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Testing and application of the computer model ‘SIMULEX’
Fire Safety Journal 24 (1995) 14%166
~) 1995 Elsevier Science Limited Printed in Northern Ireland. All rights reserved ELSEVIER
0379-7112/95/$09.50 0379-7112(95)00020-8
Testing and Application of the Computer Model 'SIMULEX' Peter A. Thompson & Eric W. Marchant Fire Safety Engineering Group, Department of Civil and Environmental Engineering, The Crew Building, The King's Buildings, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JN, UK (Received 20 February 1995; revised version received 20 April 1995, accepted 26 April 1995)
ABSTRACT A number o f computer models for the evacuation o f buildings have been produced in recent years. These models typically use a system k n o w n as ' n e t w o r k - n o d e ' modelling, which makes a number o f large assumptions concerning human motion. Methods used in the software package ' S I M U L E X ' differ from the traditional methods o f assessing motion in terms o f average parameters and 'flow rates'. The most significant feature o f the model is the geometrically accurate simulation o f the evacuation movement o f each individual person from a building space. The algorithms which achieve this movement are not based on any standard method o f evacuation modelling, so it is important to assess how realistic the algorithms prove to be, and also to investigate the performance o f the system as a whole. This paper describes a series o f tests in which S I M U L E X models the movement o f a large group o f people through a number o f exits o f different widths. The maximum sustainable flow rates that were achieved in the tests are presented and compared to data from different sources. The application o f S 1 M U L E X to the proposed design o f a large commercial store is also discussed.
1 INTRODUCTION Design guides, such as the U K regulations,t consistently regard the m o s t i m p o r t a n t aspect of crowd m o v e m e n t to be the relationship t The term 'UK regulations' is used to reference the approved regulatory guidance for Means of Escape in Approved Document B. 1 149
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P. A. Thompson, E. IV. Marchant
between the width of an exit passageway and the maximum sustainable flow rate through that passageway in terms of the number of persons per second. This relationship is regarded as linear for passage widths greater than 1.1m. Therefore, the standard form of evaluating a flow rate is by using a figure that expresses the flow rate in terms of the number of people per unit width per unit time. The usual units are: number of people; metres; and seconds respectively, although some design guides express the unit width as a multiple of a standard body breadth (0.5-0.6 m). Values of maximum flow rate per unit width, from different sources, are presented in Table 1. Very few data are available for passages that are less than 1-1 m wide. The publication 'Post War Building Studies No. 29 'lz describes a series of tests by the Paris Fire Brigade where groups of firemen moved through different width exits under controlled conditions. These tests suggested that there was no real significant difference in flow rate per unit width between a 1 m and a 1.1 m wide exit, although the validity of the results should be viewed with scepticism due to the 'unreal' nature of the experiments. The UK regulations ~ suggest a rapid reduction in flow rate per unit exit width when exits are less than 1.1 m wide. There appears to be no real evidence for this effect, other than the knowledge and judgement of the original engineers who devised the guidance on exit capacities. The computer program 'SIMULEX' has been used to model a number of specific evacuation movements and flow rates. The principles and algorithmic processes that are incorporated into the model are described by Thompson and Marchant. 13 The modelling package requires output from two other programs, D R A W P L A N and G R I D F O R M . The program D R A W P L A N allows the user to accurately define the building space, by defining a large number of wall 'units'. G R I D F O R M analyses the user-defined building space, and creates a 'map' of points whose numeric value is equal to the optimal distance to an exit from that point. This 'distance map' is used by SIMULEX to assess escape routes throughout the building plan.
2 TESTING OF FLOW R A T E S WITH SIMULEX
It is important that S I M U L E X produces realistic sustainable flow rates over a range of different exit widths because unrealistic flow rates will
151
Testing o f the computer model ' S I M U L E X ' TABLE 1
Summary of Maximum Pedestrian Flow Rates for Level Passageways Source
Maximum design flow (persons/ m/s)
UK regulations 1
1.33 (derived from exit capacities) 1"37 1.82 (unit exit width method) 1.48
1.92
Fruin 5
1.37
4-37
Daly6 Ando et al. 7
1.43
Fire and Buildings, The
1-50
Approved Document B.
SCICON report 2 Guide to Safety at Sports Grounds 3
Hankin and Wright 4
Polus et al. 11
1.3 (effective width method) 1.25-1"58
Comments
Standard British code for buildings
1.7-1"8
Aqua Group s Predtechenskii and Milinskii 9 SFPE handbook ~°
Ultimate flow capacity (persons/ re~s)
Data from football crowds Based on Japanese data and derived from 60 persons/0.55 m/min unit exit width calculation Commuters on the London Underground Max. flow is a peak regimented, 'funnelled' flow under pressure For underground stations Japanese commuters at railway stations. General design text
1'83
'Emergency conditions' for adults in mid-season dress 2 × 0.15 m boundary layers deducted from width of exit
1.58
Pedestrian movement on sidewalks in Israel
produce unreliable results when calculating the total evacuation times f o r d i f f e r e n t b u i l d i n g s . A set o f tests w e r e t h e r e f o r e c a r r i e d o u t to investigate the performance of SIMULEX by simulating the evacuation o f a specific n u m b e r o f i n d i v i d u a l s o v e r a w i d e r a n g e o f exit w i d t h s in o r d e r to assess t h e m a x i m u m s u s t a i n a b l e f l o w r a t e o f t h e g r o u p t h r o u g h different passageways. This form of testing was useful because the
152
P. A. Thompson, E. W. Marchant
motion of the individuals, moving in close proximity through a restricted opening, invoked all of the decision and movement algorithms. The tests therefore presented an overall measure of the performance of the individual calculations within SIMULEX, when applied to pedestrian movement through a fairly standard exit geometry.
2.1 Testing procedure The evacuation simulation program was used to test flow rates through exit widths over the range 0-7-3.0 m, in increments of 0.1 m. A typical 'exit flow test' geometry is illustrated in Fig. 1. The section of corridor that the exit leads into is 5 m long, and of 5 m internal width. The centre of the exit is aligned with the centre of the corridor. The initial test conditions consisted of a group of 100 individuals that possessed random initial angles of orientation and an initial population density of 4persons/m 2. The conditions were intended to simulate a fairly concentrated, non-panicking crowd. The section of corridor was placed on the other side of the exit so that the motion of the people as they passed through the exit opening and spread out into the wider passageway could be observed. It was necessary to model the movement of the occupants after they emerged from the 'test' exit because their movement could affect the motion of individuals behind them, who were in the process of moving into or through the opening. Occupants were removed from the evacuation process when they reached the end of the 5 m section of corridor. For each test on an exit greater than 1 m wide, exactly the same group of 'people' were used, in terms of initial position, orientation, and normal unimpeded walking speed. The only difference in initial conditions for each test was the lateral width of the exit. The test conditions were changed for exits less than 1.1 m wide because when narrow exits were tested with the highly concentrated group initially placed at the mouth of the exit, a permanent 'jam' of bodies occurred within the first 10-15 seconds of movement. The front two rows (20 people) were removed in order for more space to be available for movement in the initial stages of evacuation. Therefore, in the narrow exit tests, the foremost members of the group (now reduced from 100 to 80 persons) started 2 m back from the face of the exit opening. Each test was initiated by clicking on, the 'Evacuate' icon on the
Testing of the computer model "SIMULEX'
153
At the start of a test run]
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S I M U L E X screen display. W h e n the evacuation started, the individuals in the group i m m e d i a t e l y began to orientate themselves towards the exit by turning at the rate of 10 degrees per time-step (0.1 seconds), and then started to walk towards the opening. The time taken for the first 10 occupants to pass t h r o u g h the 'test' exit was noted as T~0. W h e n the evacuation p r o c e e d e d , the time at which 10 people r e m a i n e d behind the
154
P. A. Thompson, E. W. Marchant
exit (that is, the time taken for a total of 90 occupants to pass through the exit) was then n o t e d as Tg0. The exit functioned at its m a x i m u m sustainable flow rate for the duration b e t w e e n T~0 and T90. In the case of the n a r r o w e r exits, T~0 and Tg0 w e r e replaced with Ts and T70 to a c c o m m o d a t e the lower n u m b e r of occupants, and to reflect the fact that the m a x i m u m flow rate was achieved m o r e quickly than for the flow tests on the wider exits. The times were accurate to one tenth of a second. It was sometimes difficult to ascertain the exact time when a specific n u m b e r of people had passed through the exit because it was fairly c o m m o n for two people to walk through at the same time, side by side. For example, the 10th and l l t h occupants might leave the exit simultaneously, leading to the possibility that only 79 people, instead of 80 would pass through the exit b e t w e e n T~0 and Tg0. The n u m b e r of exiting persons (80 or 65) was t h e r e f o r e accurate to +1 person over the entire range of tests. 2.2 Test results
The times Tg0, T~o, TT0 and T5 obtained during the tests, were used to calculate the flow rates per m e t r e width for each exit tested. T h e formulae for the flow rate calculations are p r e s e n t e d in eqns (1) and (2). 80
Qw(
Qwhere: Q = w= T~0 = Tl0 = T70 = =
( w > =1.1 m)
(1)
-
65
w(:rTo-
(w < 1"1 m)
(2)
flow rate ( p e r s o n s / m / s ) exit width (m) time for 90 persons to pass through exit (s) time for 10 persons to pass through exit (s) time for 70 persons to pass through exit (s) time for 5 persons to pass through exit (s).
