APPENDIX H FRACTURE PROPERTIES OF ASPHALT MIXTURES
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1 APPENDIX H FRACTURE PROPERTIES OF ASPHALT MIXTURES
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3 LIST OF FIGURES Figure Page H- Loading ime under sress free emperaure... H-2 H-2 Mehod o evaluae he m mix of fracure properies for hermal case... H-3 H-3 Mehod o evaluae he m mix of fracure properies for raffic case... H-3 H-4 Mehod o evaluae he m mix-fwd... H-5 H-5 Load wave shape for single axle in bending crack propagaion... H-7 H-6 Load wave shape for andem axle in bending crack propagaion... H-8 H-7 Load wave shape for riple axle in bending crack propagaion... H-9 H-8 Load wave shape for quad axle in bending crack propagaion... H-0 H-9 Load wave shape for single axle in shearing crack propagaion... H- H-0 Load wave shape for andem axle in shearing crack propagaion... H-2 H- Load wave shape for riple axle in shearing crack propagaion... H-3 H-2 Load wave shape for quad axle in shearing crack propagaion... H-4 LIST OF TABLES Tables Page H- Tensile srengh of asphal mixures... H-2 H-2 Faigue calibraion coefficiens for four climae zones... H-5 H-3 Upper limi of inegraion of a k in differen axles... H-6 iii
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5 a k are: The equaions of he fracure properies o calculae he Paris s law coefficiens A, n and loga=g + n=g 0+ m mix g logd +g logσ mmix g (H-) (H-2) n a w() d (H-3) k 0 where g0, g, g2, g3, and g 4 are he faigue calibraion coefficiens; m mix is he slope of he graph of he relaxaion modulus (E i ) vs loading ime ( i ); D is he coefficien in he maser creep compliance power law equaion; is undamaged ensile srengh; w () is he normalized load wave shape for differen axles and hermal loading. The faigue calibraion coefficiens g0, g, g2, g3, and g 4 were developed in he SHRP A-003A projec and repored in he SHRP Repor A-357 (4). These coefficiens are shown in Table H- in all four climae zones. The variable mmix is he slope of he graph of he ANN relaxaion modulus (E i ) versus he loading ime ( i ). The hree hermal loading imes are based on he ime during which he emperaure is below he sress free emperaure (20 C) as illusraed in Figure H-. These imes are used o calculae he m mix for he hermal case Figure H-2. On he oher hand, he raffic loading ime was deermined by he eigh axle caegories shown in Figure H-3. Since he variance of pavemen emperaure could be significan, i was necessary o calculae he m mix hourly. H-
6 Table H-. Tensile srengh of asphal mixures. Tensile Srengh (psi) Temperaure ( F) r (in/m in) Thermal E(, T )( MPa) Traffic E(, T )( MPa) Temperaure Sress Free Temperaure 20 C Time, sec. Thermal Loading Time, sec. Thermal Loading Time, sec. Figure H-. Loading ime under sress free emperaure. H-2
7 log Ei (, T ) m mix 0. sress free sress free 0 sress free log Figure H-2. Mehod o evaluae he m mix of fracure properies for hermal case. log Ei (, T ) m mix 0. caegory caegory 0 caegory log Figure H-3. Mehod o evaluae he m mix of fracure properies for raffic case. H-3
8 The oher unknown erm is ensile srengh. The equaions of ensile srengh are differen in hermal and raffic cases shown in Table H-. The coefficien D is he coefficien in he maser creep compliance power law equaion which is shown in (H-4). In he Calibraion program, E is calculaed by Equaion (H-5). For he design program, he equaion for E is Equaion (H-6) which is no a funcion of he FWD modulus. D sin( mmix ) ( psi ) E m mix (H-4) FWD FWD log E (, T) log EANN (, T) mmix FWD log( ) a a T T (H-5) log E (, T) log E(, T) mmix log( ) a T (H-6) where at m mix FWD is he slope of he graph of he ANN relaxaion moduli versus loading ime; is he shif facor based on he FWD emperaure ( T FWD ) (H-7), C, C2, and T d are he parameers of he Time- Temperaure shif funcion in Table H-2; C ( TFWD Td ) C2 TFWD Td a 0 (H-7) T The mehod o obain he m mix FWD is basically he same as m mix ha we inroduced earlier in Figure H-4. Assuming he FWD loading ime is 6 second, consider hree loading imes which are FWD loading ime divided by shif facor, 0 imes he FWD loading ime divided by he shif facor, and 0. imes he FWD loading ime divided by he shif facor. Use hese loading imes and he FWD esing emperaure o evaluae he relaxaion moduli, and find he m mix FWD. H-4
