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2.5 Details of Asphalt Institute Method of Design

2.5 Details of Asphalt Institute Method of Design

of Flexible

of Flexible Pavements

Pavements

• Historical Development of AI MethodHistorical Development of AI Method •

• 1956 – 19691956 – 1969  1 1stst to 8to 8thth Editions – Empirical Approach Editions – Empirical Approach •

• 19701970  Revised 8 Revised 8thth Edition -  Edition - Empirical ApproachEmpirical Approach •

• Thickness Design – Full Depth Asphalt Pavement Structures for Highways andThickness Design – Full Depth Asphalt Pavement Structures for Highways and

Streets, The Asphalt nstitute, !anual Series "# $!S"#% Streets, The Asphalt nstitute, !anual Series "# $!S"#%

• ther !ersionsther !ersions

19811981  9 9thth Edition, M-E Approach Edition, M-E Approach

19911991  Revised 9 Revised 9thth Edition Edition

19991999  9 9thth Edition, Reprint Edition, Reprint

20012001  Revised 9 Revised 9thth Edition Edition

20082008  Revised 9 Revised 9thth Edition Edition •

• Thickness Design – Asphalt Pavement for Highways and Streets, The AsphaltThickness Design – Asphalt Pavement for Highways and Streets, The Asphalt

nstitute, !anual Series "# $!S"#% nstitute, !anual Series "# $!S"#%

(2)

"

(3)

"

(4)

• A Method is .sed to desi%n asphalt pavements composed o/ vario.sA Method is .sed to desi%n asphalt pavements composed o/ vario.s com"inations o/&

com"inations o/& a

a asphasphalt coalt concrncrete ete s.r/s.r/ace aace and "and "asese

"

" Em.Em.lsielsied asd asphalt phalt s.r/s.r/ace aace and "and "asese

c

c 3ntr3ntreateeated a%d a%%r%re%ate%ate "ae "ase ase and s.nd s."-"a"-"ase4se4

&mulsi)ed asphalt

&mulsi)ed asphalt is simply a suspension is simply a suspension of small asphalt cement glo&ules in of small asphalt cement glo&ules in waterwater,, which is assisted &y an emulsifying agent $such as soap%' The emulsifying agent which is assisted &y an emulsifying agent $such as soap%' The emulsifying agent assists &y imparting an electrical charge to the surface of the asphalt cement glo&ules assists &y imparting an electrical charge to the surface of the asphalt cement glo&ules so that they do not com&ine $(o&erts et al', #))*%'

(5)

Design Principles

Design Principles

• #avement is re%arded as#avement is re%arded as M*(+I,(A-&&D &(A/+I0 /-/+&MM*(+I,(A-&&D &(A/+I0 /-/+&M44 •

• $esi%n #roced.re is "ased on Esta"lished heor', E!perience, est $ata and a$esi%n #roced.re is "ased on Esta"lished heor', E!perience, est $ata and a

omp.ter #ro%ram $AMA ere .sed to develop a comprehensive pavement omp.ter #ro%ram $AMA ere .sed to develop a comprehensive pavement desi%n proced.re4

desi%n proced.re4

• Materials in each la'er are characteried "' Mod.l.s o/ Elasticit', E and #oisson:sMaterials in each la'er are characteried "' Mod.l.s o/ Elasticit', E and #oisson:s

Ratio, ;4 Ratio, ;4

•  ra<c is e!pressed in terms o/ra<c is e!pressed in terms o/ epetitions of '% 1epetitions of '% 1 =18,000 l" sin%le a!le load=18,000 l" sin%le a!le load

applied to the pavement on to sets o/ d.al tires i4e4

applied to the pavement on to sets o/ d.al tires i4e4 &/A( 0oncept&/A( 0oncept •

• Full Depth Asphalt 0oncrete (a3er 4 , (a3ered /3stemFull Depth Asphalt 0oncrete (a3er 4 , (a3ered /3stem •

• 3ntreated A%%re%ates & - >a'ered ?'stem3ntreated A%%re%ates & - >a'ered ?'stem •

• ?."%rade >a'er =the loest la'er?."%rade >a'er =the loest la'er   nnite in the @erticall' $onard and  nnite in the @erticall' $onard and

oriontal $irections oriontal $irections

• Bther >a'ersBther >a'ers  inite hic*ness inite hic*ness  nnite in oriontal $irections4 nnite in oriontal $irections4 •

