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1 YWXZ º º t rzyywxzhzx^ ƒ p Ž ± v x¹vƒ Prediction of Permanent Deformation for Design in Asphalt Trackbed Foundation ú ã äø ù ãã ä Ô ãã ä ãã Byeongsik Lee *, Jaebeom Park **, eunwoo Song **, Yujin Lim ** Abstract In this study, permanent deformation of asphalt trackbed is investigated by performing repetitive load test on specimen made with dense graded asphalt mixture that is prepared specially for the track. The obtained test results are compared with those computed from the prediction model proposed byaashto in 2002 called MEPD. Prediction model adaptable only for permanent deformation of asphalt trackbed foundation has not been developed yet so that the prediction model by AASHTO is used in this study to simulate permanent deformation of trackbed foundation in asphalt slab track and ballasted asphalt track. In order to do simulate permanent deformation, a finite element analysis is performed to obtain generated stresses in trackbed due to wheel load. It is found that the predicted permanent deformation is much smaller than anticipated and the asphalt track can be stable during service life of the structure. Keywords : Asphalt Trackbed, Permanent deformation, Finite Element Analysis ïy ƒ Ž ± v s m, v m w ƒ 19mm v Ž ± ¹ t ˆ³ x¹ˆ x¹ vƒ ƒ zƒ. x¹ˆ AASHTO 2002 v ¹ ³ ƒ x(kprp) ƒ ˆ x¹ ˆ, zƒ. ¹ v ¹ t x¹ ˆ v v um AASHTO Žˆ v Ž ± zƒ ˆ vƒ x¹k. p ƒ ˆˆ, x vƒ l» vƒ x¹k. ƒ k v, ƒ ºy m ±. Ž ± v x¹ ƒ ää ï º q º yˆƒ ½ v ³ w Ÿk k Ž Ÿ z v mz r ± pd Ž ƒ et Ÿ Ž ƒ q zz Ò : ø á Ò ÑÑá Ð Ñ ãñ Ñ(passion@pcu.ac.kr) * á à ò, ø á Ò ** ø á Ò ÑÑá Ð Ñ ãñ Ñ

2 y ƒ Ž ± vƒ x ƒ x¹ s p Ž ± v ¹ t w ƒ p v«m ¹ t ˆ³ y ˆ ˆˆ, ƒ. y ƒ p ˆ³ m vy ˆ ˆˆ ˆ mz ºd x¹ p m³ zž ƒ Ž ± ³ x¹ v AASHTO 2002[1] v ¹ ³ ƒ x[2] x¹ ˆ Ÿ,. p v v Ž ± ¹ t x¹ vƒ ƒ. g 3D ƒ Ž ± x x¹o vƒ± x m ˆ Ž ± v vƒ x¹ vƒª p. ääýø ö Óú ô äää ø ö Óú ô x¹ s v l ˆ, ½Monismith[3] powers n x¹o( p ) vy º (N) p ˆ(1) ¹. = A b N (1) p Ž ± ¹ tm ƒ ƒ ³ p x¹ º½ Ž. powers Ž ± ¹ t x¹ s m v ˆd p. AASHTO 2002 ƒ x ƒ Ž ± x¹ ˆ(2) x¹ ˆ. p r = 10 T N (2) ˆ(2) ƒ ºyx¹o x¹o Ž ± (T) º (N), 2 x p. ˆ(3) ¹ ³ ƒ x ƒ ˆ ˆ m ºyx¹o x¹o p Ž ± ¹ t, º v o (V a ) 3 x p. g ¹ tx ˆ (A, B, C, D)p. p r = 10 D N A T B V c a (3) äää Õ ÑñÑî Óú ô AASHTO 2002 MEPD ƒ LTPP m k n(v «m, MnRoad)p º, y k 1 [4].