9 Table H-2. Faigue calibraion coefficiens for four climae zones. We-Freeze We-No Freeze Dry-Freeze Dry-No Freeze g g g g g g g T d ( C) C C log Ei (, T ) m mix- FWD 0. FWD a T a FWD T log 0 FWD a T Figure H-4. Mehod o evaluae he m mix FWD. The healing coefficiens g 5 and g 6 are used in defining he healing shif facor which is based on he average ime beween passing vehicles, Δ. The healing shif facor is H-5
10 5 g6 SF g (H-8) healing The healing shif facor divides ino each day s raffic crack growh and hus prolongs he number of days required for he crack o reach he surface of he overlay. Fracure propery a k is a raffic facor which is a funcion of he load wave shape w () (H-3). Since he load wave shapes are differen for differen axle combinaions, herefore, we considered single axle, andem axle, ridem axle, and quadrem axle in boh he bending and shearing cases in his program for he raffic loading, and se a k for he hermal case. In order o evaluae he a k, he load wave shape for differen axles was deermined, and hen he load wave shape raised o he power n was inegraed beween he ime limis of zero and Δ. The equaions of Δ for differen axles are shown in Table H-3. L j is he lengh of he ire fooprin, V is he speed of ravel (H-9), and n is he Paris s law coefficien (H-2). Figures H-5 o H-2 are he load wave shapes for differen axles in he bending and shearing cases. n a w() d k 0 Speed of Travel, V V miles hour f 22 sec. miles 5 hour (H-9) Table H-3. Upper limi of inegraion of a k in differen axles. Δ (second) Single Axle Tandem Axle Tridem Axle Quadrem Axle Lj Lj Lj Lj 0 f V 4 f V 8 f V 22 f V H-6
11 Overlay Old Surface (Lengh of ire pach) Crack or Join 5.0 f 5.0 f W ( ) Load Wave Shape (0 + ) f. [W ()] n.00 (0.72) n (0.72) n Figure H-5. Load wave shape for single axle in bending crack propagaion. H-7
12 4.0 f Overlay Old Surface Crack or Join 2.0 f 2.0 f 5.0 f 5.0 f W ( ) Load Wave Shape (4 + ) f. [W ()] n (0.92) n (0.92) n (0.82) n (0.82) n (0.72) n (0.72) n (95) n Figure H-6. Load wave shape for andem axle in bending crack propagaion. H-8
13 4.0 f 4.0 f Overlay Old Surface Crack or Join 4.0 f 4.0 f 5.0 f 5.0 f W ( ) Load Wave Shape (8 + ) f. [W ()] n (0.72) n (0.92) n (0.92) n (0.84) n (0.84) n (0.84) n (0.76) n (0.76) n (0.72) n (95) n (95) n Figure H-7. Load wave shape for riple axle in bending crack propagaion. H-9
14 4.0 f 4.0 f 4.0 f Overlay Old Surface Crack or Join 4.0 f 4.0 f 4.0 f 5.0 f 5.0 f W ( ) Load Wave Shape (22 + ) f. [W ()] n (0.92) n (0.92) n (0.84) n (0.84) n (0.84) n (0.84) n (0.72) n (0.76) n (0.76) n (0.76) n (0.72) n (95) n (95) n (95) n Figure H-8. Load wave shape for quad axle in bending crack propagaion. H-0
15 Overlay Old Surface Crack or Join 5.0 f 5.0 f.0 W ( ) Load Wave Shape.0 (0 + ) f..0 [W ()] n.0 Figure H-9. Load wave shape for single axle in shearing crack propagaion. H-
16 4.0 f Overlay Old Surface Crack or Join 4.0 f 5.0 f f W ( ) Load Wave Shape.. (4 + ) f. (.) n (.) n [W ()] n (.) n (.) n Figure H-0. Load wave shape for andem axle in shearing crack propagaion. H-2
17 4.0 f 4.0 f Overlay Old Surface Crack or Join 4.0 f 4.0 f 5.0 f 5.0 f... W ( ) Load Wave Shape... (8 + ) f. (.) n (.) n (.) n [W ()] n (.) n (.) n (.) n Figure H-. Load wave shape for riple axle in shearing crack propagaion. H-3
18 4.0 f 4.0 f 4.0 f Overlay Old Surface Crack or Join 5.0 f 4.0 f 4.0 f 4.0 f f W ( ) Load Wave Shape.... (22 + ) f. (.) n (.) n (.) n (.) n [W ()] n (.) n (.) n (.) n (.) n Figure H-2. Load wave shape for quad axle in shearing crack propagaion. H-4
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