.. , ..

Boris RADOVSKIY Bagdat TELTAYEV

.. , ..., ,- (),

.. ..., , ()

2013

lmatyPublisher Bilim

2013

VISCO-ELASTICPROPERTIES OF ASPHALTS BASED ON PENETRATION

AND SOFTENING POINT

5

........................................................................... 7 I. .....................................10 1. 1. ..............................11 1. 2. ...................14 1. 3. .....................................................18 1. 4. ..22 1. 5. - ...................33 ....................................................................38

II. ........41 2. 1. ..............................................41 2. 2. .........................................46 2. 3. 50 ....................................................................63

III. ..66 3. 1. ......................67 3. 2. ................................70 3. 3. .............................85 3. 4. ...................................................................95 ..................................................................104

- -

( 7 8 2013 ).: ,

, .. (. , ), , .. (. , ), .. (. , ). .., ..

- / .. , .. . : , 2013. 152 .

ISBN -

, , - : -, . - , - : - .

- , , . , , , - .

ISBN .., .., 2013 , 2013

6 7

IV. .....................................107 4. 1. .................................................................108 4. 2. .............................................................115 4. 3. .........................................................119 4. 4. ..............................................................125 4. 5. ..................................................138 ..................................................................143 ..........................................................................146 ...........................................................................149

- - . - , . , , -- , - . , , .

- -, . , - , - , -, - .

- , - -, : ,

8 9

. , - : - .

. - - . - - . - : - , , - , - . - - .

- - , - [1-8]. , , - - , . -, - . , , , , - - - , -. , - , -. , -

- , , .

1. . . . . / . . . , . , , 1973, 328, II. 14, II. 15, II. 16.

2. . . , . . , . . . . , , 1989, 168.

3. . . . - . , , 2003, 252.

4. . . - / . . . -. : . , 1999. 217 .

5. , . . -- // . 2012. 2. - . 14-18.

6. . . - - // - . 2006. 1. - . 18-21.

7. . . - /- . . 17/1. - . : -, 2007. - . 68-81.

8. . . - - - - / - II . , 2007. - . 307-308.

10 11

I.

I.

, - - - . - - . , -, ( ). , -. - -, . , - , , - . - - .

- , . - -, - . , . . . . - [1] - , - 1973 ., 232 -, [2], -

, 332 , [3] 586 . - - , , - .

1.1. . . -

1943 . 1945 . - , , [4]. - . . [5]. - , : , , - . ., . . , - , , .

. , - , , - , . , , , - , - - .

12

13

I.

, , - , 1954 . SHELL [6]. . ,

S(t) = /(t) (1.1)

(t), -, , - t , , T. , - S. - [7]. - 1964 - - ( 3%) - - [8]. , - , - .

- -. , T t. - SHELL [9] S , -, - t = 0.02 . -

0.20 , 10 / (36 /).

, - . - E, T t, .

, - SHELL [10], [11], [12] [13] -.

- . . [14] : . , 0.1. - . 46-72. - , - [15,16], - , - 0.1. 00 ( - ) 100 ( ). - .

- - , , , 0.1. -, - ,

14

15

I.

. -, - , , . -, - -. , , - , , .

, - - . [17], [18], [19] .

1.2. , -

. . :

, , - , , , - , . (Maxwell, J. C. , [20], p. 276).

, - ( ) , - ( ) .

, . , :

, (1.2)

, (1.3)

, . . - .

- ( ); - ; - ; - ; G = E / 2(1 + ) - ( -); E - ( - ); - - ( ). - 1 (250 ) = 0.35, = 0.450.50. = 0.5; - E = 3G , -.

, - . , :

, (1.4)

; (1.5)

, (1.6)

(1.7)

. , , - . - -

16

17

I.

, . 3 - , - E = 3G . 200 0.001 . , , 800 3000 .

, , . [21].

-, , - , . . -, - :

, (1. 8)

(1. 9)

Gg, Eg - - , . - , , g(glassy). - Gg =1000 , - Eg = 3000 . - -, .

, , -, , :

(1. 10)

(1. 11)

= / Gg - . , - . , - .

- - (..which may be called time of relaxation of the elastic force, [21], . 53). - (t / 1, -. - - , - . , , - , - i. -, , , .

(1. 1) (1. 9) - :

(1.12)

-, -, -

18

19

I.

, - , , -, , - . - , -. - .

1.3. , -

, . - , , , -, , . - , - [22,23].

, , - , . - . - , , - - , = / E .

, - d(t) - t, d, + d ( t), d() , - D(t ) - (t ) :

(1.13)

, , D(t) - -: - , -, .

, - d(t) t - d() - (t ) - E(t ):

, (1.14)

E(t) - . (1.13) (1.14), -

t, -, , -

(1.15)

(1.16)

, - t , . , (t ) D(t). , t - , - . , - (t ) E(t).

20

21

I.

- , - . E(t) D(t) , - ( ) E 1/E.

D(t) - - . t - , :

(1.17)

(1. 1) (1. 17), , - , -

S(t) = 1/D(t) (1.18)

E(t) -. t :

(1. 19)

E(t) , E .

(1.15) (1.16), -, , - D(t) E(t) -.

(1.15), (1.16)

(1.20)

(1.20) , D(t), E(t), . . - . , . . . D(t) - E(t) - , - t.

(1.13)-(1.20) . - , -, . D(t) E(t) - J(t) = (t)/ G(t) = (t)/. (1. 20)

(1.21)

(t) -, -

D(t) = J(t)/3 , E(t) = 3G(t) (1.22) (1.18) (1.22) ,

J(t) S(t) ,

J(t) = 3/S(t) (1.23) -

. ,

22

23

I.

- , - [3, 24]. - - 1970- [25] [26, 27].

- , - , - , - , : , , - , . . , - . , - , -. , , - . , - . [28] .

1.4. J(t), D(t)

E(t), G(t) . , - - , - . - - .

-

G(t) E(t) - , - , , , . (t) = const, - E(t) = (t)/. = const - G(t) = (t)/.

- . : (1) ; (2) - , - - (t). , - , -. , - , - . , - , . - . , , -.

, , - . - J(t) D(t) - , , (t) , D(t) = (t)/. - J(t) = (t)/.

24

25

I.

. , . - , . - - , - - . . - . 1.1 0.3 320 .

- . - 1970- . . [24, 30]. - - -

. 1.1 200 [29]

: (1) - ; (2) - , - . - , - - , = const. , . .

, , - -. t, - . , , -, 0.5 , - D(t) t > 5 c. - - E(t) D(t) t.

. 1.1 - , - .. [29]. - 4040160 , - 70 , - 47.50 - 120. 6% , 40% , 13% - ( 4- [29]). - 3.3%.

.. -, - 0.0030.006

26

27

I.

. , - , - , - . - () = 0

. 1.2. 1 25

(DSR)

. 1.3.

, -: [31] - .

- . .

- (t) = 0sin(t) - 0 - - (t) = 0() sin(t ) 0, . 0 - , . 0 , -

(1.24)

- ( - ASTM D 7175) (. 1.2) DSR (. 1.3).

25 1 - 8 2 . , - , - (. 1.3). : - (. . )

28

29

I.

sin(t) 0 . - (t) = 0 () sin(t ) - 0 () , - . - 0 () () (. 1.4).

0, , 0 () - |G*()| Gd:

(1.25)

, - - , - , , .

, - Gd. , : - G' G''. G' - , G'' - . - , -

, (1.26)

G' = Gd cos(), G'' = Gd sin() tg() = G'' / G',

, - -

. = 0 , ( - (1.2)). = / 2 , - ( (1.4)). = / 4 .

. 1.4 = 10 ./ - 2 / 10 = 0.628 .

90/130 - 460. - 0 = 1.617 - 0 = 0.1183. - ( ) Gd (= 10) = |G* (= 10)| = 0 / 0(= 10) = = 1.617 / 0.1183 = 13.67 . - t = 0.129 (. 1.4). (-

. 1.4. 90/130 =460 =10 ./:

; .

DSRIIAir BohlinInstruments .

30

31

I.

) ( ). , - . 0.129 10 ./ = 1.29 740. G' = 13.67cos(740) = 3.77 , G'' = 13.67 sin(740) = 13.14 , tg() = tg(740) = 3.49.

- -. - - 1 , - . - . - [22, 23].

, , - G' G'' - G(t):

, (1.27)

, - , , . . -, - ( G(t) - t) . - ( G(t) - t, . . ) .

, G(t) - G' G'':

, . (1.28)

, - G(t). (1.27), (1.28) - G(t), - E(t).

(1.28) G(t), G'() G''() - , , , , - - . , (1.27) G'() G''(), t.

, - . - .

- J(t), D(t) G(t), E(t), - , - [22, 23]. ,

, (1.29)

gi - , i - .

i gi - . . -

32

33

I.

, (Rouse; Bueche; Doi-Edwards, Bird-Armstrong .), - i . , - .

gi i (1.29) - GM(t). - - [23]. GM(t), , 105 105 15 (1.29), . . N = 15. , N i - gi - , , 30 , GM(t). - , , .. i - gi [32]. , - - , , - i gi 2N (, 30 ).

, (1.29) , - 30 , - , . , -, - , .

1.5. - -

- [33, 34, 35]. -, -, t - T . , D(t) J(t) t T. -, t T E(t) G(t) . - , , , T - (580) , - T - t , . . 10 .