3 p r = k 10 T N (4) ƒ k depth (C 1 +C 2 depth)m depth x¹o (inch), C h ac h ac , C h ac h ac , H ac Ž ± (inch). ˆ(5) Ž ± «ƒ Hooke x ºy«ƒx¹o» ˆ(4) x¹o. x¹o r x¹k ˆ(6). ˆ(5) «ƒ (E ) ¹ t * n ƒ, v ±. rz 1 = ( σ νσ νσ ) (5) * z x y E ƒ, rz = w ºyx¹o E * = Ž ± «ƒ σ x, σ y, σ z = ¹ t x, y, zw l ν = Ž ± ³Ž n RD = ( ) p h i i i= 1 (6) ƒ, RD = x¹k(inch or mm) i = Ž ± w¹ n = Ž ± p-i = x¹o h i = Ž ± (inch or mm) ääýø ö ð ø ü äää ö ð v Ž ± ¹ t nm AP-5( Pen. 60~80, P 64-22)p yv m. ƒ ƒ ƒ º xƒž m Ž ± ¹ t w ƒ [5] ƒ v 19mm¹ t w m ˆ WC-4 p s p x ƒ. Ž ± ¹ t WC-4, ˆ³ ª D=100mm, H=75mmm pƒ v ƒº ˆ p. pƒ Ž ˆ KS F 2337 ek ˆˆ ˆ wx ¹ ˆ 5 p 60 50mm/min m ˆ ± ˆ Ž pƒ Ž ¼

4 pp. ˆ pƒ Ž ˆ ˆ v p r, 25 m ˆ. ˆ Fig. 1 m³ v ¹ t(wc-4) ( :750kgf, :800kgf, y:500kgf) y ª ³. ekƒ ˆ y ƒ w ƒ ¹ t v m m ±. g z l ƒ o 75% ºy Ž. (a)marshall Compaction Test Result (b)indirect Tensile Strength Test Result Fig. 1 Asphalt mixture Mechanics Test Results äää Óú ÑÑ þò x¹ ˆ ˆ³ D=70mm, H=100mm ¹ m NCHRP Report 465 vy ˆ wx, Ÿk vª l ¼ p m Haversine±p. Ž 138kPa, l 370kPam. ˆ Fig. 2(a) 60 ƒ ¼p zr½ º, 30, 45 ƒ 50,000º ˆ x¹o Ž ( x¹o : 30 d0.5%, 45 d0.1%) r x¹ vƒ Ž m ± Žv x ¹p. Fig. 2(b), (c), (d) AASHTO 2002 v ¹ ³ ƒ x ƒ ˆ x¹ s y ƒ ˆ v 19mm ¹ t ˆ³(V a = 3%) vy Ž ˆ mz ºd x¹ˆ p v zƒ. AASHTO 2002 ˆ KPRP v y ƒ ˆ vyˆ q ª ³ Ž. (a)permanent Deformation Test Result (b) AASHTO, KPRP and Test Measured Result(30 )

5 (c) AASHTO, KPRP and Test Measured Result(45 ) (d) AASHTO, KPRP and Test Measured Result(60 P Fig. 2 Compared Permanent Deformation Prediction: AASHTO, KPRP and Measured Test Results äää Ýø Û î Ð Ž ± ƒ ƒ m k ABAQUSp. q ƒ Fig. 3, z v ƒ x n ntƒ Table 2. (a)asphalt Slab Track Modeling and Finite Element Mesh (b)ballast Asphalt Track Modeling and Finite Element Mesh Fig. 3 3D Finite Element Analysis Modeling and Mesh l 157kN r sd ƒ ƒ¹ «ƒ m. g v Ž ± m x l beam, ±d Spring, s v v Solid m ƒ. Table 1 Asphalt Track Properties of ABAQUS FEA Model Input and Material Parameters Element Rail Pad Sleeper Ballast Asphalt Trackbed Subgrade ρ(ton/m 3 ) Elastic Model E 210Pa 40kN/mm 29.1 Pa 100 MPa 3 Pa 180 MPa 125 MPa ν

