SLOPE STABILITY ANALYSIS
Tuncer B. Edil
University of Wisconsin-Madison
LECTURE OUTLINE
 Common
Features of Slope Stability
Analysis Methods
 Water Forces on Soil
 Infinite Slope Analysis
 Finite Slopes: Plane, Circular and
Noncircular Failure Surfaces
COMMON FEATURES OF
SLOPE STABILITY ANALYSIS
METHODS
Safety Factor: F = S/Sm where S = shear
strength and Sm = mobilized shear
resistance. F = 1: failure, F > 1: safety
 Shape and location of failure is not known a
priori but assumed (trial and error to find
minimum F)
 Static equilibrium (equilibrium of forces
and moments on a sliding mass)
 Two-dimensional analysis

INFINITE SLOPE ANALYSIS
Translational failures along a single plane
failure surface parallel to slope surface
 The ratio of depth to failure surface to length
of failure zone is relatively small (<10%)
 Applies to surface raveling in granular
materials or slab slides in cohesive materials
 Equilibrium of forces on a slice of the sliding
mass along the failure surface is considered

INFINITE SLOPE
d
hp
W’

 sat
c

T

N
INFINITE SLOPE ANALYSIS
F = f(c’, ’, , , d, u)
 F = (c’/ d) seccosec + (tan’/tan)(1-ru sec2)
where ru = u/d (different ru for seepage parallel to slope face,

seepage emerging, seepage downward, etc)
For Granular Soil: F = (tan’/tan)(1-ru sec2)
Dry Granular Soil (ru = 0): F = (tan’/tan)
 For Cohesive Soil: F decreases with increasing
depth to failure plane; if c is sufficiently large, dc
for F = 1 may be large and infinite slope failure
may not apply.

WATER FORCES ON SOIL
Water fills voids and increase weight which
increases driving forces
 Water also exerts pore pressures which
decrease effective stress and therefore strength
 There are mathematically two equivalent ways
of taking water forces into account in stability
analyses

EQUIVALENT METHODS
FOR WATER FORCES
1. Boundary water force + total unit weight
u = hpw; sat consider soil element (particles
and water filled pores) as single solid mass
 2. Seepage force + submerged unit weight
Fs = i wV; ’ consider soil element as
particle skeleton with water external to it

BOUNDARY WATER FORCE
SEEPAGE FORCE
Hydraulic Gradient, i = sin  ;
Seepage Force,Fs = i w Volume
Effective Weight, W’ = ’ Volume;
’ =  - w
FINITE SLOPES: PLANE
FAILURE SURFACE
Translational Block Slides along single plane
of weakness or geological interface
 F = c’L + (W cos uL) tan’ / W sin + Fw

BLOCK SLIDES
BLOCK SLIDES
FINITE SLOPES: CIRCULAR
FAILURE SURFACE
Rotational Slides - Method of Slices
 Applies to slopes containing cohesive soils
 Ordinary Method of Slices (Fellenius’ Method)
 Bishop’s Simplified Method
 Spenser’s Method

ORDINARY METHOD OF
SLICES
Assumes that resultant of side forces on each slice
are collinear and act parallel to failure surface and
therefore cancel each other
 F = [cn ln + (Wn cosn - un ln) tann] / Wn sinn
 Undrained analysis: F = [cn ln] / Wn sinn

SIDE FORCES IN ORDINARY
METHOD OF SLICES
BISHOP’S SIMPLIFIED
METHOD
Assumes that resultant of side forces on each slice
act in horizontal direction and therefore vertical
side force components cancel each other
 F = [cn bn + (Wn - un bn) tann](1/m) / Wn sinn
 m = cosn + (sinn tann)/F
 Undrained analysis: F = [cn ln] / Wn sinn

CHART FOR m
SIDE FORCES IN
BISHOP’S METHOD
SPENCER’S METHOD
Assumes that the point of application of
resultant of side forces on each slice is at
mid-height of each slice but no assumption
is made regarding inclination of resultants;
inclination is determined as part of the
solution
 This method is more exact than Bishop’s

FINITE SLOPES: NONCIRCULAR
FAILURE SURFACE
Wedge Method
 Janbu’s Simplified Method
 Morgenstern-Price Method

WEDGE METHOD
Failure surface consists of two or more
planes and applicable to slope containing
several planes of interfaces and weak layers
 Force equilibrium is satisfied
 Assumes that resultant of side forces on
each slice either acts horizontally or at
varying angles from horizontal (typically up
to 15o)

WEDGE METHOD
1
2
Layer B

3
4
Layer A
m
WEDGE ANALYSIS
Equilibrium of Forces in
each slice is
considered to adjust
the inter-slice forces
and balance them
resulting in a correct
solution.
JANBU’S SIMPLIFIED
METHOD
A method of slices applicable to circular and
noncircular failure surfaces
 F = fo [cn bn + (Wn - un bn) tann](1/ cosnm)} /
Wn tann
 fo is a correction factor that varies with depth to
length ratio of sliding mass and type of soil
(c, or c = 0)

L
d

c,  soil
Factor, f o
c=0
Ratio, d/L
MORGENSTERN-PRICE
METHOD
No assumption is made regarding
inclination or point of application of
resultants and these are determined as part
of the solution
 Requires computers for solving the basic
equation
 Exact but not practical

REFERENCES
J.M. Duncan, A.L. Buchignani and M. De Wet (1987), An
Engineering Manual for Slope Stability Studies, Virginia Tech
Department of Civil Engineering, Blacksburg, Virginia.
L.W. Abramson, T.S. Lee, S. Sharma and G.M. Boyce (1996), Slope
Stability and Stabilization Methods, Wiley, N.Y.
Das, B. M., Principles of Geotechnical Engineering, 3rd Ed., PWS
Publishing Co., Boston, MA, 1994.
Soil Mechanics Design Manual, NAVFAC DM-7.1, Department of
the Navy, 1982.
Slide 21..- La Conchita, California-a small seaside community along Highway 101 north of Santa Barbara. This landslide
and debris flow occurred in the spring of 1995. Many people were evacuated because of the slide and the houses nearest
the slide were completely destroyed. Fortunately, no one was killed or injured. Photograph by R.L. Schuster, U.S.
Geological Survey.