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1 26ƒ 3D Á œ pp. ~ ª y w qp yw k d Predictive Equation of Dynamic Modulus for Hot Mix Asphalt with Granite Aggregates yá½x Á Lee, Kwan-HoÁKim, Hyun-OÁJang, Min-Seok Abstract The presented work provided a predictive equation for dynamic modulus of hot mix asphalt, which showed higher reliability and more simplicity. Lots of test result by UTM at laboratory has been used to develop the precise predictive equation. Evaluation of dynamic modulus for 13mm and 19mm surface course and 25mm of base course of hot mix asphalt with granite aggregate and two asphalt bindersg(ap-3 and AP-5) were carried out. Superpave Level 1 Mix Design with gyrator compactor was adopted to determine the optimum asphalt binder contentg (OAC) and the measured ranges of OAC were between 5.1% and 5.4% for surface HMA, and around 4.2% for base HMA. The dynamic modulus and phase angle were determined by testing on UTM, with 5 different testing temperatureg(-10, 5, 20, 40, & 55 o C) and 5 different loading frequenciesg(0.05, 0.1, 1, 10, 25 Hz). Using the measured dynamic modulus and phase angle, the input parameters of Sigmoidal function equation to represent the master curve were determined and these will be adopted in FEM analysis for asphalt pavements. The effect of each parameter for equation has been compared. Due to the limitation of laboratory tests, the reliability of predictive equation for dynamic modulus is around 80%. Keywords : dynamic modulus, predictive equation, master curve, shift factor, granite, gyratory compactor y w qp td yw»d yw k sƒwš, w l k š, w xk k d w t š.» w ƒ rr w w,» e w. td (13mm 19mm)»d (25mm) qp yw w š, ü t qp AP-3, AP-5 qp w w w. qpw œ 2%, 4%, 6% r œ 4% qp w Û1% q p w w r w. 5 x, -10, 5, 21, 40, 55 o C 0.05, 0.1, 1, 10, 25Hz 5 w q w x k sƒw.» k d Witczak td»d qp yw x w ü qp yw w d w. d ƒƒ w w y sƒw š, w x w d 80% sƒ. w : k, lš, d, w, y, z» 1. ü 100,000km zwš š, lj w œ w ƒ š. ù, ü AASHTO š š, w TA wš. v w * z w y œw ( ** w y œw ( *** w y œw ( š q» w wš. w,»» ƒ k l»¾ v w., z s, œ,, w s,, x, x x» ƒ v w., s»» x w» w s wwš., ù» 26ƒ 3D œ 1

2 w wš w y s š (, 2002). w x s w qp y w y 1 3 w. ü w q w qp yw yw k sƒw š, w qp yw ƒ w e k dw dœ w. 2. qp yw k 2.1 k x 1962 Papaziand w w qp yw k p sƒƒ qp yw k (Dyanmic Modulus) x w. x m x r q w w w q w š, q xk x d w. x w w q ww. x l qp yw k s w y w. z ù qp yw k sƒ ƒ w. ƒƒ w x w š, p w w» w, Witczak Root - x w š phase angle j w tw Bonnaure bending x w k sƒ w. r Õ xk w š, q w w International Union of Testing and Research qp yw k. 15 x r w x ww. x l bending x x w k x w ùký w NCHRP k ƒ w š, x r t y x w., x r x j», r, x, w, w w. 2.2 k» qp yw k p q w {» ww k d xp l ³ ƒ w, w q l w k (complex modulus, E*) w. x w d x wk. σ ε σ o e iωt E* = -- = ( φ) φ o e i ωt k wk w, (4) tx. σ o E* = ε o x l k x w w ƒƒ. w (Superposition Principle) w 1 lš (Master Curve) w. lš p qp yw w ³ w ƒ š. lš j ƒ, w q w Arrhenius qp w w w AASHTO Arrhenius lš» w w yw (shift factor) v w. w reduced frequency(f r ) w ƒƒ w q (f) ù.» a(t) y v w y w. f or f r = at ( ) log( f r ) = log( f) log[ at ( )], qp yw w p w xk wš, š p sƒ w (polynominal fitting fucntion) w. Pellinen(2001) w Sigmoidal w w lš w, w d k x w w (Kaloush, 2001, ½x & y, 2005).» š, MS EXCEL w» (Solver Function) w q l w. α log( E* ) = δ exp β γlog ( t r ) + (3) (4) (5) (6) σ = σ o sin( ωt) σ = σ o sin ωt φ ( ) (1) (2) 2 1. lš yw

