Numercal Study of Occupants Evacuaton from a Room for Requrements n Codes HL MU JH SUN Unversty of Scence and Technology of Chna State Key Laboratory of Fre Scence Hefe 2300326, CHINA muhl@mal.ustc.edu.cn FILIPPO NERI Unversty of Naples Department of Computer Scence Naples, Italy flppo.ner@unna.t SM LO Cty Unversty of Hong Kong Department of Archtecture and Cvl Engneerng Hong Kong bcsml@ctyu.edu.hk Abstract: - Durng fres or other emergences, occupants of buldngs or specfc areas need to escape from the hazardous locaton as quckly as possble. Effcent and safe evacuaton of these occupants s a core research topc n the publc securty feld. Wth reference to the provsons n varous codes, some specfc requrements are not the same, such as the requred number of occupants n a room wth a sngle ext, the mnmum wdth of the ext and the angle between two exts n a room. Combned wth the detaled evacuaton requrements, research of constructng an optmzed buldng envronment to facltate the evacuaton of occupants s of mportant realstc sgnfcance. The evacuaton smulaton model employed s based on a socal force model n order to nvestgate the effect of each nfluence factors on clearance (evacuaton) tme. The research results have the potental to provde a theoretcal foundaton and the techncal support for mprovng evacuaton processes as well as the relevant evacuaton standards mplemented n varous countres. Key-Words: - Occupants Evacuaton, Smulaton, Clearance Tme, Requrements n Codes, Socal Force Model 1 Introducton It s known that absolute preventon of fre or other hazardous events n a buldng and restrctng ther spread may be mpossble. Therefore the mmedate evacuaton of people from hazardous locatons can effectvely reduce the rsk of dsasters nvolvng the loss of human lfe. Therefore, the provson of exts n a zone s a crtcal component of buldng desgn and safety engneerng. Gven that the spatal layout of a buldng s sgnfcantly affected by relevant prescrptve requrements, especally for the escape system, t s mportant to provde a reasonable and flexble archtectural desgn on the bass of performance-based fre safety engneerng crtera. In recent years, computer modelng has been consdered as a major research method for studyng occupant evacuaton or traffc. Researchers from dfferent dscplnes around the world have proposed varous models, ncludng the optmal-controltheory-based pedestran moton model [1], socal force model [2], cellular automaton (CA) model [3], and lattce gas (LG) model [4]. Generally, these models can be classfed nto dscrete models where the space s dvded nto grds and contnuous models where pedestran can contnually move to any avalable space n accordance wth the treatment of space and tme. Both of these models treat the evacuees as partcles that occupy a gven sze of space. When a consderable number of occupants are located n a sngle zone, the number of exts and ther correspondng wdth can nfluence the clearance tme of these occupants. To help buldng desgners n desgn room exts, varous buldng and fre regulatons or codes have prescrbed a mnmum number and dmenson of exts accordng to the number of occupants n a room. Such requrements are proposed on the bass of the carryng capacty of each buldng component. However, these requrements vary across each country. Ths study examnes the evacuaton of occupants from rooms by numercal smulaton based on socal force model consderng the requred number of occupants n a room wth a sngle ext, the mnmum wdth of the ext and the angle between two exts n a room. Further extenson to ths study nvolves the exploraton of agent based smulatons and machne learnng technques to model the evacuaton process [5-7]. E-ISSN: 2224-2678 54 Volume 14, 2015