(6)

Design 0riteria

Design 0riteria

• oriontal ensile ?train, Coriontal ensile ?train, Ctt  on the 3nderside o/ the >oest Asphalt  on the 3nderside o/ the >oest Asphalt Do.nd >a'er sho.ld "e ithin the #ermissi"le @al.e4 / the ?train is Do.nd >a'er sho.ld "e ithin the #ermissi"le @al.e4 / the ?train is E!cessive

E!cessive  rac*in% o/ the reated >a'er rac*in% o/ the reated >a'er  ati%.e ail.re Bcc.rs ati%.e ail.re Bcc.rs

• @ertical ompressive ?train, C@ertical ompressive ?train, Ccc  at the ?.r/ace o/ the ?."%rade >a'er  at the ?.r/ace o/ the ?."%rade >a'er sho.ld "e s.ch that E!cessive #ermanent $e/ormation =R.ttin% sho.ld sho.ld "e s.ch that E!cessive #ermanent $e/ormation =R.ttin% sho.ld not 

(7)
(8)

Fatigue 0riterion4 Fatigue 0rac6ing

 he eF.ation /or /ati%.e criterion is&

f  7 %.%$#89:t;,.2#"9&;,%.'5<

Ghere,

• H I alloa"le no4 o/ repetitions o/ standard a!le load to control /ati%.e crac*in% • Jt I horiontal tensile strain at the "ottom o/ the asphalt la'er4

• E I d'namic mod.l.s o/ the asphalt mi!t.re

• he eF.ation /or limitin% the pavement de/ormation is&

d 7 ".85 x "%,# 9:c;,<.<$$

Ghere,

• HdI alloa"le no4 o/ repetitions to limit r.ttin% to 1247 mm /or the desi%n tra<c4 • Jc I vertical compressive strain on the s.r/ace o/ the s."%rade4

(9)

Permanent Deformation

• he eF.ation /or limitin% the pavement de/ormation is& d 7 ".85 x "%,# 9:c;,<.<$$

Ghere,

• HdI alloa"le no4 o/ repetitions to limit r.ttin% to 1247 mm /or the

desi%n tra<c4

• Jc I vertical compressive strain on the s.r/ace o/ the s."%rade4

• Resilient mod.l.s o/ .ntreated %ran.lar material varies ith stress conditions4

(10)

Design Procedures

14 np.t data&

• Tra+c loading, SA

• Su&"grade resilient modulus, !( •  Surface and &ase type

24 $etermine desi%n thic*ness /or the specic conditions descri"ed "' the inp.t data4

4 #repare sta%e constr.ction desi%n

4 Ma*e economic anal'sis o/ vario.s sol.tions4 54 ?elect the nal desi%n

(11)

+ra=c Anal3sis

• n pavement desi%n, n.m"er o/ repetition o/ each a!le load %ro.p d.rin% the desi%n period4

• he initial dail' tra<c in to directions over all tra<c lanes m.st "e m.ltiplied "' directional and lane distri".tion /actors to o"tain the initial tra<c on desi%n lane4

• he tra<c loadin% /or the A method is the E?A> on the desi%n lane anticipated over the desi%n li/e the pavement4

• >oad repetitions, e!pressed in terms o/ an 18-*ip =80-*H sin%le-a!le load, are determined /rom tra<c estimates "' .sin% AA?B eF.ivalent /actors /or a str.ct.ral n.m"er ?H o/ 5 and a terminal servicea"ilit' inde!,  pto/ 2 45

(12)

Determination of Design &/A(

• he proced.re /or determinin% the desi%n E?A> can "e s.mmaried as /ollos&

14 Estimate the n.m"er o/ vehicles o/ diKerent t'pes, s.ch as passen%er cars, sin%le-.nit tr.c*s =incl.din% ".ses, and m.ltiple .nit tr.c*s o/ vario.s t'pes, e!pected on the proposed /acilit'4

24 $etermine the n.m"er o/ each t'pe o/ tr.c* on the desi%n lane d.rin% the rst 'ear o/ tra<c4

or to-lane hi%ha's, the desi%n lane ma' "e either lane o/ the pavement /acilit'4 3nder some conditions, more tr.c*s ma' travel in one direction than in the other 4 n man' locations, heavil' loaded tr.c*s ill travel in one direction, ".t empt' tr.c*s in the other4

