SLOPE STABILITY

Chapter Four
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
o Culmann’s Method
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices
 SLOPE STABILITY

What is a Slope?
An exposed ground surface that stands at an angle with the horizontal.

Why do we need slope stability?

In geotechnical engineering, the topic stability of slopes deals with:
1. The engineering design of slopes of man-made slopes in advance
(a) Earth dams and embankments,
(b) Excavated slopes,
(c) Deep-seated failure of foundations and retaining walls.
2. The study of the stability of existing or natural slopes of earthworks and
natural slopes.
o In any case the ground not being level results in gravity components of the
weight tending to move the soil from the high point to a lower level. When
the component of gravity is large enough, slope failure can occur, i.e. the soil
mass slide downward.
o The stability of any soil slope depends on the shear strength of the soil
typically expressed by friction angle () and cohesion (c).
 TYPES OF SLOPE

Slopes can be categorized into two groups:

A. Natural slope
• Hill sides
• Mountains
• River banks

B. Man-made slope
• Fill (Embankment)
• Earth dams
• Canal banks
• Excavation sides
• Trenches
• Highway Embankments
 Case histories of slope failure

• Some of these failure can cause dramatic impact on lives

and environment.

Slope failures cost billions of $

every year in some countries
 Case histories of slope failure

Bolivia, 4 March 2003, 14 people killed, 400 houses buried

Case histories of slope failure

Brazil, January 2003, 8 people killed

Case histories of slope failure
Case histories of slope failure
 Case histories of slope failure

Slides: Rotational (slump)

Case histories of slope failure
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
o Culmann’s Method
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices
 Types of Slope Movements

o Slope instability (movement) can be classified into six

different types:

 Falls
 Topples
 Slides
 Flows
 Creep
 Lateral spreads
 Falls

• Rapidly moving mass of material (rock or soil) that travels mostly

through the air with little or no interaction between moving unit
and another.
• As they fall, the mass will roll and bounce into the air with great
force and thus shatter the material into smaller fragments.
• It typically occurs for rock faces and usually does not provide
warning.
• Analysis of this type of failure is very complex and rarely done.
 Falls
• Gravitational effect and shear strength
Gravity has two components of forces:
T driving forces: T= W. sin 

Boulder N resisting forces (because of friction)

N = W. cos 
N T
the interface develop its
resistance from friction ():
S  = friction S = N tan 

In terms of stresses:
S/A = N/A tan 
or

f =  tan 
A = effective Base Area of sliding block
Falls
 Topples

This is a forward rotation of soil and/or rock mass about an axis

below the center of gravity of mass being displaced.
 Slides

o Movements occur along planar failure surfaces that may run more-or less
parallel to the slope.
o Movement is controlled by discontinuities or weak bedded planes.
Back-Scrap

A
Slides
A. Translational (planar)

Bulging at
Toe

Weak bedding
plane
Occur when soil of significantly
different strength is presented (Planar)
 Slides

B. Rotational (curved)
This is the downward movement of a soil mass occurring on an
almost circular surface of rupture.

B
Back-Scrap

Bulging

Curved escarpment

C. Compound (curved) (Slumps)

Slides
 Slides

Reinforcement

Soil nails
 Slides

Reinforcement

Anchors
‫تادادش‬

Possible failure
surface
 Flows

o The materials moves like a

viscous fluid. The failure plane
here does not have a specific
shape.

It can take place in soil with

high water content or in dry
soils. However, this type of
failure is common in the QUICK
CLAYS, like in Norway.
Flows
 Creep

• It is the very slow movement of slope material that occur over a long
period of time
• It is identified by bent post or trees.
 Lateral spreads
o Lateral spreads usually occur on very gentle slopes or essentially flat terrain,
especially where a stronger upper layer of rock or soil undergoes extension
and moves above an underlying softer, weaker layer.

weaker layer
 Types of Slope Failures

In general, there are six types of slope failures:

1. Falls
2. Topples
Slide is the most
3. Slides common mode of
• Translational (planar) slope failure, and it will
• Rotational (curved) be our main focus in
this course
4. Flows
5. Creep
6. Lateral spreads
 Types of Slide Failure Surfaces

• Failure of slopes generally occur along surfaces known as failure surfaces.

• The main types of surfaces are:

• Planar Surfaces: Occurs in frictional, non

cohesive soils

• Rotational surfaces: Occurs in cohesive soils

Circular surface Non-circular surface

(homogeneous soil) (non-homogeneous soil)
 Types of Slide Failure Surfaces

• Compound Slip Surfaces:

When there is hard stratum at some depth that intersects
with the failure plane

• Transitional Slip Surfaces:

When there is a hard stratum at a
relatively shallow depth
 Types of Failure Surfaces

Failure surface 1

Long plane
Infinite
failure surface
Translational
2
(planar)
Plane failure
Finite
Slides

surface

3
Above the toe
Rotational
Finite Through the toe
(curved)
Deep seated
 Types of Failure Surfaces

Types of Failure Surfaces Considered in this Course are

1

Stability of infinite slopes

2
Stability of finite slopes with plane
failure surfaces

3
Stability of finite slopes with circular
failure surfaces
 TOPICS

 Introduction
 Types of slope movements
 Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
o Culmann’s Method
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices
 Concepts of Slope Stability Analysis

In general we need to check

 The stability of a given existed slope
 Determine the inclination angle for a slope that we want to
build with a given height
 The height for a slope that we want to build with a given
inclination
 Methodology of Slope Stability Analysis

It is a method to expresses the relationship between resisting forces and

driving forces

• Driving forces – forces which move earth materials downslope. Downslope

component of weight of material including vegetation, fill material, or
buildings.

