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1 565-0871 2-1tanimoto@civil.eng.osaka-u.ac.jp
565-0871 2-1tsusaka@civil.eng.osaka-u.ac.jp
162-8557 2-1ymitaras@ku.kumagaigumi.co.jp
Key Words : loosening, tunneling, strain-softening, convergence, support pressure, non-elastic zone
1.
NATM1 The New Austrian Tunnelling MethodNATM 30
L. Müller2
NATM
NATM
2
1978Convergence-Confinement Method
3 4 - 6
Hoek & Brown7
8 - 10
11
Hoek & Brown7
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440
12 - 14
15 - 17
FEM
18 19)
20
Brown21
22
23 24
25
26
3C 2
8 27 28
pi
100
pi
pi
70
Is28 29
2.
p0
a
pi
p0
pi
W1 W2
Wp
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
441
0.1, 0.2, 0.3, 0.4, 0.5
q u (MPa) 0.3, 0.9, 1.5, 2.1, 3.0
(°) 5, 10, 20, 30, 40
q u'/q u 0.1, 0.3, 0.5, 0.7, 0.9
'/ 0.1, 0.3, 0.5, 0.7, 0.9
E (MPa) 50q u, 100q u, 150q u, 200q u, 300q u
(MPa) 0.2E, 0.5E , 1.0E , 2.0E, 5.0E
ABCD
pi rr=Wp r(r=Wp)
t(r)
r(r=Wp)
pi
p0
, pi
Wp pi
pi r(r=0)
AB r(r=Wp)
t(r)
pi
8 27
pia
p0
p0
A B
CD
OW1 W2
p0
p0
r(r=Wp)
t(r)
pi
W1
W2 t(r)
D
O
B
C
A
aO
p0
p0
p0
p0
r(r=0)
t(r)t(r)
W2
W1A B
CD
r(r=Wp)
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
442
Wp (
m)
pi (MPa) 0.5 1.0 1.50.0
20
40
0
60= 0.1
= 0.4= 0.5
= 0.3 = 0.2
3pi
Wp Uw
Hoek & Brown7
30 ,31
40 D=10m 18MPa
5cm0.1MPa
pi 5cm0.1MPa
Tanimoto & Hata32
qu
qu=0.3MPa
qu=2.1MPa qu=3.0MPa
qu=1.5MPa qu=0.9MPa
= 5°
= 30°= 40°
= 20°= 10°
’ E
Wp (
m)
pi (MPa)0.5 1.0 1.50.0
20
40
0
60 =5.0E
=0.5E=0.2E
=1.0E=2.0E
Wp (
m)
pi (MPa)0.5 1.0 1.50.0
20
40
0
60
qu’
Wp (
m)
pi (MPa) 0.5 1.0 1.50.0
20
40
0
60
Wp (
m)
pi (MPa)0.5 1.0 1.50.0
20
40
0
60
’/ = 0.1
’/ = 0.7 ’/ = 0.9
’/ = 0.5 ’/ = 0.3
Wp (
m)
pi (MPa) 0.5 1.0 1.50.0
20
40
0
60 E=50qu
E=200qu
E=250qu
E=150qu
E=100qu
Wp (
m)
pi (MPa)0.5 1.0 1.50.0
20
40
0
60
qu’/qu = 0.1
qu’/qu = 0.7 qu’/qu = 0.9
qu’/qu = 0.5 qu’/qu = 0.3
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
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33
qu
qu’
p0
aW2
W1
p0 a Equ qu’
pi
pi
Wp 2
p0=3.0MPa a=5m E=300MPaE=200qu =0.3
qu=1.5MPa =20° qu’=0.3MPa’=10°
=0.4E Equ qu’
’qu’
qu qu’/qu ’’/
pi
qu
Wp
qu qu’’
qu
pi qu
qu’ ’
pi Wp
p0=3.0MPa
D=10mE=300MPa
=0.3 qu=1.5MPa =20°qu’=0.3MPa ’=10°
0.2E 1.0E 5.0Epi
pi Wp D/Da=5m
pi
pi
pi
pi=0.3MPa=0.2E 38%