(13)

4 $etermine a tr.c* /actor /or each vehicle t'pe 4 +ruc6 factor is dened as the n.m"er o/ 18-*ip =80-*H a!le load applications contri".ted "' one passa%e o/ a tr.c*4

4 he eF.ivalent 18-*ip =80-*H sin%le-a!le load applications can "e o"tained directl' "' m.ltipl'in% the total n.m"er o/ tr.c*s ith the tr.c* /actor /or all tr.c*s4 or the %iven desi%n period, nd a sin%le %roth /actor /or all tr.c*s or separate /actors /or each tr.c* t'pe, as appropriate 4

54 M.ltipl' the n.m"er o/ tr.c*s o/ each t'pe "' the tr.c* /actor and the %roth /actor and s.m the val.es determined to o"tain the desi%n E?A> 4

(14)

/ub,grade &valuation

• DR

(15)

/ubgrade /trength &valuation

• he correlation considered reasona"le /or ne %rained soils ith a soa*ed DR o/ 10 or less is&

(16)

+ra=c (evel 9&A(; Design /ubgrade !alueB ?

10 or >ess 60

Deteen 10 and 106 75

106 or More 8745

(17)

AI C Design 0harts

• he A desi%n proced.re is "ased on a series o/ charts that ere prod.ced /rom comp.ter pro%rams /or la'ered elastic s'stems4

• Reasona"le properties ere ass.med /or the properties o/ the earin% la'er and o/ the "ase and s.""ase co.rses4

• h.s, the desi%n varia"les treated in the anal'sis o/ a %iven pavement t'pe are s."%rade MR and tra<c E?A> /or  temperat.res, MAA =7, 1545 and 20

(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
(27)

Minimum +hic6ness of HMA over &mulsi)ed

Asphalt >ases

+ra=c (evel &/A( +hic6ness for +3pe I Mix

+3pe II +3pe III

n4 mm n4 "%< 140 50 2 "%5 145 50 2 "%8 240 75 "%$ 240 100 "%$ 240 10 5

(28)

Minimum +hic6ness of Asphalt 0oncrete

over *ntreated Aggregate >ase

+ra=c &/A( +ra=c 0ondition Minimum

+hic6ness of Asphalt 0oncrete 9mm;

"%< >i%ht tra<c, par*in%

lots, drivea's and li%ht tra<c r.ral roads

75L "%< but less than "%8 Medi.m tr.c* tra<c 100 "%8 Medi.m to heav' tr.c* tra<c 125

Lor /.ll depth asphalt concrete or em.lsied asphalt pavements a minim.m thic*ness o/ 100 mm applies4

(29)

Numerical Example - 1

 A pavement has to &e designed for a certain length of e-isting single lane carriageway road from the following considerations.

a%/urrent tra+c of 01 k2 e3uivalent single a-le load 4 1'5* - A67day  &%Design period 4 #1 years

c%/onstruction period 4 #0 months from the last tra+c count  d%Tra+c growth rate 4 08

e%09':th /;( values of su&grade soil from seven samples collected 4 :8 f% lastic modulus of asphalt concrete for surface course, ac 4 5:11 !Pa g%lastic modulus of emulsi<ed sta&ili=ed &ase, & 4 #511 !Pa

h%lastic modulus of granular su&&ase $/;( > ?18%, s& 4 #:1 !Pa

Draw the cross"section of <nal pavement layers considering the thickness of asphalt concrete on the surface course is not less than :1 mm'

(30)

Solution:

1 .m.lative Ho4 o/ ?tandard A!les to "e atered H I ! A ! $ or,  7 x Px D Here, # I 0426 ! EA>+da' r I 8 I 0408 n I 10 'ears ' I 18 months I 18+12 I 145 'ears

$ I 1 =Since a Single lane carriageway road =as per R& 7 – 2001

 hen,  7 x %.28x"%x "

7 ".5< x &A(

(31)

2 8745th DR val.es o/ s."%rade soil /rom seven samples collected I

5

 here/ore, $esi%n Resilient Mod.l.s o/ ?."%rade, Mr 7 "%. x 0>9?; =in M#a

I 104 ! 5 I 5".5 MPa

 or  7 ".5< x &A( and Mr 7 5".5 MPaB /rom the %iven desi%n chart,

Full Depth of Asphalt 0oncrete 7 25% mm Ho, adopt

(32)