2 Revews of Requrements n Varous Prescrptve Codes 2.1 Requred number of people correspondng to sngle ext The Code of Practce for Fre Safety n Buldngs [8] by the Buldng Department of Hong Kong suggests that the number of exts n a room s determned by the number of occupants. However, such a requrement has not been fully explaned n the code or n any practce notes ssued by the Hong Kong Government. The same stuaton s observed n the fre safety codes of other countres. Buldng codes generally suggest that a sngle enclosed space must have a mnmum of two exts, unless such space has a low rsk level and accommodates merely a lmted number of occupants. Table 1 shows the requrements n the Code of Practce for Fre Safety n Buldngs [8] by the Buldng Department of Hong Kong. Ths code does not specfy the usage of the space, whch ndcates that the hazard level of dfferent types of space usage s not consdered n the code. Ths code merely stpulates that a room wth more than 30 occupants must have two or more exts. A relatvely conservatve number of occupants (19) are examned n ths study. Smlar requrements can be found n the buldng codes of some countres. For example, the Russan Natonal Fre Safety Code [9] specfes that at least two exts must be provded for rooms wth more than 50 occupants, for rooms that are located n basements, and for rooms of specal usage (e.g., chld care centers, homes for the elderly, and ndustral buldngs) wth a specfc number of occupants. The Code of Practce for Fre Precautons n Buldngs by the Sngapore Cvl Defence Force [10] stpulates that the number of exts must comply wth the provsons presented n Table 2. Ths code also stpulates that rooms wth more than 50 occupants must have two exts. Moreover, referrng to the Internatonal Buldng Code of the by Internatonal Code Councl [11], when the occupancy maxmum occupant load s 49, one ext or ext access doorway can be permtted for the spaces. Table 1 Mnmum number and wdth of ext doors and ext routes n a room as prescrbed by the Code of Practce for Fre Safety n Buldngs [8] Occupant Capacty of room, fre compartment or storey (No. of persons) Mnmum No. of ext doors or ext routes Mnmum total wdth Mnmum wdth of each Ext doors Ext routes Ext door Ext route 4-30 1 750 mm 1050 mm 31-200 2 1750 mm 2100 mm 850 mm 1050 mm 201-300 2 2500 mm 2500 mm 1050 mm 1050 mm 301-500 2 3000 mm 3000 mm 1050 mm 1050 mm 501-750 3 4500 mm 4500 mm 1200 mm 1200 mm 751-1000 4 6000 mm 6000 mm 1200 mm 1200 mm 1001-1250 5 7500 mm 7500 mm 1350 mm 1350 mm 1251-1500 6 9000 mm 9000 mm 1350 mm 1350 mm 1501-1750 7 10500 mm 10500 mm 1500 mm 1500 mm 1751-2000 8 12000 mm 12000 mm 1500 mm 1500 mm 2001-2500 10 15000 mm 15000 mm 1500 mm 1500 mm 2501-3000 12 18000 mm 18000 mm 1500 mm 1500 mm >3000 persons - the number of ext doors, ext routes and ther wdth to be determned by the Buldng Authorty Notes: (1) In the case of Places of Publc Entertanment, the requrements n should be compled wth. (2) The wdth of an ext door should be the least clear wdth measured between the vertcal members of the door frame. (3) The wdth of a requred starcase, starcase landng, passage or corrdor comprsng an ext route should be measured between the fnshed surfaces of the walls or of the nner sdes of any balustrade and should not be decreased by the ntroducton of any projectons other than handrals the projecton of whch should not exceed 90 mm. (4) The Table shows the mnmum requrement on the assumpton that doors can be readly and freely opened by occupants n case of fre. E-ISSN: 2224-2678 55 Volume 14, 2015
Table 2 Mnmum number of exts as prescrbed by the Code of Practce for Fre Precautons n Buldngs by the Sngapore Cvl Defence Force [10] Number of Occupancy (persons) Mnmum number of Doors 51-200 2 201-500 2 501-1000 3 exceedng 600 4 Occupancy Loadng (persons) Table 3 Mnmum number of exts as prescrbed by the Ontaro Fre Code [12] Mnmum number of Exts Not exceed 60 1 61-600 2 601-1000 3 More than 1000 4 Aggregate wdth of requred means of egress (a) 6.1 mm per person for ramps wth a gradent of not more than 1 n 8, doorways, corrdors and passageways, or (b) 9.2 mm per person for ramps wth a gradent of more than 1 n 8 and stars. Remarks Floor areas n buldngs not exceedng 2 storeys n buldng heght; the floor area does not exceed 200 m 2 ; travel dstance from any pont on the floor area does not exceed 15 m The Fre Protecton and Preventon Act of 1997 by the Ontaro Regulaton [12] stpulates that the number of occupants n rooms wth a sngle ext must not exceed 60. Table 3 summarzes the requrements for assembly usage. The Scottsh Buldng Standards [13] prescrbe that the mnmum numbers of exts depend on the occupancy capacty of a room. Table 4 shows that the maxmum occupancy loadng of a sngle ext room s 60 occupants. The examples show that the prescrbed maxmum number of occupants n a room wth a sngle ext vares from 30 to 60. The prme concern of the layout desgn may be the flow pattern of the occupants and the clearance tme from the space, whch manly depend on the number of occupants. 