, - [22]. - - Tr (reference temperature) tr - t T

tr = t / aT(T) (1. 30) aT(T) - - , - T; tr - Tr.

, - aT(T) : , - E(t), D(t), - Ed() -. - ( - ) , ,

34

35

I.

tr (1.30) ; - - , , (1.30).

(T t) - , -, ( T t tr), -, - . , , 200 - 0.001, - 10150 - 1. , , aT(T).

(T), - - [22]:

(1.31)

(Tr) - Tr, - .

- aT(T) (1.32) (1.33). - , - . (1916 ) - .

(1.32)

aTr(T) - - Tr; T , ,0; Ea - -, /; R = 8.314 /( K) - -

. / R (1.32) - (K).

(1.32) - - Ea, aTr(T) T. , [6] - Ea = 50 / = 2.09 105 /.

aTr(T) . , . . () [35]:

(1.33)

: ln(10) = 2,303 -; C1, C2 - . C1 - -, C2 (K). Tr 500 , - : C1 = 8.86, C2 = 101.6 [35].

(1.33) (, -, .) , , (-, .) -. - , . , . [22] - - C1, C2. .. .. ( ) - ( ) C1 = 23, C2 = 218 [24].

36

37

I.

- - .. -, - 4040160 . - , - . 1.1 ( 4- [29]). , - (t) t = 0.1, 1, 10, 32 100 .

20, 15, 0, 5 8.50. . 1.5 S(t) = / (t) . - . - -, r = 200, - , - , - aTr(T), , - , . 1.6. aTr(T) - (1.32), Ea = 1.88 105 /.

, , = 150,

= 3.82,

50 - 3.82 Tr = 200.

, S(t), - 150 t = 0.1, 1, 10, 32 100 , - tr = 0.0262, 0.262, 2.62, 8.38 26. 2 200. , . 1.6, 200.

. 1.5. [29]:

- 200, - 150, - 00, - 50, - 8.50

. 1.6. T = 200C

- 200, - 150, - 00, - 50, - 8.50

38

39

I.

, - 0.1 100 0.00001 100 200.

- , - .

1. . . , . . . . . , , 1973, 264.

2. LesueurD, The colloidal structure of bitumen: Consequences on the rheology and on the mechanisms of bitumen modi cation, Advances in Colloid and Interface Science, 2009, V. 145, 1-2, p. 42-82.

3. Krishnan, J. M. , K. R. Rajagopal. Review of the uses and modeling of bitumen from ancient to modern times. American Society of Mechanical Engineers, Applied Mechanics Reviews, 2003, 56(2), p. 149-214.

4. Burmister, D. M. The general theory of stresses and displacements in layered soil systems, Journal of Applied Physics, 1945, Vol. 6, No. 2, pp. 89-96, No. 3, pp. 126-127; No. 5, pp. 296-302.

5. , . . -. . : , . 14, , - , 1953, . 33-46.

6. Van der Poel C. , A general system describing the visco-elastic properties of bitumens and its relation to routine test data. Journal of Applied Chemistry, London, Vol. 4, 1954, pp. 221-236.

7. Van der Poel C. , On the rheology of concentrated dispersions. Rheologica Acta, 1, 1958, p. 198205.

8. Heukelom, W. , Klomp, A. J. , Road design and dynamic loading. Proceedings of the Association of Asphalt Paving Technologists, 1964, Vol. 33, pp. 92-123.

9. Claessen, A. J. M. , J. M. Edwards, P. Sommer, P. Uge. Asphalt Pavement Design The Shell Method. Proceedings, 1977, 4th International conference on the Structural Designof Asphalt Pavements, Vol. I, Ann Arbor, pp. 39-74.

10. Shell (1978), Pavement Design ManualAsphalt Pavements and

Overlays for Road Traf c, Shell International Petroleum Co Ltd,London, UK.

11. Asphalt Institute (1982), Research and development of The Asphalt Institutes thickness design manual, Manual Series 1, Research Report 82-2, Maryland.

12. British Standards (2001), BS EN 12697: Bituminous mixtures. Test methods for hot mix asphalt, British Standards Publ. , UK; HD 23/99 (1999). Design Manual for Roads and Bridges. Vol. 7, Pavement Design and Maintenace

13. Design of Pavement Structures, Technical Guide (in French). SETRA, Laboratoire Central des PontsetChausses, Dec. 1994.

14. , . . . - , 1964, 6, . 20-21.

15. 46-83 (1985) - , . , , . 1-157.

16. 218. 046-01 (2001) - , . , . 1-152.

17. , . . , . . . . -, 1981, . 17, N. 6, c. 45-52; Privarnikov, A. K. and B. S. Radovskii. Action of moving load on viscoelastic multilayer base. Int. Appl. Mech. , Vol. 17, No. 6, 1981, p. 534-540.

18. , . . . - . . , 1982, 35.

19. Chen, E. Y. G. , E. Pan, T. S. Norfolk, O. Wang. Surface loading of a multilayered viscoelastic pavement. Road Materials and Pavement Design, 2011, V. 12, p. 849-874.

20. Maxwell, J. C. Theory of Heat. Elibron Classics, (2001) Reprint of the 1872 edition, pp. 1-312.

21. Maxwell JC (1866), On the dynamical theory of gases, Philosophical Transactions of the Royal Society. London A157, 2678.

22. , . . . . . : , 1963, 536c.

23. Tschoegl, N. W. , The phenomenological theory of linear viscoelastic behavior. Springer-Verlag, Heidelberg, 1989, 769 pp.

24. Vinogradov G. V. , A. I. Isayev , V. A. Zolotarev, E. A. Verebskaya, Rheological properties of road bitumens. Rheologica Acta, 1977, Vol. 16, p. 266281.

25. Monismith, C. L, R. L. Alexander, K. E. Secor, Rheological behavior

40

41

of asphalt concrete. Proceedings of the Association of Asphalt Paving Technologists, Vol. 35, 1966, pp. 400-450.

26. Mehta, Y. A. , D. W. Christensen. Journal of the Association of Asphalt Paving Technologists, Vol. 69, 2000, pp. 281-312.

27. , . . - . , 2010, 3, . 24-27.

28. , . . , . , 1965, 223. 29. , . . -

- . - , , 1986, 330.

30. , . . . , , 1977. 116.

31. Standard Speci cation for Performance Graded Asphalt Binder: ASTM D 6373, AASHTO M 320.

32. Friedrich, Chr. , J. Honerkamp, J. Weese. New ill-posed problems in rheology. Rheologica Acta, 1996, Vol. 35, pp. 186-193.

33. ,. . ,. . , . . . . , , 1937, 3, 329-344.

34. Leaderman, H., Textile Materials and the Time Factor: I: Mechanical Behavior of Textile Fibers and Plastics, Textile Research, 1941, V. 11, 171-193.

35. Williams, M. L. , R. F. Landel, J. D. Ferry. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. Journal of the American Chemical Society 1955, 77, 3701-3707.

II.

, - - . - - (.. 11501-78 ASTM D 5) ( , 11506-73 ASTM D 36) -, - , , , - .

2.1. , [1-3]

c (t), ..

S(t) = c / (t). (2.1)

S(t) , - [1, 2].

, ( ), - S(t), - . - 1 10 000 [2]. -

42

43

II.

- 3, - 0.5 - .

- 1 /. 1000 /. - - , .. - Ed() = |E*()| = 0/0() . -, 6% - , , - .

, - , , -, , - :

S(t) Ed ()|=1/ t (2.2)

(2.2) - , - ( (1.9)). - log S(t) log t, - S(t) Ed t , 1 /. - S(t) t 1 . - , -

log S(t) log t - 103 104.

- - , - , . 1.5. - . , . . (), - . (1.32), Ea = 50 / = 2.09 105 / [1].

47 , - (, - , , , -). S(t) - . PI (penetration index), - 1936 [4] - :

PI = , (2.3)

A - , - - P - :

A = (2.4)

P - () 250, Trb - , - (ring and ball temperature), -

44

45

II.

, 800, .. 800 ().

, (2.3) PI A , , , 250 200, - PI = 0. (2.3) - PI = 20 - ( = 0), PI = 10 , , - .

, PI 3 +5. PI +2 2. PI 2 -, - . -, 22245-90 - 40/60 200/300 1 < PI < +1.

, - 250 P ( - ASTM D5) Trb (- ASTM D36) PI.

- 2.6 +6.3, .. - - , - . - . , PI = 2.3 Trb = 660 = 5, 15, 25, 35 450, PI = +5.3 Trb = 1160 - T = 20, 0, 20, 40 600. -

t - log S(t) log t - S(t).

- [1]. P Trb S T - t . - PI, (Trb ) t 106 1010 - S 104 2.5109 .

, - , , [5, 6 .].

-, [7], - ([8] .), - ([9] .), . , - , , .

, - 50% - , . - , . , - , , -

46

47

II.

13 ( 104 2.5109 ), 50% . - . , [1], - 20 , , - .

SHELL , , P. Ullidz K.R. Peattie - PONOS [10, 11]. 2000 - Ababtech, Inc. G.M. Rowe M.J. Sharrock BitProps, -, PONOS, - . - .

2.2. , -

, - - S(t) - J(t) D(t), - G(t) E(t), |G*()| |E*()|, - ( P 250 Trb), .

S(t) - P, Trb T .