• Resisting forces – forces which oppose movement. Resisting forces include

strength of material

• Failure occurs when the driving forces (component of the

gravity) overcomes the resistance derived from the shear
strength of soil along the potential failure surface.
 Methodology of Slope Stability Analysis

The analysis involves determining and comparing the shear stress developed
along the most likely rupture surface to the shear strength of soil.
 Slope Stability Analysis Procedure

1. Assume a probable failure surface.

2. Calculate the factor of safety by determining and comparing
the shear stress developed along the most likely rupture
surface to the shear strength of soil.

3. Repeat steps 1 and 2 to determine the most likely failure

surface. The most likely failure surface is the critical surface
that has a minimum factor of safety.

4. Based on the minimum FS, determine whether the slope is

safe or not.
 Assumptions of Stability Analysis

o The problem is considered in two-dimensions

o The failure mass moves as a rigid body

o The shear strength along the failure surface is isotropic

o The factor of safety is defined in terms of the average shear

stress and average shear strength along the failure surface

 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
o Culmann’s Method
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices

39
 Factor of Safety

Factor of safety  Resisting Force

Driving Force

 Shear Strength
Shear Stress
  f= Avg. Shear strength of soil
Fs  f
d d= Avg. Shear stress developed along the failure surface

40
 Factor of Safety

• The most common analytical methods of slope stability use a

factor of safety FS with respect to the limit equilibrium condition,
Fs is the ratio of resisting forces to the driving forces, or
Shear strength (resisting movement)
(Available)
average shear strength of the soil.

Shear stress (driving movement)

average shear stress (developed)
developed along the potential
failure surface.

FS < 1  unstable
Generally, FS ≥ 1.5 is acceptable
FS ≈ 1  marginal
for the design of a stable slope
FS >> 1  stable

If factor safety Fs equal to or less than 1, the slope is

considered in a state of impending failure
41
The important geotechnical properties affecting stability of a
slope are shear strength of material.
Others
 particle size distribution
 density
 permeability
 moisture content
 Plasticity
 angle of repose.
 The strength of rock mass is a very important factor that
affects the stability of slopes. 42
 Factor of Safety

Where:
c’ = cohesion
’ = angle of internal friction
cd ,d = cohesion and angle of
friction that develop along
the potential failure surface
Other aspects of factor of safety
Factor of safety with respect to cohesion

Factor of safety with respect to friction

When the factor of safety with respect to cohesion is equal to the

factor of safety with respect to friction, it gives the factor of safety
with respect to strength, or

When Fc  F then Fs  Fc  F

43
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices

44
 Stability of Infinite Slopes

What is an Infinite slope?

• Slope that extends for a relatively long distance and has

consistent subsurface profile can be considered as infinite slope.

• Failure plane parallel to slope surface.

• Depth of the failure surface is small compared to the height of

the slope.

• For the analysis, forces acting on a single slice of the sliding mass
along the failure surface is considered and end effects is
neglected.
45
 Infinite Slope

The shear strength of the soil may be given by

 Assuming that the pore water pressure is zero, we will evaluate the
factor of safety against a possible slope failure along a plane AB
located at a depth H below the ground surface.
 The slope failure can occur by the movement of soil above the plane
AB from right to left.
 Let us consider a slope element abcd that has a unit length
perpendicular to the plane of the section shown.
 The forces, F, that act on the faces ab and cd are equal and opposite
and may be ignored.
 Infinite Slope

The weight of the soil element is

 Infinite slope – no seepage

Force parallel to the plane AB Ta =

W sin  =  LH sin 
(*)

The resistive shear stress is given by

48
 Infinite slope – no seepage

The effective normal stress at the base of the slope element is given by

(**)
Equating R.H.S. of Eqs. (*) and (**) gives

(***)

tan 
For Granular Soil (i.e., c = 0) Fs 
tan 
 This means that in case of infinite slope in sand, the value of Fs is
independent of the height H and the slope is stable as long as  < ’ 50
Case of Granular soil – Derivation From Simple Statics Extra

L Equilibrium of forces on a slice:

FS  Resisting Forces
Driving Forces

51
 Infinite slope – no seepage

Critical Depth, Hcr

The depth of plane along which critical equilibrium occurs is

obtained by substituting Fs = 1 and H = Hcr into Eq. (***)

52
 Infinite slope – with steady state seepage

Seepage is assumed to be parallel to the slope

and that the ground water level coincides with
the ground surface.

