26ƒ 3D Á 2006 5œ 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 72 86 š š, w TA wš. v w * z w y œw (E-mail : khlee@ks.ac.kr) ** w y œw (E-mail : kho1052@hotmail.com) *** w y œw (E-mail : jms03010@hotmail.com) 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 2006 5œ 1
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,. 1974 Witczak Root - x w š phase angle j w tw. 1977 Bonnaure bending x w k sƒ w. r Õ xk w š, q w w. 1980 1990 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. 1990 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 2002. 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 + ----------------------------------- 1 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
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 2006 5œ 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 3.3.1 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 58-22 (AA-1) PG 64-22 (AB-1) PG 58-22 (AA-1) PG 64-22 (AB-1) PG 58-22 (AA-1) PG 64-22 (AB-1) qpw (%) 5.2 5.3 5.1 5.1 4.3 4.5 G mm 2.462 2.458 2.475 2.468 2.481 2.487 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
x t 3. w q d w w q z d ü r qw 25 200 95-200 10 200 95-200 5 100 95-100 0.1 20 15-20 0.05 15 10-15 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. 3.3.2 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) 5 0.05 7874.3 10.72 6928.0 10.75 6589.0 9.64 0.1 8052.7 9.60 10663.0 10.21 6971.5 9.49 1 9108.0 6.65 8098.0 6.31 8032.0 6.91 10 9539.3 4.44 8370.3 4.50 8544.0 4.27 25 9265.3 3.94 8170.7 1.79 9498.5 5.88 0.05 5209.0 15.78 4662.0 15.91 4416.7 16.68 0.1 5566.3 12.66 4917.7 14.01 4694.3 15.21 1 6748.3 8.62 6060.3 10.30 5729.3 8.72 10 7735.3 6.55 6833.3 7.65 6668.3 7.16 25 7975.3 4.15 6964.7 4.35 6632.3 5.68 0.05 2479.3 26.50 2196.3 26.44 1957.0 27.02 0.1 4202.5 24.11 2150.7 24.96 2188.3 25.38 1 4111.3 14.78 3672.0 16.69 3342.3 16.29 10 5178.7 11.85 4802.7 10.37 4582.7 11.92 25 5977.0 12.06 5411.0 10.56 5013.0 11.91 0.05 739.0 18.35 715.0 19.37 653.0 20.85 0.1 818.0 19.32 791.3 19.79 739.7 20.55 1 1229.0 20.81 1143.0 19.52 1023.7 18.05 10 1948.3 21.28 1828.7 17.52 1574.3 21.61 25 2369.3 19.80 2108.3 14.12 1874.7 16.52 0.05 326.7 12.43 302.7 14.46 274.0 12.26 0.1 324.0 13.25 323.7 14.63 292.3 13.58 1 426.3 15.69 433.7 16.73 552.0 16.27 10 679.7 22.19 652.3 22.88 563.7 20.45 25 857.0 16.06 834.3 27.23 677.7 20.13 t 4. b td y 19mm + AP-3 (PG58-22) 5 0.05 7288.7 11.17 6821.7 10.70 7742.7 10.64 0.1 7495.7 10.33 7055.0 9.27 8110.3 9.55 1 8700.3 7.01 7893.0 6.42 9215.7 7.47 10 9245.7 5.46 8532.7 4.21 9757.3 5.07 25 8619.7 3.28 8515.7 3.58 9730.7 2.93 0.05 4539.0 16.10 4140.3 16.55 4525.7 17.61 0.1 4744.3 15.22 4341.3 14.58 7168.0 14.86 1 6038.7 9.09 5318.3 9.47 8989.0 10.69 10 6425.3 6.06 5834.0 6.17 10276.0 7.37 25 6601.3 5.09 5742.0 3.71 10454.0 5.08 0.05 2233.7 27.22 1926.7 26.61 1948.3 26.51 0.1 3815.5 25.75 2171.7 25.01 2215.7 24.94 1 3816.3 16.71 3228.7 16.45 3408.7 15.96 10 5245.3 11.50 4303.7 11.26 4528.7 13.13 25 5603.3 13.26 4513.0 10.55 5017.0 12.37 0.05 755.3 18.04 702.0 20.24 706.3 19.97 0.1 825.7 17.98 757.3 19.93 776.7 18.64 1 1183.0 17.02 1061.0 17.88 1086.0 17.79 10 1834.3 19.12 2432.0 16.53 1702.0 16.18 25 2165.7 15.16 2894.0 17.63 1999.0 17.98 0.05 322.3 11.19 301.7 19.08 282.7 11.70 0.1 344.0 13.27 313.3 13.53 293.7 12.93 