The probability of occurrence.
In FRAME, the combination of probability related factors is spread between P and D to fit practical design conditions, as some
parameters are more linked to the buildings’ location, the others to the design of fire protection systems.
What is really evaluated is not the probability of "a” fire, but the probability that the fire grows beyond control and reached the severity
of the worst case. Kinney proposes a single value for the probability, but in fire oriented developed methods using the event tree
approach, the final "worst case" probability is split up in several sub factors: one for the probability of ignition, one for the probability of
early control, one for extinguishing by the fire brigade, sprinklers etc., and finally one for the probability that the an uncontrolled fire
engulfs the compartment and destroys it. A similar combination of probability related factors is used in FRAME.
Probability of ignition.
A number of fire safety studies consider the probability of ignition to be more or less uniform within compartments with similar
occupancies, supported by statistical values. A few surveys have established such values for offices, housing, industrial building: they
are in a range around 10-6 events per m² per year. The probability of ignition is therefore linked to the compartment floor area: the
larger the compartment, the more likely a fire will occur. In prescriptive codes, compartment size limitations are apparently not linked
to probability, but inspired by a concern for controllability of the fire by limiting the total quantity of combustibles (area x fire load).
This approach is probably too much of a simplification: In fact the size of a compartment does not only define the number of (evenly)
distributed ignition sources, but has also an impact on the time necessary to discover the fire, the occurrence of secondary ignition
sources and the time necessary for the fire brigade to reach the seat of the fire.
In FRAME the occurrence of ignition is used as part of the exposure evaluation: A building and its users are only exposed to the fire
once ignition has occurred: The more ignition sources available in building or compartment, the higher the exposure is and hence the
less a fire risk becomes acceptable. This is included in the acceptable risk A.
Building configuration is a risk aggravating element and is built in the area factor g, the level factor e, and the access factor z. The
shape of the compartment, the presence of intermediate galleries and multiple levels and the location versus the access level are also
included.
Building configuration is a risk aggravating element and is built in the area factor g, the level factor e, and the access factor z. The
shape of the compartment, the presence of intermediate galleries and multiple levels and the location versus the access level are also
included.
In the "natural fire concept" approach the increase in compartment size from 2500 m² to 10.000 m² causes a 15 % increase of fire
severity value. For the same situation, the g-factor in FRAME doubles the value of P, which means a 100 % increase in fire severity
value, reflecting not only the increased probability of ignition but also the decrease in controllability of the fire, resulting from the
reduced capacity of occupants and fire brigade to gain early control in a large building or less accessible spot.
It should be noted that in FRAME the g-factor does not intervene in the risk assessment for the occupants. As any developing fire is
considered as "worst case for people", the size of the compartment is not considered as relevant for severity and/or probability of the
risk to persons. However, the size and shape of the compartment is considered in the calculation of A1, but this is a measure for the
"exposure" and is dealt with separately.
Probability of controlling the fire.
1/D indicates the probability that a fire develops fully into a catastrophic situation: A high level of protection reduces considerably the
probability of such event.
Statistical fire studies estimate the probability of early control of the fire by the occupants to be between 45 and 75 % of the cases,
based on comparisons of the number of insurance claims and the number of fire brigade interventions in areas where both data were
well documented.
The probability of effective control by fire brigades and sprinklers again is derived from statistical information on insurance claims: e.g.
from the ratio between medium value and high value insurance claims, an average fire brigade effectiveness (= limiting the fire to the
room of origin) of 90% is deduced. Sprinkler reliability is reasonably documented, so effective sprinkler control can be evaluated. The
main causes of sprinkler system failure are also well known and the reliability of a particular sprinkler protection can be fairly well
assessed. Anchor points are also the premium rebate percentages used by the insurance industry for active fire protection: higher
rebates mean that the final cost of the fire is statistically lower and thus that corresponding fire protection systems are more reliable.
Reliability of protection elements in FRAME.
FRAME protection degree sub factors W (water supply), N (normal protection), S (special protection), U (escape) and Y (salvage) deal
with a large number of variants of design features, active fire protection devices and systems, fire fighting organisation, etc., as well
with reliability aspects. Early control by the occupants is e.g. considered as part of the normal protection. It can be easily checked that
the values used in the evaluation of these factors reflect the relative contribution of these features to the overall probability of
successful control of fire before it reaches a critical situation. A lack of water supply on the premises results in a value for W, which just
means that the fire brigade has one chance in two to extinguish the fire with the water in their trucks. The combined result is a
"probability" correction for the risk assessment formula.
In FRAME the probability of control is written as a division by "protection factors". The values of N and W are in fact always <= 1, so
1/W and 1/N give "failure rates" >= 1: When the quality of the water supply and of the normal protection are substandard, the
probability that a fire can be controlled is reduced. The values of S, F (and U and Y) are always >= 1: the higher these reliability
factors, the lower the probability of failure.
Probability of building collapse.
The probability of a final "victory" of fire depends in the end on the fire resistance of the structural and separating elements compared
to the estimated duration of the fire. In general, codes require a certain level of fire resistance for structural and non-structural
elements, compared with the available fire load as basis combined with a safety factor to reduce the probability of ruin by fire. A typical
fire in a non-industrial environment has an average ISO 834 duration between 30 and 45 minutes.
Code requirements basically start with 30 minutes fire resistance for small and low-rise buildings, with increasing levels of requirements
for medium height; taller and high rise buildings. As the fire duration does not basically change with the height of the building, the
higher fire resisting requirements are in fact safety factor applications to reduce the probability of collapse in case the fire breaks out of
the original fire compartment into other levels of the building.
FRAME deals with this aspect in the resistance factor F and reckons with three assumptions.
The first is that the available stability in case of fire, is the joined result of the stability of structure the roof, floors, walls and internal
separations. There is no scientific proof for counting these in a 50 %, 25%, 12.5 % and 12.5 % combination, yet there is no research
done to support a better guess.
The second is that the value of F has to reflect the increased reliability of high fire resistance performance components, but also that
the higher fire resistance may not be needed, certainly if the fire load is limited. This is dealt with in the first part of the F-formula,
which gives a "bent" increase for F versus fire resistance. The absolute value of F also increases in the same way as the safety factors
applied in building codes and at the same time follows broadly the same curve as the e-factor, so that the traditional link between
building height and fire resistance requirements is also observed.
The third assumption is that building designers shall neither rely entirely on active fire protection systems or on passive fire resistance.
This is accomplished by the second term of the F-formula, where the value of the special protection S is used to decrease the final value
of F.
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