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Rutting as a function of dynamic modulus and gradation

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Virginia Transportation Research Council, Charlottesville, VA, USA; email:[email protected]

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* +,- . / 0 1 , / 2 3 45 6 6 5 7 / 8 9 : 1 22+8 1 8 / 8 9 * +,- . / 0 45 6 6 5 7 ;1 < = ;,1 9 > = = 9 - = ;;1 2/ ,+= 8 1 ,@ 1 1 8

9 A 8 / B +- B = 9 C 2C D / 8 9 ;C ,,+8 > 3 E A 8 / B +- B = 9 C 2C D = ? ,/ +8 1 9 F; = B C 8 - = 8 F+8 1 9 - = B < ;1 D D += 8 ,1 D ,D / , G H I J

/ 8 9 / , / F;1 K C 1 8 - A = F G L . @ / D - = 8 D +9 1 ;1 9 / > = = 9 +8 9 +- / ,= ; = F ;C ,,+8 >

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/ D 1 9 = 8 ,M 1 ;1 < 1 / ,1 9 2= / 9 N O ,1 D ,3

P ,M 1 ; D ,C 9 +1 D M / Q 1 ;1 < = ;,1 9 2+,,21 ,= 8 = - = ;;1 2/ ,+= 8

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1 ,@ 1 1 8 9 A 8 / B +- B = 9 C 2C D / 8 9 ; C ,,+8 > B 1 / D C ;1 9 @ +,M

,M 1 / D < M / 2, < / Q 1 B 1 8 , / 8 / 2A . 1 ; 4 R : R 7 3 S 22+9 ,. 4 T U V W 7 F = C 8 9 8 = > = = 9 - = ;;1 2/ ,+= 8 ? 1 ,@ 1 1 8 R : R ;C , 9 1 < ,M

/ 8 9 9 A 8 / B +- B = 9 C 2C D B 1 / D C ; 1 9 / , H 6 I J / 8 9 T L . F ;1 K C 1 8 - A / D 9 +9 X 0 +8 > 1 8 45 6 6 H 7 @ M = - = B < / ;1 9

9 A 8 / B +- B = 9 C 2C D =

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,/ +8 1 9 / , T L . / 8 9 H L . / 8 9 R : R ; 1 D C 2,D 3 Y = M / B B / 9 1 , / 2 3 4 5 6 6 Z 7 - = B < / ;1 9

9 A 8 / B +- B = 9 C 2C D B 1 / D C ;1 9 / , G H I J / 8 9 G L . 2= / 9 +8 > F ;1 K C 1 8 - A @ +,M ;C ,,+8 > / 8 9 ;1 < = ;,1 9 ,M / , 9 A 8 / B +

-B = 9 C 2C D - = C 29 8 = , 9 +F F1 ; 1 8 ,+/ ,1 ? 1 ,@ 1 1 8 ; C ,,+8 > D C D - 1 < ,+? +2+,A = F ,M 1 B +[ ,C ;1 D ,1 D ,1 9 3

\8 B = D , = F ,M 1 / F= ;1 B 1 8 ,+= 8 1 9 D ,C 9 +1 D ] ,M 1 1 FF1 - , = F > ;/ 9 / ,+= 8 @ / D 8 = , 1 [ < 2+- +,2A 1 Q / 2C / ,1 9 +8

- = 8 ^ C 8 - ,+= 8 @ +,M 9 A 8 / B +- B = 9 C 2C D @ M +- M B / A M 1 2< 1 [ < 2/ +8 D = B 1 = F 9 +D - ;1 < / 8 - +1 D =

?

D 1 ;Q 1 9 +8 ,M 1

;1 < = ; ,1 9 ;1 2/ ,+= 8 D M +< ? 1 ,@ 1 1 8 9 A 8 / B +- B = 9 C 2C D / 8 9 ;C ,,+8 > 3 _ M C D / 9 9 +,+= 8 / 2 D ,C 9 +1 D +8 Q = 2Q +8 > ,M 1

1 Q / 2C / ,+= 8 = F F/ - ,= ;D +8 F2C 1 8 - +8 > ; C ,,+8 > +D D ,+22 8 1 1 9 1 9 3 ` 1 D C 2,D = F D C - M D,C 9 +1 D B / A / 2D = ? 1 +B < = ;,/ 8 , +8

= ,M 1 ; / ; 1 / D / D 9 +D - C D D 1 9 8 1 [ , 3

_ M 1 1 8 = ;B = C D 2+D , = F F/ - ,= ;D +9 1 8 ,+F+1 9 / D / FF1 - ,+8 > ;C ,,+8 > +22C D ,;/ ,1 D ,M 1 9 +FF+- C 2,A = 8 1 B / A

1 8 - = C 8 ,1 ; @ M 1 8 / ,,1 B < ,+8 > ,= = < ,+B +. 1 / > +Q 1 8 / D < M / 2, B +[ ,C ;1 F= ; ;1 D +D ,/ 8 - 1 / > / +8 D , ;C ,,+8 > 3 R - 2= D1