Some variation in flow rates was expected because the different attributes of individuals (initial orientation, u n i m p e d e d walking speed) would create different patterns of m o v e m e n t when the group m o v e d through different exit widths. The actual variation in flow rates that was e n c o u n t e r e d was not regarded as excessive. The flow rate achieved for
Testing of the computer model 'SIMULEX' Graph
of
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Flaw
Rate
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/"
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-~.3.5
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values f o r doorways less than 1.1m wide apply to crowds that start at least 2m
/
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Fig. 2. Graph of crowd flow rate against passageway width---comparing SIMULEX results with other data. each width of exit was plotted on the graph presented in Fig. 2, where the results are plotted on the same graph as the values quoted by Hankin and WrighP and the U K regulations (Approved D o c u m e n t B). ~ 2.3 Analysis of results The linear relationship between flow rate and exit width was observed in the S I M U L E X test runs for widths greater than or equal to 1.1 m, at the m a x i m u m sustainable rate of 1-40persons/metre width/second. This value lies between the data points plotted from Hankin and WrighP and the UK regulations I in Fig. 2, and compares well with a n u m b e r of design values quoted in Table 1. The sustainable (design) flow rates in Table 1 vary considerably, depending on the source of the data, but values typically lie in the range 1 . 3 - 1 - 5 p e r s o n s / m e t r e width/second. The value of 1.4 p e r s o n s / m e t r e width/second, yielded by the simulation tests, therefore indicates that the algorithms and parameters incorporated into S I M U L E X combine to produce realistic sustainable exit flow rates. The difference in values between the S I M U L E X tests and A p p r o v e d D o c u m e n t B 1 for exit widths less than 1-1 m, is significant. However, there appears to be no experimental evidence for the figures in the UK regulations for exit widths of less than 1.1 m, so they may not represent realistic flow rates. In fact, the Code for Safety to Life ~4 uses the same
156
P. A. Thompson, E. IV. Marchant
figures for total flow capacity per unit width (1 occupant per 5 m m exit width) for all exit widths greater than 0.9 m. S I M U L E X produced complete stagnation of m o v e m e n t for high density groups attempting to move through narrow exits (less than 1 m) when the foremost m e m b e r s of the group were initially positioned at the face of the exit. Sustained flow was only possible by ensuring that the group began m o v e m e n t at a distance of 2 m back from the exit. By effectively moving the initial position of the group of people away from the face of the exit, the density at which the occupants entered the exit was reduced slightly. This initially reduced density enabled the maintenance of m o v e m e n t through the opening and allowed test results to be obtained, although the flow was somewhat irregular, and the 'pulsing' flow behaviour observed by Pesch115 sometimes occurred. Continuous m o v e m e n t could not be achieved for exits less than 0-75 m wide as the bodies of different individuals became 'entwined' with each other and j a m m e d against the edges of the exit opening. The m o v e m e n t of individuals emerging from the exit into the wider corridor proved to be important because it did, as expected, affect the m o v e m e n t of the occupants who were entering, or already in, the exit opening. As individuals emerged from the exit, they resumed the expected patterns of overtaking and twisting. This produced the effect of the emerging group 'spreading out' laterally across the 5 m section of corridor and produced group formations similar to the 'zone' configurations observed by Fruin, 5 where each person appears to possess a circular zone of 'personal space'. 2.4 Parameters for m o v e m e n t
The results from these tests are encouraging, because they indicate that the m o v e m e n t parameters used in the program were sufficiently realistic for the simulation of a normal, non-panicking crowd. In S I M U L E X , the most important parameters that affect the transition of people through an opening are the rate of body twist and the threshold distance. If the rate at which the bodies of individuals can turn is not restricted, then the overall flow rate of a group of people generally increases by approximately 10%. If the threshold distance (the furthest inter-person distance at which the presence of one person affects the speed of another) is reduced, then the flow rate increases dramatically. The threshold distance that corresponds to the data derived from A n d o e t a l . v is 1.1 m (assuming circular zoning). When S I M U L E X uses a threshold distance of 1-1 m instead of 1-6m, the m a x i m u m sustainable flow rate increases to 1.7 persons/m/s. This value corresponds well to
Testing of the computer model 'S1MULEX'
157
the average ' m a x i m u m ' flow rate of 1.65-1.75 p e r s o n s / m / s calculated from the data produced by A n d o et al. over the range 1.55 . 0 p e r s o n s ] m 2. This indicates that S I M U L E X may be able to model cultural a n d / o r psychological differences between different groups of people by changing the threshold distance of individuals, which hence affects the overall flow rate through a passageway. People who are in a hurry and therefore possess a higher 'anxiety level' are likely to accept more of an invasion of personal space than in normal, comfortable conditions. This could be modelled by decreasing the threshold distance and would result in an increase in the overall flow rate. The effects produced by occupants possessing different body sizes have not yet been fully explored. S I M U L E X currently assigns the average body dimensions of 0.5 m × 0-3 m to each person. It is certain that if all members of a group of people possess significantly larger body sizes than normal, then the overall flow rate will decrease as a result. A few test runs of S I M U L E X have been executed for groups of individuals with much larger body dimensions than normal, moving through an exit geometry similar to that illustrated in Fig. 1. The m a x i m u m sustainable flow rate in such tests was found to be reduced by as much as 50% due to the increase in body sizes. Unfortunately, no comprehensive real-life data are currently available to compare the effect of differences in body size upon the overall flow rate achieved by a group of people moving through a passageway of specific width. The flow rate data presented by Predtechenskii and Millinskii 9 suggest that the m a x i m u m flow rate (persons/unit width) is inversely proportional to the average plan area of the body of a single person in the group. Hankin and Wright 4 observed that schoolboys, walking through a 'test' circuit achieved a significantly higher peak flow rate than adult commuters who were unaware that their m o v e m e n t was under analysis. However, the commuters achieved a greater m a x i m u m sustainable flow rate. Comparisons of this kind become uncertain where the variation of experimental data and the form of analytical methods used, mean that it becomes very difficult to isolate the effect of changing individual parameters such as body size.
3 A P P L I C A T I O N OF S I M U L E X TO A P R O P O S E D BUILDING DESIGN S I M U L E X is intended for eventual use as a design tool, to be used by fire safety engineers, and possibly architects and building engineers when devising the geometric layout of buildings in the design stages.
