Model developmen of unenable condiions during egress and sochasic evaluaion in comparmen fires Bai-Nian Zhou 1, Yi-Chun Lin 2*, Yuan-Shang Lin 3 1 Fire Service and Disaser Prevenion Advocae Managemen, Hsinchu Couny Fire Deparmen, Hsinchu 30049, Taiwan, ROC 2 Deparmen of Fire Science, Graduae School of Fire Science & Technology, Cenral Police Universiy, Taoyuan 33304, Taiwan, ROC 3 Graduae School of Disaser Managemen, Cenral Police Universiy, Taoyuan 33304, Taiwan, ROC * Corresponding auhor. Tel.: +886 3 328 2321#4615 or +886 928 086 675; fax: +886 3 328 1114 E-mail address: linyichunw@yahoo.com.w (Y. C. Lin). Absrac This sudy aimed o develop an improved simplified wo-zone model auhenicaion echnology in order o simulae he ime o unenable condiions in comparmens less han 200 m 2 in area, which include smoe layer emperaure, visibiliy, carbon monoxide concenraion, fracional lehal dose, and radiaion hea flux. Based on reliabiliy-based design and srucure funcion, his sudy focuses on consrucing he sochasic model of egress safey/failure in a comparmen fire. Moreover, sochasic parameers and probabiliy disribuions were assumed. Random numbers of parameers were generaed by Mone Carlo simulaion. Afer several simulaions, he failure probabiliy of occupans egress due o one or more han one of he unenable condiions was obained. Afer consrucing he model, 200 m 2 occupans in a ALA PUB disco ballroom locaed in Taichung, Taiwan were aen as an example. The simulaion of polyurehane furniure fire was execued 100 imes. The resuls showed ha insallaion of auomaic fire alarm equipmens and emergency broadcasing equipmens can subsanially reduce he unenable condiions and failure probabiliy of occupans egress. Some ideas for fire officers and fuure sudies for fire researchers were also recommended. Keywords Fracional lehal dose, Radiaion hea flux, Reliabiliy-based design, Sochasic model, Srucure funcion, Unenable condiions. HIGHLIGHTS The aliude effecs on comparmens less han 200 m 2 in area was explored and an improved srenghened simplified wo-zone model auhenicaion echnology was developed. Time o unenable condiions was simulaed and elucidaed. Sochasic parameers and probabiliy disribuions was assumed. Random numbers of parameers were generaed by Mone Carlo simulaion. Based on reliabiliy-based design and srucure funcion, his sudy focused on consrucing he sochasic model of egress safey/failure in a comparmen fire. 200 occupans in a ALA PUB disco was aen as an example. I. INTRODUCTION The fire inciden of an enerainmen quarers (ALA PUB) occurred on March 06, 2011. I is siuaed in Chung Hsing Sree, Taichung Ciy, Taiwan. The fire broe ou a 1 am. I firs iniiaed from he sage area on he second floor, so cusomers saying on he mezzanine were unable o escape, hus resuling in 9 dead and 12 wounded. Afer he fire inciden, public safey in discos, bars, and musical performance places (live house) ha sell alcoholic beverages became he focus of aenion. Over he pas decades, comparmen fire has been invesigaed in deail and is growh is well undersood. From hese lieraures [1 3], i appears ha grea progress has been made in he ypical building comparmen fires wih verical openings, such as door and window. As a ypical enclosure, he buildings, such as underground srucures, enerainmen comparmens, and bars, only have he horizonal ceiling vens. Comparmen fire wih verical wall vens or horizonal ceiling vens migh have differen behaviors, because he flow exchange a he openings and vens is of considerable imporance in he comparmen fire growh and spread. Page 106
Afer sudying he fire safey engineering manuals of many advanced counries, we had deliberaely seleced he six mos common facors ha are liely o be encounered by fire vicims in a fire evacuaion process, or unenable condiions ha may incapaciae hose rying o escape from a fire. These condiions were described below: (a) Smoe layer heigh; (b) Convecive hea, usually described as smoe layer emperaure; (c) Smoe obscuraion, or visibiliy, ofen expressed as opical densiy per meer (OD/m); (d) Densiy of asphyxiaing gases, ofen described as carbon monoxide concenraion; (e) Radian hea, ofen described as radian hea flux; and (f) Fracional effecive dose (abbreviaed as FED) composed of oxic and asphyxiaing gases, he mos commonly used are fracional lehal dose (abbreviaed as FLD) and fracional incapaciaing dose (abbreviaed as FID). From he full-scale experimen made by Wang [4] for measuring main fire hazard facors in small subdivided space, i was found ha he a 1.8 m above floor level, ime for radian hea flux o reach olerance limi of 2.5 W/m 2, was less han he ime for smoe layer heigh o drop o 1.8 m above floor level. The above ime for radian hea flux o reach olerance limi can be regarded as he hreshold ime before encounering unenable condiions during subdivided space personnel evacuaion (or called he ime o unenable condiion in shor). The quesion is how o combine he above ime and ime needed for evacuaion in order o assess wheher personnel can escape safely from a fire in a subdivided space. This brough ou he following hree moives for his sudy: (1) Using an alernaive mehod (roue B) o verify he performance of subdivided space fire evacuaion, local model designers only calculaed he ime for smoe o reach heigh of 1.8 m above ground level, and hen compared he above ime wih he ime o evacuae from living quarers based on he living quarers evacuaion verificaion mehod [4]. In case of acual fire, where he number of people in subdivided space reaches he conrol limi, he ime o evacuae from living quarers has o be longer han normal. Is i possible ha he convecive hea, radian hea flux, and carbon monoxide level a he fire scene could gradually reach inolerable levels, hus leading o failure in escaping from a fire as he fire and smoe become more poen? The firs moive of his sudy was o answer he above quesion. (2) Numerous objecs in he building are combusible, so i is hard o dismiss all heir combusible characerisics. If he model designer does no cover all possible parameers, for insance, combusion hea of all combusible maerials wihin subdivided space, i leaves oo many uncerainies for he deerminisic equaions (group). Thus, a sochasic model was used o overcome he uncerainy problem of he deerminisic model. This is he second moive