ED 500

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1.7E-05

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Crown Side Wall Invert

2.45 0.002 1

2.21 0.006 2

1.96 0.010 3

1.71 0.015 4

1.47 0.019 5

1.22 0.023 yes 6

0.98 0.027 yes 7

0.73 0.032 yes yes yes 8

0.49 0.036 yes yes yes 9

0.24 0.041 yes yes yes 10

0 0.044 yes yes yes 11

Total DisplacementSupport

Pressure(Mpa)

Total

Displacement [m]

Plastic Zone

0

0.5

1

1.5

2

2.5

3

0.000 0.010 0.020 0.030 0.040 0.050

SupportPressurePi(Mpa)

Total Displacement [m]

Total Displacement

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Crown Side Wall Invert

500 0.00 1

450 0.01 2

400 0.01 yes yes 3









Total Displacement

Plastic ZoneDeformation

Modulus(Mpa)

Total Displacement

[m]

0

100

200

300

400

500

600

0.00 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

DeformationModulus(Mpa)


Total Displacement

DEF MOD VS DISPLACEMENT AT CROWN

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Tunnel Radius Ro 4.5 m

Max. Disp Uif 21.400 m

Radius of plastic zone Rpm 6.897 m

Point Ui Remarks1 6.587 FACE

2 12.059

3 16.602

4 19.239

5 20.488

6 21.027

7 21.249

8 21.339

9 21.376

10 21.390

11 21.396

12 21.39813 21.399

14 21.400

15 21.400 MAX

1

2

14

8

9

10

11

Longitudinal Displacement Profile

7

12

13

3

4

5

6

Distance to the face,X,m0

0.000

5.000

10.000

15.000

20.000

25.000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

DeformationModulus(Mpa)


Total Displacement

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Definitions of Dimensions:

b - 600 mm

t - 450 mm

b 1 - 577 mm

b 2 - 173 mm

t 2 - 150 mmd 1 - 16 mm

d 2 - 20 mm

- 30 Degree

Cover - 30 mm

h g - 400 mm

bg - 462 mm

Lo - 1500 mm

d 3 - 8 mm @ 150 mm c/c

Rock Bolts

ELEV

b

b 1

d 1

d 3

d 2

b 2

PLAN

400

462

h - t + t 2

- 600 mm

d g - h g - 0.5(d 1 + d 2)

- 372 mm

Definitions of Material Properties:

f cd - 25 Mpa

fyd - 415 Mpa

- 0.85

Lo

t

t 2

Lattice Girder

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A st 1 - 402 Sq mm

A st 2 - 314 Sq mm

A st 3 - 50 Sq mm

A c - b t + 0.5 t 2 b 2 - A st 1 - A st 2

- 290539 Sq mm

b eff - 0.2 (b-b 2) + 0.24 L o+b 2

- 618.4 mm

A s11 -

- 609 Sq mm (only in tension)

h cm -

- 237.25 mm (Calculation of center of mass)

Eight Strain conditions to derive M-N envelope:

1 Pure axial force

2 Zero strain in tensioned bars (positive Moment)

3 Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Positive Moment)

4 Pure moment (Positive)

5 Pure tension

6 Pure Moment (Negative)

7 Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Negative Moment)

8 Zero strain in tensioned bars (Negative Moment)

1 Nd - f cd A c + f yd (A st1 + A st2)

- 6471 kN

5 N tog - f yd (A s11 +A st2)

- 383 kN

3 cu - 0.0035

syd - 0.0021

d - hg - 0.5 d 2- 390 mm

X bal - d

cu + syd

- 244 mm

0.8 X bal < t

0.8 X bal - 195 mm

< 450 mm

f c - f cd 0.8 X bal b eff - 2562495 N

f s1 - f yd A st1 - 166797 N

f s2 - f yd A st2 - 130310 N

N ud - c + f s1 - f s2 - 2599 kN

M ud - f c (h cm -0.4 X bal) + f s1 (h cm - 0.5 d1) + f s2 (d - h cm)- 376.44 kN m

2 h c3 - 0.8 d - 312 mm

A c3 - t b eff + (0.5 b2 t2 - (h - h c3)2/ tan )

- 147592 sq mm

Center mass of compression zone

cu

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h cm2 - 0.5 b eff t2

+ 0.5((2(h-hc3)/tan + b2)) (t + 0.5(hc3-t))(hc3 -t)

- 62613000 + 585 -x 52578

- 156.470421 mm

f c3 - f cd A c3

- 3136325.28

N ud3 - f c3 + f s1

- 3303 kN

M ud3 - f c3 (d - h cm2) + f s1 (d -0.5 d1) - Nud3 (d-hcm)

- 244 kN m

4 x -

- 12.40 mm

Mu - f yd A st2 (d -0.4 x)

- 50.17 kN m

6 d 1 - h -0.5 d 1

- 592 mm

h c - Sqrt ((A s11 f yd tan )/ f cd)

- 82.87 mm

M u2 - f yd A s 11 (d 1 - 0.67 hc)

- 135.60 kN m

7 X bal2 - d

cu + syd

- 370 mm

h c2 - 0.8 X bal2- 296 mm

f c2 - f cd (h c2)2/tan - 3224801 N

f s11 - f yd A s 11 - 252753 N

f s2 - f yd A st2 - 130310 N

N ud2 - f c2 + f s2 - f s11 - 3102 kN

M ud2 - f c2 (h-h cm -0.67 h c2) + f s1 (d-h cm ) + f s2 (h cm - 0.5d1)

- 608 kN m

8

h c4 - 0.8 d1

- 473.6 mm

A c4 - 213089.24 Sq mm

f c4 - 4528146.35 N

N ud4 - 4658 kN

h cm3 - Center mass of compression zone

- (h c4 -t2)b eff (h -h c4 + 0.5(h c4 - t2)) + (0.5 t2 b2 (t + 0.33 t2))

f cd 0.8 b eff

cu

((h c4 -t2)b eff ) + (0.5 t2 b2)

b eff t+ 0.5((2(h-hc3)/tan + b2)) (hc3 -t)

203473

f yd A st2

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- 301.10 mm

M ud4 - f c4 (h cm3 -0.5 d1) + fs2 (d1 - co - 0.5 d2) - N ud4 (h cm - 0.5 d1)

- 368.69 kN m P M

0 0

0 0 4864.1 46.231

M ud3 244 4998.7 25.378M ud 376.44 5168 4.8295

M u 50.17 5466.2 -22.899

Moment = 0 = 0 kN m 5831.4 -44.263

-M u2 -135.60 6092 -56.669

-M ud2 -608 5980.4 -44.682

-M ud4 -368.689 5603.1 -29.967

0 0 5024 -15.153

4341.3 0.047538

N d 6471 3658.9 12.314

N ud3 3303 3058.1 25.847

N ud 2599 2618 31.249

0 0 2376.2 39.333

Nforce = -N tog = -383 kN 2380.1 35.518

0 0 2613.5 34.268

N ud2 3102 3059.1 25.947

N ud4 4658 3659.1 12.001

N d 6471 4342.3 -0.64786

5027.4 -14.769

5607.3 -30.103

5988.7 -44.797

6098.9 -56.456

5833.3 -41.294

5478.8 -14.014

5163.9 10.351

0 0

0 0

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-1000

0

1000

2000

3000

4000

5000

6000

7000

-800 -600 -400 -200 0 200 400 600

Series2Series1

ED 500

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