The impact of the egress time on the FRAME risk assessment.
"Prediction of the movement of occupants during egress is an essential aspect of performance-based building fire safety analysis
methods. In general, life safety from fire is achieved if the required safe egress time (RSET) is shorter than the available safe egress
time (ASET), where the ASET is defined as the time when fire-induced conditions within an occupied space or building become
untenable." (SFPE handbook p.3-367).
RSET means Required Safe Egress Time. This time is usually calculated by simulating the evacuation movement of the people in the
compartment, whereby some assumptions are made for the reaction of people in case of a fire, the composition of population and the
way the flow of the persons is going. The tools available vary from simplified methods with manual inputs to very powerful computer
simulations for large groups.
ASET means Available Safe Egress Time. This time is
usually calculated by simulating a "worst case" design
fire in the design compartment by zone model computer
program and checking the time necessary to reach
untenable conditions, usually expressed as the time to
reach a cold air layer of less than 2.5 m, a high CO
content of the cold air, or an unacceptable level of
vision. In most case studies , the governing factor is the
depth of the hot smoke layer (or height of the cold
layer).
How this principle is applied is shown in the following
scheme (from the SFPE handbook p 3-347)
In a scenario type fire safety analysis, it is common practice to compare a worst case RESET with a worst case ASET, but in reality the
probability of such a simultaneous occurrence is low, and in many situations there may still be a comforting safety margin. For a risk
assessment approach, measuring the gap between ASET and RSET is probably a better option, and this is applied in FRAME.
The formula for A1, the acceptable risk for the occupants, considers that margin between RSET and ASET as a contributing element for
the risk assessment. The ASET is largely defined by smoke layer conditions which are taken into account by the ventilation factor v, but
for the speed of smoke and heat production the environment factor r is used as reference measurement. A potentially fast developing
fire will result in a high value of factor r, which means a short ASET.
The evacuation time factor t is used for the RSET.
Both values are included in the formula : A1 = 1.6 - a - t - r
When a comfortable margin can be expected between the RSET and ASET, the value of A1 will be above 0.8, which means a lower risk.
On the other hand, when the calculated RSET is high, the value of A1 will be go below 0.8, indicating an increased risk.
Note : The value of A1 of 0.8 is usually compensated by a protection degree D which is around 1.25
The RSET can be subdivided into a number of time intervals, the sum of which constitute the total RSET:
RSET = td + ta + to + ti + te
where
td = time from fire ignition to detection; ta = time from detection to notification of occupants of a fire emergency;
to = time from notification until occupants decide to take action; ti = time from decision to take action until evacuation commences; te
= time from the start of evacuation until it is completed.
The RSET elements td and ta may involve hardware, such as fire detection devices and fire alarm equipment, and human response, such
as discovery of fire, or other indication of fire, and giving the alarm. The elements to and ti relate the individual and collective responses
of the occupants until they commence evacuation.
FRAME Approach
The evacuation time factor t in FRAME uses a formula which combines a calculation of the egress time with a mobility factor linked to the
human response. The evacuation factor t is calculated with the following formula:
p*x*[ (b+ l) + (X/x) + 1.25*H+ + 2* H-]*(b+l)
t = --------------------------------------------------------------
800* K* [1.4 * x * (b+l)-0.44* X]
The body of the formula for evacuation time factor t is a time calculation based on the formulas and values found in the SFPE FPE-
handbook (chapter 3-13 Movement of People: The Evacuation Timing.).
Evacuation distance
The first part of the formula concerns the calculation of the evacuation distance, and is composed of
(b+l ) + X/x + 1.25 * H^{+} + 2 * H^{ -}
FRAME assumes that the occupants will travel at a constant speed S on an exit path that has the same width as the doors. On stairs, the
speeds of movement are slightly lower and, at low densities, relatively fit people can average about 1.1 m/s descending along the stair
slope, which is slower than on level parts. But as fire safety codes require stairs to be wider than the door openings, and as people will
take staggered positions on stairs, which increases the flow capacity, it can be assumed that the descend speed is basically the same as
in the corridor. For up going stairs, the FRAME formula assumes that the movement is 60 % slower.
However, in cases where the exit path contains stairs which are narrower than the access or exit
doors , the number of exit units should be measured on the stairs, using a free width of 75 - 80
cm as minimum unit width.
( b+l ) : the sum of the length and the width of the compartment is the longest travel distance (in
meters) inside a compartment for a person when he is stays in one corner of the compartment and
has to walk to an exit in the opposite corner. This part of the formula gives the time to reach the
most remote exit at a walking speed of 1 meter/second. (see figure).
X/ x : is the passage of X persons through x exit units. Assuming the it takes about one second per person to go through the door
opening, this part of the formula translates the passage of one person into a walking distance of about one meter. The passage of one
person per second has been observed in uncontrolled total evacuation drills in well-populated office buildings.
1.25 * H^{+} : is the equivalent distance for going downstairs for a distance of H^{+} , assuming that the length of the stairs is 1.25 times the
height.
+ 2 * H ^{-} : is, alternatively, the equivalent distance for going upstairs for a distance of H^{-} , and assuming that the stair is 1.25 times the
height of the stair and that a person walks about 60 % slower on a rising stair than on a level path.
Evacuation speed
The second part of the formula concerns the calculation of the walking speed of mobile healthy people, and is composed of :
x * (b+l)
-------------------------------
[1.4 * x * (b+l)- 0.44* X]
This speed depends on the pedestrian density on the exit path, and is expressed by the formula :
S = k - a k D. = k. (1- a.D)
In this formula k is a constant ( = 1. 26 m/sec for horizontal exit route elements) , a = 0.266 and D is the density expressed in persons
per m². For a density of 0.4 persons/m², this formula gives a walking speed of 1.25 m/sec and for a density of 3.75 persons/m² the
speed has go down to 0 m/sec.
