.D., P.Eng., Don Raboud, Ph.D. and
George Hadjisophocleous, Ph.D., P.Eng. August 9,1999
ABSTRACT
The Life Hazard Model of FlERAsystem calculates the time-dependent
probability of death of occupants in a compartment due to the effects of being exposed to high heat fluxes and hot and/or toxic gases. The Life Hazard Model uses input from other FlERAsystem models that describe the heat fluxes (Fire Development and Smoke Movement Models) in the compartment, and the temperature and chemical composition of hot gases (Smoke Movement Model). Information from this model for each
compartment in the building is used along with the residual population in each
compartment (Occupant Evacuation Model) in order to calculate the expected number of deaths in each compartment (Expected Number of Deaths Model).
TABLE OF CONTENTS
...
...
Nomenclature III...
. 1 Introduction 12 . Probability of Death Due to High Heat Fluxes
...
12.1 Review of Current Models
...
1-4 3.
Probability of Death Due to Hot and/or Toxic Gases...
43.1 Probability of Death Due to Toxic Gases
...
4-5 3.2 Probability of Death Due to Hot Gases . ....
54
.
Overall Probab~llty of Death...
5-7NOMENCLATURE
Notation
A area (m2)
CO concentration of carbon monoxide (ppm) END expected number of deaths
FID fractional incapacitating dose (dimensionless)
P
probability (dimensionless)q" heat flux (kW/m2) T temperature ("C) t time (s)
V thermal dose ( ( k ~ / m ' ) ~ . s )
VC02 multiplication factor for C02
-
induced hyperventilation (dimensionless) Y probit function (dimensionless)%C02 concentration of carbon dioxide (percentage) Greek Letters
rl dummy variable for integration
C compartment CO carbon monoxide cum cumulative D death HG hot gases I ring number inst instantaneous S hot gas layer TG toxic gases TR thermal radiation
1.0 INTRODUCTION
As Canada and other countries move from prescriptive-based building codes to
performance/objective-based codes, new design tools are needed to demonstrate that compliance with these new codes has been achieved. One such tool is the computer model FiRECAMTM, which has been developed over the past decade by the Fire Risk Management Program of the Institute for Research in Construction at the National Research Council of Canada (NRC). FiRECAMTM is a computer model for evaluating fire protection systems in residential and office buildings that can be used to compare the expected safety and cost of candidate fire protection options.
To evaluate fire protection systems in light industrial buildings, a new computer model is being developed. This model, whose current focus is aircraft hangars and warehouses, is based on a framework that allows designers to establish objectives, select fire scenarios that may occur in the building and evaluate the impact of each of the selected scenarios on life safety, property protection and business interruption. The new computer model is called FlERAsystem, which stands for Fire Evaluation and Risk Assessment system.
FlERAsystem uses time-dependent deterministic and probabilistic models to evaluate the impact of selected fire scenarios on life, property and business interruption. The main FlERAsystem submodels calculate fire development, smoke movement through a building, time of failure of building elements and occupant response and evacuation. In addition, there are submodels dealing with the effectiveness of fire suppression systems and the response of fire departments.
The Life Hazard Model of FlERAsystem calculates the time-dependent
probability of death for occupants in a compartment due to the effects of being exposed to high heat fluxes and hot andlor toxic gases. The Life Hazard Model uses results from other FlERAsvstem models that describe the heat fluxes (Fire Develo~ment (e.a.. \
- . .
111) ,, and Smoke ~ b v e m e n t [2] Models) in the compartment, and the temperature and chemical composition of hot gases (Smoke Movement Modelr21).
Information from this model for each compartment-in the building is used along with'the residual population in each compartment (Occupant Evacuation Model[3])
in order to calculate the expected number of deaths in each compartment (Expected Number of Deaths Model [4]).In this report, the theory behind the equations used for each of the calculations in the Life Hazard Model is described. Particular emphasis is placed on the assumptions inherent in the equations used in the model. ~ h e i e assumptions must be kept in mind when considering any results of the FlERAsystem Life Hazard Model.
2.0 PROBABILITY OF DEATH DUE TO HIGH HEAT FLUXES
2.1 Review of Current Models
Current methods for determining the probability of death due to high heat fluxes use either thermal dosage criteria or specific heat flux thresholds. Good reviews of current models can be found in Hockey and Rew [5] and Rew
[6].
