6,0 slope stability_part 1

8/3/2019 6,0 Slope Stability_Part 1

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Slope Stability


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Causes of instability

All slopes (natural or manmade) have a tendency to

move. The main force causing movement is gravity.

Causes of instability:

inherent, such as weaknesses in the rock or soilforming the slope;

variable, such as heavy rain and changes in ground-water level;

transient, such as earthquake or volcanic activity;

human activities, such as excavations, removal ofvegetations, etc.


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Types of slope failure

Source: BS6031:1981


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Types of slope failure


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Principles of stability

Disturbing force is generated by self weight of the soil,

surface loadings, and seismic loads.

Tendency to slide is opposed by the shearing resistanceof the soil.

Sliding can be caused by either an increase in thedisturbing force or a decrease in shearing resistance ofthe soil.

Limit equilibrium method is normally used.


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Limit equilibrium method

Failure is on the point of occurring along an assumedor known failure surface.

The static force and moment equilibrium of the

assumed failed mass is analysed.

A factor of safety is obtained from the ratio of shearstrength of the soil to the mobilised shear stresswhen the slope is on the point of failing.

A search for the critical failure surface is carried outso as to obtain the minimum factor of safety for theslope.

For a slope which has failed, F = 1.


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Stability analyses may be carried in 2 ways:

Total stress analysis using undrained shear strengthparameters for short term cases

Effective stress analysis using drained shear strengthparameters for long term cases


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Infinite slope analysis

The failure plane is parallel to the surface of the slope

z

En

En+1

N = N' + U


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Infinite slope: effective stress analysis

En+1 and En are equal, opposite and co-linear.

Resolve // failure surface: Wsinb = S = tmob x l

l= b/cosb

tmob = t/F

t = c' + s' tan f'

s' = N'/l

W =g xz x b =g xz x lcosb

F = c' + (N'/l) tan f'

gz sinb cosb


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Resolve perp to failure surface: N = N' + U = WcosbN' = l(gz cos2b u)

F = c' + (gz cos2b u) tan f'gz sinb cosb

which is the general equation of infinite slope in terms ofeffective stress


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Special cases

If c' = 0, F = (1 u/gz cos2b ) tan f'tan b

If c' = 0 and u = 0, F = tan f'tan b


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Special cases

Steady seepage parallel to ground level with groundwater table verticalheight, hw, above failure surface, u =gwhw cos

2b

hw cos2b

b

hw cos b

hw


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If c' = 0 and steady seepage parallel to ground level with groundwatertable vertical height, hw, above failure surface

F = (1 m. gw/g) tan f', where m = hw/z

tan b

If m = 1, F = (g' /g) tan f'

tan b

If m = 1 and F = 1, tan b = (g' /g) tan f', which is approximately = tan f'

2


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Infinite slope: total stress analysis

Saturated soils: fu = 0

F = S = cul = cuW sinb g xz x b gz sinb cosb


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Stability analysis with circular failure surface

d

q


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Undrained analysis (fu = 0)

Disturbing moment = W x d

Resisting moment = tmob x r q x r

tmob

= cu

/ F, where F is the factor of safety

F = cu r2q

W d

The critical failure surface is found by searching for theposition of centre of rotation, O, and radius, r, with thelowest F


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Undrained/Total stress analysis (fu = 0)

Tension cracks tend in cohesive soils and can be filled with water.

For analysis, refer to Whitlow pages 363 & 364.


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Drained/Effective stress analysis (c'f' soil)

Method of slices

The assumed failed mass is divided into a number of slices, theirforce systems are analysed and are then summed up to produce anaverage factor of safety.

The minimum factor of safety is found by analysing many trialcircles.


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Method of slices


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Method of slices

a

l


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Fellenius / Swedish method

It is assumed that

(En En+1) = 0

(Xn Xn+1) = 0

F =

l

= bseca

F =

The Fellenius method underestimates F by 5 to 20%.

S [c'l+ (Wcos a ul)tan f]

S Wsina

S [c'b + (Wcos2a ub)tan f']seca

S Wsina


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Bishops simplified method

It is assumed that (Xn Xn+1) = 0, but (En En+1) 0

F =

As F appears on both sides of the equation, F is found by an iterative

process of successive approximations. First, a trial value of F is input

on the right hand side of the equation to obtain a new value of F, which

is substituted back into the right hand side of the equation until F

converges to an acceptable accuracy. The Bishops simplified method

underestimates F by less than 3%.

S Wsina

1S

[c'b + (W ub)tan f']seca

1 + tan a tan f' / F


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Slope stability analysis

Pore pressure ratio, ru

The porewater pressure at a given point in a slope is also given in terms of ru

which is the ratio of the porewater pressure to the weight of the soil per unit

area above the point.

ru

= u/gz

Bishops simplified method

ub/W = ub/gzb = ru

F =

F =

S Wsina1 S [c'b + (W ub)tan f']seca1 + tan a tan f' / F

S Wsina

1S

[c'b + W(1 ru)tan f']seca

1 + tan a tan f' / F


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6,0 slope stability_part 1

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