158
P. A. Thompson, E. W. Marchant
This section describes the application of the computer modelling system to the design of a branch of a well-known superstore. This building will subsequently be referred to as The Superstore.
3.1 Design requirements The Superstore was chosen as a case study because it was still in the design stages, and certain aspects of the design had not been finalised. One important aspect was that the design population density had not been finalised, and it was uncertain whether a population density of 7.0m2/person or 4.0mZ/person was applicable to the design. The reasons for the use of two different population densities was that The Superstore was to sell primarily do-it-yourself (hardware) goods. The figure quoted by UK regulations 1 for the occupant density of supermarkets and d e p a r t m e n t stores is 2.0 m2/person, but this concentration of people is not normally e n c o u n t e r e d in D I Y stores and was not d e e m e d to be appropriate. The occupant density quoted by the same guide for shops that sell primarily furniture, floor coverings, cycles, prams and large domestic appliances is 7-0 m2/person. The classification of D I Y stores may sometimes lie between these two categories, so a figure of 4.0m2/person is often used instead of 7.0m2/person. The designers therefore wished to assess the capacity of the building plan for evacuation for the two different initial population conditions.
3.2 Spatial analysis The single-storey plan of The Superstore was input using D R A W P L A N , 13 which took approximately 4 hours. Walls, stacks, racking and other immovable obstructions were defined with the use of 'wall units'. At two points, small 'wall units' were drawn 3 m from the boundary of the plan to ensure that the spatial analysis algorithms assessed a 3 m wide space a r o u n d the perimeter of the building in addition to the defined building plan. The program G R I D F O R M segmented the space into a mesh of 0.25 m × 0.25 m spatial blocks; assigned the perimeter of the 3 metre boundary space with a distance to exit of zero, and formed the distance map. This process required approximately 10 minutes c o m p u t e r processing time. The building plan and distance m a p were downloaded by S I M U L E X . The distance m a p was scanned, and the m a x i m u m travel distance
159
Testing of the computer model 'S1MULEX'
(using optimal route directions) was found to be 44.7 m. The perimeter space width of 3 . 0 m was deducted from 44.7 m to yield a m a x i m u m travel distance within the building of 41.7m. The travel distance of 41.7 m was just within the limit of 45 m specified by UK regulations, t 3.3 Simulated evacuations
The perimeter of the occupied sales area (95% of the building plan) was defined as input by the program user, and the area was calculated by S I M U L E X to be 7674.4m 2. The densities of 7.0m2/person and 4 . 0 m 2 / p e r s o n were entered for the two evacuations. Therefore, the n u m b e r of occupants placed initially in the building were 1097 and 1919 persons, respectively. A n evacuation was modelled for each occupancy loading, and the flow rate results stored for later analysis. A n example of one of the simulated evacuations is illustrated in Fig. 3. The simulation of the two evacuations illustrated the general patterns of m o v e m e n t and queuing that occurred during the entire escape process. The distance m a p had been formed in such a way that all
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The simulated evacuation of The Superstore, after 10s. Initial density = 4 m2/person.
160
P. A. Thompson, E. W. Marchant
occupants m o v e d towards the nearest exit. In both evacuations, Exits 1, 2, 3, 8, 9 and 10 were the only exits that approached or achieved the m a x i m u m flow rate and caused queues to form behind the face of the exit opening. The rate of flow throughput at Exit 7 was h a m p e r e d by the constrictions within the escape route before the exit. The aisle that served most of the occupants using Exit 5 was actually narrower than the width of the exit doorway. Exit 5 therefore never approached its m a x i m u m potential flow rate. Exit 4 was oversized for the n u m b e r of occupants that it served. Exits 1, 2, 3, 6, 7, 8, 9 and 10 all experienced the convergence of different flows of occupants as they emerged from different aisles and moved towards the exits. The convergence of different flows at Exit 3 is illustrated in Fig. 4. 3.4 Design calculations It is possible to apply standard approximate design calculations to The Superstore to predict the total evacuation times, and compare the values obtained with the results of the simulated evacuations carried
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161
Testing of the computer model 'SIMULEX' TABLE 2
Width of Exits for The Superstore Exit number Measured width,
1
2
3
3"5 3"6 3.5
4
5
3.4 3.6
6
7
8
9
2.4
2.4
1.8 ~]W=31"8
2-1 2.1
2.1
1.5
5-2 2.4
10
Total
W(rn) Effective width,
3.2 3.3
3.2 3.1
3.3
4.9
~] We=28"8
We(m)
out by SIMULEX. The exit widths are presented in Table 2. The effective widths quoted are based on a 0-15 m wide boundary layer at each side of the exit, as specified in the SFPE handbook. 1° The predicted evacuation times for this building will either be governed by the travel time of the person who is initially most remote from an exit (where the exits do not function at maximum capacity), or the time required for the population to 'flow' through the exits (where the maximum flow capacity of the exits dictates the evacuation time). No time is required for the crowd to arrive at the exits, because the even distribution of the occupants throughout the sales area ensures that a number of people will be at or near the exits at the start of the evacuation. No impediment to normal walking speed through the main body of The Superstore is envisaged in accordance with the observation from Hankin and Wright 4 and the SFPE handbook, 1° that walking speeds are generally unaffected for crowd densities less than 0.5persons/m 2 (7m2/person is equal to 0.14person/m 2 and 4mZ/person is equal to 0.25person/m2). The unimpeded walking speed quoted in the SFPE handbook 1° is 1.19 m/s. Equation (3) is used to calculate the evacuation time for either of the design occupancy loadings, assuming that the width of the exits does not restrict the total flow rate of people leaving the building. d 41.7 Twa,k- 35"0 (3) v 1"19 where:
Zwalk = time to walk from most remote point in building to exit (s)
d = travel distance from most remote point (m) v = unimpeded walking velocity (m/s). If we use the normal design assumption that all exits are used
162
P. A. Thompson, E. W. Marchant
optimally, then the total 'flow time' can be calculated, based on simultaneous, m a x i m u m sustainable flow through all exits. Equation (4) uses data from the SFPE h a n d b o o k , 1° which uses the effective width calculation method. This m e t h o d produces a slightly longer 'flow time' than would be produced if the exit capacities quoted in the UK regulations I were used. Qtot = E W e x q = 28"8 X 1"3 = 37"4
(4)
Nocc 1097 T7 - Q,o~- 37"~- - 29.3
(5)
Nocc 1919 37-~ - 51-3.
(6)
T4 - Qto~t -
The notation for eqns (4)-(6), applying to m a x i m u m sustainable flow through all exits is as follows: Qtot = q= ~]We = T7 =
total combined flow capacity of all exits (persons/s) flow rate per unit exit width -- 1.3 (persons/m effective width/s) total effective exit widths (m) total evacuation time for occupancy loading of 7-0 m2/ person (s) T4 = total evacuation time for occupancy loading of 4.0 m2/ person (s) Nocc = total n u m b e r of building occupants.
The results from eqns (3)-(6) suggest that an evacuation of The Superstore for an occupancy loading of 7 m2/person will be governed by the time taken to walk from the most remote point of the sales area, because Twa~kis greater than TT. The calculations predict that for this fairly low occupancy loading, stagnation or queuing will not occur because the occupants will not arrive at different rates to achieve the m a x i m u m flow rates that the exits are capable of accommodating. However, the evacuation of a population with an initial density of 4 m2/person will be influenced by the flow capacity of the exits, rather than the u n i m p e d e d walking time because T4 is greater than Twa~kTherefore, for the larger population, queues will be set up as the flow rate of people arriving at exits is greater than the m a x i m u m sustainable flow rates of the exits. The evacuation times predicted by these 'optimal' design calculations for occupancy loadings of 7 m2/person and 4 m2/person are therefore 35.0 and 51.3 s respectively.