 Ho, EF.ivalent thic*ness o/ em.lsied sta"ilied "ase co.rse,  t &

I ! I ! 200

I 2554  mm

3se "<% mm thic* emulsi)ed stabiliEed base course

 he em.lsied sta"ilied "ase co.rse eF.ivalent to %ran.lar s.""ase co.rse, t s&

 I 255 – 10 I ""5 mm

(33)

5 hen , EF.ivalent thic*ness o/ %ran.lar s.""ase co.rse, =DR N 0 I ! I ! 115

7

A ?.r/ace o.rse, Eac I 2500 M#a 5% mm

"<% mmEm.lsied ?ta"ilied Dase o.rse,E

" I 1200 M#a

2% mmOran.lar ?.""ase o.rse, =DR N 0,E

s" I 150 M#a

28% mmB A0 Eac I 2500 M#a

?."%rade, DR I 5 ?."%rade, DR I 5

(34)
(35)

Numerical Example - 2

The results of eight tests produced the following su&grade resilient modulus values. @5'0, )?'5, *1'9, 05'#, :?'0, 91'1, *:'* and *)'1 !Pa' Design the e-i&le pavement using Asphalt nstitute !ethod for a single lane 5"way road to cater the tra+c with the following considerations.

a% ;ase tra+c of 01 k2 e3uivalent single a-le load 4 0'5 - #1@ SA67year 

&% Design period 4 #1 years

c% /onstruction period 4 #: months from the last tra+c count  d% Tra+c growth rate 4 98

e% !inimum depth of asphalt concrete wearing course with the modulus of elasticity of 5:11 !Pa 4 9: mm

f% mulsi<ed asphalt &ase course with the modulus of elasticity 4 #5:1 !Pa

(36)

Solution Hints:

14 #.t the test resilient mod.l.s val.es in descendin% order&

esilient ModulusB MPa umber eual to or greater than Percent eual to or greater than 942 1 = ! 100 I 1245 8241 2 = ! 100 I 2540 7840  = ! 100 I 745 6940  = ! 100 I 5040 6546 5 = ! 100 I 6245 6047 6 = ! 100 I 7540 5.' 7 = ! 100 I '$.5 248 8 = ! 100 I 10040 esilient ModulusB MPa umber eual to or greater than Percent eual to or greater than 942 1 8241 2 7840  6940  6546 5 6047 6 5.' 7 248 8

(37)

24 .m.lative Ho4 o/ ?tandard A!les to "e atered H I ! A ! $ or,  7 x Px D 7 G Here, # I 842 ! 10 E?A>+'ear r I 7 I 0407 n I 10 'ears ' I 15 months I 15+12 I 1425 'ears

$ I 1 =Since a Single lane carriageway road =as per R& 7 – 2001

(38)

4 8745th percentile resilient mod.l.s val.e /or the desi%n,

Mr 7 548 M#a

 or  7 G and Mr 7 5".5 MPaB /rom the %iven $esi%n hart, B"tain

Full Depth of Asphalt 0oncrete 7 G

(39)

Numerical Example - 3

The results of eight tests produced the following su&grade resilient modulus values *511, 9011, 0011, ):11, #1111, ##?11, ##)11, and #?:11 psi' Design the e-i&le  pavement using Asphalt nstitute !ethod for a single lane 5"way road to cater the

tra+c with the following considerations.

a% ;ase tra+c of 01 k2 e3uivalent single a-le load 4 1'55 - #1? SA67day  &% Design period 4 #: years

c% /onstruction period 4 #0 months from the last tra+c count  d% Tra+c growth rate 4 9':8

e% !inimum depth of asphalt concrete wearing course with the modulus of elasticity of 5*11 !Pa 4 9: mm

f% mulsi<ed asphalt &ase course with the modulus of elasticity 4 #511 !pa g% Branular su&"&ase course with the modulus of elasticity 4 #:1 !pa

h% Cse )1th percentile resilient modulus value for the design'

(40)

Solution Hints:

(41)

2. raphical determination of design subgrade resilient modulus #%        $        <        '        %

rom the a"ove plot, #%th percentile design subgrade resilient

modulus value for the design 7 $<'% x "%

(42)