As FlERAsystem requires time-dependent probabilities of death, only models based on thermal dosage criteria were considered in the development of the Life Hazard Model.The time-dependent probability of death from exposure to high thermal radiation heat fluxes, P T ~ , at a given location in the compartment, is calculated using the sum of the heat flux from the fire (calculated by the Fire Development Models (e.g., [I]) and the heat flux from the hot smoke layer (calculated by the Smoke Movement Model [2]). The revised vulnerability model of Tsao and Perry [7] is used to calculate the probability of death from the heat flux data. This model uses the following probit equation:
Where:
Y =the probit function; and
V =the thermal dose ( ( k ~ / m ? ~ . s ) .
The thermal dose, V, is calculated using the following equation [S]:
Where:
q" =the incident heat flux (kW/m2); and t =the exposure duration (s).
For a square wave heat flux (i.e., a constant value), Equation (2) reduces to the following equation:
The probit function, Y, is then used to determine the probability of death due to thermal radiation heat fluxes:
Y-5
1
j
e-qx
d,,PTR
(t) = -6,
Tsao and Perry's model is based on the work of Eisenberg, et al 181, who developed a probit relation using data from the atomic explosions in Hiroshima and Nagasaki. Eisenberg used estimates of the heat fluxes at different distances from the nuclear blasts, population data and distributions of deaths to develop the following probit function:
There are several differences between the conditions associated with this data and modelling the effects of an industrial hazard today [5]:
deaths during the nuclear blasts may have been due to pressure effects, as well as high heat fluxes;
medical treatment for burns has improved substantially since 1945;
the population exposed to the nuclear blast would likely contain a much larger percentage of both very young and very old people than in an industrial setting today; and
the exposed population likely had a lower level of clothing (coverage, thickness and masslunit area) than in a typical industrial setting today.
One other major difference is that a single individual, or a small group of individuals, injured in an industrial accident, should expect to get better medical treatment for their injuries than was afforded to a large number of casualties immediately after a nuclear blast.
On the other hand, for the same heat flux, radiation from a nuclear blast should inflict less damage to human skin than radiation from a fire. This is because human skin will absorb practically all of the incident infrared radiation (as in a fire), but will absorb a
substantially smaller percentage of incident ultraviolet radiation (as from a nuclear blast). Therefore, some believe that Eisenberg's model may still be used today, as the
conservative assumptions may balance out the non-conservative assumptions.
Tsao and Perry [i'l did revise the Eisenberg model to account for the differences in the wavelengths of thermal radiation from fires and nuclear blasts. Analyzing data for the times required to produce first degree burns under different wavelengths of radiation, Tsao and Perry found that a factor of 2.23 could be used to relate first degree burn data for ultraviolet radiation to first degree burn data for infrared radiation. They assumed that the same factor could also be used to relate data on fatalities, although there is no experimental data for third degree burns to prove or disprove their assumption. Many of the same comments on Eisenberg's model are also applicable for Tsao and Perry's model.
Neither the Tsao and Perry, nor the Eisenberg models consider the effects of clothing. For example, it has been estimated that 20% of the total surface area of skin will be exposed for a typical adult who is clothed other than their face, neck, lower arms and hands (for young children the percentage would be 30%) [5]. This percentage may increase to 70% during summer. Some examples of estimated unclothed areas are given in
161.
Clothing can be beneficial or detrimental, depending on whether the incident heat fluxes are high enough to ignite the clothing. If they are smaller, then the clothing can protect the underlying skin by slowing the rate of heat transfer to the skin and thus reducing burn injuries. If the heat fluxes are high enough to ignite the clothing, then burn injuries can be more severe than those caused to bare skin by heat fluxes from the original hazard. A review of models to predict the ignition of clothing can be found in Rew[6]
and Hymes, et al [9].The Tsao and Perry, and Eisenberg models do not consider occupant
and females of all ages and physical abilities. In reality, occupant characteristics will vary by building. For example, occupant characteristics will be considerably different in seniors' residences, aircraft hangars, shopping centres and industrial settings.