163
Testing of the computer model 'SIMULEX'
3.5 Predictions of evacuation times and flow rates
The design calculations yield optimistic predictions for the building evacuation times, c o m p a r e d to the times predicted by S I M U L E X , and they tell us little about the geometric complexities of the evacuation. When S I M U L E X was used to model the two evacuations of The Superstore for occupancy loadings of 7 m2/person and 4 mg/person, the predicted total evacuation times were 58-1 and 105.1 s respectively. The evacuation times predicted by S I M U L E X are significantly greater than those predicted by using eqns (3)-(6) for both occupancy loadings, because the geometry of the building space, and the merging of different occupant groups from different aisles led to the formation of queues at some exits while others never achieved their m a x i m u m flow capacity. S I M U L E X predicted that the evacuation time for the initial density of 4m2/person was 81% longer than for the initial density of 7m2/person. This greater evacuation time occurred because the increase in occupant numbers produced significantly more queuing at a n u m b e r of exits, and all of the building exits never simultaneously achieved m a x i m u m flow throughput. In fact, some of the exits never achieved more than 50% of their m a x i m u m flow capacity. A graph representing overall evacuation flow rates from the building using the output from S I M U L E X is illustrated in Fig. 5. g
Graph of Flow Rate Against Time f o r simulated evacuation
~ 406
35
~, 30:
.....
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g 25:
20~m15-
g ~102 ~
5-
0 O
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I , I I I I I T I I I l , l l f
lo
20
30
~ l l , l l l l l l r l l ~ , l l t l l ~ l l l l l ,
40 50 oo 70 Time (seconds)
80
i
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Fig. 5. Graph of total exit flow rate against time for two simulated evacuations of The Superstore.
164
P. A. Thompson, E. W. Marchant
In both evacuations, the rate at which occupants leave the building increases rapidly in the first 10 s, and climbs to a peak between 20 and 30 s. The total flow rate then 'tails off' as some exits are completely emptied, while others are either still serving queues of people or groups of slower individuals that have taken significantly longer to arrive at the exit openings. The larger number of occupants in the 4m2/person evacuation produced slightly higher flow rates because exits that did not achieve their individual maximum flow capacities served more occupants than in the 7 m~/person evacuation. The fact that these exits were more fully utilised when more occupants were present meant that they contributed more to the total flow rate from the building at the peak flow times. The peak flow rate achieved for the whole building was 38.7persons/s at 25-30s for an initial occupancy loading of 4mZ/person. The flow throughput of each exit during the period in which the peak total evacuation flow was observed and estimated numerically by the user as a fraction of the maximum possible flow rate for that exit. These exit usage values are presented in Table 3. The figures in Table 3 demonstrate that even at the peak flow rate of numbers of occupants leaving the building, only six of the exits operate at, or near, the maximum sustainable flow rate. These 'partially used' exits could either be repositioned to serve a larger percentage of the population or reduced to a size more suitable to the number of occupants that they serve. For example, Exit 5 could be moved upwards (on the plan) to be located directly at the end of the main aisle that spans left to right across the shop floor area. This change of geometry would increase the number of people that the exit served; would directly align it with a wider passageway, and the exit would therefore operate at a higher flow rate efficiency. It would also be clearly visible to the occupants in that central aisle. However, no design changes were TABLE 3
Exit Usage at Peak Flow in The Superstore Evacuation for an Initial Occupancy Loading of 4.0 m2/Person Exit number Usage as a fraction o f maximum possible flow for each exit
1
2
3
4
max. max. max. emptied 1
1
1
0
5
6
7
8
9
10
p a r t p a r t part max. max. max. ~
½
]
1
1
1
Testing of the computer model 'SIMULEX'
165
strictly necessary because the evacuation times predicted are significantly less than the m a x i m u m stated by UK regulations.
4 CONCLUSIONS The outputs from this version of S I M U L E X have been c o m p a r e d to the figures obtained by using fairly standard methods of calculation because this version of the c o m p u t e r model makes some initial assumptions that are similar to those m a d e when using the calculations, where complex psychological aspects of evacuation are ignored. Standard design calculations and statutory guidance cannot accurately predict the evacuation performance of a building which contains complex spaces where groups of escaping people meet from different directions as they travel towards the final exits. The application of S I M U L E X to geometrically complex building designs is useful because it is capable of highlighting areas where different group 'flows' meet, queues form, stagnation of m o v e m e n t may occur, and also where exits are significantly oversized or undersized for the n u m b e r of occupants that they actually serve. It is crucial that any c o m p u t e r model that produces results which will be used to assess life safety produces consistently realistic results. The tests carried out to evaluate m a x i m u m sustainable exit flow rates indicate that S I M U L E X produces results that correlate well to the data obtained from real-life observations, when analysing m o v e m e n t through a single, open passageway. When the development of Version 3 is complete, similar tests will be carried out to evaluate parameters for egress m o v e m e n t on staircases. The final, multi-storey version of S I M U L E X will be subjected to a rigorous series of tests to investigate how the results produced by the model correlate to full-scale 'real life' evacuations in a n u m b e r of different buildings.
REFERENCES 1. Department of The Environment and The Welsh Office, The Building Regulations--Approved Document B, (Section B1, 1992 ed.) HMSO, London, 1991, pp. 9-40. 2. Poyner, B., Robinson, D., Hughes, N. & Ayles, P., Safety in football stadia; a method of assessment. Report for SCICON, Scientific Control Systems, London, 1972. 3. Home Office/Scottish Office, Guide to Safety at Sports Grounds. HMSO, London, 1991.
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4. Hankin, B. D. & Wright, R. A., Passenger flows in subways. Operational Res. Quart. 9 (1958) 81-8. 5. Fruin, J., Pedestrian Planning and Design. The Metropolitan Association of Urban Designers and Environmental Planners, New York, 1971. 6. Daly, P. N., Pedestrian speed/flow relationships for underground stations. Traffic Engng Control, 32 (1991) 76-8. 7. Ando, K., Ota, H. & Oki, T., Forecasting the flow of people (in Japanese). Railway Res. Rev., 45 (1988) 8-14. 8. The Aqua Group, Fire and Buildings. Granada, London, 1984. 9. Predtechenskii, V. M. & Millinskii, A. I., Planning for Foot Traffic Flow in Buildings. Amerind, New Delhi, 1978 (translated from original publication in Russian, 1969). 10. Nelson, H. E. & MacLennan, H. A., Emergency movement. In The SFPE Handbook of Fire Protection Engineering, ed DiNenno, P. J. National Fire Protection Association, Quincy, MA, 1995, pp. 3-286-3-295. 11. Polus, A., Schofer, J. L. & Ushpiz, A., Pedestrian flow and level of service. J. Transportation Engng, 109 (1983) 46-7. 12. Joint Committee on Fire Grading of Buildings (Ministry of Works), Fire grading of buildings, part III, personal safety. In Post War Building Studies No. 29, HMSO, London, 1952 pp. 71-87. 13. Thompson, P. A. & Marchant, E. W., A computer model for the evacuation of large building populations. Fire Safety J., 24 131-48 (1995). 14. NFPA, Capacity of means of egress, Section 5-3. In NFPA lO1--Code For Safety to Life. National Fire Codes, National Fire Protection Association, Quincy, MA, 1991. 15. Peschl, I. A. S. Z., Doorstromingscapaciteit van deuropeningen bij panieksituaties, B O U W nr 2 9-1-1971. Private translation of Flow Capacity of Door Openings in Panic Situations, 1971, pp. 62-7.
