19 19 1
1.. 3.
5cm 10cm 5 10cm :(Binder course Base course ) 5 10cm 5cm 5 0cm 10 0cm base course subbase course 1m 3
4 (Boussinesq Boussinesq, 1885), 1885) 1 ( ) θ π π σ 5 5/ 3 cos 3 3 z Q z r z Q z = + = ( ) ( ) + = + + + + = θ θ υ θ θ π υ π σ cos 1 cos 1 cos 3sin 1 3 3 5 / z Q z r z z r z r z r Q r ( ) ( ) ( ) + = + + + + 1 = θ θ θ υ π υ π σ cos 1 cos cos 1 1 3 3 / z Q z r z z r z r z Q t ( ) θ θ π π τ 4 5 / cos sin 3 3 z Q z r rz Q rz = + =
1901 1901 5
6 (Boussinesq Boussinesq 1885 1885 ) (Westergaard Westergaard 195 195 ) (PR PR ) 199 199 1940 1940 (Hubbard (Hubbard 1940 1940 ) Poeter Poeter 194) 194) CBR CBR (Burmister Burmister 1943 1943 ) (Burmister Burmister 1945 1945 ) 3 (Odemark Odemark 1949 1949 ) (Fergas Fergas 1950 1950 ):CBR ):CBR 1955 1955 WASHO WASHO 196 196 AASHO AASHO
1955 CBR 1964 CBR (1967 ) 1967 3 (1967 (1967 1969,197 7
Hubbard (1940 AI ) 1.5cm 1.5cm 1/ 5mm 5mm 0.35kgf/cm 0.7kgf/cm 3 8
CBR Porter 1930-194 CBR A 8.t B (Corps of Engineer, CE) 9
CBR CBR CBR A (1943 (1943 ) 4.kgf/cm 4.kgf/cm 0% 0% 10
CBR CBR 4.1tf 4.1tf B.7tf 11
CBR CBR (Corps of Engineer, CE) A 5.4t 4.kgf/cm 1
13 CBR CBR (1) (1) ( ) α σ 3 3 / 3 3 / cos 1 1 1 1 1 1 = + = + = p a z a z p z a p z 3 1 1 cos 1 + = = a z p σ z α Z>a
CBR () CBR CBR p CBR 0 z z CBR z CBR CBR z 0 σ z = p = 1 cos σ z = k CBR z k CBR p z = 1+ 1 z a 3 α = 1+ 1 z a z a = p 1 k CBR z h h = a k p CBR 1 14
CBR (3) P p a P= a p h = P 1 π k CBR 1 p k CBR in lb k=8.1/ 1 1 A a h = P 0.57CBR πp p 1 h = A 0.57CBR π 1964 1964 P 10 6 P h = 46.8 ( 1+ 5logCBR) CBR 1965 0.4 58.5P H = 15 0.6 CBR
CBR (4) AASHO CBR3 H = 58.5P CBR 0.4 0.6 16
17 Palmer Palmer Barber) Barber) Boussinesq Boussinesq (E) (a) (p) (z) ( ) 1/ 3 z a E pa w + = P p a P= a p 3 a Ew P H = π
Palmer Barber) 3Pm n H 3 = πc ω a C C p (H) P(4100kg) (m) (n) (C) (Cp) kgf/cm.5mm C 3 barber, C p z 1/ 3 E1 Z = H E 18
(Shell (Shell 1963 E(kgf/cm )=30,530,710,1060,1770 (CBR 3,6,8,1,0% ) 5 As 19
(Shell (Shell 5tf As ( CBR ) 1967 As T A E(kgf/cm )=30(CBR 3% ) T A = 10 log N LogE + 13 3 0
1967 1967 0 ( / ) 000 / 000-7500 / 7500 / 10 6 1960 1967 1
1967 1967 5t 5t 5
3 1967 1967 P 5t 5t 4 10 10 6 10 365 10 5 6 4 = a N P 4 4 5 3 1. 10 365 5 a N a N P = P (t) (t) N 5t 5t / a 5 1.5 1.5
1967 1967 3 67 67 4 CBR CBR CBR 100cm CBR = n i= 1 { ( ) } 3 1/3 h i CBR i 100 h i i (cm) CBR i i CBR %) CBR = CBR m CBR n 1 ( σ ) CBR CBR-CBR 16% 16% COE /3 5% 5% 4
1967 1967 H = 58.5P CBR 1.5P T A = CBR 0.4 0.6 0.64 0.3 H (cm) T A cm) P (t) CBR CBR (%) AASHO AASHO 5
τ z p 3 4 = 3 z 1 + a z z a p z a (kgf/cm ) (kgf/cm ) (cm) (cm) 80% 80% h=1.5 a 6
JH ( ) JH 7
JH ( ) 10t 10t 1 1 3 1 1 80% 80% t 8
JH ( ) T A T A 10t 10t T A ( CBR=3 ) 9
JH ( ) CBR CBR T A CBR3 CBR3 CBR T A 10t T A 30
( max) 8 cm T 50 5 50 T 1,000 10 5 1,000 T 3,000 15 10 3,000 T 0 15 1 3cm 31
ω f π ω = r ( 1 ) υ = E ( 1 υ ) E pa E : (MPa) p : (kpa) : a : (m) : (mm) pa 3