+8 D < 1 - ,+= 8 = F ,M 1 F/ - ,= ;D / FF1 - ,+8 > ;C ,,+8 > +9 1 8 ,+F +1 9 +8 < ;1 Q += C D D ,C 9 +1 D D C > > 1 D ,D ,M 1 D 1 F/ - ,= ;D - = C 29

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- 2/ D D +F +1 9 +8 ,= ,@ = > ;= C < D 3 N +;D , +D ,M 1 ? +8 9 1 ; < ;= < 1 ;,A - = 8 ,;= 22+8 > ,M 1 Q +D - = 1 2/ D ,+- / 8 9 Q +D - = < 2/ D ,+

-? 1 M / Q += ;] / 8 9 D 1 - = 8 9 / ;1 / > > ;1 > / ,1 < ;= < 1 ; ,+1 D +8 - 2C 9 +8 > > ;/ 9 / ,+= 8 ,M / , - = 8 ,;= 2D ,M 1 1 2/ D ,+- 4/ 8 9 < = D D +? 2A

< 2/ D ,+- 7

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1 M / Q += ; = F ,M 1 B +[ 3 R 2D =

?

1 - / C D 1 = F ,M 1 Q +D - = 1 2/ D ,+- 8 / ,C ;1 = F / D < M / 2, B +[ ,C ;1 ;1 D < = 8 D 1 ,= 2= / 9 ]

D 1 21 - ,+= 8 = F / D C +,/

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21 9 A 8 / B +- B = 9 C 2C D Q / 2C 1 4/ , / > +Q 1 8 ,1 D ,+8 > ,1 B < 1 ;/ ,C ; 1 / 8 9 F;1 K C 1 8 - A 7 F= ;

1 Q / 2C / ,+8 > ; C ,,+8 > ;1 B / +8 D / - M / 221 8 > 1 ,= ? 1 D = 2Q 1 9 3 \, +D / 8 ,+- +< / ,1 9 +8 ,M +D D ,C 9 A ,M / , 9 A 8 / B +- B = 9 C 2C D

/ 8 9 - 1 ;,/ +8 0 1 A > ; / 9 / ,+= 8 < / ;/ B 1 ,1 ; D - = C 29

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1 C D 1 9 / D D C ;;= > / ,1 D F= ; ,M 1 8 C B 1 ; = C D F / - ,= ; D +9 1 8 ,+F+1 9 +8

< ;1 Q += C D D ,C 9 +1 D ,= / FF 1 - , ;C ,,+8 > = F / D < M / 2, B +[ ,C ;1 D 3 a A C D +8 > = 8 2A / F1 @ ;1 21 Q / 8 , B / ,1 ;+/ 2 < ;= < 1 ; ,+1 D ] +,

+D M = < 1 9 ,M / , ,M 1 / < < ; = / - M < ; = < = D 1 9 +8 ,M +D D ,C 9 A - = C 29 21 / 9 ,= / B = ;1 1 FF+- +1 8 , / 8 9 ;/ ,+= 8 / 2 B 1 / 8 D = F

1 Q / 2C / ,+8 > ; C ,,+8 > 9 C ; +8 > / ; = C ,+8 1 B +[ 9 1 D +> 8 < ;= - 1 D D 3 : ;1 9 +- ,+= 8 B = 9 1 2D C ,+2+. +8 > ,M 1 - = B ? +8 1 9 1 FF 1 - ,D

= F 9 A 8 / B +- B = 9 C 2C D / 8 9 - 1 ; ,/ +8 > ; / 9 / ,+= 8 < / ;/ B 1 ,1 ;D @ +22

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G ; < < E

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I9 ; = @A 9 ? ; 8 8 ; D IN 7 < 9 F Z [ 8 EJ @7 :9 < ED f E:H ED E> K X A 9 8 EJ @7 : 9 < ? ; D @> ED 9 F o Z g > 8 ; 7 D @< : > D H ED H

=:; 8 e @; c S p

C

N P 9 EH A @ K X A :9 9 F E== 9 :9 D @

C

ED F 9 : @N G 9 < P 9 : 9 7 < 9 F ^ g q \ r Tc c = ; : 8 EJ 9 < P E@A Z

F 9 < EH D > @E; D d g q s e Tc c =; : 8 EJ 9 < P E@A t F 9 < EH D > @E; D d > D F g q s \ Tc c = ; : 8 EJ 9 < P E@A u F 9 < EH D > @E; D > D F

? ; D @> ED ED H G ; IN 8 9 : 8 ; F E=E9 F T> < G A > I@a K _ EJ 9 < Z M t M > D F u > :9 F 9 < EH D 9 F =; : G > B 9 8 9 D @< ? > ::N ED H 7 G @; n

8 EIIE; D u ` Z v < M n T R e 8 EIIE; D u ` Z v > D F w R e 8 EIIE; D u ` Z v M :9 <G 9 ? @EB 9 IN ^f t x X M c e e \ a K

(5)

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* + + ,- ,. / - 1 2 . 3 + - 4 5 6. + 1 7 ,8 . 4 1 + , 9 1 4 4 1 : 6; < + . / 4 => ,< ?. ,; 5 . + @ . ?. 9 1 66. 9 ,. / 7?1 4 - ?1 < : /

,8 . A 1 4 4 1 : @ . - 6,8 1 7 B =?C =: =- D E -F 1 ?=,; 1 7 ,8 . 4 => . + + - 4 5 6. / @ . ?. + < ?7- 9 . 4 => GH E I 71 661 @ . / 0 ; 0 - + .