Hymes, et al [lo] have indicated that the two most important factors in predicting deaths from burn injuries are the patients' age and area of skin bum. In addition, the models do not consider the fact that medical treatment for burns have advanced considerablv since 1945. The treatment an individual or small group of casualties receive today would be considerably different than the treatment afforded to a large percentage of the population of a city, which has just been destroyed by a nuclear blasi. '
-
As the revised vulnerability model of Tsao and Perry does consider the
differences between the nuclear blasts, which the Eisenberg vulnerability model is based on, and fires, which are being modelled here, it is used in the FlERAsystem Life Hazard Model. In addition, it is more conservative than the Eisenberg model. However, the assumptions inherent in the model in terms of occupant characteristics, effects of clothing and medical treatment should be considered when analyzing any results from the FlERAsystem Life Hazard Model.
3.0
PROBABLITY OF DEATH DUE TO HOT AND/OR TOXIC GASES 3.1 Probability of Death Due to Toxic GasesThe orobabilitv of death due to toxic aases is calculated usina the same techniques briginally developed for F~RECA~~~M[I I ] , NRC's compute; model for
evaluating fire protection systems in office and apartment buildings. The FlERAsvstem Life ~ a z a i d ~ o d e l only considers the toxic effects of CO and CO;, because, in most practical fire situations, the effects of CO are the most important. C02 will affect the rate of breathing and hence will affect the intake of CO. The fractional incapacitating dose due to CO (FIDco) is calculated using the following equation and the concentration of CO at a height of 2 m in the compartment of interest:
Where:
FIDco =the fractional incapacitating dose of CO; and CO(t) =the concentration of CO at time t (ppm).
The FID is defined such that the dose will be lethal when FID
=
1.The concentration of C02 is used to calculate a factor, VC02, which is used to increase the FIDco to incorporate the increase in the breathing rate due to C02.
VCO, (t) = exp((0.2496. %CO, (t))+ 1.9086)
Where:
VC02 = the multiplication factor for C02-induced hyperventilation; and %C02 =the percentage of C02 in the compartment of interest.
The total fractional incapacitating dose for toxic gases is calculated using the following equation:
This FID is then used as the probability of death due to breathing toxic gases (i.e., PTG
=
F 1 4 ~ ) .3.2 PROBABILTY OF DEATH DUE TO HOT GASES
The FlERAsystem
Life
Hazard Model also considers the probability of death due to breathing or being exposed to hot gases, PHG. This probability is equal to the FID for exposure to hot gases, calculated using the following equation 1121:t
1
FIDHG (t) =
J
dto
60.
exp(5.1849-
0.0273-
Ts (t))Where:
Ts(t) = the temperature of the hot gases at a height of 2 m in the compartment of interest ("C).
Equation (9) is based on data from the literature for human tolerance times in
experimental exposures to dry and humid air at elevated temperatures. A FIDHG of 1.0 is said to represent the point where a person would become incapacitated by the exposure to the hot gases. This equation should be conservative, as it is based on tolerance times rather than exposure times necessary for death. While the effects of breathing hot gases are not explicitly considered in this equation, Purser
[I21
states that tenability limits, such as Equation (9) that are based on the effects of exposures on human skin should also be adequate to protect them from burns to the respiratory tract.It should be noted that the calculations for the probability of death due to hot or toxic gases are done using temperatures and concentrations at a height of 2 m. While this is considerably higher than the height of most people and it can be argued that all individuals can crawl under a smoke layer of this height, this height was chosen so as to be conservative.
4.0 OVERALL PROBABILTY OF DEATH
The overall probability of death, Po(t), at a given location in the compartment is calculated using the union of the individual probabilities of death from being exposed to high thermal radiation heat fluxes, and breathing hot or toxic gases.
In order to calculate the total probability of death in any compartment using the FlERAsystem Life Hazard Model, the compartment is first divided into a number of rings from the fire, which is assumed to be located at the centre of the compartment, to the compartment walls. The average of the heat fluxes at the inside and outside diameters of each of these rings are used to calculate the probability of death for the ring due to thermal radiation heat fluxes. Equation (10) is then used to calculate the total probability of death for each of the rings. The total probability of death for the compartment is then calculated using a weighted sum of the probabilities of death in each of the rings.