(SN) ESAL h 33
400 AI 41mm AASHTO H AS 0 1.7 87.3% 34
400 50% 50% A B C 90% 90% 35
36
49kN 37
1 3 4 5 6 7 8 9 10 11 1-4.1-3.5 0.1 6.7 1.1 16.3 0.5.0 17.6 11.3 4.6-1.0-0.9-0.3 3.5 11.1 17.0 1.1 5.0 6.1.0 15.8 8.1.1-1. -0.4 4.9 15.5 3.8 9.5 35.0 36.5 30.8.1 11.3.9 1 3 4 3 1 1 3 4 ( ) 0 10 0 30 1,,3,1 4,11 5,6,10 7,8,9 (MPa) 16,000 9,000 4,800,800 As (MPa) 9,000 6,000 3,300 1,400 4 38
N fa { ( )( 0.854 )} 5 3.91 18.4 C 6.167 10 ε = S E A t N fa 49kN A C C = 10 M M M = 4.84(V /(V b b +V v )-0.69) V (%) b V v (%) t (MPa) V b ( %) = (%) C (g/cm 3 ) ( %) ( %) (13).400 3.5 5.8 13.7 3.6 (13F).40 3.4 6.0 13.8 3.47 (0).350 4.5 5.0 11.5 1.38.300 6.5 4. 9.5 0.34 As.338 6.1 4.0 9.0 0.35.356 7.0 4.3 9.8 0.31 39
1) E Asleq = h 1 E 1 3 1 h 1 + he + h 1/ 3 3 Asleq (MPa) (MPa 1 MPa) (MPa MPa) h 1 (mm) h (mm) 40
N { } 9 4.477 1.365 10 ε fs = S s c N fs 49kN c S 0% 0% 15mm 41
AASHTO 4
(1948 ) 3 1948 5 1950 43
44
9 1954 30 1955 31 (1956 ) Reports on Kobe-Nagoya expressway survey-1956 by Ralph J. Watkins The roads of Japan are incredibly bad. No other industrial nation has so completely neglected its highway system. 45
38 1963 71km 39 1964 47 55 59 44 1969 13 001 46
33 1958 10 5 47
or 48
Arlington 1936 1956 USA 49
50
51
Westergaard K 75 ) 5
K 75 ) 53
K 30 ) 54
K kgf/cm 0 P 0.15cm (1.5mm) K =P/w K 75 75cm K K 30 30cm w 55
K 75 cm 75cm 56
K 75 K / K 75 6 5 4 3 1 0 75 75cm 0 50 100 150 57
B,C,D K 30 0 kgf/cm /cm L,A K 30 15 kgf/cm /cm K 75 7.0 kgf/cm /cm K 30 K 75 K 75 Westergaard K 75 K 30 /. K 75 K 30 /.5 197 58
CBR K30 1984 cm 60 50 40 30 0 CBR (%) 3 4 6 8 1 K30 (kgf/cm 3 ) 4 5. 6 7.5 9 11 p k1 h1 a E1, v1 k 10 0 0 1 3 4 5 6 k1/k Ef, vf h= E, v Burmister 59
(1) () 60
61
1990. 6
σ = Westergaard (196) ( + υ ) 3 1 P l (ln + πh b 0.6159) P h Co. b a: a 1.74h b=a a<1.74h b= 1.6a h 0.5-0.675h 63
Westergaard l = 4 3 Eh 1 K ( 1 υ ) 75 E Co. Co. 64
Westergaard 3 P Eh ( 1+ 0.54υ ) log 0. σ = 0.59 71 10 4 h K 75b Teller & Sutherland 1935 σ = 0.59 1 079 10 4 10 h K75b 1 υ 3 P Eh b ( + 0.54υ ) log + log 1. a 1.74h b=a a<1.74h b= 1.6a h 0.5-0.675h 65
( N,mm ) P (log10 l 0.75log10 a σ = ( 1+ 0.54υ ) C L h 100 0.18) C L (.1, 1.59) Teller & Sutherland 66
67
σ t = 0. 35 C w α E θ C w E T B T S T S -T B 68
( ) ( ) bk 69
1) bk ) bk FD = k i= 1 n N i i FD 1.0 n i i / bk N i i 70
1 0.9 0.8 0.7 0.6 1 0.9 0.8 0.7 0.6 Pf=10% Pf=0% Pf=5% Pf=30% Pf=40% Pf=50% 0.5 1 100 10000 1000000 0.5 1 100 10000 1000000 10000000 71
1tf N 1 tf N 3tf N 3 4tf N 4 5tf N 5 6tf N 6 7tf N 7 8tf N 8 9tf N 9 10tf N 10 1tf N 1 14tf N 14 19 Tp 19 17 Tp 17 15 Tp 15 13 Tp 13 11 Tp 11 9 Tp 9 7 Tp 7 5 Tp 5 3 Tp 3 1 Tp 1-1 Tm 1-3 Tm 3-5 Tm 5-7 Tm 7-9 Tm 9 15cm 45cm 75cm 105cm f15 f45 f75 f105 Temp>0 Rp Temp<0 Rm FD<1.0 OK 7
50, 75, 90 50 1 75 90 4 AASHTO Guide for Design of Pavement Structures(1986) 73
( ) 1 8,000 / 30% 5% 65% 4% % CBR 6% P9, P30 P30 T A 74