R. Saal [13], . 11 12 [1]. - t = 0.4 :

(2.5)

. . -, -

- . -, - - , - = 250. -, (2.5), t = 0.4 - , .. . -, P = 100 (2.5) S0.4 = 0.4 . , P = 100 - Trb = 38.80C, 47.50C 59.50C, - PI = 3,0 +3, ( BitProps) S = 0.26 , 0.40 0.52 -. , - PI = 0, - PI = 3 +3 , (2.5) PI .

P. Ullidz B. Larsen [12] -

S(t) = 1.157 107 t0.368 ePI (Trb T)5 (2.6) . -

, , (2.6) , , t. T = Trb (2.6) - , -

48

49

II.

, T > Trb , - . , - , Trb. (2.6) P.Ullidz B. Larsen [12] - 0.01 < t < 0.1, - 1 < PI < 1 100C < (Trb T) < 700C.

, - , - . , PI = 1, P = 54.5 Trb = 500C, T = 300C t = 0.1 (2.6) S = 2.35 , ( - BitProps) S = 1.27 , . - . PI = +1, P = 109.5 Trb = 500C, T = 300C t = 0.01 (2.6) - S = 0.742 , BitProps S = 2.021 , . . , (2.6) , - [12], 40%.

, , - , (2.6) , - [14], - 200C < (Trb T) < 600C. , Trb = 500C - 10 300, - (2.6) , .

(2.6), M.Y.Shahin [15], - - . - lg(t), PI - (Trb T).

- - lg(t), PI (Trb T), , . - lg(S), -, .

M. Shahin [15] , , - S < 1 ( (2) [15]), S > 1 ( (3) [15]).

, , - -. , , PI = 1, P = 54.5 Trb = 500C, T = 230C t = 1 S = 0.826 , - S = 13.34 , -, , . 23 350C. - .

A.A.A. Molenaar [16], . [15], - 2 < PI < 2, -. , . -. , PI = 1 = 150 t = 0.01 (3) [15] - 16000 . : 6-7 - .

, , , - . - [12,13,15] . ,

50

51

II.

- - .

2.3. , ,

-. S(t) ( . 2.1). P = 80 250 Trb = 500C ( - PI = 0). 150 32 - t 106 103 BitProps 32 , .

c - t 0 (t)

- = c / Eg, , (2.1), t 0 Eg (glassy modulus). S(t).

- . - , ( (1.7)), (t) = c t / 3, -, (2.1), t - S(t) = 3 / t. log(S) log(t) , 450.

() () - S(t) . 2.1. , - , Eg = 3 / t, t0 = 3 / Eg. t0 = 0.005 . - S(t).

(2.7)

. . [17], - -, . - v = w 1992 . - |G*()| . . [18,19] CA (Christensen-Anderson model). t0 , v -. . . v - [18]. -

. 2.1 :

, (2.8); ()

() S(t)

52

53

II.

0.1 ([19], . 198).

. . - - v w [20] ( CAM). - . [21], - t0, v w . , - - .

-

(2.8)

Eg - ; - , - ; - (0 < < 1), . (2.8) , [18] |G*()|. (2.8) .2.1.

(2.8) - Eg, , S = 3 / t. - . S(t) , .. - .

Eg, P Trb .

Eg -

S(T, t) T - t, .. t 0. - , .. - [22]. - 8- t = 0.00005, 0.0001, 0.0002, 0.0005, 0.001, 0.002, 0.005 0.010 , - , BitProps - S t = 0.00005 . - 420 PI = +2 90 PI = 3. S . (18) (37) [22] , - , - .

, PI 2 +3 Eg = 2460 7%, - Eg (. 2.2).

Eg = 2460 . , , Eg = 2500 [2]; . Gg = 1000 [23], Eg = 3000 ; . . - - , Gg = 720 Gg = 1120 , Eg = 2160 - 3360 , Eg = 3000 [18].

, - (. 2.3). (2.8) - S .

54

55

II.

, - aTr(T).

. 1.5, aTr(T) , t T, - - tr Tr, .. - - tr = t / aTr(T) log(t) , . ,

aTr(T) = t / tr, (2.9)

t tr - T Tr, -.

, PI = 0.5, Trb = 500C, - . 2.3, - - - T = 150C - Tr = 400C. BitPros ( - , ) , T = 150C t = 100 S = 0.0807 . Tr = 400C - - tr = 0.2205 . (2.9) , aTr(T) = 100 / 0.2205 = 454. , 40 15 = 250C t 454 . -, -. T = 150C t = 10 ( 100 , -). - S = 0.5395 . Tr = 400C - - tr = 0.02153 , aTr(T) = 10 / 0.02153 = 464. - 2%. , S(t, T = 150C) S(t, T = 400C) . 2.3 -

. 2.2. ,

( Eg = 2460 )

. 2.3. : PI = 0.5, Trb=500C

56

57

II.

log (t) log (460) = 2.663 .

(2.9) aTr(T) PI . , aTr(T), , .

aTr(T) .- .-.-. () [24], - . 1.5:

(2.10)

(2.11)

< Tr , > Tr - . ( -) , 100C - , .

Tr = (Trb 10) , Tg 50-700C Trb [25, 26], , C1 = 8.86, C2 = 101.6 Tr = (Tg + 50). (Tg + 100) . , Tr = (Trb 10), - -. , - (Trb 10) -. PI = 3 PI = +2 (T Tr) 100 +140 100C

(2.9) aTr(T) Ea(PI), - C1 (PI) C2 (PI).

Ea = 9.745104 ,

, - Ea = 1.56105 / PI = +2 Ea = 2.25105 / PI = 3. , [2] - Ea = 50 / = 2.09 105 /, Tr = Trb, Ea = 2.5 105 / [19] Ea = 2.61 105 / [18] Trb.

C1 = , C2 =104.5

C1 = 7.97 PI = +2 C1 = 11.5 PI = 3, PI. , , [24], C1 = 8.86, C2 = 101.6. , - - aTr(T):

(Trb 10):

(2.12a)

> (Trb 10):

(2.12b)

- -

((

))

58

59

II.

. 2.4. T = Tr: - (2.12)

Tr = 400C

, t tr = t / aTr(T). - . 2.3, S(t) (. 2.4), - (2.12). -, . 2.3 106 103 , 1010 105 , .. 6 .

(2.12) aTr(T), (T) , (Tr ), .. [24]

(2.13)

- (Tr),

(Tr) = 0.00124

(2.14)

(2.13) (2.12) -:

= aTr Ahrr(T) (Tr) T Trb 10; = aTr WLF(T) (Tr) > Trb 10

(2.15)

- , aTr Ahrr(T), aTr WLF(T), (Tr), (2.12a), (2.12b) (2.14), .

- (2.15) . 2.5. SHELL [16, . 70] [27, . 68].

. 2.5.

60

61

II.

(2.8) - Eg , - . - - , - t / aTr(T). - - PI = 3 PI = +2 , (T Trb) 450C 100C - S(t), (2.8), - . -

(2.16)

= 0.1285 PI = +2 = 0.5476 PI = 3.

, S - , , (2.8), Eg = 2460 , - (2.15), - (2.16).

, P = 80 250 Trb = 500C, PI = 0 S 150C 1 . (2.12a) - - - = 150 Tr = 400 - aTr Ahrr(T) = 347.5. (2.14) (Tr) = 0.01222 . - (2.15) 150 = 4.25 . (2.16) = 0.1794. , (2.8)

= 2.042

BitProps S = 2.107, . - 3%. - . 2.1 -. BitProps, - - , MathCAD Excel, . 2.1 .

S, - (2.8), ( - BitPtops) 1910 , PI = 3 PI = +2, (T Trb) 450C 100C t 0.0001 10 000 , 14.6%. 540 .2.6.

. , - - , Trb = 500, : P = 54.5; 80 109.5 (- PI = 1, 0 1, ).

, - t = / S(t). - = / Eg, visc = t / 3 - del, -. . , -

(2.17)

62

63

II.

(. 2.7) , - t = 0.1 , - -, -1 0 - 50 - 450 . - - . - , - PI = 1. (PI = +1), - - 40 600.

. 2.6. ,

(2.8) (2.15), (2.16): PI = 3, 0 1, = 5 , 15, 30, 40, 50, 600C, t = 106 104

, Trb = 500 109.5 ( 250) -, - .

- , - -.

1. Van der Poel C., A general system describing the visco-elastic properties of bitumens and its relation to routine test data. Journal of Applied Chemistry, London, Vol. 4, 1954, pp. 221-236.

2. Van der Poel C., Representation of rheological properties of

. 2.7. :

Trb = 5 00, , t = 0.1 .

64

65

II.

bitumens over a wide range of temperature and loading times. Proceedings of 1st International Congress of Rheology, N. 2, Oxford, 1954, London: Butterworths Scienti c Publications, pp. 331-337.

3. Van der Poel C., On the rheology of concentrated dispersions. Rheologica Acta, V. 1, No. 2-3, 1958, pp. 198-205.

4. Pfeiffer J.Ph., P.M. van Doormal. The rheological properties of asphaltic bitumens. Journal of the Institute of Petroleum Technologists USA, 1936, vol. 22, pp. 414-440.

5. Heukelom, W., Klomp, A. J., Road design and dynamic loading., Proceedings of the Association of Asphalt Paving Technologists, 1964, Vol. 33, pp.92-123.

6. Bonnaure, F., G.Gest, A.Gervois, P. Uge. A New Method of Predicting the Stiffness of Asphalt Paving Mixtures. Proceedings, Association of Asphalt Paving Technologists, Vol. 46. 1977. pp. 64-100.