4 => GJ E I3 - : / H E * 4 => . + D

K . ,- =6+ 1 7 ,8 . 4 => ,< ? . + + - 4 5 6. / =: 9 6< / =: C ,8 . - + 5 8 - 6,

0

=: / . ? C ? - / . 3 - 4 1 < : , 1 7 L * M 3 - : / 4 => ,< ?.

+ 1 < ? 9 . - ?. + 8 1 @ : =: N - 0 6. O D * 66 + - 4 5 6. + @ . ? . 5 6- : ,P4 => . / - : / @ . ?. + - 4 5 6. / 61 1 + . - , ,8 . 5 ? 1 F . 9 , + =,. - : /

+ . : , ,1 6- 0 1 ?- ,1 ?; 7 1 ? 7< ?,8 . ? 5 ? 1 9 . + + =: C - : / ,. + ,=: C D H - 4 5 6. + @ . ?. + ,1 ?. / =: - ,. 4 5 . ? - ,< ?. 9 1 : ,?1 66. /

. : 2 =?1 : 4 . : , =: + . - 6. / 9 1 : ,- =: . ?+

0

. 7 1 ?. ,. + ,=: C D * / / =,=1 : - 6 / . ,- =6+

-0

1 < , ,8 . 4 => ,< ?. + =: 9 6< / =: C Q . ;

C ? - / - ,=1 : 5 - ?- 4 . ,. ?+ - : / 4 => ,< ?. 2 1 6< 4 . ,? =9 + - ? . + 8 1 @ : =: N - 0 6. R - : / N - 0 6. S 3 ?. + 5 . 9 ,=2 . 6; D N 8 . 61 1 + .

4 => ,< ?. + @ . ? . 5 ?1 9 . + + . / =: ,1 9 1 4 5 - 9 ,. / + 5 . 9 =4 . : + 71 ? 4 . 9 8 - : =9 - 6 ,. + ,=: C - + / . ,- =6. / =: +< 0 + . T < . : ,

+ . 9 ,=1 : + < : / . ? 6

-0

1 ?- ,1 ?; ,. + ,=: C D N 8 . 4 - =: 4 . 9 8 - : =9 - 6 6

-0

1 ?- ,1 ? ; ,. + ,+ 9 1 : / < 9 ,. / =: 9 6< / . / / ; : - 4 =9

4 1 / < 6< + - : / 761 @ ,. + ,+ < + =: C - : - + 5 8 - 6, 4 - ,. ? =- 6 5 . ?71 ?4 - : 9 . ,. + ,. ? G* E M N I D

U V W X Y V Z X Y [ \ X ] ^ V _ Z ` X a b c Z d X e f

* H < 5 . ?5 - 2 . C ; ?- ,1 ?; 9 1 4 5 - 9 ,1 ? @ - + < + . / ,1 7

-0

? =9 - ,. + 5 . 9 =4 . : + < + . / 71 ? ,8 . / ; : - 4 =9 4 1 / < 6< + - : / ,8 .

g h ,. + ,+ D N 8 . 4 => ,< ?. + 71 ? ,8 . 2 - ? =1 < + ,. + ,+ @ . ?. 9 1 4 5 - 9 ,. / ,1 - ,- ?C . , - =? 2 1 =/ 6. 2 . 6 1 7 i j k Dl m D N 8 =+ @ - +

- 9 9 1 4 5 6=+ 8 . /

0

; / . ,. ?4 =: =: C ,8 . 9 1 4 5 - 9 ,=1 : 8 . =C 8 , : . . / . / ,1 1

0

,- =: ,8 . ?. T < =?. / ,- ? C . , - =? 2 1 =/ 9 1 : ,. : ,D

n, @ - + / . ,. ?4 =: . / ,8 - , ,8 .

0

- + . 4 => . + G h E * H R l Dk 4 4 I ? . T < =? . / ,1

0

. 9 1 4 5 - 9 ,. / ,1 - 8 . =C 8 , 1 7 R k k 4 4

@ 8 =6. ,8 . H E - : / H E * 4 => . + Go Dl 4 4 - : / O R Dl 4 4 h E * H I ? . T < =?. / ,1 0 . 9 1 4 5 - 9 ,. / ,1 8 . =C 8 , 1 7 O i l

4 4 D h . > , - 9 1 ?=: C ? =C @ - + < + . / ,1 1 0 ,- =: ,8 . ?. T < =?. / O l k 4 4 ,- 66 0 ; O k k 4 4 / =- 4 . ,. ? + 5 . 9 =4 . : 7?1 4

,8 . C ; ? - ,1 ?; 9 1 4 5 - 9 ,. / + 5 . 9 =4 . : 7 1 ? ,. + ,=: C D N 8 . + - 4 . + 5 . 9 =4 . : + @ . ?. < + . / 71 ?