~) 1995 Elsevier Science Limited Printed in Northern Ireland. All rights reserved ELSEVIER
0379-7112/95/$09.50 0379-7112(95)00020-8
Testing and Application of the Computer Model 'SIMULEX' Peter A. Thompson & Eric W. Marchant Fire Safety Engineering Group, Department of Civil and Environmental Engineering, The Crew Building, The King's Buildings, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JN, UK (Received 20 February 1995; revised version received 20 April 1995, accepted 26 April 1995)
ABSTRACT A number o f computer models for the evacuation o f buildings have been produced in recent years. These models typically use a system k n o w n as ' n e t w o r k - n o d e ' modelling, which makes a number o f large assumptions concerning human motion. Methods used in the software package ' S I M U L E X ' differ from the traditional methods o f assessing motion in terms o f average parameters and 'flow rates'. The most significant feature o f the model is the geometrically accurate simulation o f the evacuation movement o f each individual person from a building space. The algorithms which achieve this movement are not based on any standard method o f evacuation modelling, so it is important to assess how realistic the algorithms prove to be, and also to investigate the performance o f the system as a whole. This paper describes a series o f tests in which S I M U L E X models the movement o f a large group o f people through a number o f exits o f different widths. The maximum sustainable flow rates that were achieved in the tests are presented and compared to data from different sources. The application o f S 1 M U L E X to the proposed design o f a large commercial store is also discussed.
1 INTRODUCTION Design guides, such as the U K regulations,t consistently regard the m o s t i m p o r t a n t aspect of crowd m o v e m e n t to be the relationship t The term 'UK regulations' is used to reference the approved regulatory guidance for Means of Escape in Approved Document B. 1 149
150
P. A. Thompson, E. IV. Marchant
between the width of an exit passageway and the maximum sustainable flow rate through that passageway in terms of the number of persons per second. This relationship is regarded as linear for passage widths greater than 1.1m. Therefore, the standard form of evaluating a flow rate is by using a figure that expresses the flow rate in terms of the number of people per unit width per unit time. The usual units are: number of people; metres; and seconds respectively, although some design guides express the unit width as a multiple of a standard body breadth (0.5-0.6 m). Values of maximum flow rate per unit width, from different sources, are presented in Table 1. Very few data are available for passages that are less than 1-1 m wide. The publication 'Post War Building Studies No. 29 'lz describes a series of tests by the Paris Fire Brigade where groups of firemen moved through different width exits under controlled conditions. These tests suggested that there was no real significant difference in flow rate per unit width between a 1 m and a 1.1 m wide exit, although the validity of the results should be viewed with scepticism due to the 'unreal' nature of the experiments. The UK regulations ~ suggest a rapid reduction in flow rate per unit exit width when exits are less than 1.1 m wide. There appears to be no real evidence for this effect, other than the knowledge and judgement of the original engineers who devised the guidance on exit capacities. The computer program 'SIMULEX' has been used to model a number of specific evacuation movements and flow rates. The principles and algorithmic processes that are incorporated into the model are described by Thompson and Marchant. 13 The modelling package requires output from two other programs, D R A W P L A N and G R I D F O R M . The program D R A W P L A N allows the user to accurately define the building space, by defining a large number of wall 'units'. G R I D F O R M analyses the user-defined building space, and creates a 'map' of points whose numeric value is equal to the optimal distance to an exit from that point. This 'distance map' is used by SIMULEX to assess escape routes throughout the building plan.
2 TESTING OF FLOW R A T E S WITH SIMULEX
It is important that S I M U L E X produces realistic sustainable flow rates over a range of different exit widths because unrealistic flow rates will
151
Testing o f the computer model ' S I M U L E X ' TABLE 1
Summary of Maximum Pedestrian Flow Rates for Level Passageways Source
Maximum design flow (persons/ m/s)
UK regulations 1
1.33 (derived from exit capacities) 1"37 1.82 (unit exit width method) 1.48
1.92
Fruin 5
1.37
4-37
Daly6 Ando et al. 7
1.43
Fire and Buildings, The
1-50
Approved Document B.
SCICON report 2 Guide to Safety at Sports Grounds 3
Hankin and Wright 4
Polus et al. 11
1.3 (effective width method) 1.25-1"58
Comments
Standard British code for buildings
1.7-1"8
Aqua Group s Predtechenskii and Milinskii 9 SFPE handbook ~°
Ultimate flow capacity (persons/ re~s)
Data from football crowds Based on Japanese data and derived from 60 persons/0.55 m/min unit exit width calculation Commuters on the London Underground Max. flow is a peak regimented, 'funnelled' flow under pressure For underground stations Japanese commuters at railway stations. General design text
1'83
'Emergency conditions' for adults in mid-season dress 2 × 0.15 m boundary layers deducted from width of exit
1.58
Pedestrian movement on sidewalks in Israel
produce unreliable results when calculating the total evacuation times f o r d i f f e r e n t b u i l d i n g s . A set o f tests w e r e t h e r e f o r e c a r r i e d o u t to investigate the performance of SIMULEX by simulating the evacuation o f a specific n u m b e r o f i n d i v i d u a l s o v e r a w i d e r a n g e o f exit w i d t h s in o r d e r to assess t h e m a x i m u m s u s t a i n a b l e f l o w r a t e o f t h e g r o u p t h r o u g h different passageways. This form of testing was useful because the
152
P. A. Thompson, E. W. Marchant
motion of the individuals, moving in close proximity through a restricted opening, invoked all of the decision and movement algorithms. The tests therefore presented an overall measure of the performance of the individual calculations within SIMULEX, when applied to pedestrian movement through a fairly standard exit geometry.
2.1 Testing procedure The evacuation simulation program was used to test flow rates through exit widths over the range 0-7-3.0 m, in increments of 0.1 m. A typical 'exit flow test' geometry is illustrated in Fig. 1. The section of corridor that the exit leads into is 5 m long, and of 5 m internal width. The centre of the exit is aligned with the centre of the corridor. The initial test conditions consisted of a group of 100 individuals that possessed random initial angles of orientation and an initial population density of 4persons/m 2. The conditions were intended to simulate a fairly concentrated, non-panicking crowd. The section of corridor was placed on the other side of the exit so that the motion of the people as they passed through the exit opening and spread out into the wider passageway could be observed. It was necessary to model the movement of the occupants after they emerged from the 'test' exit because their movement could affect the motion of individuals behind them, who were in the process of moving into or through the opening. Occupants were removed from the evacuation process when they reached the end of the 5 m section of corridor. For each test on an exit greater than 1 m wide, exactly the same group of 'people' were used, in terms of initial position, orientation, and normal unimpeded walking speed. The only difference in initial conditions for each test was the lateral width of the exit. The test conditions were changed for exits less than 1.1 m wide because when narrow exits were tested with the highly concentrated group initially placed at the mouth of the exit, a permanent 'jam' of bodies occurred within the first 10-15 seconds of movement. The front two rows (20 people) were removed in order for more space to be available for movement in the initial stages of evacuation. Therefore, in the narrow exit tests, the foremost members of the group (now reduced from 100 to 80 persons) started 2 m back from the face of the exit opening. Each test was initiated by clicking on, the 'Evacuate' icon on the
Testing of the computer model "SIMULEX'
153
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S I M U L E X screen display. W h e n the evacuation started, the individuals in the group i m m e d i a t e l y began to orientate themselves towards the exit by turning at the rate of 10 degrees per time-step (0.1 seconds), and then started to walk towards the opening. The time taken for the first 10 occupants to pass t h r o u g h the 'test' exit was noted as T~0. W h e n the evacuation p r o c e e d e d , the time at which 10 people r e m a i n e d behind the
154
P. A. Thompson, E. W. Marchant
exit (that is, the time taken for a total of 90 occupants to pass through the exit) was then n o t e d as Tg0. The exit functioned at its m a x i m u m sustainable flow rate for the duration b e t w e e n T~0 and T90. In the case of the n a r r o w e r exits, T~0 and Tg0 w e r e replaced with Ts and T70 to a c c o m m o d a t e the lower n u m b e r of occupants, and to reflect the fact that the m a x i m u m flow rate was achieved m o r e quickly than for the flow tests on the wider exits. The times were accurate to one tenth of a second. It was sometimes difficult to ascertain the exact time when a specific n u m b e r of people had passed through the exit because it was fairly c o m m o n for two people to walk through at the same time, side by side. For example, the 10th and l l t h occupants might leave the exit simultaneously, leading to the possibility that only 79 people, instead of 80 would pass through the exit b e t w e e n T~0 and Tg0. The n u m b e r of exiting persons (80 or 65) was t h e r e f o r e accurate to +1 person over the entire range of tests. 2.2 Test results
The times Tg0, T~o, TT0 and T5 obtained during the tests, were used to calculate the flow rates per m e t r e width for each exit tested. T h e formulae for the flow rate calculations are p r e s e n t e d in eqns (1) and (2). 80
Qw(
Qwhere: Q = w= T~0 = Tl0 = T70 = =
( w > =1.1 m)
(1)
-
65
w(:rTo-
(w < 1"1 m)
(2)
flow rate ( p e r s o n s / m / s ) exit width (m) time for 90 persons to pass through exit (s) time for 10 persons to pass through exit (s) time for 70 persons to pass through exit (s) time for 5 persons to pass through exit (s).