W2/Wp=3.7/9.7 =1.0E77% W2/Wp=15.3/19.8 =5.0E
94% W2/Wp=23.2/24.7pi
=0.2E 1.50MPa 0.57MPa0.93MPa =1.0E 1.50MPa 1.12MPa0.38MPa =5.0E 1.50MPa 1.38MPa0.12MPa =5.0E
3pi 0.4MPa 0.3MPa 0.1MPa
=0.2ED/D 6.67% 10.72% 4.05%
Wp 6.7m 9.7m 3.0mpi 0.1MPa 200mm
3.0m Wp
=1.0ED/D 17.51% 27.70% 10.19%
Wp 14.9m 19.8m 4.9mpi 0.1MPa
500mm 4.9mWp
=5.0ED/D 25.63% 40.39% 14.76%
Wp 18.8m 24.7m 5.9mpi 0.1MPa 740mm
5.9m Wp
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
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0.1MPapi
pi
0.7MPa 0.6MPa 0.1MPaD/D 1.88% 2.64% 0.76%
Wp 2.2m 2.9m 0.7mpi 0.1MPa 38mm
0.7m Wp
pi
pi
rt r
pi
pi 0.3MPa 0.4MPa 1.2MPa1.3MPa 1.5MPa
pi
4.5MPa1.5MPa pi
t(r)
pi 0.4MPa11.4m 4.5m
D/D Wp pi
=0.2E D/Dpi
pi (MPa)
D/D
(%)
25.63
0.3 0.4 0.0 0.00
50.00
1.5
pi=1.38MPa
40.39
pi=1.50MPa
pi (MPa)
D/D
(%)
10.72 6.67 2.64
50.00
1.88
pi=0.57MPa pi=1.50MPa
25.00
0.3 0.4 1.3 1.2 0.0 pi (MPa)
D/D
(%)
27.70
17.51
0.00
50.00
0.92 0.78
pi=1.12MPa
pi=1.50MPa
=1.0E D/Dpi
=5.0E D/Dpi
pi (MPa)
Wp (
m)
9.7
2.2 0.0
30.0
6.7
2.9
pi=0.57MPa
0.3 0.4 0.0 0.6 0.7 1.5
pi=1.50MPa
pi (MPa)
Wp (
m)
19.8
0.4 0.3 0.4 0.0 0.0
30.0
1.2 1.3
14.9
0.6
pi=1.12MPa
pi=1.50MPa
30.0
pi (MPa)
Wp (
m)
24.7
0.3 0.4 0.0 0.0
18.8
1.5
pi=1.50MPa
pi=1.38MPa
=0.2E Wp
pi
=1.0E Wp
pi
=5.0E Wp
pi
0.3 0.4 0.0 0.6 0.7 1.5
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
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pi 0.3MPa 0.4MPa
5cmpi=0.1MPa
28 , 29
Is p0
pi Cf
Cf
Wp D/D
Is Cf
Is Cf
Wp D/D
E qu
3Is Cf
Cf 2 pi
r (m)
r (m)
=1.0E
r (m)
=5.0E
(MPa
)
=0.2E
pi
2.27
1.501.39
3.00
4.50
0.00
pi=1.5MPapi=1.4MPa
pi=1.5MPapi=1.4MPa
pi=0.3MPapi=0.4MPa
(MPa
)
pi=0.4MPapi=0.3MPa
(MPa
)
1.821.501.12
3.00
4.50
0.00
pi=0.3MPa
pi=0.4MPa
pi=0.3MPa
pi=0.4MPa
pi=1.2MPapi=1.3MPapi=1.5MPa
pi=1.5MPapi=1.3MPa
pi=1.2MPa
5 10 15 20 250
1.501.07
0.58
3.00
4.50
0.00
pi=0.6MPa pi=0.7MPa
pi=1.5MPa
pi=0.4MPapi=0.3MPa
pi=0.3MPa
pi=0.4MPa
pi=0.6MPa pi=0.7MPa
pi=1.5MPa
5 10 15 20 250
5 10 15 20 250
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446
Is 0
Is
Wp D/D
=0.2ECf 0.85 0.85
Cf pi
3.0m
D/D Cf
Cf 0.5 p0 20%pi D/D 3.0%
p0 50% pi
=1.0ECf 1.5 1.5
Cf pi
1.0m
D/D Cf
Cf 0.5 p0 40% pi
1.0%=5.0E
Cf 1.851.85 Cf
pi
0.5mD/D Cf
Cf 1.0p0 30% pi
0.5%Is Cf Wp
D/D
3.