1 427.3 16.41 403.7 15.71 539.5 14.97 10 640.3 28.33 577.0 21.12 511.3 19.94 25 796.0 23.88 733.0 21.28 616.0 18.09 t 4. c td y 13mm + AP-5 (PG 64-22) 5 0.05 9035.7 8.85 8253.0 7.90 7299.7 9.30 0.1 9291.3 7.67 12769.0 7.71 7547.3 8.29 1 10068.7 5.52 14170.0 5.81 8528.3 4.90 10 11050.3 3.47 15863.5 3.82 8784.0 4.75 25 10275.3 3.55 15445.0 5.03 8931.0 3.12 0.05 5536.7 15.01 5050.7 15.72 4485.3 15.55 0.1 5689.7 13.63 5413.0 13.95 6975.5 14.35 1 7028.0 9.32 6701.7 8.36 8480.5 9.02 10 8226.7 6.04 7496.3 6.79 10127.0 7.16 25 7683.7 5.31 7734.3 6.04 9983.0 4.88 0.05 2426.7 25.61 2293.3 25.58 1982.0 27.05 0.1 4141.0 24.00 2545.0 24.36 2254.0 24.45 1 4253.7 16.14 3869.7 15.24 3372.3 16.60 10 5937.3 10.01 4923.7 11.10 4475.7 11.86 25 5961.7 8.04 5337.7 11.74 4968.7 13.23 0.05 855.0 18.19 770.7 20.90 738.0 23.27 0.1 856.3 19.94 870.0 21.53 825.3 22.34 1 1401.0 18.86 1327.7 19.45 1279.0 18.25 10 2340.0 19.87 3087.0 20.00 1967.3 16.98 25 2807.7 17.47 3895.0 17.85 2190.7 17.57 0.05 341.0 9.91 324.7 13.05 317.7 13.78 0.1 357.0 12.27 342.3 14.27 327.0 14.52 1 469.0 15.94 468.3 18.35 694.0 18.15 10 726.3 20.99 727.7 19.16 712.3 22.25 25 891.0 21.77 933.0 22.79 908.3 23.51 4
t 4. d td y 19mm + AP-5 (PG 64-22) 5 0.05 8732.0 8.10 8299.3 8.09 7641.7 8.52 0.1 8876.7 7.77 8635.3 8.28 7803.7 8.16 1 9901.0 5.31 9372.7 5.94 8741.7 6.23 10 10263.7 3.88 10031.0 4.49 9271.0 4.14 25 10025.3 4.01 9983.0 2.53 8972.7 1.97 0.05 5666.3 13.33 5298.7 14.65 4780.7 16.85 0.1 9043.0 11.93 8520.5 13.68 7886.0 15.53 1 7047.3 7.26 7113.0 8.60 6350.3 9.44 10 8045.3 5.98 7787.7 6.24 7291.3 6.89 25 7823.3 6.27 7536.0 6.63 7359.0 6.77 0.05 2706.0 24.29 2351.7 25.75 2173.0 26.45 0.1 3140.3 23.78 2669.0 23.95 2474.3 24.22 1 4463.3 14.23 4004.7 15.36 3679.3 15.33 10 8419.5 8.78 5241.3 11.04 5084.3 11.12 25 6286.3 11.07 5575.0 8.18 5820.3 9.98 0.05 940.0 19.57 881.7 21.03 1262.0 19.97 0.1 1036.0 19.53 975.0 19.55 1365.5 21.09 1 1564.3 16.80 1453.0 17.13 1306.0 18.44 10 2482.7 17.22 2267.0 22.13 2030.7 19.75 25 2670.0 17.85 2443.0 18.86 2312.3 19.46 0.05 394.7 12.82 379.3 13.38 367.3 11.64 0.1 410.7 12.68 402.3 11.69 393.7 12.19 1 788.5 17.30 540.0 17.59 743.0 15.20 10 846.0 22.42 818.3 23.10 714.7 15.92 25 1087.3 24.89 1004.7 10.11 853.7 21.57 t 4. e»d y 25mm + AP-3 (PG58-22) 5 0.05 8042.3 7.48 5546 9.95 7788 10.76 0.1 8066 8.72 5658.5 10.36 7920.7 9.7 1 8387.7 6.26 4161.3 4.89 9011.7 5.22 10 9672 7.14 6563.5 13.9 9114.7 3.41 25 9157.3 7.61 5983.5 0.75 9312.3 3.91 0.05 6698 8.98 4955 12.6 5241 15.91 0.1 5472.3 11.17 5172.5 12.6 5629.7 14.31 1 6375 7.14 5864 9.2 6582 10.11 10 6678.3 4.39 6365.5 3.2 7380.3 6.27 25 6335 3.32 6203 3.1 7327 6.43 0.05 2823.3 23.2 2044.5 23.8 2647.3 24.3 0.1 3032.3 21.24 1519.7 23 2992.3 22.9 1 4127.7 14.43 3030 14.9 4069 12.25 10 4974.7 10.15 3778.5 12.2 5216.3 9.8 25 4585.3 13.24 3499 11.8 5596.3 6.7 0.05 829.3 17.1 720.5 17.5 802.3 16.3 0.1 931 17.2 777 18.2 866.7 17.3 1 1294 17.1 1077.5 17.4 1205.3 17 10 2091 17.4 1653.5 17.5 1747.7 18 25 2413 17.8 2002 22 2098.3 18.7 0.05 342.3 14.8 332 17.1 327 12.5 0.1 384 15.1 369.5 18.8 333 12.4 1 522 17.8 527.5 18.4 452.7 17.6 10 781 21.8 756 22.9 660.3 20 25 933 23.4 932 21.8 711 20 t 4. f»d y 25mm + AP-5 (PG 64-22) 5 0.05 6707.7 9.23 6522.3 9.96 5900 11.16 0.1 6863.7 9.02 6684.0 9.10 6018.5 10.30 1 7434.3 