2.2 Requred mnmum wdth of sngle ext The mnmum ext wdth requrements of varous codes have been nconsstent. For nstance, the Code of Practce for Fre Safety n Buldngs [8] by the Buldng Department of Hong Kong suggests that the ext of rooms or floors wth more than three occupants must not be less than 750 mm n wdth. The Code of Practce for Fre Precautons n Buldngs stpulates that the mnmum clear wdth of an ext door openng shall be not less than 850 mm [10]. The Internatonal Buldng Code by the Internatonal Code Councl [11] suggests that mnmum wdth of each door openng shall be suffcent for the occupant load thereof and shall provde a clear wdth of 32 nches (813 mm). The Buldng Regulatons Part B - Fre Safety [14] by the government of Ireland suggests that the wdth of escape routes and exts depends on the number of persons who need to use them and must not be less than the dmensons lsted n Table 5. Moreover, Table 6 summarzes the mnmum ext wdth requrements prescrbed by varous codes. 2.3 Requred angle between two exts n a room Wth respect to the requrements of a room wth two exts, the way of placng the two exts s a major concern n relevant codes. However, the codes of several dstrcts have varyng prescrptons wth regard to the placement of two exts n a sngle room. For example, the Code for Fre Protecton Desgn of Buldngs GB 50016-2014 by the Mnstry of Publc Securty of Chna [15] prescrbes that the dstance between the nearest edges of two ext doors n a sngle room must be longer than 5 m. The Buldng Regulatons Part B - Fre Safety [14] by the government of Ireland suggests that choosng from multple escape routes s nsgnfcant f such routes tend to be blocked or dsabled smultaneously. Every escape route n a buldng level must be ndependent of any other escape route that can be drectly E-ISSN: 2224-2678 56 Volume 14, 2015
accessed by the occupants. Alternatve escape routes should satsfy the crtera that they are n drectons 45 or more apart. Fg. 1 shows that two drectons of escape are assumed f the escape routes are more than 45 away from each other. Addtonally, n shaded areas where the angle s less than 45 at any pont, only one drecton of escape must be assumed and dead-end condtons wll be appled. Table 4 Mnmum number of exts as prescrbed by the Scottsh Buldng Standards [13] Occupancy capacty (persons) Mnmum number of room exts Not more than 60 1 61-600 2 More than 600 3 Table 5 Wdth of escape routes and exts as prescrbed by Buldng Regulatons Part B - Fre Safety [14] Maxmum number of Mnmum wdth (mm) persons (1)(2)(3) 50 750 (4) 100 850 150 950 220 1050 More than 220 5 mm per person (5) Notes: (1) Refer to Para B1.0.10 (c) Methods of Measurement - Wdth. (2) The mnmum wdths gven n the table may need to be ncreased n accordance wth the gudance n TGDM: Access for People wth Dsabltes. (3) Wdths less than 1050 mm should not be nterpolated. (4) May be reduced to 530 mm for gangways between fxed storage rackng other than n publc areas of buldngs of purpose group 6 or 7. (5) 5 mm/person does not apply to an openng servng less than 220 persons. Table 6 Mnmum wdth of exts as prescrbed by varous codes Requrement n Dstrct Mnmum Wdth Prescrptve Code Hong Kong 750 mm (BD, 2011) [8] Ireland 750 mm (TGB, 2006) [14] IBC 813 mm (IBC, 2012) [11] Sngapore 850 mm (SCDF, 2013) [10] Chna 900 mm (MPS, 2014) [15] Shaded areas Fg. 1 Alternatve escape routes as prescrbed by the Buldng Regulatons Part B - Fre Safety by the government of Ireland [14] The Code of Practce for Fre Safety n Buldngs by the BD of Hong Kong (2011) assumes two drectons of escape f the angle between the two exts s greater than 30 [8]. For any room or story where two or more ext doors are requred to be provded as shown n Table 1, a lne that s drawn from any pont on the floor of that room or level to one of the ext doors must form an angle of not less than 30 wth a lne that s drawn from the same pont to the other ext door. Fg. 2 llustrates such a requrement of alternatve escape routes. Fg. 2 Alternatve escape routes as prescrbed by the Code of Practce for Fre Safety n Buldngs by the Buldng Department of Hong Kong [8] 3 Smulaton Model The socal force algorthm s employed n ths study to descrbe the essental movement rule of the evacuees. In the socal force model, the nteracton among people and that between people and the buldng envronment can be descrbed and adopted to affect the movement dynamcs [2]. Each person occupes a gven space n tme, and the moton of one person s governed by Newton s law of moton. For the sake of completeness, the man equatons of the socal force model are presented as follows: E-ISSN: 2224-2678 57 Volume 14, 2015