of his sudy. (3) Among he resuls of he fire ris assessmen, he one ha is more commonly seen is expeced casualies in he fire inciden [5]. If he inciden wih personnel casualies is se equivalen o he inciden coupled wih evacuaion failure aribuable o one or more unenable condiions under he same fire condiions, he quesion is: Does auomaic fire alarm and emergency broadcas equipmen insalled in subdivided space mae a difference in calculaing he ris of personnel casualies? Therefore, analyzing he probabiliy of reduced personnel casualy rae when such equipmen is insalled in a subdivided space was he hird moive of his sudy. II. METHODOLOGY Based on he above research moives, his paper endeavored o explore all unenable condiions and oher facors ha may cause evacuaion failure when a fire breas ou in a subdivided space. Accordingly, he following objecives were esablished for his sudy: (a) Using a predicable hea release rae and smoe generaion rae of he Simple Two-Layer Auhenicaion [6] in conjuncion wih he modeling equaion for predicing unenable condiions during fire evacuaion in subdivided space, o consruc a dynamic fire and smoe growh model o predic he hreshold ime o unenable condiion in subdivided space fire evacuaion. This ime is hen compared wih he ime for one or more people o escape from a fire in subdivided space obained from personnel evacuaion model, o se up a deerminisic model o predic he oucome of fire evacuaion in subdivided space. (b) The above deerminisic model was based on a reliabiliy-based design [7], and supplemened by he Mone Carlo simulaion mehod o esablish a sochasic model for predicing he oucome of fire evacuaion in subdivided space. Page 107
(c) Using a place used for specific purposes wih he same dimensions, we will hen compare he probabiliy of evacuaion failure when fire vicims are faced wih one or more unenable condiions in wo scenarios: One wih a conrol limi on accommodaing capaciy of subdivided space, and he oher wihou. This can be a reference model for he building adminisraion and fire deparmens in deermining he life hrea severiy o personnel being caugh in specific purpose quarers in he even of a fire. Main research mehods used for his sudy were described as follows: (1) Lieraure review mehod: Using a sochasic model assessmen mehod o review he main poins in relaed lieraure and applicaions and collec relevan parameers appropriae for applicaion in subdivided space fire evacuaion. For insance, if flaming combusion is observed a he fire scene, relevan combusion parameers such as carbon monoxide producion raes, hea combusion, and combusion efficiency of combusible maerials should be incorporaed in he equaion. Furhermore, referring o he unenable condiions for fire evacuaion in all inds of subdivided space as defined by developed counries, a predicion equaion should be esablished for subdivided space fire evacuaion. (2) Experimenal analysis mehod: Se he presence or absence of auomaic fire alarm and emergency broadcasing equipmen in subdivided space as an independen variable in he research; and se he probabiliy of failure for personnel evacuaion in subdivided space as a dependen variable in he research, when fire vicims were faced wih one or more unenable condiions in subdivided space. A subdivided space wih similar condiions, size and combusibles were hen se up o observe he effec of independen variable on dependen variables. (3) Compuer simulaion mehod: Using he Mone Carlo simulaion mehod wih compuer simulaion o generae random numbers corresponding o parameer-deermined probabiliy disribuions, he deerminisic simulaion model developed by his sudy was run several imes o verify he probabiliy of failure for subdivided space fire evacuaion if fire vicims are faced wih one or more unenable condiions. The scope of his sudy was se as follows: III. SCOPE OF OUR RESEARCH (a) In his sudy he so called subdivided space may refer o enclosed living quarers or comparmens according o he Archiecural Technology Rules. Enclosed living quarers generally include space used for living, woring, meeing, recreaion, cooing, ec., whereas hallways, corridor, saircases, coarooms, oiles, bahrooms, sorage rooms, mechanical rooms, garages, ec. are no viewed as living quarers. However, for hoels, residenial houses, muli-sory residenial buildings, and hosels, he crierion in principle is ha he oal area of coa rooms and sorage rooms do no exceed 1/8 of he oal floor area. (b) A fire scene in his sudy refers o a fire ha is iniiaed and spread ou seing combusible maerials nearby ablaze, bu confined in he subdivided space where i iniially sared. The scope of his sudy did no cover oher condiions, such as when he fire spread beyond he limi of he subdivided space, or when i was pu ou or burned ou. (c) Accumulaed calorific value of combusible maerials sored in places defined by his sudy, or referred o as fire load per uni area, was limied o 960 mj/m 2. If he fire load per uni area exceeded he above sandard, hen he places were considered o have a high fire load, and were no included in he scope of his sudy. (d) For he purpose of his sudy, he oal floor area of subdivided space should be less han 200 m², and ceiling heigh less han 8 m, forming a single recangular space. Any dimensions greaer han he above sandard should no be included in he scope of his sudy. (e) For his sudy, he building needed o be consruced wih a fire-proof srucure and had fire proecion equipmen insalled, such as fire-exinguishers and smoe exhaus equipmen. Their operaions were no included in he scope of his sudy. (f) Personnel in he subdivided space should be conscious and had he abiliy o escape on heir own. Personnel sleeping or canno escape on heir own will no be included in he scope of his sudy. (g) In his sudy, only he cener of he subdivided space was used o represen he locaion of combusibles, all oher locaions were no included in he scope of his sudy. (h) Inerior decoraion and rimming maerials (ceilings, walls and oher pars) used in he subdivided space were all in Page 108