6 «ƒ m ƒ mz Ž ± x¹ Ž ± v l. ºd l Table 3. Table 2 Calculated Stresses for Asphalt Trackbed Division Asphalt Slab Track(kPa) Ballast Asphalt Track(kPa) x y z x y z Stress Result ˆ (5)p «ƒx¹o ˆ, p l Ž ± v «ƒ p (30 = 2Pa, 45 = 1Pa, 60 = 0.8Pa) r p ƒ. Fig. 4 AASHTO 2002 x¹ ˆ(ˆ (4)) v Ž ± ƒ m l º x¹o p, vy ˆ m z ºd x¹. xm ˆ 30 ƒ x¹ o ˆ ª py vy º m º pvy ˆ ˆ ¹ t v l º½s s um tp (a)compared Asphalt slab track N - p with Temperature (b) Compared Ballast Asphalt track N - p with Temperature Fig. 4 Compared permanent deformation Predicted by AASHTO and FEA Result (N - p ) äääã Ñ ú Ï Ñ ô æñ Óú í Table 3 «ƒ xºp v AASHTO2002ˆ, ƒ r( )x x ¹o,. ƒ r Ž º mƒ ˆ ƒ º Ÿ. l Ž ± ¹ t 60, ƒ r 60 k x¹k k 5mm 50% 2.45mm z Ž.

7 Table 3 Predicted permanent deformation with change of temperature at the end of design life Division 20 Years 40 Years 60 Years mm mm mm [\ mm mm mm ]W mm mm mm Ž ± v «ƒ p x m ƒ ƒ ˆˆ nz Ž ± v l. Table 4 ƒ Ž ± x «ƒ p p. Fig. 5 l «ƒ p º Ž ± v x x¹o vƒ±. Table 4 Seasonal temperature and dynamic elastic modulus Season Dynamic Elastic Modulus(Pa) Temperature( ) Spring 6 15 Summer Fall 4 20 Winter 12 0 (a) Permanent deformation for 20 years (b) Permanent deformation for 40 years (c) Permanent deformation for 60 years Fig. 5 Expected permanent strain variation with depth of asphalt trackbed at representative dynamic modulus Žƒ ƒr v p m x¹k ƒzºˆ«xm x¹o( p )» p s x x¹k. x¹k ƒ Ž ± v x «ƒ ƒ r vy º p r Ž. x¹k Ž ± v ƒ r( ) Ÿ [6] ƒ½. e x¹k m (1) x Ž ± ¹ t «ƒ (E * ) (2) ¼ v «ƒ (E s ), (3) (P), (4) (MT) v (5) º (N) d v.

8 p, s r Ž ± v Ž(Ž 450kPa) Ž ± m³ ƒ ˆ «Ž(680kPa)y et x¹k(rd) wx y m. (ƒ r) vy º N ˆ(7). N = MT (20,40,60 4 P Year) p (7) ƒ, MT = (10,000,000ton), p = x (10kN), P = (KTX =153kN) ääñï y ƒ x¹ˆ ««ª v ¹³ ƒ x ªªªª ƒ ˆ x¹ ˆ zƒ ¹ v ¹ t x¹ ˆ v v um ««ª Žˆ v Ž ± zƒˆvƒ x¹k p ƒ ˆˆ xvƒ l» vƒ x¹k ƒ k v ƒºy m±. Õ t ƒv ƒ v º Ž ± vv v vž ƒ tm ƒ dp Ñö [1] AASHTO (2002) 2002 Design uide of New and Rehabilitated Pavement Structures, Research Report, National Coopertative Highway Reasearch Program, USA. [2] Ministry of Land, Transport and Maritime Affairs(2011) Korea Pavement Research Program. [3] C. L. Monismith, N. Ogawa, C. R. Freeme (1975) Permanent Deformation Characteristics of Subgrade soils due to Repeated Loading, Transportation Research Record, (537), pp [4] R. B. Leahy (1989). Permanent Deformation Characteristics of Asphalt Concrete, PhD Dissertation, University of Maryland. [5] Ministry of Land, Transport and Maritime Affairs(2005) Hot mix asphalt design guidelines. [6] B. S. Lee (2012) Analysis of Dynamic Modulus and Permanent Deformations in Asphalt Mixtures for Design of Asphalt Trackbed Foundation, Master s Thesis, Paichai University.