0

1 ,8 ,8 . / ; : - 4 =9

4 1 / < 6< + - : / ,8 . g h ,. + , + =: 9 . ,8 . 71 ?4 . ? =+ 9 1 : + =/ . ?. / - : 1 : P/ . + ,?< 9 ,=2 . ,. + , D

p [ a V ] ` _ b X e q r q f s c fZ f

K ; : - 4 =9 4 1 / < 6< + ,. + ,+ @ . ?. 5 . ?7 1 ?4 . / @ =,8 - : nM A * E M N - 9 9 1 ?/ =: C ,1 * * H t N u N M v R D N . + ,+ @ . ?.

5 . ?71 ?4 . / 1 : O k k 4 4 / =- 4 . ,. ? 0 ; O l k 4 4 ,- 66 + 5 . 9 =4 . : + =: ,8 . < : =- > =- 6 9 1 4 5 ?. + + =2 . 4 1 / . D N . + ,+ @ . ?.

9 1 : / < 9 ,. / - , l ,. 4 5 . ? - ,< ?. + ?- : C =: C 7?1 4 P O k w A ,1 l x w A - : / + => 61 - / =: C 7? . T < . : 9 =. + ?- : C =: C 7?1 4 k DO t y

,1 R l t y D N 1 =: + < ? . - C - =: + , / - 4 - C . ,1 ,8 . ,. + , + - 4 5 6. + 3 ,8 . ,. + ,+ @ . ?. 9 1 : / < 9 ,. / + ,- ? ,=: C 7?1 4 ,8 . 9 1 6/ . + ,

(6)

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.0 - @ 0 += .7 +0 A*+0 6 7 0 8 9 : 9 , - B 18 = .1, 8 C = @ @ 410 > 3 .+= 18 5 = 3 18 ./ 0 += 8 2 0 , * D E A F G E - 19 + , A3 .+= 18 ; H / 13 5 = 3

> , 8 0 ., 0 8 3 7 +0 ./ = . .0 3 .18 2 5 = 3 9 , 8 > 7 9 .0 > 18 ./ 0 418 0 = + ? 13 9 , 0 4= 3 .19 += 8 2 0 , * ./ 0 I J - 1K 0 3 C = 8 0 9 0 3 3 = +:

+0 6 7 1+0 - 0 8 . *, + = ? = 41> > : 8 = - 19 - , > 7 47 3 .0 3 . ; L .+0 3 3 ? 0 +3 7 3 3 .+ = 18 ? = 47 0 3 5 0 +0 9 = @ .7 +0 > 9 , 8 .18 7 , 7 3 4: = 8 >

7 3 0 > ., 9 = 49 7 4= .0 > : 8 = - 19 - , > 7 47 3 ? = 47 0 3 ; M : 8 = - 19 - , > 7 47 3 5 = 3 9 , - @ 7 .0 > = 7 ., - = .19 = 44: B : ./ 0 .0 3 .

3 , *.5 = +0 ; N 0 3 7 4.3 = . 0 = 9 / .0 - @ 0 += .7 +0 A* +0 6 7 0 8 9 : 9 , - B 18 = .1, 8 *, + 0 = 9 / - 1K .7 +0 .: @ 0 = +0 +0 @ , +.0 > *, + ./ +0 0

+0 @ 419 = .0 3 @ 0 9 1- 0 8 3 ;

O P Q R S Q S

H / 0 T U .0 3 .3 5 0 +0 @ 0 +*, +- 0 > , 8 F V V - - > 1= - 0 .0 +

B

: F E V - - .= 44 3 @ 0 9 1- 0 8 3 7 3 18 2 U J W N X X +, Y 0 9 . Z A F Z

@ +, 9 0 > 7 +0 3 ; I 8 [X J \ X ] I ] X H 5 1./ G E A^ U 4, = > 9 0 44 5 = 3 7 3 0 > ; H 0 3 .3 5 0 +0 @ 0 + *, + - 0 > , 8 3 @ 0 9 1- 0 8 3

./ = . 5 0 + 0 @ +0 ? 1, 7 3 4: 7 3 0 > * , + ./ 0 > : 8 = - 19 - , > 7 47 3 .0 3 .3 ; H / 0 T U .0 3 .3 18 ? , 4? 0 > 3 7 B Y 0 9 .18 2 = 3 @ 0 9 1- 0 8 , *

= 3 @ / = 4. 9 , 8 9 + 0 .0 3 @ 0 9 1- 0 8 3 ., = +0 @ 0 = .0 > / = ? 0 + 318 0 = K 1= 4 9 , - @ +0 3 3 1? 0 4, = > @ 7 43 0 , * V ;F 3 0 9 0 ? 0 + : F ;V 3 0 9 ;