conformance wih grade 2 or higher fire resisan maerials. Grade 3 fire resisan maerials or oher decoraion maerials no in conformance wih fire resisan sandards were no included in he scope of his sudy. The limiaions of his sudy can be summarized ino he following four poins: A. The developmen of he sochasic model of predicing he arge oucome of fire evacuaion in subdivided space was based on he probabiliy of failure wih respec o fire evacuaion in subdivided space when fire vicims were faced wih one or more unenable condiions. B. The developmen of fire and smoe growh model was based on Simple Two-Layered Auhenicaion. We had sudied he defecs [8] or limiaions of his verificaion echnology, and made he following assumpions for he fire and smoe growh model: (1) Targe building was consruced wih no openings, and canno reflec ouside emperaure, wind speed and energy exchange. (2) The model can only reflec he smoe layer changes in a single subdivided space and canno simulae smoe layer changes in adjacen subdivided space. (3) The fire growh ime should be in line wih he fire growh model, and he fire source should be locaed a he cener of he recangular space. (4) Use of a wo-layer fire zone model for calculaing he decrease of smoe layer heigh. (5) Only using fire radian hea from fire source for calculaing he fire radian hea flux received a he locaion of individual people, while he smoe layer or radian hea from surrounding walls were no considered. C. Using he fire and smoe growh model o calculae he hreshold ime o unenable condiion during he fire evacuaion process in he subdivided space, also called available safe egress ime (ASET). Facors influencing he ASET can be broen down ino physical, physiological, and psychological componens. This sudy only examined he physical and physiological componens, while hose involving psychological facors (sress and panic) were no considered in his sudy. D. The developmen of he personnel evacuaion model had referenced he compuaion of waling ime o reach he subdivided space and ime needed o pass hrough he egress of subdivided space described in he Technical Manual for Srucure Fire Evacuaion Safey Verificaion, so he following assumpions are made for he personnel evacuaion model : (1) Personnel remaining in subdivided space were evenly disribued. (2) In he subdivided space wih no auomaic fire alarm devices insalled, he saring ime for one or more persons o escape from a fire was evenly disribued, meaning personnel do no evacuae a he same ime; he subdivided space se up wih auomaic fire alarm and emergency broadcas equipmen, regardless of he accumulaed ime for he fire deecor cenral conrol and emergency broadcas sysems, he sar ime for one or more persons o escape from a fire was se equal o he fixed emperaure deecor acivaion ime, and personnel would sar evacuaing all a once. (3) All evacuees should ae he given evacuaion roue, wih no urn bacs. (4) The flow of evacuaion was subjeced o he widh of exis. (5) During evacuaion, no one pu ou he fire nor urns on he smoe exhaus sysems insalled on windows for effecive venilaion. 4.1 Ris-based assessmen mehods IV. LITERATURE REVIEW When Ramachandran [9] conduced research on fire disasers in various ypes of buildings, he aenion was placed on he fire growh of differen periods, wih is muliple ineracions producing uncerainies in fire developmen models. I was possible hrough compuaion of probabiliy (uncerainy) occurrence of various ypes of fire and esimaed limi of confidence o derive a non-deerminisic fire model. Such a model can be developed as eiher a probabilisic model, or a sochasic model. The firs ype ha involved he compuaion of probabiliy can be called a saic model, because i oo ino Page 109
accoun he collecive ris in fire proecion and insurance for differen ypes of buildings, his model can provide sufficien research ools, bu he compuaions of probabiliy disribuions and faul ree had no examined he basic physical process and variance [10] in he fire growh period (ime). The second ype was a dynamic model, which can be seen as an inference model, and can forecas he fire growh and change capabiliy [10] in he building. Hadjisophocleous [11] poined ou ha he judgmen crieria used for performance ype designs can be roughly divided ino wo ypes: 1. Deerminisic crieria involve personnel safey, fire growh, and fire spread condiions, damage effecs from exposure o fire scene, building srucures and funcions. 2. Probabilisic crieria involved he exen of inciden damage and he possibiliy of occurrence. Hasofer s research [12] ransformed he deerminisic model ino a sochasic model, using wo mehods: 1. Deerminisic model inpus are ransformed o sochasic model inpus, and is he more common mehod. This sudy chooses o ransform deerminisic ype inpus o sochasic ype inpus, and he deerminisic ypes flame growh model and personnel behavior model are ransformed ino sochasic ypes flame growh model and personnel behavior model. 2. The number of random enries in he modeling program was increased, which means ha he exising deerminisic ype modeling program canno precisely forecas he values acually observed. Therefore, i is necessary o inroduce random enries. This mehod can be applied o he smoe flow model. Alhough Hasofer and Qu [13] explained ha he use of deerminisic ype fire growh predicion model had a sound predicabiliy for fire developmen process, he inpu parameers are no readily available, and some of he inpu parameers were essenially random in naure, so he equaion canno be deduced from pure physics, meaning ha he program designer canno precisely predic he fire developmen wih a deerminisic model. The way o cope wih his problem was o rea unnown inpu parameers as random variables. Supposedly, here were sochasic parameers, so heoreically a - dimensional oupu space can be obained, and hen using he reliabiliy-based design [14] he chance of success or failure can be calculaed. However, because he compuer-based fire simulaion model involved evaluaion equaions ha were oo complicaed, i is no suiable for he above calculaion. A his poin, his sudy decided o swich o he Mone Carlo simulaion model, and all predeermined parameer disribuions were alered o corresponding random number disribuions. Afer several simulaion runs, his sudy can analyze he oupu probabiliy disribuion obained so as o assess he reliabiliy of model design. The aricle of Nysed [15] discussed he insallaion of fire proecion measures in residenial buildings such as smoe deecors or waer sprinler sysems ha can effecively reduce fire deahs. According o Nysed s research mehod, he ris of