3 log( t r ) = log t ( ) c log η», log( E* )= w k», δ = minimum modulus ( )», α = range of possible value», β & γ = shape parameter», η, η Tr = qp 2 ùkù, γ w»» wš, β s w» (turning point) w. k x k (k, E 1 ) x (, E 2 ) w š, v t w Cole & Cole Plane Complex plane w. f k ƒ(phase angle) ùkü v Black space w. Black space ùkù w q k ƒ ƒ š, ƒ 0 k p. w - x AASHTO 2002 Design Guide dk w s x w wš, w s eƒ k. qp (viscosity) w yw (shift factor) wš, w qp yw k w (½ x, 2005). 3. x x { ( ) log( η Tr )} 3.1 x x ü r ƒ w qp yw 2. Shape parameter 26ƒ 3D œ 3 (7) y, qp AP-3 AP- w. x l AP-3 PG58-22, AP- PG64-22 y. qp yw td 13mm, td 19mm,»d 25mm w. 3.2 w qp yw w Superpave Level 1 w š, z» w. z» z y œ y d w 4% œ ƒ qp w w š, t 1 ùkü. x r z» w 150mm, 160mm mx r w z, g (coring)w 100mm, 150mm mx œ x r w. 3.3 k x x x»(utm) w k x k sƒ w x»(utm) w. k sƒ x w xw x Pellinen(2001) w w Simple Performance Test(SPT) ü ü x»» š w ü y w w. k x 5 5 w q w š, t 2 x, w x w. x k x k w w x p sƒw. qp yw p w (mobilizing the aggregate friction) w x p sƒ w. ù, yw xp sƒ q ƒ w y ƒ q. k x ƒƒ x r 5, 5 w q w x ww. x w x» wš, w {»ƒ qx k w. k q x š p w k ƒ r w x ww. x š, w q û w q xk yw ww. w -w q x x w x r w x (½x, 2005). (-10 t 1. qp yw w td 13mm (SGA-11) td 19mm (SGA-12)»d 25mm (BGA-11) qp PG (AA-1) PG (AB-1) PG (AA-1) PG (AB-1) PG (AA-1) PG (AB-1) qpw (%) G mm t 2. k xw x xw x ( o C) q (Hz) k x (µstrain) Dynamic Complex Modulus -10, 5, 20, 40, 55 25, 10, 1, 0.1, 0.05 x < 150

4 x t 3. w q d w w q z d ü r qw o C, 5 o C, 20 o C) 138kPa(20psi) 965kPa(140psi) w w š,» 965kPa w xp w w. š, 40 o C w 46-68kPa(7-10psi), 55 o C 21kPa(3psi) w. x w q y w q ¾ 60 {» w z xw. w x w q yw. t 3 x w q x d š x x» w ƒƒ qp yw k ƒ t 4 w. d k w d. ü wš qp yw ƒ w ù kü q. t 4. a td y 13mm + AP-3 (PG58-22) t 4. b td y 19mm + AP-3 (PG58-22) t 4. c td y 13mm + AP-5 (PG 64-22)

5 t 4. d td y 19mm + AP-5 (PG 64-22) t 4. e»d y 25mm + AP-3 (PG58-22) t 4. f»d y 25mm + AP-5 (PG 64-22) d 4.1 d qp yw k x šƒ x x w w., š w ù k x» DB d w v w sƒw. ü w w,» Witczak & Fonseca (1996) d» w, x w k d ù y w. 3» d xw w wù, š sƒ š, š sƒ. ü xk w ³ qp ³». š, Witczak d w w x z ƒ. x ü k x y w td yw (13mm, 19mm)»d yw (25mm) 2ƒ qp w», Witczak d ù w.,» 26ƒ 3D œ 5

6 4. d» x 3. Witczak d x Witczak d w x w, ƒ û wš, m mw w. t z w. Sigmoidal w x», w, x xkƒ w. 4 z w» w Sigmoidal w p w w w. D š w w š, q w š, w w ƒ D=f(P200, P4, Va, V beff /(V beff +Va)) w. A k cetipoiseƒ 12 ƒ p ƒ kƒ» ƒ., w A=f(P4, P38, P34) w ƒ. ƒ š»» E t 5. d k (10 5 psi) η qp,10 6 posie f V beff V a w q (Hz) z qp w (%) yw œ (%) P 34 19mm ƒ (%) P mm ƒ (%) P mm ƒ (%) P mm m (%) q w ƒ xk w tx. B=f(logf, logη). t 6 ü k x w td yw (13mm, 19mm)»d yw (25mm) w w» e, t 7 qp. d. (8) k x ù Sigmoidal w q l w, z w ù d. 13mm 19mm 25mm 2% 4% 6% 2% 4% 6% 2% 4% 6% t 6. qp yw» e no V a V beff P 34 P 38 P 4 P