7. The SHELL Bitumen Handbook. 5th Edition. Thomas Telford Ltd, London, 2003, 460p.

8. Roberts, F. L., P. S. Kandhal, E. R. Brown, D.-T. Lee, and T. W. Kennedy, 1996, Hot Mix Asphalt Materials, Mixtures, and Construction. National Asphalt Pavement Association, Lanham, MD, 585 pp.

9. Yang H. Huang. Pavement Analysis and Design. Prentice Hall, Inc., New Jersey, 1993, 805pp.

10. Bats, F.Th. A computer simulation of Van der Poel nomograph. Journal of Applied Chemistry and Biotechnology, Vol. 23, 1973, pp. 139-140.

11. Ullidtz, P., K. R. Peattie. Pavement Analysis by Programmable Calculators. ASCE Journal of Transportation Engineering, Vol. 106, No. TE5, 1980, pp. 581-597.

12. Ullidz, P., B.K. Larsen. Mathematical model for predicting pavement performance. Transportation Research Record 949, TRB, 1984, pp. 45-54.

13. Saal, R.N.J. Mechanical testing of asphaltic bitumen. 4th World Petroleum Congress, Rome, 1955, Section VI/A, Paper 3, pp. 1-17.

14. Collop, A.C., D. Cebon. A parametric study of factors affecting exible pavement performance. ASCE Journal of Transportation Engineering, 1995, Vol. 121, No 6, pp. 485494.

15. Shahin, M. Y. Design system for minimizing asphalt concrete thermal cracking, Proceedings of 4th International Conference on the Structural Design of Asphalt Pavements, Ann Arbor, 1977, University of Michigan, pp. 920 932.

16. Molenaar A.A.A. LECTURE NOTES ROAD MATERIALS, PART III, Delft, 2005, 97pp.

17. Havriliak, S., S. Negami, Complex plane analysis of -dispersions in some polymer systems. Journal of Polymer Science, Part C: Polymer Symposium, 1966, Vol. 14, p. 99.

18. Christensen D.W., D.A. Anderson. Interpretation of dynamic mechanical test data for paving grade asphalt cements. Journal of AAPT, V. 61, 1992, 67-116.

19. Christensen, D.W. Mathematical modeling of the linear viscoelastic behavior of asphalt cements. Ph. D. Dissertation Thesis. The Pennsylvania State University, 1992, 278p.

20. Marasteanu, M. O., Anderson, D. A. Improved model for bitumen rheological characterization, Eurobitume Workshop on Performance Related Properties for Bituminous Binders, Paper No. 133, Luxembourg, May 1999.

21. Lesuer D., J-F. Gerard, P. Claudy, J-M. Letoffe, J-P. Planche, D. Martin. Relationships between the structure and the mechanical properties of paving grade asphalt cements. Journal of AAPT, V. 66, 1997, pp. 486-505.

22. Drozdov, A.D. A model for the viscoelastic and viscoplastic responses of glassy polymers. International Journal of Solids and Structures, 2001, Vol. 38, pp. 8285-8304.

23. Dobson, G.R. The dynamic mechanical properties of bitumen. Journal of AAPT, V. 38, 1969, pp. 123-135.

24. , . . . . .: , 1963, 536c.

25. Schmidt, R.J., L.E. Santucci. A practical method for determining the glass transition temperature of asphalts and calculation of their low temperature viscosities. Journal of AAPT, V. 35, 1965, pp. 61-85.

26. Bahia, H.U., D.A. Anderson. Glass transition behavior and physical hardening of asphalt binders. Journal of AAPT, V. 62, 1993, pp. 93-125.

27. Claessen, A. J. M., J. M. Edwards, P. Sommer, P. Uge. Asphalt Pavement Design The Shell Method. Proceedings, 1977, 4th International conference on the Structural Design of Asphalt Pavements, Vol. I, Ann Arbor, pp.39-74.

66 67

III.

III.

- : - J(t) D(t), G(t) E(t), |G*()| |E*()|, S(t), , . S(t) - , - , - - .

- G(t) E(t). , , - , - 40/60, 6000 , - , - 0.1 00 E(t) = E(t = 0.1) = 6000 . - -. : - , -. - -; , -

-.

3.1. S(t) = c / (t)

- ( - CA)

(3.1)

, , S, - - :

= aTr Ahrr (T) (Tr) (T Trb 10);

= aTr WLF (T) (Tr) (T > Trb 10) (3.2)

(Tr) = 0.00124

(3.3)

aTr Ahrr (T)=exp

(3.4)

aTr WLF (T) = exp (3.5)

= (3.6)

68

69

III.

: S - , ; Eg - , - Eg = 2460 ; - -, ; (Tr) - Tr = (Trb 10); aTrAhrr (T) - - Trb 10; aTr WLF (T) - > Trb 10; Trb - , 0C; PI - PI = (20 500A) / (1 + 50A); A = (lg (800 / P)) / (Trb 25) - ; P - () 250; t - , ; T - , 0C.

(3.1)-(3.6) , - : Trb P. - PI = 3 PI = +2, - (T Trb) 450C 100C t 0.0001 10000 S (3.1) 14.6%. - (3.1)-(3.6) , . [1]. , .. - . - , - (3.2)-(3.6) , - . -, PI = 3 Trb = 500C T = 300C S t > 300 .

, - t - D(t) = (t) / c, , - : D(t) = 1 / S(t). , (3.1), -

D(t) = (3.7)

( (1.23)) -

J(t) = = (3.8)

Gg = E g / 3 Gg = 820 . , (3.8)

, 250 - P = 80 Trb = 500 ( PI = 0), 150. (3.6) = 0.1794. (3.2) 150 = 4.247 . (3.8) (. 3.1):

. 3.1

70

71

III.

J(t) = (3.9)

. 3.1 - .

3.2. E(t) G(t)

, E G. , - , E(t) T.

, - , (, (3.7) (3.8)), - - . - , Trb P.

, -

, - t - [2,3]:

(3.10)

(3.11)

,

, - , D(t) - - J(t) E(t) - - G(t).

, - D(t) - E(t), J(t) - G(t). , , - D(t) E(t), , (3.10) (3.11) -. D(t) E(t) - [3,4], -. - . re ( re - -) (t) = ret. (3.10) (3.11)

ret = , (t) =

d(t) / dt = reE(t) ,

(3.12a) (3.12b)

(3.12) - x = t . - (3.12), - , - . , D(t), E(t) , - (3.12) .

72

73

III.

, - J(t) G(t):

(3.13a) (3.13b)

J(t) , G(t) , (3.13).

(3.12) . . - [4], . - . [5]. , - - , - D(t) E(t).

, - -. D(t), t, - E(t) . - [4] [0, t] - (3.12) , - ( - ), , - , -. - - - , . - - [5]. . [3] - - -

, , - [6].

- - , , [7, 8, 9] . - , - - : ASTM D 6816-02 AASHTO PP 42-07 [10,11]. , , .

, , , -. (3.12), -

(3.14)

(3.12) t - (3.10), (3.11). (3.14)

[a, b] , :

(3.15)

(3.14), E(t) tm D(t) 0 < t < tm. ti ( i = 0, 1, 2m 1, m). (3.14) -

74

75

III.

E() , - .

(3.15), -

(3.16)

(3.16) (m-) , E(ti ) = Ei:

Em, -

(3.17)

0 < t < tm [ti 1, ti ]. , , -

, - ti log t.

, (3.17) t = 1 - t0 t1, . -, ,

E0 = 1 / D(0) (3.18)

-, E1 t1. - (3.17):

(3.19)

(3.18) (3.19) - (3.17). (3.19) , D(t1 ) / D(0) 3. - t1 , 1.5. - -, D(t), .

, D(t) E(t) - (3.12) , .. . - (3.17) E(t) - D(t), - D(t) E(t), - .

, D(t) E(t) -, - J(t) G(t) . -, (3.17) - G(t):

76

77

III.

(3.20)

, (3.21)

(3.17), (3.20), - [4], - - , . ([3], . 407). - (3.17) (3.20) - , 0.1 10 11 , - 22000 . J(t) - G(t) , - . , - t , 0 t. - 100 t (3.20) 0.09%.

, (3.20) - G(t) , 250 - P = 80 Trb = 500 ( PI = 0), 150. -, (3.9) . 3.1.

t0 = 0 (3.21)

G0 = 1 / J(0) = 820 , - - Eg = 2460 . t1 = 109, - t = 1000. 5 - , .. . - ti = ti 1 101/5, - log (t). G(t) - . 3.2. - - 0.15.

(3.17) (3.20) -, , - , - , 3.1 3.2.

, . . - [12] -

. 3.2. , (3.20) ,

. 3.1

78

79

III.

1:1 125000 750000 1800 [13]. J(t) (. 1 [12]), (3.20) G(t) . t1 = 104 100 50 300 . 2.5 . - G(t) . 3.3 ( ), [12] . - 0.0001 100 - 0.4%.

- t ( ), , [13] (. 3.3). G(t) - . G(t) , [12], - , (3.17) (3.20) ( -

(3.1) -(3.6)) , - .

(3.17)

(3.20) , , Trb P, .

E(t) D(t) - , -

(3.22)

a, d, m - , 0 < m < 1. - - (3.14), - (3.17).

( t E(t) 1 / D(t), (3.14)

(3.23)

-

(3.14),

.