Numerical Example - 4

 A pavement has to &e designed for a speci<ed stretch of e-isting two lane road from the following considerations.

a% /urrent tra+c of 01 k2 e3uivalent single a-le load 4 #'10 - A67day  &% Design period 4 #1 yrs'

c% /onstruction period 4 # year fro the last tra+c count  d% Tra+c growth rate 4 98

e% !inimum /;( values in percent o&served on si- locations for that stretch of the road are. ?'?, :'1, *'5, @'#, :'@ and ?'1 respectively for su&grade'

f% Design resilient modulus of su&grade in !Pa is to &e taken as 09':th

 percentile value as is re3uired fro the design' Eou are re3uired to design the  pavement from Asphalt nstitute !ethod'

Draw the cross"section of <nal pavement layers considering the thickness of asphalt concrete on surface course is not less than :1 mm'

(43)

Solution Hints:

1 o determine the $esi%n ?."%rade Resilient Mod.l.s, Mr4

or this, ta".late the DR res.lts, determine the correct val.e /or the tra<c percentile and then convert the $esi%n DR val.e to the $esi%n ?."%rade Resilient Mod.l.s .sin% the e!pression,

Mr 7 "%. x 0> 9?; =in M#a

#.t the test DR val.es in descendin% order40> 9?; umber eual to or greater than Percent eual to or greater than 642 1 = ! 100 I 1647 54 2 = ! 100 I 4 540  = ! 100 I 5040 41  = ! 100 I 6647 4 5 = ! 100 I 84 0> 9?; umber eual to or greater than Percent eual to or greater than 642 1 54 2 540  41  4 5

(44)

• rom the interpolation or /rom the plot "eteen percent eF.al to or %reater than v s DR =, the '$.5th percentile Design /ubgrade 0> !alue 7 .2?.

• here/ore the $esi%n ?."%rade Resilient Mod.l.s, Mr I 104 ! 42  Mpa

2 .m.lative Ho4 o/ ?tandard A!les to "e atered

H I ! A ! $ or,  7 x Px D 7 G Here, # I 1408 ! EA>+da' r I 7 I 0407 n I 10 'ears ' I 1 'r4

$ I 0475 =Since two lane carriageway road =as per R& 7 – 2001

 or  7 G and Mr 7  MPaB /rom the %iven $esi%n hart, B"tain Full Depth of Asphalt 0oncrete

7 G

 hen, /ollo the steps as e!plained in #revio.s E!amples4 •

(45)

Numerical Example - 5

/alculate the accumulated e3uivalent single a-le load for a proposed 5" lane rural highway' The <rst year AADT will &e ?111, the annual growth rate 4 :8 and the design period 4 51 years' The proected vehicle mi-for that highway during the <rst year of operation is given in the ta&le &elow'

/. 

!ehicle +3pes +ruc6

FactorB +F

? of !ehicles "; /ingle *nit +ruc6s

a% 5"A-le, @"Tire 1'15 #0

&% 5"A-le, *"Tire 1'5# 0

c% ?"A-le or !ore 1'9? @

2; +ractor /emitrailers and

0ombination

a% ?"A-le 1'@9 ?

&% @"A-le 1'0? #

(46)

Solution:

1 alc.lation o/ Oroth actor F 7 I I .%8

/ . 

!ehicle +3pes o. of !ehicles

for "st -ear of peration +ruc6 FactorB +F F &/A( 9"; 92; 9; 9"; J 92; x 9; " ; /ingle *nit +ruc6s a  % 5"A-le, @"Tire )0,::1 1'15 ??'1 * *:,#*# &  % 5"A-le, *"Tire @?,011 1'5# ??'1 * ?,1@,*0* c  % ?"A-le or !ore 5#,)11 1'9? ??'1 * :,50,:?1

(47)

/ample 0alculation4 !alues *nder 0olumn o."