dv v () t e () t v () t m m f f 0 0 = + j + W dt τ j( ) W (1) In equaton (1), a person of mass m moves 0 wth a desred speed of v n a drecton 0 e, whle the actual velocty v n a characterstc tme τ s adjusted n tme as nfluenced by other people f j and walls f W [2]. f = { A exp[( r d ) / B ] + kg( r d )} n j j j j j j t + κgr ( d) Δν t j j j j (2) havng a fxed target pont at the ext. The desred velocty refers to the speed at whch an evacuee s wllng and able to walk n uncongested condtons. (b) When the evacuees arrve at the outer sde of the ext zone or ts extenson lne, whch s defned beforehand, the nearest pont at one of the doors would be chosen for approachng. (c) The destnaton pont wth the shortest dstance s updated at every tme step (0.1 s for ths smulaton) n the model. The evacuees then reach and pass through the ext. Besdes, n each smulaton, when all people have escaped at tme T, the tme T they leave from the space s recorded as the evacuaton or clearance tme. f = { Aexp[( r d )/ B] + kg( r d )} n κg( r d )( v t ) t W w w w w w w In equaton (2) and (3), r j = r + r j, dj = r rj denote the sum of the rad and the dstance between person and j, respectvely. Furthermore, the repulsve and attractve psychologcal forces follow the form that s assumed n these two equatons. For example, the socal force among people s descrbed r as Aexp[( rj dj) / B] nj, n whch A and B are constants. In accordance wth the orgnal socal force model, physcal nteractons are determned by these parameters, τ =0.5 s, k =1.2 10 5 kg -2, κ =2.4 10 5 kgm -1 s -1, A =2 10 3 N and B =0.08 m [2]. The evacuees are represented by crcle dots wth dfferent dameters because representng the human body as a pont s unreasonable. Gven that the mean horzontal projecton area of an adult body s 0.113 m 2 [16], the dameters follow a unform dstrbuton from 0.35 m to 0.42 m (from 0.096 m 2 to 0.138 m 2 ) to add the essental factor of dfferent body szes. The partal person-to-person and person-to-wall overlaps are allowed. The socal force model does not focus on modelng a complcated escape system from an overall perspectve. However, ths model can descrbe the evacuaton process accordng to the behavoral characterstcs of the evacuees by representng ther nteractons. To be dfferent wth the orgnal socal force model, certan movement rules have been ncluded, such as allowng the evacuees to move and choose the doors randomly. The other rules are descrbed as follows: (a) The evacuees move forward wth a specfc desred velocty n a rectlnear drecton nstead of (3) 4 Results and Dscusson 4.1 Effect of number of people on evacuaton wth sngle ext 4.1.1 Examnaton of desred velocty In the aforementoned expressons of pedestrans movement, the parameter v 0 n the socal force model represents the desred velocty for a person to move toward a specfc object. To examne f the desred velocty v of a person can affect 0 evacuaton tme, the dfferent value of must also be analyzed n the smulaton. The nputs for the analyss are presented as follows. The numbers of persons are selected as 19, 30, 50, and 60. The desred veloctes vary from 0.8 m/s to 2.2 m/s. The room sze s 10 m 10 m and the wdth of the ext s 0.75 m, whch s consstent wth Hong Kong s Code of Practce for Fre Safety n Buldngs. In the begnnng of the smulaton, all people are generated and randomly dstrbuted n the room, as shown n Fg. 3 (a). After the people are placed n ther respectve locatons, they wll be actvated to move toward the ext smultaneously. The orgnal postons of the agents can also be manually assgned n the plan. The model also has a constant or random delay tme for each agent before movng. For nstance, f the maxmum delay tme s 1 mnute, every agent stays at the ntal poston for no more than 1 mnute and then starts to evacuate when the tme followng a stochastc dstrbuton has already passed. In these smulatons, the delay tme s assumed as zero. Fg. 3 (b) shows a screenshot of the smulaton of occupants evacuaton from a room wth a sngle ext. E-ISSN: 2224-2678 58 Volume 14, 2015