Some variation in flow rates was expected because the different attributes of individuals (initial orientation, u n i m p e d e d walking speed) would create different patterns of m o v e m e n t when the group m o v e d through different exit widths. The actual variation in flow rates that was e n c o u n t e r e d was not regarded as excessive. The flow rate achieved for
Testing of the computer model 'SIMULEX' Graph
of
Crowd
Flaw
Rate
against
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155 Width
/"
~-.4.0 0 ©
-~.3.5
/"
O3
03.0 ~..~ 2.5
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away
from
/
.~-~'/~ ~" *C~./~"/
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~
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values f o r doorways less than 1.1m wide apply to crowds that start at least 2m
/
/-
/
/
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/
O.O 0.6
xxH. - -- -......
/
~ 0.5 c.D
/ ,
,
i
0.9
,
,
i
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Values from SIMULEX test runs 'Best Fit' for SIMULEX test runs values from Approved Document B1, Table 5 max. design values from Hankin & Wright ( 1 9 5 8 ) '
,
i
1.5
,
,
i
1.8
,
,
i
2.1
,
,
i
2.4
,
,
i
2.7
,
'
q
3.0
Passageway Width (m)
Fig. 2. Graph of crowd flow rate against passageway width---comparing SIMULEX results with other data. each width of exit was plotted on the graph presented in Fig. 2, where the results are plotted on the same graph as the values quoted by Hankin and WrighP and the U K regulations (Approved D o c u m e n t B). ~ 2.3 Analysis of results The linear relationship between flow rate and exit width was observed in the S I M U L E X test runs for widths greater than or equal to 1.1 m, at the m a x i m u m sustainable rate of 1-40persons/metre width/second. This value lies between the data points plotted from Hankin and WrighP and the UK regulations I in Fig. 2, and compares well with a n u m b e r of design values quoted in Table 1. The sustainable (design) flow rates in Table 1 vary considerably, depending on the source of the data, but values typically lie in the range 1 . 3 - 1 - 5 p e r s o n s / m e t r e width/second. The value of 1.4 p e r s o n s / m e t r e width/second, yielded by the simulation tests, therefore indicates that the algorithms and parameters incorporated into S I M U L E X combine to produce realistic sustainable exit flow rates. The difference in values between the S I M U L E X tests and A p p r o v e d D o c u m e n t B 1 for exit widths less than 1-1 m, is significant. However, there appears to be no experimental evidence for the figures in the UK regulations for exit widths of less than 1.1 m, so they may not represent realistic flow rates. In fact, the Code for Safety to Life ~4 uses the same
156
P. A. Thompson, E. IV. Marchant
figures for total flow capacity per unit width (1 occupant per 5 m m exit width) for all exit widths greater than 0.9 m. S I M U L E X produced complete stagnation of m o v e m e n t for high density groups attempting to move through narrow exits (less than 1 m) when the foremost m e m b e r s of the group were initially positioned at the face of the exit. Sustained flow was only possible by ensuring that the group began m o v e m e n t at a distance of 2 m back from the exit. By effectively moving the initial position of the group of people away from the face of the exit, the density at which the occupants entered the exit was reduced slightly. This initially reduced density enabled the maintenance of m o v e m e n t through the opening and allowed test results to be obtained, although the flow was somewhat irregular, and the 'pulsing' flow behaviour observed by Pesch115 sometimes occurred. Continuous m o v e m e n t could not be achieved for exits less than 0-75 m wide as the bodies of different individuals became 'entwined' with each other and j a m m e d against the edges of the exit opening. The m o v e m e n t of individuals emerging from the exit into the wider corridor proved to be important because it did, as expected, affect the m o v e m e n t of the occupants who were entering, or already in, the exit opening. As individuals emerged from the exit, they resumed the expected patterns of overtaking and twisting. This produced the effect of the emerging group 'spreading out' laterally across the 5 m section of corridor and produced group formations similar to the 'zone' configurations observed by Fruin, 5 where each person appears to possess a circular zone of 'personal space'. 2.4 Parameters for m o v e m e n t
The results from these tests are encouraging, because they indicate that the m o v e m e n t parameters used in the program were sufficiently realistic for the simulation of a normal, non-panicking crowd. In S I M U L E X , the most important parameters that affect the transition of people through an opening are the rate of body twist and the threshold distance. If the rate at which the bodies of individuals can turn is not restricted, then the overall flow rate of a group of people generally increases by approximately 10%. If the threshold distance (the furthest inter-person distance at which the presence of one person affects the speed of another) is reduced, then the flow rate increases dramatically. The threshold distance that corresponds to the data derived from A n d o e t a l . v is 1.1 m (assuming circular zoning). When S I M U L E X uses a threshold distance of 1-1 m instead of 1-6m, the m a x i m u m sustainable flow rate increases to 1.7 persons/m/s. This value corresponds well to
Testing of the computer model 'S1MULEX'
157
the average ' m a x i m u m ' flow rate of 1.65-1.75 p e r s o n s / m / s calculated from the data produced by A n d o et al. over the range 1.55 . 0 p e r s o n s ] m 2. This indicates that S I M U L E X may be able to model cultural a n d / o r psychological differences between different groups of people by changing the threshold distance of individuals, which hence affects the overall flow rate through a passageway. People who are in a hurry and therefore possess a higher 'anxiety level' are likely to accept more of an invasion of personal space than in normal, comfortable conditions. This could be modelled by decreasing the threshold distance and would result in an increase in the overall flow rate. The effects produced by occupants possessing different body sizes have not yet been fully explored. S I M U L E X currently assigns the average body dimensions of 0.5 m × 0-3 m to each person. It is certain that if all members of a group of people possess significantly larger body sizes than normal, then the overall flow rate will decrease as a result. A few test runs of S I M U L E X have been executed for groups of individuals with much larger body dimensions than normal, moving through an exit geometry similar to that illustrated in Fig. 1. The m a x i m u m sustainable flow rate in such tests was found to be reduced by as much as 50% due to the increase in body sizes. Unfortunately, no comprehensive real-life data are currently available to compare the effect of differences in body size upon the overall flow rate achieved by a group of people moving through a passageway of specific width. The flow rate data presented by Predtechenskii and Millinskii 9 suggest that the m a x i m u m flow rate (persons/unit width) is inversely proportional to the average plan area of the body of a single person in the group. Hankin and Wright 4 observed that schoolboys, walking through a 'test' circuit achieved a significantly higher peak flow rate than adult commuters who were unaware that their m o v e m e n t was under analysis. However, the commuters achieved a greater m a x i m u m sustainable flow rate. Comparisons of this kind become uncertain where the variation of experimental data and the form of analytical methods used, mean that it becomes very difficult to isolate the effect of changing individual parameters such as body size.