fire deah is defined o be equivalen o he probabiliy of evacuaion failure in he ime period from fire iniiaion o he momen when fire vicims were faced wih unenable condiions, and he Mone Carlo simulaion mehod was used o overcome uncerainies in he model. From he research resuls, we found ha he insallaion of smoe deecors and waer sprinler sysems in residenial buildings can effecively reduce he ris of fire deah by 11% and 53%, respecively. Summary: Through he above lieraure review, his sudy had decided o swich deerminisic ype inpu parameers ino sochasic ype inpu parameers, and he fire model was swiched from a deerminisic ype o a sochasic ype. 4.2 Modeling program o simulae unenable condiions during he fire evacuaion process in subdivided space According o he research of Mingjin e al. [16], he emperaure of smoe layer can be esimaed wih he following Eq. (1): T T0 C 0 p Q Q d Z A s w s (1) According o he sudy made by Jin [17] and Mulholland [18], he visibiliy of ligh-emiing equipmen (referred o egressmaring lighs and emergency lighs) can be esimaed according o he following Eq. (2): S 8 K 10 8Vroom 2.3 D M m (2) Page 110
According o he research of Mile e al. [19, 20], he concenraion of carbon monoxide in smoe layer can be esimaed according o Eq. (3): M ppmco M air CO Y CO 10 6 M M air CO fcoq H A H Z s c s 10 6 (3) According o he research made by Purser [22,23], he concenraion of carbon monoxide in he blood o reach olerance limis, or when changed o fracional incapaciaing dose (abbreviaed as FID), can be esimaed according o Eqs. (4) and (5): FI CO 2 5 COHb 3.31710 ppmco % D 30 exp0.2468 % CO2 1.9086 6.8 RMV 1.036 % CO2 V CO (5) According o he research of Drysdale [24], he fire radian hea flux can be esimaed according o Eq. (6): q r Q Q 2 r r r 2 2 2 4R 4R 4R (6) Afer sudying he SFPE Handboo of Fire Proecion Engineering [25], he olerance limis of all unenable condiions during he fire evacuaion process in subdivided space are shown in Table 1. TABLE 1 TOLERANCE LIMITS OF ALL UNTENABLE CONDITIONS DURING THE FIRE EVACUATION PROCESS IN SUBDIVIDED SPACE Unenable condiion Smoe layer emperaure Visibiliy Carbon monoxide concenraion V Radian hea flux (4) Fracional incapaciaing Dose(FID) Tolerance limi 200 C 5 m 1, 400 ppm 2.5 W/m 2 1 Summary: Afer he above lieraure review, his sudy used he Simple Two-layered Auhenicaion Technique o obain smoe layer emperaure per uni ime and relaed fire and smoe parameers. Using he above compuaion equaion for visibiliy, carbon monoxide concenraion, fracional incapaciaing dose (abbreviaed as FID), and radian hea flux, as well as olerance limis, his sudy was able o consruc he fire and smoe growh model for esimaing he hreshold or provisional ime for individuals o encouner unenable condiions. 4.3 Time needed for personnel evacuaion Nysed [26] defined several scenarios depending on he locaions of individual persons (in living quarers on fire or oher rooms), physiological saus (awae or asleep) and alarm device (insalled or uninsalled), using probabiliy disribuion o deermine he individual deecion ime and response ime in some specific siuaions. The resuls are summarized as in Table 2; for oher specific siuaions, his sudy used he alarm acivaion ime o represen he sum of he above 2 ime values. TABLE 2 PROBABILITY DISTRIBUTION OF DETECTION AND RESPONSE TIME FOR INDIVIDUALS DURING FIRE Parameer Scenario Random variable Mean value Range disribuion No alarm devices, fire iniiaed in living quarers, conscious Fire deecion ime 30 s Even disribuion (20, 40) Response ime 20 s Even disribuion (10, 30) Page 111
The differen ypes of deecors used in he ess. All hermal deecors are based on he differenial deecors and emperaures deecor principle. The reason ha no ionizaion smoe deecors, aspiraing smoe deecors and phooelecric smoe deecors were esed was due o he fac ha he hea deecors were more common among he comparmen fires alarm and suppression sysem suppliers. According o research made by Schifilii e al. [27], if he fixed emperaure deecor and alarm device were insalled on he ceiling, he emperaure o be deeced by he sensor can be calculaed according o Eq. (7). If ha emperaure is greaer han he nominal emperaure for deecor acivaion, he acivaion ime can be obained. u T 1/ 2 n g, n d, n1 T d, n Td, n Td, n1 Td, n1 (7) RTI T If fire breas ou in subdivided space, he above menioned gas can be separaed ino wo componens: Fire plume and ceiling je flow Schifilii e al. [27] used a series of exended saic-sae hea release rae models o simulae he fire growh process. The emperaure and speed of he fire plume and ceiling je flow in he nh sage can be calculaed as follows: If 1 T T g, n T g, n n Tg, n 1, 5.38 Q H 16.9 Q H r 5 3 2 3 n n Tg, n 1, un 5 6 T n, le g, n1 a and u n 0 2 3 u n 0 Q.946 n H 1 3, r 0. 18H (Fire plume) (8) 1 3 1 2 0.197Q H, r 0. 18H (Ceiling je flow) (9) r According o he invesigaion made by Chen [28], he waling ime o reach he exis of enclosed living quarers can be calculaed as Eq. (10) shown: li v ravel max (10) Taeyoshi [29] acually measured he free waling speed of individuals, ranging from 1.0 o 2.0 m/s, in which he free waling speed of men is abou 1.4 m/s, while he free waling speed of women is abou 1.2 m/s. Moreover, under differen condiions, he waling speeds of individuals will be somewha differen, as lised in Table 3. TABLE 3 WALKING SPEEDS OF INDIVIDUALS UNDER DIFFERENT CONDITIONS Condiion Speed Condiion Speed Jogging 3.00 m/s In he dar (unnown place) 0.30 m/s Running 4.00 m/s Crawling wih elbows and nees 0.30 m/s Running quicly 6.00 m/s Crawling wih hands and nees 0.40 m/s Sprining 8.00 m/s Crawling wih hands and fee 0.50 m/s In he dar (nown place) 0.70 m/s Waling wih low-profile 0.60 m/s According o he research made by Chen [30], he ime needed o pass hrough he egress of enclosed living quarers can be calculaed as follows: paarea queue (11) N B eff eff Summary: Following he above lieraure review, his sudy used 2 scenarios, one wih auomaic fire alarm and emergency broadcasing equipmen insalled, and he oher wihou. Having he acivaion ime of fixed emperaure deecor, personnel deecion ime and response ime o represen he saring ime for evacuaion and adding waling ime, in evacuaion and Page 112