The data of the average desred velocty are collected from the evacuaton smulaton, whch s conducted 50 tmes correspondng to each parameter. Table 7 shows the clearance tme for a seress of desred veloctes. In accordance wth the clearance tme, the curves n Fg. 4 show the relatonshp between the clearance tme and the dfferent desred veloctes of the evacuees. From ths fgure, t can be found that an ncrease n the desred velocty of a specfc number of evacuees can sgnfcantly decrease the clearancee tme when the desred velocty ranges from 0.8 m to 1.2 m, slowly decrease the clearancee tme when the desred velocty ranges from 1.3 m to 1.7 m, and can slghtly decreasee the clearance tme when the desred velocty ranges from 1.8 m to 2.22 m. Ths result reflects a phase change from a normal condtonn when people move at an ordnary speed to an emergency condton when people begn to move at a comparatvely rapd velocty. In addton, n ths present study of examnng the relevant standards on the specfc number of occupants n a room wth a sngle ext, t s notced that a faster desred velocty s not consdered n vew of the faster s slower phenomenonn [2]. 140 120 100 Clearance tme (s) 80 60 40 (a) (b) Fg. 3 Screenshot of the evacuaton smulaton from a room wth a sngle ext: (a) Random dstrbuton of people n the room, and (b) evacuaton though a sngle ext Number of people 19 30 50 60 20 0 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 Desred velocty (m/s) Fg. 4 Relatonshp between clearance tme and desredd veloctes for dfferent numbers of people E-ISSN: 2224-2678 59 Volume 14, 2015
Table 7 Clearance tme n the evacuaton smulaton for a seres of desred veloctes Number of people Desred velocty (m/s) 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 19 Clearance tme (s) 48 40 31 25 21 18 15 13 12 10 9 8 8 7 7 30 78 53 48 33 32 26 24 22 21 17 13 14 10 9 8 50 104 78 65 52 47 42 37 34 32 30 28 26 24 21 19 60 115 86 73 62 56 50 44 41 40 35 31 27 28 25 23 4.1.2 Mean evacuaton tme per person Furthermore, the evacuaton effcency of the escape s measured based on the mean evacuaton tme per person. Correspondng to each specfc number of people, Fg. 5 shows the mean evacuaton tme per person of three ranges of desred velocty. It can be dscovered that when the desred velocty ranges between 1.3 m/s and 1.7 m/s, the mean evacuaton tme per person remans at approxmately 0.7 s for each specfc number of people. When compared wth the curve of the desred velocty that ranges from 0.8 m/s to 1.2 m/s, the mean evacuaton tme for each person sgnfcantly decreases by approxmately 50%. Buldngs, whch ndcates that no more than 30 people can be placed n a room wth a sngle ext. However, the requrements of codes from other dstrcts wth regard to the maxmum number of people n a room wth a sngle ext may have to be examned further. 4.2 Effect of Sngle Ext Wdth on Evacuaton Furthermore, several ext wdths are examned n ths study, namely, 650, 700, 750 1600, 1650, and 1700 mm. The szes of rooms n the smulaton model are 10 m 10 m (Room 1), 10 m 5 m (Room 2), and 13.33 m 7.5 m (Room 3). The ext s placed n the mddle of the long sde of the rectangular room. Thrty agents are selected and randomly dstrbuted n the room at the begnnng of the smulaton. To reflect an emergency stuaton better, the desred velocty of people follows a unform dstrbuton (from 1.8 m/s to 2.0 m/s). The relatonshps between sngle ext wdth and clearance tme for each room are calculated and shown n Fg. 6. Fg. 5 Mean evacuaton tme per person correspondng to the specfc number of people for three ranges of desred velocty As mentoned above, emergences are generally accompaned by a comparatvely rapd velocty. When the desred velocty ranges from 1.8 m/s to 2.2 m/s, the mean evacuaton tme per person s sgnfcantly reduced as compared wth the data from other curves. Especally, the shortest mean evacuaton tme per person can be acheved when a room only contans 30 people. Therefore, the evacuaton from a sngle-ext room wth 30 occupants s consdered the most effcent. Ths result s consstent wth the requrements prescrbed n Hong Kong s Code of Practce for Fre Safety n Fg. 6 Relatonshp between sngle ext wdth and clearance tme for rooms wth dfferent szes and 30 occupants E-ISSN: 2224-2678 60 Volume 14, 2015