H / 0 .0 3 . 13 9 , 8 > 7 9 .0 > = . = .0 - @ 0 += .7 +0 ./ = . +0 @ +0 3 0 8 .3 ./ 0 0 K @ 0 9 .0 > @ = ? 0 - 0 8 . .0 - @ 0 + = .7 + 0 = . ./ 0 31.0 = 8 >

4= : 0 + , * ./ 0 @ = ? 0 - 0 8 . 3 0 9 .1, 8 ; [8 ./ 13 3 .7 > : ./ 0 T U .0 3 . 5 = 3 9 , 8 > 7 9 .0 > = . E _ ` J 5 / 19 / + 0 @ +0 3 0 8 .3 ./ 0 E V a

+0 41=

B

141.: - = K 1- 7 - / 12 / @ = ? 0 - 0 8 . .0 - @ 0 += .7 +0 = 3 > 0 .0 +- 18 0 > 7 3 18 2 ./ 0 < H X X b 18 > 3 , *.5 = + 0 c X = ? 0 - 0 8 .

L : 3 .0 - 3 G V V E d *, + 4, 9 = .1, 8 3 18 ./ 0 3 , 7 ./ 0 = 3 .0 +8 @ , + .1, 8 , * ./ 0 \ L ; H / 0 T U .0 3 .3 5 0 +0 = 44 @ 0 +* , +- 0 > 18 ./ 0

7 8 9 , 8 *18 0 > - , > 0 7 3 18 2 = > 0 ? 1= .1, +19 3 .+0 3 3 , * G V e ^ X = ; H / 0 .0 3 .3 5 0 +0 9 , 8 .18 7 0 > ., F V CV V V 9 : 9 40 3 , + =

@ 0 +- = 8 0 8 . 3 .+= 18 , * * 1? 0 @ 0 +9 0 8 . 5 / 19 / 0 ? 0 + 9 = - 0 *1+3 . ;

f R S g hQ S i j k l m S n g S Sm o j

[8 ./ 13 3 0 9 .1, 8 C ./ 0 0 **0 9 .3 , * > : 8 = - 19 - , > 7 47 3 = 8 > 2 += > = .1, 8 , 8 +7 ..18 2 = +0 0 ? = 47 = .0 > ; T 1+3 . > : 8 = - 19

- , > 7 47 3 > = .= = . *1? 0 .0 - @ 0 += .7 +0 3 = 8 > 3 1K .0 3 .18 2 *+0 6 7 0 8 9 10 3 *, + 0 = 9 / , * ./ 0 F e - 1K .7 +0 3 = +0 @ +0 3 0 8 .0 > ; I

- = 3 .0 +9 7 +? 0 9 , 8 3 13 .18 2 , * > : 8 = - 19 - , > 7 47 3 ? = 47 0 3 5 = 3 > 0 ? 0 4, @ 0 > *, + 0 = 9 / - 1K .7 +0 = 8 > @ 4, ..0 > .,

1447 3.+= .0 ./ 0 .0 - @ 0 += .7 + 0 = 8 > *+0 6 7 0 8 9 : > 0 @ 0 8 > 0 8 9 : , * ./ 0 = 3 @ / = 4. - 1K .7 +0 3 = 8 > / , 5 1. - = : 9 , - @ 419 = .0

./ 0 9 / , 19 0 , * = > : 8 = - 19 - , > 7 47 3 ? = 47 0 ., 7 3 0 *, + 0 ? = 47 = .18 2 +7 ..18 2 ; U 0 K . ./ 0 + 0 3 7 4.3 , * ./ 0 T U .0 3 .3 = +0

@ +0 3 0 8 .0 > 5 1./ = 8 1447 3 .+= .1, 8 , * / , 5 ./ 0 T U 13 > 0 .0 +- 18 0 > 8 7 - 0 +19 = 44: 7 3 18 2 3 .= 8 > = +> I I L W H p H X e G

(7)

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* +, 0 23 /2. ? @ A 1 - 1 = 4 . 3 /28 . 8 = 0 > . 1 ; 23 ; 8 0 4 94 - 1 . 0 ? + 1 0 1 /28 . B 4 - 2. ? C D ; 2E /4 + , - =+8 ; * +, < 28 4 - 9>

* 4

F

92- 7 , 0 +, - , 1 +3 7 5

G H I J K L M N O P Q R Q S T U SV S

W , - 4 9/- = 8 + /7 , - 2E /, , . 0 2== , + , . / 1 - * 7 1 9/ ; 2E /4 +, - /, - /, 0 2. 4 . 21 E 21 9 3 8 ; * +, - - 28 . ; 8 0 , 1 / =2< , /, ; * , +1 /4 +,