- 855.51 [17], 1 < m < 1. (3.14)

. 3.3. , (3.20) ( ), [12] ( )

80

81

III.

, m / sin (m). - (3.22) (3.23), (3.24)

(3.24)

(3.22) (3.24) (3.14) -.

. (3.24) - [14], - [16,17] . - (3.22) - (3.24), -, , .. - - -. (3.22) (3.24) - , [12,18].

, , [19], D(t) E(t) - - . , - log (D) log (t) log (E) log (t) (3.22) (3.24) m log (t), D(t) E(t) - . (3.22) (3.24) :

(3.25)

(3.26)

D(t) m

(3.27)

(3.28)

(3.25), (3.26) D(t) J(t) 0 < m < 1, m > 0.5 .

(3.8) (3.26) - :

(3.29)

m (3.8) (3.28):

(3.30)

- (3.2) (3.6).

, (3.29) - G(t) , 250 - P = 80 Trb = 500 ( PI = 0), 150. (3.6) = 0.1794. (3.2) = 4.247 . Gg = Eg /3 = 820 . (3.29) . 3.4 ( ) , (3.20) ().

82

83

III.

, - (3.29) , - : t = 0.01 3.5%, t = 0.1 5%, t = 10 12%, - m m = 0.795 , .. 0.80.

- , , . - - , . . [20] ( , CAM):

(3.31)

, [22] , - (3.7) (3.8), - (Gg, ), (3.31) -

k, , - . [20] . , , , - , [2, .70, - (51)):

. (3.32)

(3.31) (3.32) - t = x / Gg.

, ,

. - ([21], 3.241.4) b > 0, k > 1

(3.33)

(x) - -, - . (3.33) k = 1 + b. , , - (3.31), [20], k - -, b - k = 1 + b.

- :

(3.34a)

. 3.4. , (3.20) () (3.29) ()

, . 3.1

84

85

III.

(3.34b)

b , t0 = / Gg (3.29). - (3.30) m = 1/2 (3.29) - 3%. t = t0 (3.29)

, (3.34)

. , - b :

(3.35)

(3.6). = 0.1285 PI = +2 = 0.5476 PI = 3, b - b = 0.1346 PI = +2 b = 0.6767 PI = 3.

(3.34) - G(t) , 250 P = 80 Trb = 500 ( PI = 0), - 150. (3.6) = 0.1794 - (3.35) b = 0.1914. (3.2) = 4.247 . Gg=Eg / 3 = 820 . - (3.34) . 3.5 ( -) -, (3.20) ().

(3.34) - 4%. - (3.32) , -

= 4.23 ,

= 4.247 0.4% . , - : (3.29) (3.34).

3.3. ,

- . - 1960- - [1, 20, 21, 22].

- AASHTO T315 ASTM D7552-09, - -

. 3.5. , (3.20) () (3.34) ()

, . 3.1

86

87

III.

AASHTO M 320-05 [23]. , [24]. - , .

,

G*() = G'() + iG''(), i = - ; G- ; G- - .

, - |G*| Gd, (), - . - - , -

(3.36)

- Gd

G' = Gd cos (), G'' = Gd sin () (3.37) , -

Gd , - : .

, G G G(t), [2]:

, (3.38)

(3.34) -, . . . [19], (3.25) (3.26). , J(t) G(t) - - , (3.38) , , - log (t). , -

(3.39)

(3.13), (3.24) -

(3.40)

(3.40) (3.38) - ([15], 858.812), -

= . (3.41)

a(d)m (3.39), (3.39) , (t 1/), a(d)m = 1 / J (1/). -

88

89

III.

(3.42)

(3.43)

, (3.42), (3.43) (3.36) (3.37), - :

, (3.44)

(3.42)-(3.44) [12,16,17], - , , -. (3.39), .

- (3.8), (3.2) (3.6). - (3.44) (3.8) m ,

(3.45)

= m () / 2 (3.46)

m (3.8) (3.28):

(3.47)

Ed

(3.48)

= m () / 2 (3.49)

(3.50)

(3.45) - , 250 P = 80 Trb = 500 (PI = 0) = 150. , - = 0.1794 , = 4.247 Gg = 820 (. 3.6).

. . ,

. 3.6. (3.45): P = 80 Trb = 500 (PI = 0), = 150

90

91

III.

[25] [26] , [27] AAB-1.

AAB-1 . , -10 (.. 600 1000 200 = 100 20 ), PG-58-22 ( 580 220). [27] ( ), 17.3% , -; 2% , ; 38.3% , 33.4% 8.6% . -1 P = 98 250 - Trb = 47.80, .. PI = 0.

- RMS-803 - 0.1 100 /c 35, 25, 15, 5, 5, 15, 25, 35, 45 600. [25] - - - - 250 (. 3 [25] . 3.3 [26]). - 3.7 3.8. Gd, - , - 16% (.. - , ). - - (3.46) 12.2%.

. - Gd 10 25% 15% ([26], . 100), 0.4 0.9 . , -

- .

- (3.45), (3.46) -

. 3.7. Gd -1: [25,26]; (3.45)

. 3.8. -1: [25,26]; (3.46)

92

93

III.

, - (3.1)-(3.7), - .

-, - . , . H() - , .. , .

. ([26], . 31, . 3.4) AAB-1 = 250. . 3.9. .

- Gd , 3.7 3.8, . . [28].

(3.34) G(t) - (T. Alfrey). ([2], . 81), - G(t)

(3.51)

(3.34) (3.51), -

(3.52)

-1 (P = 98 250 Trb = 47.80) (3.3), (3.6) (3.35) = 4.247 , b = 0.1914 , , Gg = 820 . , - (3.52), . 3.10, , . 3.9.

- = 1.9 108 . , -, (3.52)

(3.53)

, - , . - b, (3.34) , -

. 3.9. -1 250 [26]:

G, G

H(), ( . )

94

95

III.

(. 3.11). b ( - (3.35)), b = 0.1346 PI = +2 b = 0.6767 PI = 3. b, .

- , , H() log (), , .. . 3.11 Gg = 820 . H - , .. - - . . - - H .

. 3.10. -1 250, (3.52)

b:

Hmax = bGg / 3 (3.53)

, - , : - , - .

3.4.

, -

(.. - - Ed () - ()) ,

. 3.11. b

96

97

III.

E(t). , , - - .

- , - - . - : - - , , . - , . , - , - , - E(t), - - [29, 30, 31,32]. E(t) - [33, 34, 35].

- E(t) Ed(). . (3.1) (3.48), :

S(t) = (1 + m())Ed ()|=1/t (3.54)

m() log (Ed()) log () (. . 3.12). (1 + m) 1 m = 1 , 0.886, m = 0.46, 1 m = 0. , (1 + m) 0.886 1 . - 11.4% (1 + m) 1 (3.54)

S(t) = Ed()|=1/t (3.55)

(3.55) [1], t S(t) -, t < 1 c Ed(), - . - , 13%, .. 1/0.886=1.13, .. S(t), - .

, Ed() E(t):

1) Ed(i) - i , 1 / ti, - - :

S(ti ) = Ed (1 / ti ) (3.56)

2) 1 1 (3.1):

(3.57)

, S1(t) S(ti).3) 1 1 b1

(3.35)

98

99

III.

23 , . 3.12 , - -, .. = 103 = 108 /c.

(3.56), - Ed (i ) S(ti) ti = 1/i - t = 108 t = 103 .

1 1

. 3.12. Ed () Tr = 200C 460C 100 250C

(3.58)

- :

(3.59)

. Gd () () - . - , 1.5 (. . 1.5 1.6) 2.3 (. . 2.3 2.4), - 200C - Gd (). - -, Ed () = 3Gd (), , , - . 3.12.

3.1. 200C

, /c

1

0.001

0.004

0.01

0.04

0.1

0.4

1

Ed(),

2

1.26 103

4.64 103

1.08 104

3.83 104

8.64 104

2.86 105

6.14 105

, /c

1

103

4 103

104

4 104

105

4 105

106

Ed(),

2

6.98 107

1.37 108

2.03 108

3.38 108

4.52 108

6.54 108

8.01 108

1

4

10

40

100

400

2

1.86 106

3.72 106

9.97 106

1.83 107

4.23 107

1

4 106

107

4 107

108

2

1.03 109

1.19 109

1.40 109

1.54 109

100

101

III.

(3.57). 3.1 S(108) = 1.54 109 S(103)=1.26 103 (- ), , . - , - , , . 1 1 - S1(t) , :

dev(1, 1) = , min[dev(1, 1)]

1 = 5.34 105 , 1 = 0.2071.

S1(t)

(3.60)

. 3.13, S(ti), - Ed (1 / ti) 3.1. -, (3.60), . 3.13, 0.3% ( -). (3.58) b1 = 0.2232 (3.59) - (. 3.14), .

Ed()

= 1 / t, S(t) - E(t). , , - 250 P = 80 Trb = 500 (PI = 0) = 100 0.1 ,

. 3.13. , Ed ()

. 3.14. E(t), Ed ()

102

103

III.

(3.49) Ed(), (3.1) S(t) (3.34b) E(t). Ed(10) = 23.7 , S(0.1) = 21.1 E(0.1) = 11.3 .

(3.54), S(t) Ed(=1/t), , 13%. -, [25] 18%. Ed(=1/ t) - E(t) (. 3.15), - .

, - t = 0.1 Ed(=1/ t) E(t) 1.6 00, 2.1 100 2.9 200.

