1 2 3

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

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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)

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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

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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

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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

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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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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%

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447

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]

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450

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

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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)

土木学会論文集Ｃ Vol.62 No.2, 440-456, 2006. 5

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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)

土木学会論文集Ｃ Vol.62 No.2, 440-456, 2006. 5

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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

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