3 A P P L I C A T I O N OF S I M U L E X TO A P R O P O S E D BUILDING DESIGN S I M U L E X is intended for eventual use as a design tool, to be used by fire safety engineers, and possibly architects and building engineers when devising the geometric layout of buildings in the design stages.
158
P. A. Thompson, E. W. Marchant
This section describes the application of the computer modelling system to the design of a branch of a well-known superstore. This building will subsequently be referred to as The Superstore.
3.1 Design requirements The Superstore was chosen as a case study because it was still in the design stages, and certain aspects of the design had not been finalised. One important aspect was that the design population density had not been finalised, and it was uncertain whether a population density of 7.0m2/person or 4.0mZ/person was applicable to the design. The reasons for the use of two different population densities was that The Superstore was to sell primarily do-it-yourself (hardware) goods. The figure quoted by UK regulations 1 for the occupant density of supermarkets and d e p a r t m e n t stores is 2.0 m2/person, but this concentration of people is not normally e n c o u n t e r e d in D I Y stores and was not d e e m e d to be appropriate. The occupant density quoted by the same guide for shops that sell primarily furniture, floor coverings, cycles, prams and large domestic appliances is 7-0 m2/person. The classification of D I Y stores may sometimes lie between these two categories, so a figure of 4.0m2/person is often used instead of 7.0m2/person. The designers therefore wished to assess the capacity of the building plan for evacuation for the two different initial population conditions.
3.2 Spatial analysis The single-storey plan of The Superstore was input using D R A W P L A N , 13 which took approximately 4 hours. Walls, stacks, racking and other immovable obstructions were defined with the use of 'wall units'. At two points, small 'wall units' were drawn 3 m from the boundary of the plan to ensure that the spatial analysis algorithms assessed a 3 m wide space a r o u n d the perimeter of the building in addition to the defined building plan. The program G R I D F O R M segmented the space into a mesh of 0.25 m × 0.25 m spatial blocks; assigned the perimeter of the 3 metre boundary space with a distance to exit of zero, and formed the distance map. This process required approximately 10 minutes c o m p u t e r processing time. The building plan and distance m a p were downloaded by S I M U L E X . The distance m a p was scanned, and the m a x i m u m travel distance
159
Testing of the computer model 'S1MULEX'
(using optimal route directions) was found to be 44.7 m. The perimeter space width of 3 . 0 m was deducted from 44.7 m to yield a m a x i m u m travel distance within the building of 41.7m. The travel distance of 41.7 m was just within the limit of 45 m specified by UK regulations, t 3.3 Simulated evacuations
The perimeter of the occupied sales area (95% of the building plan) was defined as input by the program user, and the area was calculated by S I M U L E X to be 7674.4m 2. The densities of 7.0m2/person and 4 . 0 m 2 / p e r s o n were entered for the two evacuations. Therefore, the n u m b e r of occupants placed initially in the building were 1097 and 1919 persons, respectively. A n evacuation was modelled for each occupancy loading, and the flow rate results stored for later analysis. A n example of one of the simulated evacuations is illustrated in Fig. 3. The simulation of the two evacuations illustrated the general patterns of m o v e m e n t and queuing that occurred during the entire escape process. The distance m a p had been formed in such a way that all
~:..-
:-~:
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~ [g2i~l
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'(.:...
.2:
Fig. 3.
The simulated evacuation of The Superstore, after 10s. Initial density = 4 m2/person.
160
P. A. Thompson, E. W. Marchant
occupants m o v e d towards the nearest exit. In both evacuations, Exits 1, 2, 3, 8, 9 and 10 were the only exits that approached or achieved the m a x i m u m flow rate and caused queues to form behind the face of the exit opening. The rate of flow throughput at Exit 7 was h a m p e r e d by the constrictions within the escape route before the exit. The aisle that served most of the occupants using Exit 5 was actually narrower than the width of the exit doorway. Exit 5 therefore never approached its m a x i m u m potential flow rate. Exit 4 was oversized for the n u m b e r of occupants that it served. Exits 1, 2, 3, 6, 7, 8, 9 and 10 all experienced the convergence of different flows of occupants as they emerged from different aisles and moved towards the exits. The convergence of different flows at Exit 3 is illustrated in Fig. 4. 3.4 Design calculations It is possible to apply standard approximate design calculations to The Superstore to predict the total evacuation times, and compare the values obtained with the results of the simulated evacuations carried
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=~
161
Testing of the computer model 'SIMULEX' TABLE 2
Width of Exits for The Superstore Exit number Measured width,
1
2
3
3"5 3"6 3.5
4
5
3.4 3.6
6
7
8
9
2.4
2.4
1.8 ~]W=31"8
2-1 2.1
2.1
1.5
5-2 2.4
10
Total
W(rn) Effective width,
3.2 3.3
3.2 3.1
3.3
4.9
~] We=28"8
We(m)
out by SIMULEX. The exit widths are presented in Table 2. The effective widths quoted are based on a 0-15 m wide boundary layer at each side of the exit, as specified in the SFPE handbook. 1° The predicted evacuation times for this building will either be governed by the travel time of the person who is initially most remote from an exit (where the exits do not function at maximum capacity), or the time required for the population to 'flow' through the exits (where the maximum flow capacity of the exits dictates the evacuation time). No time is required for the crowd to arrive at the exits, because the even distribution of the occupants throughout the sales area ensures that a number of people will be at or near the exits at the start of the evacuation. No impediment to normal walking speed through the main body of The Superstore is envisaged in accordance with the observation from Hankin and Wright 4 and the SFPE handbook, 1° that walking speeds are generally unaffected for crowd densities less than 0.5persons/m 2 (7m2/person is equal to 0.14person/m 2 and 4mZ/person is equal to 0.25person/m2). The unimpeded walking speed quoted in the SFPE handbook 1° is 1.19 m/s. Equation (3) is used to calculate the evacuation time for either of the design occupancy loadings, assuming that the width of the exits does not restrict the total flow rate of people leaving the building. d 41.7 Twa,k- 35"0 (3) v 1"19 where:
Zwalk = time to walk from most remote point in building to exit (s)
d = travel distance from most remote point (m) v = unimpeded walking velocity (m/s). If we use the normal design assumption that all exits are used
162
P. A. Thompson, E. W. Marchant
optimally, then the total 'flow time' can be calculated, based on simultaneous, m a x i m u m sustainable flow through all exits. Equation (4) uses data from the SFPE h a n d b o o k , 1° which uses the effective width calculation method. This m e t h o d produces a slightly longer 'flow time' than would be produced if the exit capacities quoted in the UK regulations I were used. Qtot = E W e x q = 28"8 X 1"3 = 37"4
(4)
Nocc 1097 T7 - Q,o~- 37"~- - 29.3
(5)
Nocc 1919 37-~ - 51-3.
(6)
T4 - Qto~t -
The notation for eqns (4)-(6), applying to m a x i m u m sustainable flow through all exits is as follows: Qtot = q= ~]We = T7 =
total combined flow capacity of all exits (persons/s) flow rate per unit exit width -- 1.3 (persons/m effective width/s) total effective exit widths (m) total evacuation time for occupancy loading of 7-0 m2/ person (s) T4 = total evacuation time for occupancy loading of 4.0 m2/ person (s) Nocc = total n u m b e r of building occupants.
The results from eqns (3)-(6) suggest that an evacuation of The Superstore for an occupancy loading of 7 m2/person will be governed by the time taken to walk from the most remote point of the sales area, because Twa~kis greater than TT. The calculations predict that for this fairly low occupancy loading, stagnation or queuing will not occur because the occupants will not arrive at different rates to achieve the m a x i m u m flow rates that the exits are capable of accommodating. However, the evacuation of a population with an initial density of 4 m2/person will be influenced by the flow capacity of the exits, rather than the u n i m p e d e d walking time because T4 is greater than Twa~kTherefore, for the larger population, queues will be set up as the flow rate of people arriving at exits is greater than the m a x i m u m sustainable flow rates of the exits. The evacuation times predicted by these 'optimal' design calculations for occupancy loadings of 7 m2/person and 4 m2/person are therefore 35.0 and 51.3 s respectively.