- -, -. , -

- , , - .

, - :

1. (3.17), (3.20) E(t) G(t) - - D(t) J(t).

2. (3.29) - - - ( P 250 - Trb) - (3.34a) (3.34b) E(t) G(t) P Trb.

3. (3.45) - (3.49) - Gd Ed - - P Trb. - , - - .

4. - E(t) Ed() - .

. 3.15.

104

105

III.

1. Van der Poel C., A general system describing the visco-elastic properties of bitumens and its relation to routine test data. Journal of Applied Chemistry, London, Vol. 4, 1954, pp. 221-236.

2. Ferry, J.D. Viscoelstic Properties of Polymers, 3rd edition, John Willey & Sons, Inc., New York, 1980, pp. 1-641. 1- : , . . . . .: , 1963, 536c.

3. Tschoegl, N.W., The phenomenological theory of linear viscoelastic behavior. Springer-Verlag, Heidelberg, 1989, 769pp.

4. Hopkins I.L., R.W. Hamming. On creep and relaxation. Journal Applied Physics, 28, 1957, pp. 906-909.

5. Secor K.E., C.L. Monismith, Analysis and interrelation of stressstraintime data for asphalt concrete. Transactions of the Society of Rheology, V. 8, 1964, pp. 1932.

6. Mead, D.W. Numerical interconversion of linear viscoelastic material function. Journal of Rheology, V. 38, 1994, pp. 1769-1795.

7. Bouldin, M.G., R.N. Dongre, G.M. Rowe, M.J. Sharrock, D.A. Anderson. Predicting thermal cracking of pavements from binder properties: theoretical basis and eld validation, Journal of AAPT, V. 69, 2000, pp.455496.

8. Marasteanu, M. Low temperature testing and speci cations. Transportation Research Circular E-C147. Development in Asphalt Binder Speci cations, TRB, Washington, DC, 2010, pp.34-40.

9. Bahia, H.U., M. Zeng, K. Nam. Consideration of strain at failure and strength in prediction of pavement thermal cracking. Journal of AAPT, V. 69, 2000, pp.497535.

10. ASTM D 6816-02. Standard practice for determining low-temperature performance grade (PG) of asphalt binders.

11. AASHTO PP 42-07 Determination of low-temperature performance grade (PG) of asphalt binders.

12. Baumgaertel,M., H.H. Winter. Determination of Discrete Relaxation and Retardation Time Spectra from Dynamic Mechanical Data, Rheologica Acta, V. 28, 1989, pp. 511-519.

13. Schausberger, A. A simple method of evaluating the complex moduli of polystyrene blends. Rheologica Acta, V. 25, 1986, pp. 596-605.

14. Leaderman, H. Viscoelasticity phenomena in amprphous high polymeric systems. Rheology, Vol. II, edited by F.R. Eirich, Academic Press, New York, 1958, pp.1- 61. : :

. . . . . . . - .. .. ., - . ., 1962. 824.

15. , .. . - , ., 1966, 228.

16. Schwarzl, F.R.L., C.E. Struik. Analysis of relaxation measurements. In: Advances in Molecular Relaxation Processes, 1968, 1, pp. 201-255.

17. Schapery, R.A., S.W. Park, Methods of interconversion between linear viscoelastic material functions. Part II - an approximate analytical method. International Journal of Solids and Structures, 1999, Vol.36, pp.1677-1699.

18. Winter, H.H., F. Chambon. Analysis of linear viscoelasticity of a crosslinking polymer at the gel point. Journal of Rheology, 1986, Vol. 30, pp.367-382.

19. Ferry J.D., M.L. Williams . Second approximation methods for determining the relaxation time spectrum of viscoelastic material. Journal of Colloid Science, 1952, 7, pp. 347-353.

20. Marasteanu, M. O., Anderson, D. A. Improved model for bitumen rheological characterization, Eurobitume Workshop on Performance Related Properties for Bituminous Binders, Paper No. 133, Luxembourg, May 1999.

21. Sayegh, G. Variation des modules de quelques bitumes purs et btons bitumineux. Confrence au Groupe Franais de Rhologie, 1963, 51-74, France.

22. , .. . , , 1977. 116.

23. Standard Speci cation for Performance Graded Asphalt Binder: ASTM D 6373, AASHTO M 320.

24. Mechanistic-Empirical Pavement Design Guide, Interim Edition: A Manual of Practice. AASHTO, 2008, pp. 1-212.

25. Christensen D.W., D.A. Anderson. Interpretation of dynamic mechanical test data for paving grade asphalt cements. Journal of AAPT, V. 61, 1992, 67-116.

26. Christensen, D.W. Mathematical modeling of the linear viscoelastic behavior of asphalt cements. Thesis. The Pennsylvania State University, 1992, 278p.

27. The SHRP Materials Reference Library, SHRP A-646, Washington, DC, 1993, pp. 1-228, (Appendix A).

28. Ninomiya, K., J.D. Ferry. Some approximate equations useful in the phenomenological treatment of viscoelastic data. Journal of Colloid and Interface Science, 1959, Vol. 14, pp. 36-48.

29. Elliot, J. F., F. Moavenzadeh. Analysis of stresses and displacements

106

107

in three-layer viscoelastic systems. Highway Research Record 345, 1971, pp. 4557.

30. Huang, Y. H. Stresses and strains in viscoelastic multilayer systems subjected to moving loads. Highway Research Record 457, 1973, pp. 6071.

31., .., .. . - - . -, 1981, . 17, No. 6, pp. 45-52.

32. Chen, E.Y.G., E. Pan,T.S. Norfolk, Q. Wang. Surface loading of a multilayered viscoelastic pavement. Road Materials and Pavement Design. Vol. 12, No. 4, 2011, pp. 849-874.

33.Monismith, C.L, Secor, G.A. and Secor, K.E., Temperature induced stresses and deformations in asphalt concrete. Journal of the Association of Asphalt Pavement Technologists, Vol. 34, 1965, pp. 245-285.

34. Radovskiy, B., V. Mozgovoy. Ways to Reduce Low Temperature Cracking in Asphalt Pavements. 4th Eurobitume Symposium, 1989, Madrid, Vol. 1, pp. 571-575.

35. Bouldin, M.G., R.N. Dongre, G.M. Rowe, M.J. Sharrock, D.A. Anderson, Predicting thermal cracking of pavements from binder properties: theoretical basis and eld validation, Journal of the Association of Asphalt Paving Technologies, Vol. 69, 2000, pp. 455496.

IV.

, - , , - , , - - , - -, - .. - (3.1) (3.2)-(3.6) - - , - - , - . - - - .

, - , - , , , - . , - - . , , -

108

109

IV.

, - , . - - -, , , -.

4.1 , -

- . . - - , - -, , - () .

[1,2], 1980- - - [3,4]. , - , - , , - -, - . - , -.

- 140-1600 -

- 700. - , - . - -, , , - - . - : (RTFO), - , - , (PAV), (1000 2 ) , - 4-8 - [5, 6]. - . , - - .

-. . [7] - 65% : = 0.65 . -, [8], -, - 5.7% : = 50 - Trb= 52.90, = 32.5 , Trb= 59.30. , 3.5% -, =100 Trb= 44.90, - = 65 Trb= 51.40 (.

110

111

IV.

4.1 [8]). [9] , : 0.70-0.75 ( 250), 1.08 2.08 600.

. [10] , - , , - . , - 0.6-0.8 , - 0.6-0.8 . , - . . [11], - , -, -

P1 = 0.52P 2

60 29.2 , 90 44.8 , - .

[12], 8 -, , - ( 250) 0.59 ( 0.53 0.70), ( 600) 2.5 ( 1.8-3.2), - 1.13 . , , 0.6 - - 1.1 .

-. , 5 15 , -

- , - - 250 [13]. -. ( 4%) - 5 0.7 , 10 0.5, - ( 8%) - 0.6 0.4, .

. , . . 18 [14]. 60 , 4 - 31-34 , 11 26-29 , .. 4 0.55 -, 11 0.45. - 11 520 660, .. 27%. . [11], , , 14

P(t) = P1 b log (t)

t - , P1 - - , P1 = 0.52P 2, b - , -, . , - 14 9 ( 0.95).

b = 9.7 - 69 . 4.1 [4]. - -.

112

113

IV.

- . 5 - , 10 20% . - -.

[15] -, - 10 10 . . 5-10 60-70 20-25 , . , , 5-7 3 -, 600 - .

. . [12], -

8 , - , ( 250) - 0.34 ( 0.28 0.43), ( 600) 7.5 ( 4.2-10.5), 1.13 . , , - - 0.6 - 1.25 ( 1.12-1.32).

, , - - 5-7 - 0.3-0.4 -, 1.2 , 600 5-10 . - , - 0.3-0.4 - 20-25% .

, , - , , , -, - . [16] - , 4 13 , US 93 (. 4.2). PG 76-16 . , - .

. 4.1. [15]

114

115

IV.

4.2. -

, , . - -, . - , - , - . - .

. , Ste. Anne - 1250 ./ (10% -) 8 (1967-75 .) - 29 120 [17]. - - ( , 1% 0.5% ), . 380, 400. , - . - , - , , [18]. - .

, -, - S - , ,

,

./

c

.

4.2

.

:

,

4

1

3

;

(

)

Gd(

)

,

,

,

(

)

;

4

00

Gd,

116

117

IV.