=0.2E
Wp=1m Wp=3m
Wp=5m
Wp=10m
=1.0E
=5.0E
Is Cf
Cf
I s
0.6
0.4
0.2
0.8
1.0
0.02.00.4 0.8 1.2 1.60.0
D/D=1.0% D/D=3.0% D/D=5.0% D/D=10.0%
Wp=0.5mWp=1m
Wp=3m
Wp=5m
D/D=1.0%D/D=3.0%
D/D=0.5%
Wp=0.5mWp=1m
Wp=2m
Wp=5m
Cf
I s
0.6
0.4
0.2
0.8
1.0
0.02.00.4 0.8 1.2 1.60.0
Cf
0.6
0.4
0.2
0.8
1.0
0.0
I s
2.00.4 0.8 1.2 1.60.0
D/D=1.0%D/D=3.0%
D/D=0.5%
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
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5.6km 70220m 80 100m2 2
5.6km 2.3km76
3 300m
34 CIDII
19
K0
50m 0.71.1
35
80m 0.5 0.8 1.0 1.2
3
70 220m
Wp
36
1 37 1D38 0.3D
38
38 dU/dLD 0.3 D
0.3Dmm/m
D/D DD
D/D0
1mdU/dL
D/D
D/D dU/dLD=11m 31
dU/dL (mm/m)
I
II
III
IV
V
DI / / )
CII / / )
0.01 1000.1 1 10
D/D
(%)
0.01
0.1
1
10CIICII
DI
CII
DI
CII
DI
DIIDII / / )
Cf dU/dLD/D 31
Initialdeformation
Observeddeformation
rate (mm/m) D/D (%)
I Slight over 1.5 less than 0.1 less than 0.07
II Midium 1.0 - 1.5 0.1 - 1 0.07 - 0.3
III Heavy 0.75 - 1.0 1 - 5 0.3 - 0.8
IV Very heavy 0.5 - 0.75 5 - 12 0.8 - 1.5
V Extremelyheavy
less than 0.5 over 12 over 1.5
Supportload
Competencefactor C f
Class
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31 60
CDI DII
38
Wp
D
2D
D’2D’
2D
2D
dU/dL D/D
dU/dL 1mm/mD/D 0.25 0.30%
0.3D D 6mm
C 19 2Class I II
DII 9
Class III IV DI 34
Class IIIV Class II
Class IV
dU/dL0.1 1.0mm/m Class II CII
dU/dL 1.0 5.0mm/m Class IIIDI dU/dL 5.0 12.0mm/m
Class IV DII
D=11mdU/dL 0.5mm/m
D=11m
dU/dL 5.0mm/m
16
161 121 7
Class VI 8 12Class III13 16
15 16
16
Uw
Uw=0.5 D pi Wp
D/D dU/dLCf 1
Tanimoto & Hata32
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449
Uw Wp
pi Uw Wp
pi31
39 - 42
20 30%
pi
Cf
Wp
FEM 38
Cf 1.5 1.0 0.5
Cf=1.5(Wp=0 - 0.03D)
Cf=1.0(Wp=0.1 - 0.15D)
Cf=0.5(Wp=0.45 - 0.6D)
:pi=0.00MPa:pi=0.15MPa
200
100
0 0 8040
D(m
m)
(m)
200
100
00 8040
D(m
m)
(m)
1 16
No.1, 2, 10, 11, 13, 14, 15, 16
No.3, 4, 5, 6, 7, 8, 9, 12
D/D dU/dL
dU/dL (mm/m)
D/D
(%
0.1
1
10
1001 10
III
IV
V
8 7 6
2 1
415 16
14
101112
35
9
13
DI / / )
CII / / )
DIDI
CII
DIIDII / / )
37)
100
200
300
(D 11 )
Uw (mm)
L(m)
5 4 3 2 1 0 -1 -2 -3 [×D]
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
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Wp
Uw
Cf pi=0.0MPapi=0.15MPa
Cf
pi=0.0MPa Cf
20 30%pi=0.15MPa
Cf
50%Cf
Cf
pi
Cf 0.5 1.0 1.565mm 24mm 15mm Cf
Cf
1.0
2030%
1 3m
20%1
Wp
DWp 1
D1
D 4.0D 4.5D D=11m
Wp 5.5 6.8mp0
H=104m 25kN/m3
E D.Deere43
E50 qu
modulus ratio E50/qu
E50/qu 200qu Cf p0
Cf dU/dLD/D 31
Class 1
1
1
1r(r=0) Wp Uw
Uw (mm)
r(r=0)
(MPa
)
1500 300
3
9
0
6
(109mm) (101mm)
0.3D
W2
Uw
W1
Wp
1
3
0
2
2.6
1.18
0.3 0.480.55 0.62 2.0
5.7
3.4
2.7
(W1=2.2m)(W1=2.4m)
(W1=3.0m)
36 124 21081 101
Wp (
m)
U w (mm) 98 109
W p (m) 5.5-6.8 5.71
p i (MPa) 0.28 0.3
a (m) 5.5
p 0 (MPa) 2.6
0.3
E (MPa) 312 (E = 200q u)
q u (MPa) 1.56 (C f = 0.6)
(°) 20
(MPa) 125 ( = 0.4E )
q u' (MPa) 0.62 (q u'= 0.4q u)