This formula comes from the SFPE handbook and is in line with observation that: "Expressed quantitatively, when the pedestrian density
is less than about 0.5 persons/m2 (21 ft2/person), people are able to move along walkways at about 1.25 m/s (4.1 ft/s), an average
unrestricted walking speed. With greater density, speed decreases, and it decreases very markedly with very high densities, reaching a
standstill when density reaches 4 or 5 persons/m2 (2.1 to 2.6 ft2/person)"
To calculate the density of the occupants, FRAME uses an imaginary exit corridor where all the occupants (X) are gathered at the same
time.
Mobility of the occupants
The third element in the formula is the mobility factor p, and corrects the calculated time estimation for such complications as people
who need guidance or help, panic, unclear evacuation schemes, etc. Factor p considers the evacuation time under such conditions as a
multiple of the calculated time for healthy mobile and independent persons. Table 7 of the handbook gives an overview of the most
common situations.
TABLE 7. The mobility factor p
Type of occupants
value of p
A. Mobile and independent persons ( e.g. workers)
1
B. Mobile but dependent persons ( pupils)
2
C. Immobilized persons (patients, elderly)
8
D. There is no clear evacuation plan
+2
E. There is a danger for panic
+2
F. People with limited perception capacities, such as patients,
elderly, disabled persons, sleeping guests in hotels, etc.
+2
Using the same idea that in unfavourable conditions the evacuation time will be a multiple of a "standard" situations, this table could be
replaced in a future version of FRAME by a more detailed one, that takes into account more aspects of human response and behaviour,
such as : response to perception of fire and smoke; recognition of the emergency situation; time delays to start the movement;
composition of the occupant group, gender and age distribution; nonadaptive and panic behaviour; handicapped and impaired occupants,
alertness; crowd behaviour and management; familiarity with the location; building layout and way finding.
These elements are somehow included in the FRAME time calculation , but are more developed in evacuation time models. The FRAME
calculation sheet provides the possibility to use the result of an evacuation model in the risk assessment calculation.
Multiple and distinct exit paths.
The fourth element in the formula is k.
The sub factor k is the number of separate exit directions or exit paths available. The total evacuation time is reduced as people when
people have more than one way to find an exit. In buildings with a moderate to high occupant load, such as offices and places of
assembly, the fire safety codes require more than one exit path and a more or less even distribution of the exit units along the perimeter
of the compartment.
The national requirements how to calculate the required width of the exits differ considerably from one country to an other. The basis is
always the occupant load of the compartment, multiplied by a width coefficient. In some countries the calculated width is required for
each exit, while others calculate the total required width for all exits together and impose limiting conditions on the differences.
In "FRAME" the X/x part of the factor t formula corresponds with an exit speed of one person per second per exit unit of 60 cm useful
width. But the maximum capacity of such an exit unit is 120 persons per minute. If more people try to use this exit, they will be cueing
to pass, which slows down the exit movement.
"FRAME" reckons with that maximum capacity to define the number of available exit paths. When all the exit units are needed to satisfy
the evacuation need for the occupants at 120 persons/ unit , all exits together shall be considered as a SINGLE useful exit path. Only
where there is an excess of exit units present , FRAME will consider these as extra exit paths. This may be the case in buildings with low
density occupant loads ( factories, warehouses), where the number of doors is defined by operational requirements and/or by maximum
allowable travel distances imposed by codes.
To define the number of DISTINCT exit paths, the maximum capacity of all exit units together shall thus be compared with the number of
persons that need to use these exits.
Two directions are considered as separate if one must turn for 90\260 ° or more to go from one exit path to another. A maximum of 4
separate exit paths is thus possible.
Evacuation time target.
The fifth element in the formula is the value 800 = 1.11 x 720 in the denominator, which compares the calculated evacuation time with a
preset value.
The value of 720 had been "backward engineered" with the assumption that an adequate level of protection is obtained when the people
in the building have already evacuated the building at the time the fire brigade arrives at the fire scene, for a low hazard situation such
as : a non industrial activity in a modern non-combustible building, with a basic manual fire protection but no automatic fire detection,
located in a small urban area with a semi-professional fire brigade.
For such a situation, the value of P1 = 1 and the value of D1 = 1.20 . This means that the value of A1 can be = 0.83 for a well protected
building with R1 =1 .
Further on, assume for the activation factor a = 0.1 (e.g. electrical installation in compliance with the rules without regular checks, no
other special hazards) and for the environment factor r = 0.1 log (Qi + 1 ) + M/10 = 0.25 , i.e. Qi = 0 and M = 2.5 ( medium to slowly
burning surfaces) .
This means that for A1 = 0.83 the value of t can be: 1.6 - 0.1 - 0.25 - 0.83 = 0.42 .
With 720 as correction factor, this corresponds with an evacuation time 0.42 *720 = 300 seconds or approx. 5 minutes, after the
evacuation signal is given.
In a building with a higher hazard which is either expressed by a higher activation factor a and/or a higher environment factor r, the
margin left for t will be smaller, or otherwise the longer the evacuation time is, the higher the risk is estimated.
When a building is equipped with automatic fire detection and alarm systems, the value of D1 increases to 2.16 , which means that for
R1 = 1, the value of A1 can be = 0.46 or t = 1.6 - 0.2 - 0.2 - 0.46 = 0.74 or an acceptable evacuation time of 0.74 * 720 = 532 or
approx. 9 minutes. This can also be accepted , as with automatic detection and alarm, the detection and reaction times will be shorter,
leaving more time for the evacuation itself.
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