. - S - t = 7200 200 . S - , - 6.2512.5125 102 . - - 100 , t = 60 , S(60) = 300 .

, - S(t) , - , - , . m, - - S(t) , 0.30, ..

> 0.30

t = 60 . S(60) = 300 mS > 0.30 AASHTO M 320-05. - .

(3.1) , -

mS = (4.1)

, - -

, - .

. , 60 48.80 ( PI = 1.08) , 5-7 ( 45 , 59.30 ( - PI = 0.68).

t = 60 c (3.1) - (. 4.3).

. 4.3. ,

, : ( ), RTFOT PAV;

, mS = 0.30; t = 60c S 180,

> 280C.

118

119

IV.

S(60) = 300 () . , - (4.1) - mS = 0.30.

, - . - T = 210C, - T = 180C. T = 180C - (P = 45, Trb = 59.30, PI = 0.68) t = 60 - (3.1) S = 302 , (4.1) mS = 0.356, - S < 300 .

(S < 300 , mS > 0.30) - 60 10 . , -, - , - , , 280.

, - [19] S m . - - , - [20]. -. , [21], - .

4.3. , -

- - - , - - .

- - [19]. - [22]. , PG 64-34 , - - - 64C, 34C. , , 6C.

- - , - . , 20 , [23]. , - - , - 20 , - 20 -. -

120

121

IV.

, .

[19] ( -) - 10 . 80 -. - (, ) - , ( ), -, PG 64 PG 58. - ( ), , PG 70 PG 58. - .

. - , - , - , 10 . . - - 10 30 . , - ( 6 -) . - 30 . , - . 76 820 - - . PG 76 PG 82 .

- , , , - , - ,

( 1).

, AASHTO M 320-05 [19] - :

1) . - |G*| / sin () - - 10 /c. , - 1 2.2 , .

2) -. , [19] , - - 60 100 : S < 300 , mS > 0.30.

3) - . , - 10 /c , , - - . [19] . , PG 64-34 190. |G*| sin () < 5 .

, , , - [19] ,

122

123

IV.

, , , . [19] - , - (. [20]).

, . - , .

, -, - , - . , - - - - (SHRP). , 32 ( 4000 -), 11 ( 30 ) 82 [24]. 32 SHRP 8 11 4 . - , -. - [24], .

AAB-1 . , - [24] , , [12]. Trb = 47.80, -

P = 98 ( 250C), PI = 0. - :

TFOT: Trb = 520, P = 92 , PI = 0.95.

TFOT - PAV: Trb = 570, P = 34 , PI = 0.455.

1) - .

= 580. Trb = 47.80, P = 98 , PI = 0 (3.6) = 0.1794, (3.2) = 4.115104 . , Gg = 820 , (3.47) m = 0.8993 (3.46) = 1.413. - ( ) (3.45) |G*| = 2.368103 = 2.368 . - |G*| / sin () = 2.398 , , 1 .

Trb = 520, P = 92, PI = 0.95 |G*| / sin () = 2.768 , - 2.2 , .

= 640. , - |G*| / sin () = 1.148 , .. , |G*| / sin () = 1.874 , 2.2 . PG 58.

2) - .

PG 58 [19] -: 16, 22, 28, 34 400 ( -

124

125

IV.

). , - 60 - - 6, 12, 18, 24, 300.

= 280, = 180 t = 60c. - Trb = 570, P = 34 , PI = 0.455 (3.6) = 0.1984 (3.2) = 3.928105 . (3.1), , Eg = 2460 , S = 190 , S < 300 . (4.1) mS = 0.398, - 0.300.

, 340. = 240 t = 60 c. -, (3.6) = 0.1984, (3.2) = 3.072106 , (3.1) S = 391 , - 300 . , - 28.

3) - .

-1 PG 58-28. [19] - - 190 . - (3.6) = 0.1984, (3.2) = 7.885 , (3.47) m = 0.6141, (3.46) = 0.965. - (3.45) |G*| = 7.547 . |G*| sin () = 6.20 , , 5 . - -1 - PG 58-28.

,

PG 58-22. [19] - 220. = 0.1984, (3.2) - = 3.695 , (3.47) m = 0.6491, (3.46) = 1.02. - (3.45) |G*| = 7.547 . - |G*| sin () = 3.96 , , 5 . -1 - PG 58-22 .

, (- ), - -1 - . , - PG 58-22 , [24], [12] - . - .

, - [25], (. 4.4).

4.4. ,

- - [26].

126

127

IV.

, [27] - .

, - Ec, E1 E2, c1 c2, ( c1 + c2 = 1). . (A. Reuss, 1929 [28]), - -

(4.2)

= (4.3)

. (W. Voigt, 1928 [28]),

EV :

EV = c1 E1 + c2 E2 (4.4)

, Ec, E1 E2, - , - [28]:

ER Ec EV (4.5)

- . (. 4.5 ), E1 E2, - -.

, - . l = (l1 + l2) -

,

c1 = l1 / l, c2 = l2 / l - E1 E2 . -, - Ec,

-

. 4.4. [25]

128

129

IV.

:

, ER (4.2). (. 4.5 -

), a l1 l2 - E1 E2, . -

, :

1 = E1 , 2 = E2 .

, -

Q = 1 l1 a + 2 l2 a

= = 1c1 + 2c2 = (E1c1 + E2c2)

c1 = l1 / (l1 + l2), c2 = l2 / (l1 + l2) - - - E1 E2 - .

, Ec,

= Ec .

- -:

Ec = E1c1 + E2c2

, EV (4.4)., -

( ) (4.3), (- ) (4.4).

, -, - ( (4.2)) (- (4.4)) . , - (c1 = c2 = 0.5) (E1 = 1 , E2 = 2 ) , ER = 1.33

. 4.5. ,

,

130

131

IV.

EV = 1.50 , .. Ec 1.33-1.50 . 100 (E1 = 1 , E2 = 100 ), - Ec - 1.98 50.5 .

, - (4.3) (4.4) -: , - (), (-), .. - , - -. 1962 . . - , (4.2) (4.4):

(4.6)

k , - . , , - k = 0 -, . 4.5 . , k = 1, - (4.6) (4.4), (. 4.5 ).

. . , . - . [27] - . - .

. -

. - Pc . - [27]:

(4.7)

-

(4.8)

P0 , P1 P2 - . : Eagg - -

; Eb - ; VMA - - ( -); VFA - , . (1 VMA) (4.7) , VMA VFA - . Pc = 1 (4.7) (4.4) ( ), Pc = 0 (4.2) (- ).

(4.7) [27] - , .. - Ed() = |E*()|. , [27] Emix (4.7) Emix d(). [27] Eagg = 29000 , [29] 19000 . , - (4.7) [27] Eb=Eb d(), .

132

133

IV.

- , [27] - P0 , P1 P2 (4.8), VMA = 0.137 0.216, VFA = 0.387 0.68, - 5.6-11.2%. 0.1 5 /c, - 100 +540. - SSP (Superpave Shear Tester) SPT (Simple Performance Tester). - 9.5, 19 37.5 . - DSR (Dynamic Shear Rheometer) , .

[27] - (4.8) . (4.8) : - P0 P2 -. - , P0 = 0.138, P1 = 0.58 P2 = 36.25. Pc . 4.6.

, Pc , - , - Emix d() Emix (t). - (4.7) - E(t). (4.7) Emix = Emix (t) Eb = E(t), (3.34b):

(4.9)

1. . , - Trb = 500 - 80 ( PI = 0), - T = 200 t = 0.1 . - 1.03 /3, - 2.703 /3, 2.442 /3. 5.6%, .. 5.6 100 / (100 + 5.6) = 5.3% - 94.7% . , 0.8%. , ( ), 5.3 0.008 94.7 = 4.54% .

- 4.54 2.442 / 1.03 = 10.8% = 0.108. 94.7 2.442 / 2.703 = 85.6% = 0.856. -

. 4.6. VMA = 0.144, VFA = 0.75.

134

135

IV.

VMA - VMA = 1 0.856 = 0.144. - 0.144 0.108 = 0.036 (.. 3.6%). , - , (4.7) (4.8), - VFA = 0.108 / 0.144 = 0.75. - (3.34b) - b. PI = 0 (3.6) = 0.1794 (3.35) b = 0.1914. T = 200 (3.2) = 1.217 . t = 0.1 - (3.34b):

E = 2.46103 =1.637

(4.8)

= 0.088

- (4.7):

Emix (t) = 0.088[1.9 104(1 0.144)+1.636 0.144 0.75] +

+ =1440

- . 4.7, . 4.8 - 250 +400 - 0.1 . , - , -14, - , 65 -

. 4.7.

. 4.8.

136

137

IV.

. 4.8 0.09 .

-, , 5-7 - 0.4 , - 25%. - , - (4.7), . 4.9 , , - Trb = 450 P = 90 . , - - 50 t = 0.1 , - VMA = 0.144 VFA = 0.75 - 6600 , 8700 . - 200 2.5 .

Emix (4.7) . - 46-83 -, - - 0.1 . , - - 1979 . - , - 90/130 Trb=470 P = 114 . 5.5% . 40% , - . 4%. ( - ) 12%.

4 4 16 t = 0.1 - : 4130 , 1830 1090 = 0, 10 200, . - (4.7) VMA = 0.16 VFA = 0.75 5400 , 2500 920 . - , , - 10-30% . , 3 - 90/130 0, 10 200 3600, 2400 1200 , .

