Fire growth curves and the FRAME fire spread factor i.


In FRAME, the impact of fire growth on the overall fire risk is taken into account by the fire spread factor i, which is a component of the potential risk P :


The formula shows how factor i is calculated with the average dimension of the content m, the flame propagation class M, and the destruction temperature T.


In zone models, the impact of fire growth is typically expressed by a fire growth curve, usually a t² – curve, whereby 4 growth curves are used for the development of the fire from 0 tot 1 MW. These 4 growth rate curves are used for simplicity and convenience. In most zone model programs, the user can adapt the value of the heat release rate to simulate other design fires.
  • slow: the fire grows from 0 tot 1 MW in 600 seconds
  • medium: the fire grows from 0 tot 1 MW in 300 seconds, the burning or heat release rate (HRR) is 250 kW/m².
  • fast : the fire grows from 0 tot 1 MW in 150 seconds, the burning or heat release rate (HRR) is 500 kW/m²
  • and ultrafast: the fire grows from 0 tot 1 MW in 60 seconds

The fire spread factor i of FRAME can be directly linked to the heat release rate of the design fire by the following formulas:

i = log ( HRR / 25 kW/m² )

OR:
HRR = 25 * 10 (i) kW/m²


This link can be explained as follows:

  • For a Medium growth fire, the HRR of 250 kW/m² is typical for a medium growth fire, e.g. an fire in an office environment. In such environment, typical values to define factor i are : m = 0.3, M = 2, T = 250 , resulting in factor i = 1.
  • For a slow growth fire: The slower fire can be found in ordinary hazard group 1 fire risks, like metal workshops. In such environment, typical values to define factor i are : m = 0.1, M = 0, T = 400 , resulting in factor i = 0.7, which gives a HRR of 125 kW/m²
  • For fast growth fires: Fast growth fires are found where combustible liquids or melting plastics are found, say OH3 type activities. In such environment, typical values to define factor i are : m = 0.1, M = 3, T = 100 , resulting in factor i = 1.3, which gives a HRR of 499 kW/m²
  • For Ultrafast growth fires: This growth type is typical for fires with flammable liquids. In such environment, typical values to define factor i are : m = 0.05, M = 5, T = 0 , resulting in factor i = 1.63, which gives a HRR of 1066 kW/m²
  • For Ultraslow growth fires: The lowest value to be found for i is 0.5, for something which is almost impossible to ignite, and corresponds to a HRR of 80 kW/m².
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The added value of fire spread factor i.


The advantage of using factor i, instead of the conventional 4 growth curves, is that a finer tuned approach is possible.
For example, to demonstrate that adding combustible padding for noise insulation in a room will result in a much faster fire growth. This was one of the major contributing factors to the catastrophic The Station night-club fire on February 20, 2003.
The FRAME factor i for a non-combustible night-club environment would be i = 0.85 ( m = 0.3, M = 1, T = 250 ), resulting in a HRR of 177 kW/m².

Bringing in combustible foam padding would change M=1 to M= 4 and i = 1.15 , resulting in a HRR = 353 kW/m² , but it would also change the environment factor r from 0.3 to 0.6, reducing considerably the acceptable risk A1 . These two changes of the values of the influence factors reflect faithfully how the risk increases by using combustible padding in a otherwise low hazard environment.


Typical values for i, the flame-spread factor.


The value of i will vary in the range of 0.5 to 1.65. The first value is representative for a storage of large blocks of concrete. The last one is typical for a heap of chips of expanded polystyrene. For most residential buildings, the value of i will be about 1.2, assuming e.g. that m= 0.1, T = 200 and M = 3.


The components of fire spread factor i


The sub factors m, M and T identify 3 aspects of fire growth, in order to obtain a representative fire curve.
The average dimension m
We know that the smaller an object is, the easier it will burn. In fact, smaller objects have a higher surface to mass ratio. A solid block of wood has a much smaller total surface than the same mass of sawdust. So, in order to define how much surface a fire will find on a certain amount of combustibles, one have to reckon with the ratio between the total volume (m3) and the total surface (m²). This can be done by using the average dimension m of the content (expressed in meter). For average dimensions above 1 m, the value of the factor is reduced, for smaller sizes it is increased.

The most commonly used value for m is 0.3 (equal to 12” or 1 ft). This is the average dimension of most objects found in our daily environment. For palletised storage of goods m = 1 (40”), as this is the average size of palletised packs. For industries where smaller objects are produced or assembled, use m = 0.1 (4”), for industry where film type goods are produced or where a lot of dust is present, one can use 0.01 (1/2 “) as average dimension.
The flame propagation class M.
We also know that some materials can help a fire to spread rapidly and that others do not burn at all. Various test methods have been developed to define the flame-spread characteristics of products, and classifications have been made accordingly.
For the purpose of this method, 6 flame propagation classes, called M are used:
M = 0 is used for incombustible materials,
M = 1 for difficult to ignite (self extinguishing)
M = 2 for slow burning
M = 3 for combustible
M = 4 for flammable
and M = 5 for highly flammable materials.
It is important to notice that these classes apply for the surfaces. A closed metal container with gasoline can be classified as M = 0, and a TV-set in a polystyrene box will be classified M = 4 or even M = 5. For mixed environments, such as in warehouses, an average class as M = 2.5 can also be used in the formula. The flame propagation classes can be linked to material tests, such as the SBI test.
The destruction temperature T.
Finally, we know that most materials will react to fire, even if they do not necessarily burn. For most materials, one can indicate a temperature level where destruction starts. This destruction temperature T, expressed in °C is used as the third element in the calculation of the factor i. Representative values are found in the next table.

TABLE 3 : RECOMMENDED VALUES FOR T, the destruction temperature
Inflammable liquids 0 °C
Human beings, plastics, electronics 100 °C
Textiles, wood, paper, food 200 °C
Average content of residential buildings 250 °C
Machinery, household appliances 300 °C
Metals 400 °C
Non combustible construction materials 500 °C