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SLOPE STABILITY

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DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT 1. SLOPE STABILITY ... Failure scarp in glacial till 'Scarp' 'Toe' 'Scarp' DIVISION OF ... – PowerPoint PPT presentation

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Title: 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?
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