'(°) 10 ( '= 0.5 )
D(m
m)
(m)
1
-20 80200 40 60
225
100
0
200
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
451
Class IV Cf
0.5 0.75 Cf 0.5 0.60.7 0.75
15° 20° 25° 30° E/E ’
’ 20% 40% 60% 80%qu qu’ qu’/qu 10% 30%
50% 70% 90%
Uw r(r=0)
Wp
r(r=0)
pi
1Wp 5.7m
W1 W2 3.0m 2.7mWp
r(r=0)
Wp 2.7m W1 2.2mW2 0.5m r(r=0)
0.55MPa p0=2.6MPa 21%3 4m 0.3D
Wp 3.4mW1 2.4m W2 1.0m
r(r=0)
0.07MPa
r(r=0) 0.25MPap0=2.6MPa 10% Wp
W2 0.25MPa
r(r=0)
109mm Wp 3mW2
Uw 81mm 40 50%D 65-81mm D/D 0.59
0.74%1 2 16 15
p0
dU/dL D
1 16
A SC RB dU /dL D L o-c W p W 2 p i
(m2) (mm) (m)- (mm/m) (mm) (m) (m) (m) (MPa) (m) ( )
1 2.60 96.8 150 H125 4-30 8.38 196 4.0D-4.5D 5.7 2.7 0.30 0.60 0.12 13 26 IV
2 2.75 96.8 150 H125 4-28 5.97 167 3.5D-4.0D 5.0 2.2 0.30 0.65 0.11 28 22 IV
3 4.00 96.8 150 H125 4-19 9.82 127 2.5D-3.0D 3.1 0.8 0.30 0.85 0.08 21 17 IV
4 2.50 99.5 200 H150 6-19 6.40 126 3.0D-3.5D 4.1 1.5 0.35 0.65 0.14 7 20 IV
5 4.13 99.5 200 H150 4-19 5.85 124 3.0D-3.5D 3.2 0.8 0.40 0.80 0.10 28 16 IV
6 3.00 96.8 150 H125 4-25 6.03 77 2.5D-3.0D 2.7 0.5 0.29 0.85 0.10 72 40 IV
7 3.03 96.8 150 H125 4-26 9.00 83 2.5D-3.0D 2.6 0.4 0.29 0.85 0.10 56 38 IV
8 2.90 83.0 100 H125 3-16 3.83 72 2.5D-3.0D 2.0 0.1 0.21 0.95 0.07 92 42 III
9 4.25 99.5 200 H150 4-19 4.77 70 2.5D-3.0D 1.7 0.0 0.34 1.00 0.08 17 8 III
10 1.88 99.5 200 H150 4-19 2.40 46 2.5D-3.0D 1.5 0.0 0.34 0.80 0.18 142 70 III
11 1.58 96.8 150 H125 4-19 1.71 37 2.5D-3.0D 1.1 0.0 0.28 0.90 0.18 130 61 III
12 2.25 96.8 150 H125 4-19 1.83 37 2.0D-2.5D 0.4 0.0 0.28 1.35 0.12 66 32 III
13 2.50 99.5 200 H150 6-23 7.76 124 3.0D-3.5D 3.6 1.1 0.32 0.75 0.13 0 2 IV
14 2.48 99.5 200 H150 4-9, 6-14 2.75 148 3.5D-4.0D 3.4 0.9 0.34 0.80 0.14 13 5 III
15 2.23 100.7 250 H200 4-9, 6-14 2.13 104 3.0D-3.5D 2.8 0.6 0.41 0.80 0.18 38 14 III
16 1.98 100.7 250 H200 4-9, 6-14 3.35 100 3.0D-3.5D 1.7 0.0 0.43 0.95 0.22 30 8 III
key: p 0: A : SC: SS: RB: dU /dL : D :L o-c: W p: W 2: p i: C f: I s:
I sC fp 0
(MPa)No. ClassSS
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
452
Wp
W2 pi Cf Is
31 Class
Class IVdU/dL 5mm/m
1 12
0.3DWp
r(r=0)
1 2 4 5 91 2 4 2.0 2.5m
3 4m 12
Class IV1 7 2m
50 60%
1 3.5m 2 4 2.5mClass III
8 12 1m
r(r=0) 3 4mp0 20%
8 0.40MPa 40.13MPa
3 4m1 7
5mm/m 3 4m
A
pi
1.510 6m
1 2 1314 200mm
15 16
dU/dL DU
DL
D
dU /dL D U D L DNo. (mm/m) (mm) (mm) (mm) (m) ( )1 8.38 - - 196 13 26
2 5.97 - - 167 28 22
13 7.76 89 35 124 0 2
14 2.75 82 66 148 13 5
15 2.13 45 60 104 38 14
16 3.35 36 64 100 30 8
Wp (
m)
2
6
0
4
121 8 2 9 3 10 4 11 5 6 7
0.29
0.56
0.30
0.51
0.30
0.540.61
0.30
0.48
0.55
0.35
0.48
0.56
0.40
0.65
1.10
0.29
0.460.21
0.650.28
0.48 0.28
0.34
0.48
0.34
0.72
2.40
0.3D (3-4m)
r(r=0)(MPa)
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
453
dU/dL1 2 13 Class IV
15 1630%
13 1415 16
DL 14 15 1613 2
132
145 1D
15 14 4D16 8
3DD
1 2
1413
15 16
Wp
dU/dL 5mm/m
D 70 80mm
4.