-XY C Z [ \ B ] [ \ B D Z [ \ B ^ _ [ \ B 1 . 0 ` ] [ \ a 1 . 0 - 2E =+, b 4 , . 3 2, - XD ` c d B C Z c d B ` c d B C c d B Z 5` c d B 1 . 0 Z 5C c d a

1 +, - 7 8 : . 2. @ 2? 4 +, - C /7 +8 4 ? 7 ^ 5 6 7 , +, - 4 9/- 1 +, ? +8 4 * , 0 1 3 3 8 + 0 2. ? /8 /7 , /> * , 8 = /7 , ; 2E /4 +, Xe f B g f B

e f h a 1 - 0 , =2. , 0 1 F 8 < , 5

6 7 , ; , 1 . 0 > . 1 ; 23 ; 8 0 4 94 - 0 1 /1 = 8 + , 1 3 7 ; 2E /4 +, /> * , - 7 8 : 1 0 , 3 +, 1 - 2. ? /+, . 0 : 2/7 1 . 2. 3 +, 1 - ,

2. /, ; * , + 1 /4 +, 5 6 7 , /+, . 0 2- +, < , +- , 0 : 7 , . 3 8 . - 20 , +2. ? = +, b 4 , . 3 > 1 - 0 > . 1 ; 23 ; 8 0 4 94 - < 1 94 , - 2. 3 + , 1 - , 0

: 2/7 2. 3 +, 1 - 2. ? =+, b 4 , . 3 > 5 6 7 , 3 7 1 . ? , 2. 0 > . 1 ; 23 ; 8 0 4 94 - : 2/7 /, ; * , +1 /4 +, 2- 7 8 : , < , + . 8 / 3 8 . - 2- /, . /

1 ; 8 . ? /7 , < 1 +28 4 - ; 2E /4 +, - 5 @ 8 + , E 1 ; * 9, 2. @ 2? 4 +, C - * , 3 2; , . Z _ Y C Z ] ` i 2- + 1 . j , 0 /7 , 7 2? 7 , - / 2. /, + ;

-8 = - /2==. , - - 1 ; 8 . ? /7 , - 4 +=1 3 , ; 2E , - 1 / , 1 3 7 /, -/2. ? /, ; * , +1 /4 +, 5 6 7 2- 2- . 8 / /7 , 3 1 - , =8 + /7 , e f h - 1

-- * , 3 2; , . Z _ Y C Z D ` k : 7 23 7 : 1 - +1 . j , 0 /7 , - /2== , - / 1 / /7 , 3 8 90 , - / /, ; * , +1 /4 +, , . 0 , 0 1 - /7 , - 8 =/, - / +1 . j , 0

; 2E /4 +, - 1 / /7 , 7 2? 7 , + /, - /2. ? /, ; * , +1 /4 +, - : 7 23 7 ; 2? 7 /

F

, 0 4 , /8 * 8 9> ; , + ; 8 0 2=23 1 /28 . 1 - 1 99 ; 2E /4 + ,

-with the “E” designation are required to contain polymer

Y; 8 0 2= 2, 0 1 - * 7 1 9/

F

2. 0 , + 5 6 7 2- 2- 1 . , E 1 ; * 9, 8 =

0 2==23 4 9/> 8 . , ; 1 > , . 3 8 4 . /, + 2= /7 , , < 1 94 1 /28 . 8 = + 4 //2. ? 2- F 1 - , 0 - 8 9, 9> 8 . 0 > . 1 ; 23 ; 8 0 4 94

-; , 1 -4 + , ; , . /- 5

@ 8 + 1 99 /7 , ; 2E /4 +, - B /7 , 1 ; 8 4 . / 8 = W h l 1 * * , 1 +- /8 7 1 < , 1 - 2? . 2=23 1 . / , ==, 3 / 8 . 0 > . 1 ; 23 ; 8 0 4 94

-< 1 94 , - 2. F 8 /7 , E * , 3 /, 0 1 . 0 4 . , E * , 3 /, 0 : 1 > - 5 6 7 , 3 9, 1 +, - / , E 1 ; * 9, 8 = /7 , * 8 - 2/2< , , ==, 3 / 8 = W h l 8 .

+4 //2. ? 3 1 . F , - , , . 2. /7 , - 4 +=1 3 , ; 2E , - : 7 , +, /7 , - /2== , - / - 4 + =1 3 , ; 2E 1 / /7 , 7 2? 7 , - / /, ; * , +1 /4 +, =8 + /7 ,

- 4 +=1 3 , ; 2E , - : 1 - Z _ Y C Z ] ` i : 7 23 7 1 9- 8 3 8 . /1 2. , 0 /7 , 7 2? 7 , - / XD Z m a W h l 1 ; 8 4 . / =8 + /7 2- 3 91 - - 8 =

; 2E /4 +, 5 6 7 , /+ , . 0 2- 3 8 . =8 4 . 0 , 0 2. /7 , g f 1 . 0 e f h ; 2E , - * +8

