SLOPE STABILITY

1
SLOPE STABILITY

• D. A. Cameron, UniSA
• Rock and Soil Mechanics 2006

2
Hummocky ground
3
Failure scarp in glacial till
Scarp
4
Infinite slopes?
b
Vertical slice
Sliding surface
h
b
5
Force equilibrium the slice
WN Wsin?
W
6
STABILITY

• Stability IF, WP ? (C F)
•  
• where C cl resistance due to cohesion
  (kN)
• and F WNtan?' frictional resistance
  (kN)
•  
• Factor of Safety (FoS) restoring force
  disturbing force

7
CASE 1 c? 0, so C 0
The natural angle of repose ?
8
Case 2 c 0, seepage down the slope

• Phreatic surface at slope surface
• Pore force, U, on sliding base due to pore water
  pressure

• Effective normal force reduced less friction!

9
Case 2 solution

• almost only half the FoS!

10
Stable Slope Angles (FoS of 1.3) in c 0 Soils
11
CIRCULAR SLIPS More common in cohesive soils
centre of circle
crest of slope
slope
12
CIRCULAR SLIPS
centre of circle
crest
W
A potential sliding surface
x
toe
13
CIRCULAR SLIPS Stability? Limit equilibrium
Case 1 ?? 0 c cu
centre of circle
14
Taylors Charts slope stability for undrained
shear strength, cu

• Simple slopes
• Homogeneous
• Relative depth, D
• Stability number, Ns
• WARNING slopes are rarely homogeneous

15
Taylors Charts F FoS
Shear strength cu
H
?
Unit weight of soil ?
Bedrock?
16
Example

• H 10 m, DH 13 m
• ? 20º, F 1.25
• 18 kN/m3, cu 30 kPa

Ns 30/1.25(18)10 30/225 0.133 D
13/10 1.3
D ?
0.2
Stability Number, Ns
0.1
D 1
D 1.3
Slope angle (º)
0.0
45
90
?20?
17
CIRCULAR SLIPS Stability - Case 2 ?? ? 0
centre of circle
W
What do the green arrows now represent?
x
18
Force on Slip Plane c', ?? soil

• ? varies with position
• ? c? ?n?tan ??

Near crest
W
?
Near toe
?
19
CIRCULAR SLIPS Method of Slices
centre of circle
20
Reasons for Slices

• Frictional shear resistance varies with both ?N
  and ??
• Varying cohesion with depth
• Non-uniform pwps from seepage analysis

21
PWP influence - u from flownet
ui ?whwi
22
General Method of Slices

• FoS by summation over all slices for trial
  failure surface
• 100s of trial surfaces evaluated
• thank you for the pc!
• XSLOPE and GALENA
• Lowest FoS ? the critical failure surface

23
centre of circle
Stability of a Vertical Slice
Slice i
Wi
24
Stability of a Slice (no pwp)
centre of circle
Wi
25
PWP influence
Wi
Wicos?
Wisin?
26
Slices - overall too many unknowns! - need
simplifying assumptions to get a solution!

• Side Forces
• Assumptions re these forces
• differences in methods
• e.g. Fellenius v. Bishops simplified method
• Fellenius

27
Fellenius Method

• Resultant of side forces zero
• i.e. Xi Xi1 and Ei Ei1
• For homogeneous soil
• restoring shear force c?Larc tan???N?
• where, Ni? Wicos?i - uili
• and li arc length of slice, i

28
Factor of Safety - Fellenius
Warning method regarded as simplistic and
non-conservative
29
Simplified Bishop Method - a superior method

• Resultant of side forces acts horizontally
• Apply FoS (F) to restoring shear force
• T l(c? ?N?tan??)/F
• Sum all vertical forces
• W ?N?cos? (c?l N?tan??)sin?/F
• Solve for N?
• Substitute in

30
The Bishop Equation
Where
31
Simplified Bishop Method

• Requires iteration
• Assume initial F, then solve for F
• When trial F and determined F are equal, its a
  solution
• Spreadsheet for simple slopes
• XSLOPE and GALENA otherwise
• 1000 trial surfaces in 1 minute

32
XSLOPE (University of Sydney)
33
(No Transcript)
34
(No Transcript)
35
Other Methods

• More exact solutions exist, but little
  improvement on accuracy
• Choosing the soil shear strength factors and soil
  layers are far more important

36
What strength should be applied?

• MUST be appropriate to the field stress levels
• stresses may be quite low
• Undrained or Drained
• short term (just constructed) or long term
  stability?

37
What strength?

• Peak strength
• First time slides? Or compacted soils
• Softened strength (critical state)
• Fissured, stiff clays?
• Residual strength
• Evaluation of stability of slips or pre-existing
  slides
• Bedding shear planes

38
Typical strength values

• Peak effective friction angle, ??
• For NC soils (Kenney 1959)
• sin?? fn log(Plastic
  Index)
• e.g. 30? for PI 20 18? for PI ? 120
• RETAINING WALL STANDARD,
• AS4678 2002
• gives guidance on c?- ?? soils (see lecture
  notes)

39
Residual strengths, ?r?
London Clay ?16? - Skempton (1964)
40
Numerical Approach to Slopes

• FEA or Finite Difference
• Benefits
• Progressive failure
• shear strength mobilization not uniform along
  sliding surface
• Distortions as well as safe slope angle
• But more effort

41
SUMMARY KEY POINTS

• Angle of repose for dry granular soils
• Influence of seepage on granular soils
• Slope stability for homogeneous slopes in
  saturated clay (NC)
• simple analyses
• Taylors charts
• Frictional soils more difficult
• Method of slices
• Slope stability programs use limit equilibrium

42
POINTS, continued

• Slope stability programs search for the failure
  surface with lowest FoS
• circular or non-circular slips?
• Bishops simplified method for circular slips
• further refinement unwarranted?
• Importance of shear strength parameters
• drained and/or undrained?
• peak, ultimate or critical state?