=o"tained /rom the rst 'ear AA$ and the desi%n lane /actor • or 2-lane hi%ha', desi%n lane /actor, f  I 50 I 045

• For -ample. or 2,AxleB 8,+ire /ingle *nit +ruc6s, the Ho4 o/ @ehicles d.rin% rst 'ear o/ operation $i'e at the end of the construction% 7 AAD+ x 85 x ? of !ehicles x f d

I 000 ! 65 ! 0408 ! 045 I <B'%% and so on4

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Numerical Example - 6

(esults of seven tests produced the following su&grade resilient modulus test values @@'0, *9'?, *0'?, :0'*, *0'?, #1*') and 01'1 !Pa' The tra+c classi<cation at the end of construction is proected as &elow.

o. of !ehicles 9both directions; +ruc6 Factor 000 0400 2050 04280 1000 14060 1100 04620 1200 14050

(49)

Design the e-i&le pavement using Asphalt nstitute !ethod for two lane two way road to cater the a&ove tra+c with the following details.

a% !inimum depth of Asphalt /oncrete wearing course with modulus of elasticity 5:11 !Pa 4 :1 mm

&% mulsi<ed asphalt &ase course with modulus of elasticity 4 #5:1 !Pa c% Branular su&"&ase course with modulus of elasticity 4 #:1 !Pa

d% Annual growth rate of tra+c 4 *':8 e% Design period 4 #5 yrs'

f% Cse 09':th percentile resilient modulus value for the design

(50)

Solution Hints:

14 Oroth /actor I I I "$.$ 24 alc.lation o/ E?A> • o. of !ehicles 9both directions; +ruc6 Factor roth Factor &/A( 9"; J 92; x 9; =1 =2 = = 000 0400 1747 2084 2050 04280 1747 997048 1000 14060 1747 181242 1100 04620 1747 11864 1200 14050 1747 2188642 +otal 9; 822.58 7

(51)

4 alc.lation o/ 8745th #ercentile $esi%n ?."%rade Resilient Mod.l.s, Mr #.t the test resilient mod.l.s val.es in descendin% order&

• #lot "eteen #ercent eF.al to or %reater than v s Mr to %et 8745th #ercentile $esi%n ?."%rade Resilient Mod.l.s4

• or  and Mr /rom the %iven $esi%n hart, B"tain  Full Depth of Asphalt 0oncrete.  hen, /ollo the steps as e!plained in #revio.s

E!amples4 esilient ModulusB MPa umber eual to or greater than Percent eual to or greater than 10649 1 = ! 100 I 1428 8040 2 = ! 100 I 28457 684  = ! 100 I 2485 684  = ! 100 I 5741 674 5 = ! 100 I 7142 5846 6 = ! 100 I 85471 48 7 = ! 100 I 100 esilient ModulusB MPa umber eual to or greater than Percent eual to or greater than 10649 1 8040 2 684  684  674 5 5846 6 48 7

(52)

Numerical Example - 7

/alculate the accumulated e3uivalent single a-le load for a proposed 0"lane highway' Tra+c volume forecasts indicate that the average annual daily tra+c $AADT% in &oth directions during the <rst year of operation will &e #5,111 with the following vehicle mi- and a-le loads'

Gehicle mi- is e-pected to remain the same throughout the design life of the  pavement' f the e-pected annual tra+c growth rate 4 @8 for all the vehicles

and the design period 4 51 years'

!ehicle +3pes (oad

&uivalenc3 Factors

? of !ehicles

#assen%er ars =45 *H+a!le 0400002 50

2-A!le ?in%le 3nit r.c*s =22425 *H+a!le

0400500 

2-A!le ?in%le 3nit r.c*s =1415 *H+a!le

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Solution:

"; 0alculation of roth FactorB F4

F 7 I I 2#.$'

2 #ercenta%e r.c* @ol.me on $esi%n >ane, f d  I 5 =Ass.me PRan%e I 25 – 8 /or Ho4 o/

>anes

; o. of &uivalent Accumulated Axle (oads in the Design (ane 7 AAD+ x F x ? of !ehicles x 85 x  x F&x f d

a #assen%er ars I 12000 ! 29478 ! 045 ! 65 ! 2 ! 0400002 ! 045 7 %.%%" x "%8

" 2-A!le ?in%le .nit r.c*s I 12000 ! 29478 ! 04 ! 65 ! 2 ! 0400500 ! 045 I %."#$ x "%8

c -A!le ?in%le .nit r.c*s I 12000 ! 29478 ! 0417 ! 65 !  ! 0401960 ! 045 I %.5'8$ x "%8

+otal &/A( 7 %.$'" x "%8

Note: t can "e seen that the contri".tion o/ passen%er cars to the E?A> is ne%li%i"le so, the passen%er cars can "e omitted hen calc.latin% E?A> val.es4

(54)
(55)

References

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