F

1

F

9> 0 4 , /8 /7 , , ==, 3 / 8 = /7 , 0 2== , + , . /

F 2. 0 , + ? +1 0 , - X* 8 9> ; , +Y; 8 0 2=2, 0 a 4 - , 0 2. /7 , - , ; 2E /4 + , - 5 6 7 , =8 +, ? 8 2. ? 1 . 1 9> - 2- : 7 23 7 - 7 8 : - 0 2== , + , . /

/, ; * , +1 /4 +, - 4 - 3 , * /2

F

292/> 2. /7 , < 1 +28 4 - ; 2E , - - 4 ? ? , - / /7 , . , , 0 /8 3 8 ;

F

2. , /7 , , ==, 3 / 8 = /, ; * , +1 /4 +, 1 . 0

98 1 0 2. ? +1 /, 2. 1 ; 8 + , =8 +; 1 9 : 1 > 5 6 7 , 3 8 ;

F

2. , 0 , = =, 3 /- 8 = /, ; * , + 1 /4 +, 1 . 0 = +, b 4 , . 3 > 8 . 0 > . 1 ; 23

(8)

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* + , - ., / * 010/ 2 , .02 3 0, 4- 5 6 7 - 108 - 91- 8 , - .: 1+ .- * + , - ., / * 010/ 2 , .02 3 0, 4- * 08 , 4; 08 , 40- * 1- * 1 < : 1: / 1: 02 - < : 1

4/ > 1- 8 , - .: 1+ .- * 0* - ? + 0@ : 4- 2 1 1/ < : 1: / = 1: 02 - < : 1 7 0A 7 B. - ? + - 2 3 0- * : 2 < @ 03 - @ - .* : 5

6 7 - < : 1: : 1 17 - B0@ - 1- * 102 A 1- 8 , - . : 1+ .- * : 2 < * 0C 1- * 102 A B.- ? + - 2 3 0- * B/ . - : 3 7 8 0C > - . - 3 / 8

=

02 - <

1/ 3 / 2 *1.+ 3 1 < ; 2 : 8 03 8 / < + 4+ * 8 : * 1- . 3 + .@ - * 5 D * 0A 8 / 0< : 4 8 / < - 4 EF ? + : 10/ 2 G H > : * + * - < 1/ < - * 3 .0

=

- 17

-8 : * 1- .3 + .@ - * : 1 : .- B- .- 2 3 - 1- 8 , - .: 1+ .- / B I J K L 5 D 2 / 2 9402 - : . : 2 : 4; * 0* > : * , - .B/ .8 - < + * 02 A :

3 / 8 8 - . 3 0: 44; : @ : 04: = 4- / , 108 0M : 10/ 2 . / + 102 - EN 03 ./ * / B1 F C 3 - 4 O / 4@ - .H 1/ / = 1: 02 17 - 8 / < - 4 , : . : 8 - 1- . * / B

17 - 8 : * 1- . 3 + . @

-=

; 8 02 08 0M 02 A 17 - * + 8 / B * ? + : . - * / B - ../ .

=

- 1> - - 2 17 - , .- < 03 1- < : 2 < 17 - 8 - : * + . - <

< ; 2 : 8 03 8 / < + 4+ * @ : 4+ - * 5 P ; 2 : 8 03 8 / < + 4+ * 8 : * 1- . 3 + .@ - * B/ . 17 - 8 0C 1+ .- * : .- * 7 / > 2 02 Q 0A + . - * G

17 ./ + A 7 R , 4/ 11- < / 2 : * - 8 094/ A * 3 : 4- 5

6 7 - .- : .- * - @ - .: 4 .- : * / 2 * B/ . 3 / 2 * 1.+ 3 102 A < ; 2 : 8 03 8 / < + 4+ * 8 : * 1- . 3 + .@ - * B/ . : * , 7 : 41 8 0C 1+ .- * 02

17 0* * 1+ < ; 5 Q 0.* 1 : 8 : * 1- . 3 + .@ - / B < ; 2 : 8 03 8 / < + 4+ * , ./ @ 0< - * 17 - :

=

0401; 1/ , .- < 03 1 < ; 2 : 8 03 8 / < + 4+ * : 1

1- 8 , - .: 1+ .- * : 2 < S/ . B.- ? + - 2 3 0- * > 7 03 7 > 044 = - < 0BB03 + 41 / . 08 , / * * 0= 4- 1/ < - 1- .8 02 - 02 17 - 4: = / . : 1/ .; < +

-1/ - ? + 0, 8 - 2 1 408 01: 10/ 2 * / . 108 - 3 / 2 * 1. : 02 1* 5 D 2 / 17 - . : < @ : 2 1: A - / B : 8 : * 1- . 3 + .@ - .- 4: 1- * 1/ 17 - : = 0401; 1/

8 / < - 4 , : @ - 8 - 2 1* : 3 ./ * * : 44 , / * *0

=

4- , : @ - 8 - 2 1 3 408 : 103 : 2 < 4/ : < 02 A 3 / 2 < 010/ 2 * 5 D 8 : * 1- . 3 + . @ - 0* : 4* /

+ * - B+ 4 B / . .: 2 T 02 A 8 0C 1+ .- , - .B / . 8 : 2 3 - 5 Q / . 02 * 1: 2 3 - 02 Q 0A + .- * G 17 . / + A 7 R U 8 0C 1+ .- * > 017 7 0A 7 - .