163
Testing of the computer model 'SIMULEX'
3.5 Predictions of evacuation times and flow rates
The design calculations yield optimistic predictions for the building evacuation times, c o m p a r e d to the times predicted by S I M U L E X , and they tell us little about the geometric complexities of the evacuation. When S I M U L E X was used to model the two evacuations of The Superstore for occupancy loadings of 7 m2/person and 4 mg/person, the predicted total evacuation times were 58-1 and 105.1 s respectively. The evacuation times predicted by S I M U L E X are significantly greater than those predicted by using eqns (3)-(6) for both occupancy loadings, because the geometry of the building space, and the merging of different occupant groups from different aisles led to the formation of queues at some exits while others never achieved their m a x i m u m flow capacity. S I M U L E X predicted that the evacuation time for the initial density of 4m2/person was 81% longer than for the initial density of 7m2/person. This greater evacuation time occurred because the increase in occupant numbers produced significantly more queuing at a n u m b e r of exits, and all of the building exits never simultaneously achieved m a x i m u m flow throughput. In fact, some of the exits never achieved more than 50% of their m a x i m u m flow capacity. A graph representing overall evacuation flow rates from the building using the output from S I M U L E X is illustrated in Fig. 5. g
Graph of Flow Rate Against Time f o r simulated evacuation
~ 406
35
~, 30:
.....
Initial density=4.m2/persan
g 25:
20~m15-
g ~102 ~
5-
0 O
E
I , I I I I I T I I I l , l l f
lo
20
30
~ l l , l l l l l l r l l ~ , l l t l l ~ l l l l l ,
40 50 oo 70 Time (seconds)
80
i
90
i
i
i
I
loo
f
Iq
I
11o
Fig. 5. Graph of total exit flow rate against time for two simulated evacuations of The Superstore.
164
P. A. Thompson, E. W. Marchant
In both evacuations, the rate at which occupants leave the building increases rapidly in the first 10 s, and climbs to a peak between 20 and 30 s. The total flow rate then 'tails off' as some exits are completely emptied, while others are either still serving queues of people or groups of slower individuals that have taken significantly longer to arrive at the exit openings. The larger number of occupants in the 4m2/person evacuation produced slightly higher flow rates because exits that did not achieve their individual maximum flow capacities served more occupants than in the 7 m~/person evacuation. The fact that these exits were more fully utilised when more occupants were present meant that they contributed more to the total flow rate from the building at the peak flow times. The peak flow rate achieved for the whole building was 38.7persons/s at 25-30s for an initial occupancy loading of 4mZ/person. The flow throughput of each exit during the period in which the peak total evacuation flow was observed and estimated numerically by the user as a fraction of the maximum possible flow rate for that exit. These exit usage values are presented in Table 3. The figures in Table 3 demonstrate that even at the peak flow rate of numbers of occupants leaving the building, only six of the exits operate at, or near, the maximum sustainable flow rate. These 'partially used' exits could either be repositioned to serve a larger percentage of the population or reduced to a size more suitable to the number of occupants that they serve. For example, Exit 5 could be moved upwards (on the plan) to be located directly at the end of the main aisle that spans left to right across the shop floor area. This change of geometry would increase the number of people that the exit served; would directly align it with a wider passageway, and the exit would therefore operate at a higher flow rate efficiency. It would also be clearly visible to the occupants in that central aisle. However, no design changes were TABLE 3
Exit Usage at Peak Flow in The Superstore Evacuation for an Initial Occupancy Loading of 4.0 m2/Person Exit number Usage as a fraction o f maximum possible flow for each exit
1
2
3
4
max. max. max. emptied 1
1
1
0
5
6
7
8
9
10
p a r t p a r t part max. max. max. ~
½
]
1
1
1
Testing of the computer model 'SIMULEX'
165
strictly necessary because the evacuation times predicted are significantly less than the m a x i m u m stated by UK regulations.
4 CONCLUSIONS The outputs from this version of S I M U L E X have been c o m p a r e d to the figures obtained by using fairly standard methods of calculation because this version of the c o m p u t e r model makes some initial assumptions that are similar to those m a d e when using the calculations, where complex psychological aspects of evacuation are ignored. Standard design calculations and statutory guidance cannot accurately predict the evacuation performance of a building which contains complex spaces where groups of escaping people meet from different directions as they travel towards the final exits. The application of S I M U L E X to geometrically complex building designs is useful because it is capable of highlighting areas where different group 'flows' meet, queues form, stagnation of m o v e m e n t may occur, and also where exits are significantly oversized or undersized for the n u m b e r of occupants that they actually serve. It is crucial that any c o m p u t e r model that produces results which will be used to assess life safety produces consistently realistic results. The tests carried out to evaluate m a x i m u m sustainable exit flow rates indicate that S I M U L E X produces results that correlate well to the data obtained from real-life observations, when analysing m o v e m e n t through a single, open passageway. When the development of Version 3 is complete, similar tests will be carried out to evaluate parameters for egress m o v e m e n t on staircases. The final, multi-storey version of S I M U L E X will be subjected to a rigorous series of tests to investigate how the results produced by the model correlate to full-scale 'real life' evacuations in a n u m b e r of different buildings.
REFERENCES 1. Department of The Environment and The Welsh Office, The Building Regulations--Approved Document B, (Section B1, 1992 ed.) HMSO, London, 1991, pp. 9-40. 2. Poyner, B., Robinson, D., Hughes, N. & Ayles, P., Safety in football stadia; a method of assessment. Report for SCICON, Scientific Control Systems, London, 1972. 3. Home Office/Scottish Office, Guide to Safety at Sports Grounds. HMSO, London, 1991.
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4. Hankin, B. D. & Wright, R. A., Passenger flows in subways. Operational Res. Quart. 9 (1958) 81-8. 5. Fruin, J., Pedestrian Planning and Design. The Metropolitan Association of Urban Designers and Environmental Planners, New York, 1971. 6. Daly, P. N., Pedestrian speed/flow relationships for underground stations. Traffic Engng Control, 32 (1991) 76-8. 7. Ando, K., Ota, H. & Oki, T., Forecasting the flow of people (in Japanese). Railway Res. Rev., 45 (1988) 8-14. 8. The Aqua Group, Fire and Buildings. Granada, London, 1984. 9. Predtechenskii, V. M. & Millinskii, A. I., Planning for Foot Traffic Flow in Buildings. Amerind, New Delhi, 1978 (translated from original publication in Russian, 1969). 10. Nelson, H. E. & MacLennan, H. A., Emergency movement. In The SFPE Handbook of Fire Protection Engineering, ed DiNenno, P. J. National Fire Protection Association, Quincy, MA, 1995, pp. 3-286-3-295. 11. Polus, A., Schofer, J. L. & Ushpiz, A., Pedestrian flow and level of service. J. Transportation Engng, 109 (1983) 46-7. 12. Joint Committee on Fire Grading of Buildings (Ministry of Works), Fire grading of buildings, part III, personal safety. In Post War Building Studies No. 29, HMSO, London, 1952 pp. 71-87. 13. Thompson, P. A. & Marchant, E. W., A computer model for the evacuation of large building populations. Fire Safety J., 24 131-48 (1995). 14. NFPA, Capacity of means of egress, Section 5-3. In NFPA lO1--Code For Safety to Life. National Fire Codes, National Fire Protection Association, Quincy, MA, 1991. 15. Peschl, I. A. S. Z., Doorstromingscapaciteit van deuropeningen bij panieksituaties, B O U W nr 2 9-1-1971. Private translation of Flow Capacity of Door Openings in Panic Situations, 1971, pp. 62-7.