ime needed o pass hrough egress o consruc he personnel evacuaion model in order o calculae he ime needed for one or more persons o evacuae. V. USING DETERMINISTIC MODEL TO PREDICT THE OUTCOME OF FIRE EVACUATION IN SUBDIVIDED SPACE 5.1 Modeling and compuer simulaion Afer using his model o assess a fire experimen in subdivided space, his sudy used a deerminisic model o predic he probabiliy of success if he h person is no faced wih any unenable condiions; or predic he probabiliy of failure if he h person is faced wih one or more condiions leading o evacuaion failure. The assessmen mehod is described as follows: When 0, i indicaes ha he h person has encounered he i h unenable condiion, which criical_ i, escape, means failure o evacuae; conversely, when 0, i represens he h person has no encounered he i h criical_ i, escape, unenable condiion, meaning a successful evacuaion. Wherein, subscrip represens he h person, while subscrip i annoaes he ih unenable condiion for he subdivided space fire evacuaion. criical i, _, i 1, 2, 3, 4, 5 : Means he ime needed for he h person o encouner 5 unenable condiions for he subdivided space fire evacuaion (s), o be calculaed wih he fire and smoe growh model., : Means he ime needed for he h person o evacuae from subdivided space (s), o be calculaed using he escape personnel evacuaion model. Then, by adding all persons facing one or more unenable condiions, he oal number of persons ha failed o evacuae can be obained; conversely, by adding all persons ha did no face any unenable condiions, he oal number of persons wih a successful evacuaion can be obained. (A) Fire and smoe growh model In his sudy, we se he ime for he h person o encouner he i h unenable condiion, denoed by criical_ i,, i 1, 2, 3, 4, 5 and se n i, i 1, 2, 3, 4, 5 o represen he cumulaive ime o encouner he i h unenable condiion for i=1 o 5. The calculaion procedures using compuer compuaion wih he fire and smoe growh model are given as follows: (1) Inpuing all nown parameers, subdivided space, personnel, and deerminisic parameers of combusible maerials (which are ofen used as consans in one or more simulaions) ino he modeling program (he deailed procedures and values are given in Table 4); (2) Using he smoe layer hicness, densiy, and relaed condiions of preceding uni ime o calculae he fire and smoe growh a he specific uni ime, when he smoe layer emperaure mees he convergence crieria, he smoe densiy a he specific uni ime can be calculaed. If he smoe layer emperaure does no mee he convergence crieria (refer o he research by Wu and Xiao (2007) [31]), he calculaion of smoe layer emperaure is pu in ieraion (using inerval of 10 6 K), so he smoe layer emperaure is recalculaed as illusraed in sep 2 of Fig. 1. (3) Using he fire and smoe condiions, breahing rae and locaion of personnel o calculae he hreshold ime o encouner he 5 unenable condiions. (4) The program will end afer compleing he calculaion of hreshold ime for he 5 unenable condiions. The calculaion procedures of he fire and smoe growh model are given in Fig. 1. Noe 1: This sudy has reaed he inerior rimming maerials as surrounding walls, so he inerior rimmings are in compliance wih grade 2 fire-resisan fiber requiremens. Noe 2: Using he example of Rohr [32] who surveyed a residenial fire deah in U.S. Rohr discovered ha wo iems, furniure maresses and upholsered chairs, are mos liely o burn in a fire, because hese wo ypes of furniure consis of PU foam. No surprisingly, he srucure of his ind of furniure found in his counry is very similar. In his sudy, PU made furniure is seleced as represenaive furniure in subdivided space. Page 113
Assuming he combusion efficiency is 0.8, he combusion hea of PU is 23,900 J/g [33], and a combusion hea parameer value of 0.059 W/s 2 will be slighly higher han he rapid fire growh coefficien of 0.04689 W/s 2. FIG. 1. COMPUTATION FLOW CHART WITH THE FIRE AND SMOKE GROWTH MODEL. Page 114
TABLE 4 DETERMINISTIC PARAMETERS FOR THE FIRE AND SMOKE GROWTH MODEL. Subdivided space Value Iniial physical condiion Value parameer Toal floor area of subdivided space Ceiling heigh of subdivided space Hea radiaion rae from surrounding walls Thicness of surrounding walls Densiy of surrounding walls Specific hea of surrounding walls Smoe discharge rae from exhaus por Personnel parameers Number of persons 200 2 m Experimen coefficiens 0.076 g/s W 1/3 m 5/3 3 m Iniial emperaure 303 K 0.04 W/m K Calculaed ime inerval 0.1 s 0.125 m Parameers of combusible maerials Value 300 g/m 3 Fire growh rae 0.059 W/s 2 1.63 J/g K Combusion hea 23900 J/g 0 m 3 /min Combusion efficiency 0.8 Parameer value Same as accommodaing capaciy Opical densiy per uni mass of smoe Carbon monoxide producion rae 420 db m 2 /g 0.03 g CO /g fuel Breahing rae per minue 25 L/min Carbon dioxide producion rae 1.5 g CO2 /g fuel (B) Personnel evacuaion model In his sudy, he ime needed for he h person o evacuae from subdivided space is denoed as,, ha represens he escape sum of sar ime for he h person o escape from a fire, waling ime o reach he egress (, ), and ime needed o pass ravel hrough he egress (, ). The above ime values are compued by he compuer program wih he personnel evacuaion queue model developed by his sudy. The compuaion procedures are narraed as follows: (1) Inpuing all nown iniial parameers, subdivided space, personnel, and deerminisic parameers for combusible maerials (as consans used in one or more simulaions). The deailed procedures are given in Table 5. TABLE 5 DETERMINISTIC PARAMETERS OF THE PERSONNEL BEHAVIOR MODEL. Subdivided space parameer Parameer value Iniial physical condiion Parameer value Lengh of subdivided space 14.2 m Iniial emperaure 30 C Widh of subdivided space 14.2 m Compue ime inerval 0.1 s Ceiling heigh of subdivided space 3 m Effecive flow coefficien 1.5 persons/s m Widh of egress 2 m Combusible parameer Value Personnel parameer Value Fire growh rae 0.059 W/s 2 Individuals waling speed 1.3 m/s Combusion efficiency 0.8 Fire deecion ime 30 s Deecor parameer Value Response ime 20 s Nominal acivaion emperaure 57 C Locaion of individual person Uniform disribuion Response ime index 50 m 1/2 s 1/2 Page 115