pi
0.1MPapi
2
dU/dL 0.1 1.0mm/mCII dU/dL 1.0 5.0mm/m
DI dU/dL 5.012.0mm/m DII
3 4m Wp
r(r=0)
3 4mdU/dL 5mm/m
3 4mA
dU/dL 5mm/m
D 70 80mm
1) Rabcewicz, L.v. : The New Austrian Tunnelling Method, Water Power,
pp.453-457, Nov. 1964 (part I), pp.511-515, Dec. 1964 (part II), and pp.19-
24, Jan. 1965 (part III).
2)
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3) Gesta, M. P., Kerisel, M. J., Londe, M. P., Louis, M. C. and Panet, M. M. :
Tunnel Stability by Convergence-Confinement Method, Underground
Space, Vol.4, No.4, pp.225-232, 1980.
4)
5)
6)
7) Hoek, E. and Brown, E. T. : Underground Excavations in Rock, The
Institution of Mining and Metallurgy, London, England, 1980.
8)
9) Tanimoto, C. and Iwasaki, Y. : Allowable Limit of Convergence in
Tunnelling, 24th U.S. Symposium on Rock Mechanics, pp.251-263, 1983.
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21) Brown, E. T., Bray, J. T., Ladanyi, B. and Hoek, E. : Ground response
curves for rock tunnels, Journal of Geotechnical Engineering, ASCE,
Vol.109, No.GE1, pp.15-39, 1983.
22)
23)
24)
25)
26)
27)
28)
29)
30) Tanimoto, C., Hata, S., Fujiwara, T., Yoshioka, H., and Michihiro, K. :
Relationship between Deformation and Support Pressure in Tunnelling
through Overstressed Rock, Proc. of the 6th International Comgress on Rock
Mechanics, pp. 1271-1274. 1987.
31)
32) Tanimoto, C. and Hata, S. : Fundamental Concept of Designing Tunnel
Supports in Consideration of Elasto-plastic and Strain Softening Behavior of
Rock, Memoris of the Faculty Eng., Kyoto University, Vol. 42, 1980.
33)
34)
35)
36)
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37)
38)
39)
40)
41)
42)
43) Deere, D. U. : “Geological Consideration”, Rock Mechanics in
Engineering Practice, Editors K.G. Stagg and O.C. Zienkiewicz, pp.1-20,
John Wiley and Sons, 1968.
2005. 5. 26
QUANTITATIVE DETERMINATION OF LOOSENING ZONE IN ROCK TUNNELING
Chikaosa TANIMOTO, Kimikazu TSUSAKA and Yoshio MITARASHI
From the experience with many tunnel projects in rocks it is suggested that the ground arch effect in rock can be obtained by controlling a loosening zone. The loosening is considered as the post-peak behavior of rocks. The authors investigated the motorway tunnel which was driven through the tertiary sedimentary rocks in the northern Osaka, and confirmed as follows: Such a small change as 0.1 MPa in the confining pressure, which acts onto the tunnel wall as the resultant effect of support elements, remarkably influences the extent of loosening zone. A magnitude of loosening zone can be quantified through the rock classification and the strain-softening model proposed by Tanimoto et al.
土木学会論文集C Vol.62 No.2, 440-456, 2006. 5
456
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