- . ASTM D 36 , - - - 0.20 0.50. 0.720, -

. 4.9. : Trb = 450 P = 90 ,

5-7 Trb = 560 P = 36 ; 0.1

138

139

IV.

1.080. ASTM D 5-06 - = 0.8 60 , 60 - = 0.8 + 0.03(P 60) . , 80 1.4 . - .

, - . P = 80 Trb = 500 PI = 0 t = 0.1 c T = 100 (3.34b) E(t) = 11.2 , (4.7) - Ed = 3730 , . 4.5 4.6. - P = 78 Trb = 490 (PI = 0.342), - E(t) = 13.6 , (4.7) - Emix = 4050 . , - - 20%, - 9%.

4.5. , -

- - . - , .. Emix d mix .

. - [27] , (3.48)

Eb d . - .

[27]:

Emix d = Ec d [ Eagg ( 1 VMA)+Eb d VMA VFA] +

+ (4.10)

mix = 21 (log ( Pcd))2 55 log ( Pcd) (4.11)

[27]

(4.12)

P0 = 0.138, P1 = 0.58 P2 = 36.25.

(3.48)

Ebd() = , m() =

(3.3), - - (3.6).

2. - , 1, T = 200 = 10 /. - VMA = 0.144; , - , VFA = 0.75. - PI = 0 (3.6) = 0.1794. T = 200 (3.2) = 1.217 . - (3.48)

((

))

140

141

IV.

m() = = 0.68,

Eb d ()= =4.713 .

(4.12)

Pc d = = 0.15.

(4.10):

Emix d = 0.15[ 1.9 ( 1 0.144)+4.713 0.144 0.75] +

+ = 2461 .

- ( ) (4.11) [27]:

mix = 21 (log (0.15))2 55 log (0.15) =310.

, - = 10 /c - t = 0.1 2461 / 1440 = 1.78 . . 4.10 - ( t = 0.1 ) ( = 10 /c) -.

. 4.10, - , -, t = 1 /. Emix d Emix - 2.1 340.

. 4.11 (4.11) [27]. - , - - .

- . - , - , . - . . , - [31].

48 , - . - 40 200 . - 19 , 3 (

. 4.10. ( , t = 0.1 ) ( , = 10 /c)

= 200

))

((

142

143

IV.

). - 16 500 . , 8 - 60% , 34% 6% - 39 ( 250) - 610. : 81.6%, 14.2%, 4.2%. 100 16 8500 .

. 0.63. - = 2 16 = 100.5 /c. - VMA = 18.4%. , , VFA = 14.2 / 18.4 = 0.772. (4.10), 100 - Emix d = 7996 , - 6%.

1 - 95.3% 4.7% - 197 ( 250) -

400 ( PI = 0.095). - : 82.6%, 10.5%, 6.9%. - 100 16 5100 . (4.10), - 100 = 2 16 = 100.5 /c - Emix d = 4376 , - 14.2%.

, (4.7) (4.10) . . , - , - -, .

1. Hubbard, P., H. Gollomb. The Hardening of Asphalt with Relation to Development of Cracks in Asphalt Pavements. Proceedings of AAPT, Vol. 9, 1937, pp.165-194.

2.Traxler, R.N. Relation between asphalt composition and hardening by volatilization and oxidation. Proceedings of AAPT, V.30, 1961, pp.359372.

3. Welborn, J.Y. Relationship of Asphalt Cement Properties to Pavement Durability. TRB, NCHRP Report 59, 1979.

4. Bell C. Summary Report on Aging of Asphalt-Aggregate Systems, SHRP Report A-305. Washington D. C.: National Research Council, 1989, pp. 1-121.

5. Lesueur D, The colloidal structure of bitumen: Consequences on the rheology and on the mechanisms of bitumen modi cation, Advances in Colloid and Interface Science, 2009, V. 145, 1-2, p. 42-82.

6. Anderson, D.A., D.W. Christensen, H.U. Bahia, R., Dongre, et al. Binder Characterization and Evaluation. Volume 3: Physical Characterization, SHRP report A-369.Washington D. C.: National Research Council; 1994.

. 4.11. = 10 /c

144

145

IV.

7. S.Brown. Introduction to Analytical Design of Asphalt Pavement, Nottingham, 1980.

8. Brunton J.M., Developments in the analytical design of asphalt pavements using computers. University of Nottingham, 1983, 406p.

9. Airy, G., S.F. Brown. Rheological Performance of Aged Polymer Modi ed Bitumens. AAPT, V.67, 1997, pp. 66-100.

10. Culley, R. Relationships between hardening of asphalt cement and transverse cracking pavements in Saskatchewan. AAPT, V. 38, 1969, pp.629-645.

11. Benson, P. E. Low temperature transverse cracking of asphalt concrete pavements in Central and West Texas. Texas Transportation Institute, Texas A&M University, 1976.

12. Christensen D.W., D.A. Anderson. Interpretation of dynamic mechanical test data for paving grade asphalt cements. Journal of AAPT, V. 61, 1992, 67-116.

13. . ., - , , 1989, .128-133.

14. Corbett, L. W., and Merz, R. E. Asphalt binder hardening in the Michigan Test Road after 18 years of service, Transportation Research Record 544, Washington, D.C, 1975, pp. 27-34.

15. Kandhal, P.S. Low Temperature Ductility of Asphalt in Relation to Pavement Performance. American Society for Testing and Materials. Special Technical Publication No. 628, June, 1977.

16. Harnsberger, M. Doing with WRI: An overview of FHWA research, Rocky Mountain Asphalt Conference, Denver, Colorado, February 23, 2011.

17. Deme, I.J., F.D. Young. Ste. Anne Test Road revisited twenty years later, Proceedings of Canadian Technical Asphalt Association V. 32, 1987, 254-283.

18. Finn, F. Asphalt properties and relationship to pavement performance. Literature Review, SHRP Task 1.4, 1990, ARE Inc., 1990, pp. 1-404.

19. AASHTO M 320-05 Standard Speci cation for Performance-Graded Asphalt Binder.

20. Bouldin, M. G., R. Dongr, G. M. Rowe, M. J. Sharrock, D.A. Anderson. Predicting Thermal Cracking of Pavements from Binder Properties, AAPT, V. 69, pp. 455-496, 2000.

21. ASTM D 6816 02 Standard Practices for Determining Low-Temperature Performance Grade (PG) of Asphalt Binders.

22. Performance Graded Asphalt Binder Speci cation and Testing. Superpave Series No. 1 (SP-1). Third Edition, Asphalt Institute, Inc., pp.

1-59, 2003. : - , . . .. , ., 2004.

23. AASHTO R 29, Grading or Verifying the Performance Grade (PG) of an Asphalt Binder.

24. Mortazavi, M., J.S. Moulthrop. The SHRP Materials Reference Library, SHRP-A-646, Washington, DC, 1993, pp. 1-228.

25. Teltayev, B., E. Kaganovich. Evaluating the Low Temperature Resistance of the Asphalt Pavement under the Climatic Conditions of Kazakhstan. In: 7th RILEM International Conference on Cracking in Pavements, 2012, pp. 211-221; Teltayev, B., E. Kaganovich. Bitumen and asphalt concrete requirements improvement for the climatic conditions of the Republic of Kazakhstan /CD. Proceedings of the XXIVth World Road Congress, 2011, pp. 1-13.

26. . 2: - , . . . . . . .. .. . ., , 1978, 563.

27. Christensen, D., T. Pellinen, R. F. Bonaquist, Hirsch model for estimating the modulus of asphalt concrete. Journal of Association of Asphalt Paving Technologists, Vol. 72, 2003, pp. 97-121.

28. Hill, R. Elastic properties of reinforced solids: some theoretical principles. Journal of Mechanics and Physics of Solid, Vol. 11, 1963, pp. 357-372.

29. Hirsch, T. J., Modulus of elasticity of concrete affected by elastic moduli of cement paste matrix and aggregate. Journal of the American Concrete Institute, Vol. 59(3), 1962, pp. 427-452.

30. Zofka A., M. Marasteanu, X. Li, T. Clyne, J. McGraw. Simple Method to Obtain Asphalt Binders Low Temperature Properties from Asphalt Mixtures Properties. Journal of the Association of Asphalt Paving Technologists, 2005, Vol. 74, pp. 255-282.

31. Pell, P.S., K.E. Cooper. The effect of testing and mix variables on the fatigue performance of bituminous materials. Journal of the Association of Asphalt Paving Technologists, 1975, Vol. 41, pp. 1-37.

146 147

XXI - - - - - -.

- - , - . - . - , - : -. - - - .

- , , : , . . -, -

, , .

, - - (.1). , , - ( ), - (. 2). , 60 , -, . , - ( (3.1)-(3.6)) - .

- - - (. 3). - - (- (3.17)). - - - ( (3.29)). (3.34) - . - . - . , (3.17), (3.34), (3.35), (3.52) (3.53).

148

149

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XIX - . , . , . , - . , , . , , , - , .

- . 1961-63 . 1 . . 1964-66 . - - - (-) ( ). 1966 . 1986 . - - (. ). - (, 1966 .) (, 1983 .) . 1986-95 . - - - . 1996 .. - .

150

1991 - . 1991 . 1999 . ( . . -) -, , - , . 1999 . 2006 . -. 2006 . - . (1994 .) (1998 .) - - .

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20.11.13. 84x108 1/32. Times New Roman. .. 9,5.

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