(2) If he subdivided space has auomaic fire alarm and emergency broadcas equipmen insalled, se he value of fixed emperaure deecor acivaion ime equal o he sar ime for one or more persons o escape from a fire ; if he subdivided space has no auomaic fire alarm and emergency broadcas equipmen insalled, se he sum of individual fire deecion ime and individual response ime equivalen o he sar ime for one or more persons o escape from a fire. (3) Using parameers lie locaions of individuals, and waling speed o calculae he ime needed for personnel o reach he egress of subdivided space and ime needed o pass hrough he egress of subdivided space. (4) The program will end afer compleing he calculaion of he ime needed o evacuae all personnel from subdivided space. The calculaion process wih he personnel behavior model is demonsraed in Fig. 2. FIG. 2. CALCULATION FLOW CHART WITH PERSONNEL BEHAVIOR MODEL. Noe 1: This sudy has made reference o he research of Nysed [34]. Under he conex of no fire alarms and emergency broadcas equipmen, fire iniiaion in subdivided space, and personnel in conscious sae, he parameer value of an individual s fire deecion ime is se o 30 s and response ime is se o 20 seconds, respecively; also, by reference o he research of Taeyoshi [35], using he average free waling speed of men and women o se he parameer value of personnel waling speed as 1.3 m/s. Noe 2: In his sudy, he subdivided space is defined as a recangular space, wih no person holding up he egress. Therefore, he effecive flow coefficien is se wih a sandard value of 1.5/s m. Since he represenaive combusible is placed on ground a he cener of he subdivided space, he burning of combusible will no hamper personnel movemen near he egress. For he sae of simplificaion, he effecive widh of egress is se and equivalen o he widh of subdivided space wih a parameer value of 2 m. 5.2 Concep of convering deerminisic model o become sochasic model Using he fire and smoe growh model and personnel evacuaion model developed by his sudy, he subdivided space parameers (floor area, ceiling heigh, surrounding walls, ec.), fire parameers (fire growh rae, combusion hea of combusibles, combusion efficiency, and so on), and personnel evacuaion parameers (fire deecion ime, response ime, waling speed, effecive widh of egress, and effecive flow coefficien, and so fors) are assumed o be fixed values (or called deerminisic parameers). However, considering ha he fire parameers and personnel parameers are random in naure, if a deerminisic model is used for predicing number of persons failed o escape from a fire in subdivided space, he obained resuls may no be objecive. Page 116
In he nex paragraph, his sudy will use he reliabiliy-based design (wih 5 performance funcions) and srucural funcion o consruc a sochasic model for predicing oucome of subdivided space fire evacuaion. In he process, par of he deerminisic parameers will be convered o sochasic parameers, and supplemened by he Mone Carlo simulaion mehod. Evenually, he model can simulae he fire es wih differen ypes of subdivided space. VI. STOCHASTIC MODEL FOR PREDICTING THE OUTCOME OF SUBDIVIDED SPACE FIRE EVACUATION 6.1 Modeling and compuer simulaion (A) Model for esing wheher fire vicims are faced wih one or more unenable condiions leading o evacuaion failure. Le A 1,2,..., A, A N. There are M rials in he es, and A o be a se wih posiive inegers from 1 o A, ha is in each rial here are numbers of individuals involved, and all will encouner differen unenable condiions. Any one rial is called he mh rials; any one person is called he h person; and any one unenable condiion is called he ih unenable condiion. Using reliabiliy-based design o consruc a model for predicing he oucome for subdivided space fire evacuaion when personnel may be faced wih one or more unenable condiions (including 5 performance funcions), he deailed seps are given as follows: Le G i m,, be he performance funcion for predicing he oucome of fire evacuaion depending on wheher he h person, afer he mh rial, is faced wih he ih unenable condiion ha may resul in evacuaion failure. where Defining i 5, m M, K G i, m, criical _ i, m, escape, m, (12) When he performance funcion produces he oucome (G i,m, < 0), ha means, afer he mh rial, he h person has encounered he ih unenable condiion, hus resuling in evacuaion failure. Conversely, when he performance funcion produces he oucome G 0, ha means, afer he mh rial, he h person i, m, has no encounered he ih unenable condiion, hus resuling in successful evacuaion. (B) Model for predicing he oucome of subdivided space fire evacuaion depending on wheher fire vicims are faced wih one or more unenable condiions. Using srucure funcion o consruc a model for predicing he oucome of subdivided space fire evacuaion ha depends on wheher fire vicims are faced wih one or more unenable condiions. The deailed seps are given as follows: where x i m, Le 0, 1, if G 0 i, m, x i, m,, 5 if Gi, m, 0 i, m M, K (13), is an indicaor variable used for predicing he oucome of fire evacuaion depending on wheher he h person is faced wih he ih unenable condiion afer he mh rial. If he h person has encounered he ih unenable condiion afer he m h rial, resuling in evacuaion failure, which means he i h performance funcion has produced a failed operaion, so x 0. i, m, Conversely, if he h person has no encounered he i h unenable condiion afer he m h rial, resuling in successful evacuaion, which means he i h performance funcion has produced a successful operaion, so x 1. Le 0, 1, 5 if xi, m, 0 i1 m, 5, m M, K if xi, m, 1 i1 i, m, (14) Page 117
where m, is a srucure funcion used for predicing he oucome of fire evacuaion depending on wheher he h person has encounered one or more unenable condiions afer he m h rial. If afer he m h rial, he h person is faced wih one or more unenable condiions leading o evacuaion failure, ha indicaes one or more performance funcions have produced failed oucome i 5 s.. G i,m, < 0, so 0. m, Conversely, if afer he m h rial, he h person is no faced wih any one unenable condiion leading o successful evacuaion, revealing ha all five performance funcions have produced successful operaion [36 37] i 5 s.. G 0, so 1 i, m,. m, Assume ha each rial is an independen even, hen afer he mh rial, he MKh person is faced wih he ih unenable condiion leading o he probabiliy of evacuaion failure. [38-39] P M K M Psafe _ i, M xi, m, MK m1 1 1, 5 fail _ i, 1 i (15) Similarly, afer he m h rial, he MK h person is faced wih one or more unenable condiions leading o he probabiliy of evacuaion failure. P M K M K 5 M 1 Psafe, M 1 m, MK xi, m, MK (16) m1 1 m1 1 i1 fail, 1 The above probabiliy value was obained from compuer compuaion using he sochasic model for predicing he oucome of subdivided space fire evacuaion. The calculaion seps are depiced in Fig. 3. FIG. 3. CALCULATION FLOW CHART USING THE STOCHASTIC MODEL TO PREDICT THE OUTCOME OF PERSONNEL EVACUATION IN SUBDIVIDED SPACE. Page 118