7 t 7. qp p PG PG64-22 A VTS V eff ( V a ) log E * V ( P ) ( 200 P eff + V = + a ) P P P e ( log( f) * log( η) ) (8)», E* : k (105 psi)», η: qp (106 poise)», f: w q (Hz)», V a : œ (%)», V beff : z qp w (%)», P 34 : 19mm ƒ (%)», P 38 : 9.5mm ƒ (%)», P 4 : 4.76mm ƒ (%)», P 200 : 0.075mm m (%) d k x y w. t , ƒ t 8. d m R 2 t (MPa) t r (MPa) d x 6. d x ù. t t r MPa, MPa, , ù. ¾ w l t w, d f, 6 d x g sƒ. r r ƒ q ƒ 10Hz, 25Hz w š, 1.2 ù š 0.7~0.8 sƒ, š ƒ 0.8~ d d y g, d y. x ù qp yw» w š» d ƒ wd š w. 7 1, 4, 16, 25Hz 4ƒ q y k. k q ù w š, k ƒ w.»»ƒ w qp y w p ƒ k w. 8 w q k ùkü. ƒ w q k j w ƒ. w q - w lf 26ƒ 3D œ 7

8 7. dw k 9. œ d k 8. w q d k» w w. 7» w ƒ w w q ƒ yw ƒw o C 0.1Hz 16Hz w z qp w d k A VTS α log( + ) A VTS = ( 10 + log( + ) ) = 2.11 (9) (9) d ù w p ùkü w ù ƒ w. k ƒ œ z qp w y jš, w q 10Hz š wš,. ƒ œ ƒw k ƒ w. z qp w z qp w y w. ù, z qp w qp w Û0.6% w ƒ», 9 w ƒ ¼ j y w. 11 q 10Hz š k z, k y ùkü. t š ùkü P 200, P 4 j 25mm 19mm yw k, j» k P 38, P 34, P 4 j 25mm 19mm ƒw. ù, w k e w š w. 5. wz AP-3 AP- w td y qp y w (13mm 19mm) k x ww š, ¾ x l w.» Witczak d ù» ü x š, w xk» ü x w,» Witczak w (6) xk w. 1.2~1.3 šsƒ, š w š,

9 0.8 sƒƒ. ü x qp w w, ü x l w q. d» w ƒ» x l ù Sigmoidal w w wù, Sigmoidal w mw w q w ƒ ü» j w. d w q ƒ k ƒ j w, d w w», w q - w. w q w œ, z qpw, w ƒ j. ù, qp yw x w p tx. k d w, w x ù x ƒ w. ü k x ƒ wœ x ü 2~3œ ƒ w. ü x š w w x ƒ w. š, -10 o C¾ ü ƒ x w», x ƒ, d» ƒ ü w d ƒ w ƒ. d d 1000 ƒ ù, qp ƒ w, d ü qp s w. x d ƒ 80% w»» w y ü r, n w ƒ w. qp, (VTS : Viscosity Temperature Susceptibility) w ù, ü l w, ƒw w ƒ w w. qp yw y w w,» y» y w w d w w,»d yw ¾ w q y, mw s e q y w ƒ v w q m w x s s w w,. š x m (2002) w x s s, KPRP- -02, pp ½x (2005)»d qp yw k sƒ d, w, w y œw, pp. 60. ½x, y(2005) w qp yw k sƒ, w wz, w wz, 7«1y, pp Kaloush, K.E. (2001) Simple Performance Test for Permanent Deformation of Asphalt Mixtures, Ph.D Thesis, Arizona State University, pp Pellinen, T.K. (2001) Invesitgation of the Use of Dynamic Modulus as an Indicator of Hot-Mix Asphalt Performance, Ph.D Thesis, Arizona State University, pp. 788 Witczak, M. W., and Fonseca, O. A. (1996) Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures, TRB Record ( : / : / : ) 26ƒ 3D œ 9

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