5.85 7516.3 4.83 6802.5 6.14 10 7710.3 2.27 7672.0 2.33 7300 3.37 25 7641.0 2.25 7581.3 2.48 7048 3.87 0.05 4511.3 11.94 4559.3 13.49 3644 15.29 0.1 4620.3 10.78 4716.7 12.02 3891.5 13.48 1 5233.7 6.5 5463.7 8.81 4685.5 8.88 10 5667.7 5.74 5973.3 6.58 5216 7.38 25 5590.0 5.84 5694.3 6.17 5235 4.65 0.05 2306.7 21.55 2205 23.45 1739.5 26.54 0.1 2545.0 20.47 2476.7 22.39 1929 24.33 1 3468.0 12.65 3495.3 14.81 2867.5 10.13 10 4203.0 8.99 4366.0 9.43 3552.5 12.01 25 4384.0 11.87 4464.0 7.57 3519.5 9.33 0.05 934 19.12 901.3 17.99 740 22.34 0.1 1029.7 18.1 969.7 19.50 798 20.07 1 1489.0 16.33 1382.0 17.76 1133 18.78 10 2175.0 15.13 2107 16.04 1688 18.23 25 2507.7 13.22 2232.7 17.85 1840 16.73 0.05 326 20.06 359 12.95 290 12.42 0.1 444 14.85 416 17.45 334 15.1 1 559 49.15 600 17.71 491.5 15.9 10 950 18.5 833.3 18.6 690.5 17.7 25 1302 27.02 999.3 1592 848 18.49 4. 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 2006 5œ 5
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 2.7 10 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 38 9.5mm ƒ (%) P 4 4.76mm ƒ (%) P 200 0.075mm 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 200 1 2.212 9.8 0 16.2 32.5 7 2 2.467 9.8 0 16.2 32.5 7 3 2.117 9.8 0 16.2 32.5 7 4 4.268 9.6 0 16.2 32.5 7 5 3.795 9.6 0 16.2 32.5 7 6 4.13 9.6 0 16.2 32.5 7 7 6.573 9.4 0 16.2 32.5 7 8 6.137 9.4 0 16.2 32.5 7 9 6.036 9.4 0 16.2 32.5 7 16 2.436 9.7 2.5 24 45 5 17 2.375 9.7 2.5 24 45 5 18 2.562 9.7 2.5 24 45 5 19 4.363 9.5 2.5 24 45 5 20 4.321 9.5 2.5 24 45 5 21 4.768 9.5 2.5 24 45 5 22 6.396 9.3 2.5 24 45 5 23 6.463 9.3 2.5 24 45 5 24 6.306 9.3 2.5 24 45 5 31 1.654 7.8 13 35 51 4 32 1.568 7.8 13 35 51 4 33 1.591 7.8 13 35 51 4 34 3.687 7.6 13 35 51 4 35 3.589 7.6 13 35 51 4 36 3.571 7.6 13 35 51 4 37 5.561 7.4 13 35 51 4 38 5.571 7.4 13 35 51 4 39 5.689 7.4 13 35 51 4 6
t 7. qp p PG 58-22 PG64-22 A 10.896-3.717 VTS -3.658 11.067 0.828V eff 0.0823( V a ) --------------------- log E * V 1.25 0.016( P ) 0.0031( 200 P eff + V = + a ) 4 3.851 0.0021P + 4 0.00361P + 38 0.00611P 34 + --------------------------------------------------------------------------------------------------------- 1 + e ( 0.65 0.241log( f) 0.191 * 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 8 0.899, 0.810 ƒ t 8. d m R 2 t (MPa) t r (MPa) 0.810 53.86 2482.34 0.899 0.00088 0.406 5. d x 6. d x ù. t t r 53.86 MPa, 2482.34MPa, 0.00088, 0.406 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 0.8~0.9. 4.2 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 2006 5œ 7
7. dw k 9. œ d k 8. w q d k» w w. 7» w ƒ w w q ƒ yw ƒw. 8 21 o C 0.1Hz 16Hz w -2.. 10. z qp w d k A VTS 70 459.6 α 1.037 10 + log( + ) A VTS 40 459.6 = ( 10 + log( + ) ) = 2.11 (9) (9) d ù w p ùkü w ù ƒ w. k ƒ -. 9 10 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, 8 11. 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,
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. 2003 m w x s s w w,. š x m (2002) w x s s, KPRP- -02, pp. 142. 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. 49-61. Kaloush, K.E. (2001) Simple Performance Test for Permanent Deformation of Asphalt Mixtures, Ph.D Thesis, Arizona State University, pp. 413. 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 1540. ( : 2005.7.5/ : 2005.8.19/ : 2005.10.10) 26ƒ 3D 2006 5œ 9