Fg. 6 shows a rapd decrease n clearance tme as the ext wdths ncrease from 650 mm to 750 mm for Room 1 (10 m 10 m), from 750 mm to 800 mm for Room 2 (10 m 5 m), and from 950 mm to 1050 mm for Room 3 (13.33 m 7.5 m). The clearance tme then reduces slowly and remans constant when the wdth exceeds 1500 mm. The result ndcates that along wth ext wdth, other factors such as travel tme (from the ntal poston of the evacuee to the ext) and watng tme (watng to pass through the ext) can sgnfcantly nfluence the tme for the occupants to evacuate ther rooms. Moreover, t s observed from the evacuaton smulaton that an ntense congeston of agents around the ext can extend the clearance tme. The occupants n Room 2 requre more tme to escape than those n Room 1 even though Room 2 s half the sze of Room 1. The occupants of a smaller room need lesser tme to approach the ext, whch easly causes congeston around the ext area. By comparng Rooms 1 and 3, whch have the same acreage, the occupants n a rectangular room need more tme to evacuate when the ext wdth of s less than 1050 mm. The reason s stll that the ext areas of rectangular rooms are congested more easly than those of square rooms because of the lmt capacty of ext wth. In ths case, the occupants may not be able to evacuate quckly despte reachng the ext at an earler tme. However, as shown n Fg. 6, the clearance tme for the occupants n a rectangular room s slghtly shorter than that for the occupants n a square room when the ext wdth s more than 1050 mm. In general, the mnmum ext wdth as prescrbed n Hong Kong and Ireland (750 mm) can cause a relatvely effcent evacuaton for Room 1 (10 m 10 m). However, there s a sgnfcant mprovement for occupants evacuaton when the ext wdth s 800 mm n Room 2 (10 m 5 m). However, gven that the factors that nfluence evacuaton tme are complex, t s dffcult to determne the mnmum wdth of exts of a specfc buldng space wthout a systematc numercal computaton. 4.3 Examnaton on Angle between Two Exts n a Room 4.3.1 Examnaton of dfferent ext choce of pedestrans In consderaton of there are two exts n a room, the ext choces of occupants are then examned. Fve patterns of ext choce are consdered, namely, the ratos of 50 50, 60 40, 70 30, 80 20, and 90 10. In the smulaton model, the room has a floor area of 10 m 10 m and 100 randomly dstrbuted occupants. Two 1-m wde exts are placed at the same sde of the room. The desred velocty of the occupants ranges from 1.8 m/s to 2.0 m/s and s subject to a unform dstrbuton. The angle between the two exts ncreases from 11.42 to 48.46 as the spacng between the two exts s ncreased. In the evacuaton smulaton, the agents reman stll n the room and then move toward the exts smultaneously n accordance wth each rato of ext choce. The tme for these people to evacuate from the room s recorded as the clearance tme. The curves n Fg. 7 demonstrate the relatonshp between dfferent angles and clearance tme for each rato of ext choce. Fg. 7 Relatonshp between dfferent angles and clearance tme for each rato of ext choce Each curve n Fg. 7 shows that an ncrease n the angle between two exts slghtly reduces the clearance tme and especally may rapdly reduce the clearance tme when the angle almost reaches the maxmum value correspondng to the room. For the ext choce rato of 90 10, the clearance tme s sgnfcantly reduced when the angle between the two exts exceeds 38.58. Moreover, when the ext choce rato ncreases from 50 50 to 90 10, the clearance tme of the occupants s extended for each ncrease n angle. The result ndcates that the mbalanced use of exts has a negatve effect on evacuaton effcency. In the followng smulaton, the ext choce rato of 50 50 s employed to determne the target destnatons of the occupants. E-ISSN: 2224-2678 61 Volume 14, 2015