< ; 2 : 8 03 8 / < + 4+ * : 1 4/ > - . E.- < + 3 - < H B. - ? + - 2 3 0- * E- ? + 0@ : 4- 2 1 1/ 7 0A 7 1- * 1 1- 8 , - .: 1+ .- * H > / + 4< = - - C , - 3 1- <

1/ - C 7 0

=

01

=

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iligiri, K. P., Kaloush, K. E., Mamlouk, M. S., and Witczak, M. W. (2007). “Rati

: < - J 9 : 3 0 J>< D : /

tertiary flow for asphalt mixtures.”

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>< D 2: < = d BN B

H >?D >. . : < = H B= - < 3 6 : S ; 0 = 6 B= • >9 = – B= 8

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(2004). “The use of complex modulus to characterize

the performance of asphalt mixtures and pavements in Florida.”

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ru t „ † p ‚ w q x

= 6 0 @ : ?2 + : B ™ š › k C

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e 3 .

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] R I T Q ^ OQ K [ \ M _b ` b | [ ` } } d ` ~ c [

e 3 .

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+0 - A/ 0 1 f 2g

Kanitpong, K., and Bahia, H. (2005). “Relating adhesion and cohesion of asphalts to the effect of

moisture on laboratory performance of asphalt mixtures.”

G H I J KL M H NI NOM J P Q K Q I H R S P Q R M H T U

V M W H J I X MY NS Q G H I J KL M H NI NOM J P Q K Q I H R S Z M I H T [ G H I J KL M H NI NOM J P Q K Q I H R S Z M I H T MY NS Q \ I NOM J I X

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1 ˆ / 2

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“Standardized p

78 3 2 D 1 72 J8 7 = - = K> . 0. 8 J D > - = G 03 G 8 D 1 K1 . L

M N

L D = /=

/8 O 72 D 03 / = . O

C

= K/ O = P 2 G 2 - / D 0. /72 . . 2 . 4

Q R S T UV W R XS XYW T Z [ U[ S R \ ] Z [ \ W R ^ _ ` W a R T S b Wc X] [

Q R S T UV W R XS XYW T Z [ U [ S R \ ] d W S R ^ e Q R S T UV W R XS XYW T Z [ U [ S R \ ] d W S R ^ Wc X] [ f S XYW T S b g \ S ^ [ h Y[ U

5 ? 8 4

: B i 9 5 O O 4 : B ;

–

: i @ 4

Witczak, M. W. (2007). “Specification criteria for simple performance tests for rutting.”

f S XYW T S b

j W W V [ R S XYk [ l Ym ] n S o Z [ U [ S R \ ]

p

R W m R S h e Z [V W R X f W q f j l Z

p

Z [ V W R X r s t e u S U ] YT m XW T e v q j

4

w 0/3 x = y 5 z 4 w 45 = - D * 1 KK0P = - 5 { 4 H@ A A @ I 4 |* 1 O 2 7O = P 2 . 1 O O 8 7 / = - D O 2 7J 8 7G = - 3 2 G 8 D 2 K. G = - = } 2 G 2 - /4|

f S XYW T S b j W W V [ R S XYk [ l Ym ] n S o Z [ U [ S R \ ]

p

R W m R S h

5 ~  € 4

w 0/3 x = 3 y z 4w 5  = K8 1 .

C

 5 E 2 KK0- 2

45

M

Kƒ{ = . > 8 1 - > z 45 „ 1 0- /1 . … 46 4 H @ A A @ I 4

“Simple

E 2 7J 8 7 G = - 3 2

‚

2 . / J 8 7 * 1 O 2 7O = P 2 z 0† ‡ 2 . 0} - 4

”

f j l Z

p

Z [ V W R X ˆ ‰ r

5 ? = /08 - = K < 8 8 O 2 7= /0P 2 … 0}

C

Š = > F 2 . 2 = 73

C

E 78 } 7= G 5 O O 4 4

‹

C

8 1 5

F., and Scullion, T. (2007). “Preliminary

J02 KD P = K0D = /08 - 8 J . 0G O K2 O 2 7J8 7G = - 3 2 /2 . /. J8 7 O 2 7G = - 2 - /

D 2 J8 7G = /08 - Œ 3 = . 2 .

tudy.”

Q R S T UV W R XS XYW T Z [ U[ S R \ ] Z [ \ W R ^ _ ` W a R T S b Wc X] [ Q R S T UV W R XS XYW T

Z [ U [ S R\ ] d W S R ^ e Q R S T UV W R XS XYW T Z [ U [ S R \ ] d W S R ^ Wc X] [ f S XYW T S b g \ S ^ [ h Y[ U e f W q

: i ; @ @ A A ; 5

References

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