6.2 Defining sochasic parameers and simulaion mehods In his sudy, by referencing he research of Nysed [40] and Williams [41], we used he average values of deerminisic parameers as sochasic parameer values o define he sandard deviaion for all parameers, and assume ha all parameer disribuions are log normal disribuions. Deails of he sochasic parameers defined by his sudy (i.e., inpu of variables for one or more simulaions) and pre-deermined probabiliy disribuions are presened in Table 6. TABLE 6 STOCHASTIC PARAMETERS AND PRE-DETERMINED PROBABILITY DISTRIBUTIONS Random parameer Mean value Sandard deviaion Parameer disribuion Fire growh rae 0.059 W/s 2 0.0059 W/s 2 Lognormal disribuion Combusion hea 23,900 J/g 956 J/g Lognormal disribuion Combusion efficiency 0.8 0.08 Lognormal disribuion Carbon monoxide producion rae 0.03 g CO /g fuel 0.006 g CO /g fuel Lognormal disribuion Carbon dioxide producion rae 1.5 g CO2 /g fuel 0.3 g CO2 /g fuel Lognormal disribuion Breahing rae per minue for individual persons 25 L/min 5 L/min Lognormal disribuion Waling speed of he h person 1.3 m/s 0.2 m/s Lognormal disribuion Fire deecion ime of he 4h person 30 s 5.7 s Uniform disribuion Response ime of he h person 20 s 5.7 s Uniform disribuion Nominal emperaure for acivaion of fixed emperaure deecor 57 C 2 C Lognormal disribuion Using he Mone Carlo simulaion mehod, random numbers [42] corresponding o predeermined probabiliy disribuion of sochasic parameers can be produced. Subsiue he parameers of deerminisic models wih random numbers o predic he oucome of subdivided space fire evacuaion, he resuls are reaed as a se of experimenal values. Afer several simulaions, using he sochasic model for predicing he oucome of subdivided space fire evacuaion o calculae number of persons failed o evacuae, which is he probabiliy of failure in fire evacuaion if some persons are faced wih one or more unenable condiions. This model can overcome he uncerainies of deerminisic models, and he assessmen resuls are also more objecive. 7.1 Model illusraion VII. MODEL APPLICATIONS The arge building is classified under as enerainmen quarer (discos, hoels, pubs, ec.) caering o he usage of nonspecific people. Since i is of special business in naure, lie ohers i only has one enrance. When a lo of people gaher ino he quarers and a fire inciden breas ou, he siuaion ofen leads o heavy casualies, herefore his ype of enerainmen quarers is chosen as an applicaion model for our sudy. The oal floor area of he enerainmen comparmen is 200 m 2, and is heigh is 3 m, and an egress or enrance is locaed a he opposie corner wih a widh of 2 m. In his sudy, following he guiding principles for special business quarer, we se an accommodaing capaciy limi of 200 for special business quarers. We also considered wheher he quarer has insalled auomaic fire alarms and emergency broadcas equipmen. We hen used a sochasic model for predicing he oucome of subdivided space fire evacuaion o esimae he probabiliy of failure in personnel evacuaion under he above wo es condiions respecively. 7.2 Evacuaion modeling resuls, analysis, and discussions Afer 100 rials under he above wo es condiions, we calculaed he probabiliy of failure in personnel evacuaion when fire vicims are faced wih one or more unenable condiions, ha is P fail _ i, 100, i 5 and P fail, 100, where personnel refers o 20,000 persons remaining in he quarer. Deailed numbers relaing o he model are displayed in Table 7. From he probabiliy saisics given in Table 7.1, i can be seen ha when he enerainmen quarers (discos) are insalled wih auomaic fire alarms and emergency broadcas equipmen, he probabiliy of failure in personnel evacuaion when fire vicims are faced wih one or more unenable condiions is close o 0; however, if he enerainmen quarers (discos) are no Page 119
insalled wih auomaic fire alarms and emergency broadcas equipmen, he firs unenable condiion ha personnel are mos liely o encouner is visibiliy, which may reach he olerance limi of 5 m, followed by radian hea flux, which may reach he olerance limi of 2.5 W/m², and hen smoe layer emperaure, which may reach he olerance limi of 200 C, followed by carbon monoxide conen in blood, which may reach he olerance limi of 30%, and he final unenable condiion concenraion of carbon monoxide in smoe layers, which may reach he olerance limi of 1,400 ppm. TABLE 7 PROBABILITY OF FAILURE IN PERSONNEL EVACUATION WHEN FIRE VICTIMS ARE FACED WITH ONE OR MORE UNTENABLE CONDITIONS UNDER THE ABOVE TWO TEST CONDITIONS Tes condiion P fail _1, 100 P fail _ 2, 100 P fail _ 3, 100 P fail _ 4, 100 P fail _ 5, 100 P fail, 100 w/ fire equipmen 0.00005 0.00010 0.00005 0.00010 0.00005 0.00015 w/o fire equipmen 0.00095 0.12640 0.00010 0.00015 0.04765 0.13395 Noe: wih or wihou fire equipmen means wheher he place is insalled wih auomaic fire alarms and emergency broadcas equipmen. Furhermore, regardless of es condiions, if he probabiliy of failure of individual persons in personnel evacuaion faced wih any unenable condiion are added ogeher, i is greaer han he probabiliy of evacuaion failure when fire vicims are faced wih one or more unenable condiions. This indicaes ha personnel may be faced wih up o 5 unenable condiions simulaneously leading o evacuaion failure. No maer wha ind of es condiions, he probabiliy of failure wih he hird unenable condiion is less han he probabiliy of failure wih he second unenable condiion. However, his does no necessarily mean ha he second unenable condiion mus have occurred before he hird one. Overall speaing, i only implies ha he probabiliy of occurrence of he second unenable condiion is higher han he hird one. If he average hreshold ime o he second unenable condiion 2 is deduced by 3 sandard deviaions, i may be less han he average hreshold ime o he hird unenable condiion added wih 3 sandard deviaions, bu