4.3.2 Influence of number of people and dfferent room szes The nfluence of number of people on clearance tme for dfferent angles s then nvestgated after examnng the ext choces. Fg. 8 shows the relatonshp between dfferent angles and clearance tme for the evacuaton of 60 people and 100 people. The two curves demonstrate smlar tendences, except that the clearance tme decreases at 33.4 for the evacuaton nvolvng 60 people, but decreases at 38.58 for the evacuaton nvolvng 100 people. partcularly useful when used to assess the valdty of laws and regulatons that control the constructon of buldngs. For nstance, wth reference to the provsons n varous codes, some requrements are gven explctly, such as the requred number of occupants n a room wth a sngle ext, the mnmum wdth of the ext and the angle between two exts n a room. And the evacuaton smulaton method here proposed can nvestgate the effect of each factor on the clearance (evacuaton) tme. Therefore, we beleve that the reported results have the potental for provdng a theoretcal foundaton and a methodologcal support for mprovng the factors affectng the evacuaton process n a new buldng as well as the relevant evacuaton standards mplemented n varous countres. Fg. 8 Relatonshp between dfferent angles and clearance tme for the evacuaton wth 60 people and 100 people Therefore, the requrements n the Code of Practce for Fre Safety n Buldngs by the Buldng Department of Hong Kong [8] may not be sutable for ths scenaro because such code stpulates that the angle between two drectons of escape should be greater than 30. However, the Buldng Regulatons Part B - Fre Safety [14] by the government of Ireland suggests that the angle between two exts exceeds 45, whch can acheve a relatvely effcent evacuaton. Gven that the evacuaton of 100 people requres more tme, performng a systematc numercal computaton s crucal for a specfc scenaro and condton. 4 Concludng Remarks The behavour of room occupants durng fres or other emergences s a complex phenomena that can be studed wth specally desgned smulatve methodologes such as that here descrbed. Ths study examnes the evacuaton process by numercal smulaton based on a socal force model fully dscussed n the paper. We have then shown a detaled and reproducble methodology that can be used to study the same phenomena under dfferent type of constrants. Such a methodology may be Acknowledgments The study was jontly supported by Natonal Basc Research Program of Chna (973 Program, Grant. No. 2012CB719702); Natonal Natural Scence Foundaton of Chna (91024025) and the Research Grant Councl of Government of the Hong Kong Admnstratve Regon (No. CtyU119011). References: [1] Hoogendoorn, S. and Bovy, P., Smulaton of pedestran flows by optmal control and dfferental games. Optmal control applcatons and methods, 24 (3), 2003, pp. 153-172. [2] Helbng, D., Farkas, I. and Vcsek, T., Smulatng dynamcal features of escape panc. Nature, 407 (6803), 2000, pp. 487-490. [3] Alzadeh, R., A dynamc cellular automaton model for evacuaton process wth obstacles. Safety Scence, 49 (2), 2010, pp. 315-323. [4] Kuang, H., Song, T., L, X.L. and Da, S.Q., Subconscous effect on pedestran counter flow. Chnese Physcs Letters, 25 (4), 2008, pp. 1498-1501. [5] Ner, F., Quanttatve Estmaton of Market Sentment: a dscusson of two alternatves. WSEAS Transactons on Systems, WSEAS Press (Athens, Greece), 11 (12), 2012, pp. 691-702. [6] Ner, F., Agent based modelng under partal and full knowledge learnng settngs to smulate fnancal markets. AI Communcatons, IOS Press, 25 (4), 2012, pp. 295-304. [7] Ner, F., Learnng and Predctng Fnancal Tme Seres by Combnng Evolutonary Computaton and Agent Smulaton. E-ISSN: 2224-2678 62 Volume 14, 2015
Transactons on Computatonal Collectve Intellgence, Sprnger, Hedelberg, vol. 7, 2012, pp. 202-221. [8] BD., Code of Practce for Fre Safety n Buldngs, Buldng Department. Hong Kong Government, 2011. [9] RNS., Russan Natonal Fre Safety Code. Russan Natonal Standards, 1998. [10] SCDF., Code of Practce for Fre Precautons n Buldngs, Sngapore Cvl Defence Force. Sngapore Government, 2013. [11] IBC., Internatonal buldng code. Internatonal Code Councl, Inc. (formerly BOCA, ICBO and SBCCI), 4051, 60478-5795, 2012. [12] OR., Fre Protecton and Preventon Act 1997, Ontaro Regulaton 194/14. Prnted n the Ontaro Gazette: November 1, 2014. [13] SG., Scottsh Buldng Standards, Techncal Handbook-Non-Domestc. Scottsh Government, 2013. [14] TGB., Buldng Regulatons Part B - Fre Safety. Government of Ireland, 2006. [15] MPS., Code of fre protecton desgn GB 50016-2014. Mnstry of publc securty of the People's Republc of Chna, 2014. [16] Smth, R.A., Densty, velocty and flow relatonshps for closely packed crowds. Safety scence, 18 (4), 1995, pp. 321-327. E-ISSN: 2224-2678 63 Volume 14, 2015