Where:
PD.c(t) =the total probability of death for compartment c; PD.~(~) = the probability of death for ring i;
Ai =the area contained inside ring i; and
A, =the total area of compartment c.
The probability of death is then used by the FlERAsystem Expected Number of Deaths Model to estimate the number of people who may die in each compartment in the building.
The Life Hazard Model also calculates the overall probability of death with time for evacuation routes. This calculation consists of taking the average of the probability of death at each time step for all of the compartments in the building, which have been identified as having an exit. The probability of death with time for evacuation routes is then used by the Expected Number of Deaths Model to estimate the total number of deaths in the building. If there are no doors in any of the compartments in the building being considered, then this calculation is not performed.
The probability of death at each time step calculated using the techniques described in this report is the cumulative probability of death up to and including that time step. In other words, the overall probability of death is based on the dosages received by occupants up to and including the time step of interest. As some
calculations in other FlERAsystem models also require the instantaneous probability of death during a particular time step, the instantaneous probability of death is also calculated in the following manner. The cumulative probability up to and including time step i can be calculated using the following equation:
pcum(i) = Pam(i-x) pinst(i) ' -pcum(i-t)
)
(12)Where:
Pinst = the instantaneous probability; and i-1 = the previous time step.
cumulative probability of death in a compartment during a particular time step can be calculated using the instantaneous probability of death and residual population at the previous time step. This was done in order to simplify the calculations. Rearranging Equation (1 2 ) produces the following equation:
5.0 REFERENCES
1. TON^, D., Raboud, D. and Hadjisophocleous, G., "FIERAsystem Model Theory Report: Enclosed Pool Fire Development Model", IRC lnternal Report No. 784, lnstitute for Research in Construction, National Research Council, Ottawa, ON, 1999 2. Fu, Z. and Hadjisophocleous, G., "FIERAsystem Model Theory Report: Smoke
Movement Model", IRC lnternal Report No. 795, lnstitute for Research in Construction, National Research Council, Ottawa, ON, 1999
3. Raboud, D. and Hadjisophocleous, G., "FIERAsystem Model Theory Report:
Occupant Evacuation Model", IRC lnternal Report No. 792, lnstitute for Research in Construction, National Research Council, Ottawa, ON, 1999
4. Raboud, D. and Hadjisophocleous, G., "FIERAsystem Model Theory Report: Expected Number of Deaths Model", IRC lnternal Report No. 788, lnstitute for Research in Construction, National Research Council, Ottawa, ON, 1999
5. Hockey, S.M. and Rew, P.J., Review of Human Response to Thermal Radiation, HSE Contract Research Report No. 9711 996, Health and Safety Executive (HSE) Books, Suffolk, U.K., 1997.
6. Rew, P.J., LD5, Equivalent for the Effects of Thermal Radiation on Humans, HSE Contract Research Report No. 12911997, Health and Safety Executive (HSE) Books, Suffolk, U.K., 1997.
7. Tsao, C.K. and Perry, W.W., "Modifications to the Vulnerability Model: A Simulation System for Assessing Damage Resulting from Marine Spills (VM4)", ADA 075 231, US Coast Guard NTIS Report No. CG-D-38-79, 1979.
8. Eisenberg, N.A., et al., "Vulnerability Model: A Simulation System for Assessing Damage Resulting from Marine Spills (VMI)", Report CG-D-137-75 (NTIS
AD-A01 5 245), U.S. Coast Guard Office of Research and Development, Washington, DC, 1975.
9. Hymes, I., Boydell, W. and Prescott, B., 'Thermal Radiation: Physiological and Pathological Effects", lnstitute for Chemical Engineers, Rugby, UK, 1996.
10. Hymes, I., Brearley, S., Prescott, B.L. and Zahid, M., 'The Prognosis of Burn Injury Victims", SRDIHSE Report R600, February, 1993, SRD, Culcheth, Chesire.
11. Hadjisophocleous, G.V. and Yung, D., "A Model for Calculating the Probabilities of Smoke Hazard from Fires in Multi-Storey Buildings", Journal of Fire Protection Engineering, Vol. 4, 1992, pp. 67-80.
12. Purser, D.A., 'Toxicity Assessment of Combustion Products", SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA, 1995, pp. 2-85