such probabiliies are very small. Neverheless, he hird unenable condiion could occur before he second one. The saisics of hreshold ime for various unenable condiions lised can be referred in Table 8. TABLE 8 STATISTICAL DATA RELATING TO PERSONNEL EVACUATION AFTER 100 TRIALS, INCLUDING THRESHOLD TIME TO ENCOUNTER 5 UNTENABLE CONDITIONS AND TIME NEEDED FOR SAFE EVACUATION. Tes condiion Saisical daa criical_ 1, m, criical_ 2, m, criical_ 3, m, criical_ 4, m, criical_ 5, m, escape, m, Mean value 158.0 s 133.1 s 174.3 s 181.3 s 140.4 s 61.8 s w/ equipmen Sandard deviaion 6.1 s 13.0 s 7.9 s 6.8 s 6.9 s 24.1 s Mean value 158.2 s 131.1 s 173.8 s 181.4 s 140.6 s 92.9 s w/o equipmen Sandard deviaion 5.4 s 18.3 s 7.7 s 7.2 s 6.3 s 28.8 s Noe: wih or wihou equipmen refers o he condiion wheher he quarer is insalled wih auomaic fire alarms as well as emergency broadcas equipmen. Afer 100 rials, his sudy had colleced evacuaion saisics relaing o 20,000 persons ha may say in he quarers, including he hreshold ime o unenable condiions, i 5, m100, 200, ime needed for safe evacuaion (, m100, 200 Table 8. escape, m, criical_ i, m, ), average values, and sandard deviaions. The deailed numbers are shown in From he mean ime values lised in 7.2, i can be seen ha regardless of es condiions, if he riss of one or more unenable condiions are sored according o he mean values of hreshold ime o encouner unenable condiion, he above lising order is similar o he order of life hrea proposed by Purser [43]. Purser has conduced an analysis wih respec o fire in a single quarer (using a sofa conaining PU maerials as furniure), and lised he order of life hreas in he firs six minues of fire. The life hreas lised in order are fracional smoe visibiliy dose(abbreviaed as FSVD), fracional radiaion Page 120
hea(abbreviaed as FRH), convecive hea dose (abbreviaed as CHD), emperaure, carbon monoxide concenraion, and finally fracional asphyxiaing gas dose (asphyxiaing gas refers o carbon monoxide). 8.1 Brief resuls and discussion VIII. CONCLUSION (A) This sudy used he sochasic subdivided space personnel evacuaion predicion model, supplemened by he Mone Carlo simulaion mehod, o assess he probabiliy of personnel evacuaion failure. Personnel may be faced wih unenable condiions in enerainmen quarers (discos) during evacuaion process. The fire is iniiaed from PU 2 (polyurehane) furniure in he quarers (where fire growh rae is according o he fire growh model, while he average fire growh rae is 0.059 W/s². The unenable condiions faced by personnel include visibiliy less han 5 m, radian hea flux greaer han 2.5 W/m², smoe layer emperaure higher han 200 C, fracional incapaciaing dose of carbon monoxide in blood 30%, and lasly he concenraion of carbon monoxide over 1,400 ppm. (B) In his sudy, seing he accommodaing capaciy conrol limi for he enerainmen quarer (discos) o 200 persons, equipped wih auomaic fire alarm and emergency broadcas equipmen, he probabiliy of failure in personnel evacuaion due o one or more unenable condiions will be decreased by 13.3%. Such a decrease is close o he resul of Nysed [44]. Nysed made a simulaion wih residenial quarers equipped wih smoe deecors, in which he ris of fire deah was decreased by 11%. The apparen difference may be due o several facors. The fire growh model used by his sudy is differen from Nysed; he accommodaing capaciies for he business quarers are differen; he personnel behavior and deecor ypes used are differen; and he sandards for unenable condiions are also differen. However, he insallaion of auomaic fire alarms and emergency broadcas equipmen will indeed reduce he probabiliy of fire casualies overall. (C) The personnel evacuaion model developed by his sudy has made several assumpions. The fire is flaming combusion; people remaining in he comparmen will lisen o he auomaic fire alarms and follow insrucions from he emergency broadcas equipmen o escape; no one says behind o figh he fire, or opens he windows o release smoe. In fac, if considering he smoldering effec or ha some people will no observe he fire warning and escape bu choose o say behind o assis he fire fighing or open he windows o release smoe, such circumsances should be discussed and elucidaed separaely wih anoher research opic o analyze he probabiliy of evacuaion failures due o he above condiions. 8.2 Recommendaions (A) In he pas, fire proecion sysems have been designed based on prescripive codes and requiremens which have been proven o be effecive and adequae for radiional building developmens. Neverheless, prescripive approach ofen fails o provide saisfacory and safer fire engineering designs and sysems for modern buildings [45], where fire scenarios can be far more complicaed by he possible involvemen of a wide variey of combusible iems and ineracions of comparmen surfaces wih fire. I is recommended he fire auhoriy should enforce he Fire Proecion and Safey Equipmen Se-up Sandard for Various Buildings (hereinafer referred o as Insallaion Sandards ). Based on Aricle 4 of he Insallaion Sandards relaing o floor characerisics (floors wihou ouside opening), and Aricle 12 of he Insallaion Sandards relaing o building usage classificaion (caegory A buildings), oal floor area provided for such usage, and conrol limi on accommodaing capaciy (reaching or exceeding he conrol number), he fire auhoriies should deermine wha ypes of buildings are difficul for fire rescue operaions. For caegory buildings wihou wide-open floors and where conrol limi on accommodaing capaciy is ofen exceeded, such buildings should be seleced and argeed as a high prioriy for fire fighing and rescue exercises. (B) A his sage, only he Taipei Ciy Governmen and Taoyuan Ciy Governmen have heir own regulaions for he accommodaing capaciy conrol limi o be applied on various buildings. These regulaions are currenly enforced by he auhoriies. Taichung Ciy Governmen has drawn up is own regulaions and has sen i o he municipal council for review. The Minisry of Inerior (MOI) (Taiwan) has recenly sen a leer o auonomous regions or ciies, asing local governmens o reference he guiding rules relaing o accommodae capaciies of special business quarers, and urges hem o formulae heir own regulaions for direc enforcemen, which needs o be sen o local municipal councils for Page 121