slope paper

8/12/2019 Slope Paper

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H

1.2 H 2 H

R o l l e r s

Fixed


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Bishop & Morgenstern (1960)FOS 1.380

0.250.5

0.751

1.3

1.51.8

22.32.52.8

33.3

3.53.8

4

E

m a x

/ H 2

0.8 1 1 .2 1 .4 1 .6

FOS

D 1 .0 (Example 1)D 1 .5 (Example 2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.60 0 .2 0 .4 0 .6 0 .8 1 1 .2

E

m a x

/ H 2

Gravity factor

1 increment2 equal increments3 equal increments5 equal increments


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(a)

(b)

DH

H

(a)

(b)


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H

H

2H 2H

0.6H 1.2H

c u2

c u1

c u1

21

2

1

2H

1.2H

1

0.6H

1

0.4H

0.4H

c u2 c u1

u 0


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2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

F O S

0.20 0 .4 0 .6 0 .8 1c u2 / c u1

Finite elements

c u1 / H 0 .25Taylor (1937)FOS 1.47

Slope programwedgesSlope programcircles

(a)

(b)

(c)


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2H 2H

H

H

c u1

c u2

2H

21

u 0

Finite element analysisBase circle analysisToe circle anlaysis

Taylor(c u2 c u1 )FOS 2.10

Taylor(c u2 c u1 )FOS 1.47

c u1 / H 0.25

0 0 .5 1 .5 2 .5 3 .51 2 3 4c u2 / c u1

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

FOS


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(a)

(b)

(c)


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Free surface

Embankment

A

h A

u A h A W

u B h B W

h B

h W

B

Reservoir Level

Free surface

Embankment

Reservoir Level

Linearly increasingnormal stress fromzero to h W W h W

Constant normal

stress h

W W

H

L 0L (negative)

L (positive)


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Finite elementsLimit equilibrium

F O S

2

1.8

1.6

1.4

1.2

Morgenstern(1963)

FOS 1.85

Bishop &Morgenstern(1960)

FOS 1.4

L / H 0 0 .10.10.2 0.2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 1 .1

Reservoir level

17 .1

33 .5

7.318 23

124 .4 33 .5

H 21 .3

7.3

Dimensions in metres

F r e e s u r f a c e


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(a)

(b)

R 62 .7m

5.4m

62 .4m

5

10

15

20

25

30

351.2

E

m a x

/ H 2

1 1 .4 1 .6 1 .8 2 2 .2 2 .4 2 .6FOS

FOS 1.90 FOS 2.42

Limitequilibriumsolutions

No free surfaceWith a free surface


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(a)

(b)

R 47 .8m

11 .5m

43 .9m

(b)

FOS 1.9

(a)

FOS 2.4


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slope paper

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