The shear stress at the base of

the slope element can be given

(*)

The resistive shear stress developed at

the base of the element is given by

(**)
53
 Infinite slope – with steady state seepage

Equating the right-hand sides of Eq. (*) and Eq. (**) yields

(***)

Recall

(****)

Substituting Eq. (****) Into Eq. (***) and solving for Fs gives

c tan 
Fs  
 H cos2  tan  tan 
No seepage

53
EXAMPLE

54
EXAMPLE

55
EXAMPLE

56
 Stability of Infinite Slopes

• Cohesive Soils
With seepage No seepage

tan '
tan ' tan'
c'
c ' c' tan ' c '
d F d F d Fs d F
s s s
Fs  c'   ' tan' Fs  c'  tan'
 sat H cos2  tan  sat tan H cos2  tan  tan 

Hcr  c'
Hcr  c' 1
cos2  ( sat tan   'tan')  cos2  (tan tan ')
d

57
 Stability of Infinite Slopes

Granular Soils
With seepage No seepage

c' 0.0 c' 0.0

 ' tan '
 tan'
c' c'
Fs   Fs 
 sat H cos 2  tan   sat tan 
H cos2  tan  tan 
Fs   ' tan ' Fs  tan'
 sat tan  tan 

Independant of H Slope is stable as long as  < 

58
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Circular Failure Surface
o Mass Method
o Method of Slices

59
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
o Culmann’s Method
 Stability of Finite Slopes with Circular Failure Surface
o Method of Slices

60
 Finite Slopes with Circular Failure Surface

Modes of Failure
i. Slope failure
• Surface of sliding intersects the slope at or above its
toe.

1. The failure circle is referred to as a toe circle if it passes

through the toe of the slope
1. The failure circle is referred to as a slope circle if it
passes above the toe of the slope.

ii. Shallow failure

Under certain circumstances, a shallow slope failure
can occur.
Shallow slope
failure 73
 Finite Slopes with Circular Failure Surface

iii. Base failure

o The surface of sliding passes
at some distance below the
toe of the slope.

o The circle is called the H

midpoint circle because its
center lies on a vertical line
drawn through the midpoint of
the slope.
Firm Base
o For   53o always toe
o For  < 53o could be toe, slope, or midpoint and that depends on depth
function D where:
Depth function:

62
 Types of Stability Analysis Procedures

Various procedures of stability analysis may, in general, be divided into two major
classes:
1. Mass procedure
• In this case, the mass of the soil above the surface of sliding is taken as a unit.

• This procedure is useful when the soil that

forms the slope is assumed to be
homogeneous.
2. Method of slices

• Most natural slopes and many man made

slopes consist of more than on soil with
different properties.
• In this case the use of mass procedure is inappropriate.
76
 Types of Stability Analysis Procedures

• In the method of slices procedure, the soil above the surface of

sliding is divided into a number of vertical parallel slices.
• The stability of each slice is calculated separately.

• It is a general method that can be used for analyzing irregular slopes

in non-homogeneous slopes in which the values of c’ and ’
are not constant and pore water pressure can be taken into
consideration.

77
 TOPICS

 Introduction
 Types of slope movements
 Concepts of Slope Stability Analysis
 Factor of Safety
 Stability of Infinite Slopes
 Stability of Finite Slopes with Plane Failure Surface
 Stability of Finite Slopes with Circular Failure Surface
o Method of Slices

65
 Finite Slopes with Circular Failure Surface

• Fellenius (1927) and Taylor (1937) have analytically solved for

the minimum factor of safety and critical circles.
• They expressed the developed cohesion as
cd   H m
Where
• We then can calculate the min Fs as m  Stability number
H  height of slope
γ  unit weight of soil
c
or m  d
 H

• The critical height (i.e., Fs = 1) of the slope can be evaluated by

substituting H = Hcr and cd = cu (full mobilization of the undrained shear
strength) into the preceding equation. Thus, 66
 Finite Slopes with Circular Failure Surface

 The results of analytical solution to obtain critical circles was represented

graphically as the variation of stability number, m , with slope angle 

Toe slope Toe, Midpoint or slope circles

Firm Stratum

m is obtained from this chart depending on angle  83

Finite Slopes with Circular Failure Surface

Failure Circle

 For a slope angle  > 53°, the critical circle is always a toe circle. The
location of the center of the critical toe circle may be found with the aid of
Figure 15.14.
 For  < 53°, the critical circle may be a toe, slope, or midpoint circle,
depending on the location of the firm base under the slope. This is called
the depth function, which is defined as

68
 Location of the center of the critical toe circle

The location of the center of the

critical toe circle may be found with
the aid of Figure 15.13

(radius)

Figure 15.13

69
Finite Slopes with Circular Failure Surface

When the critical circle is a midpoint circle (i.e., the

failure surface is tangent to the firm base), its position
can be determined with the aid of Figure 15.14.

Figure 15.14

Firm base
86
Critical toe circles for slopes
with  < 53°

The location of these circles can be

determined with the use of Figure 15.15
and Table 15.1.

Figure 15.15

Note that these critical toe circle are not necessarily the most critical circles that exist.87
How to use the stability chart? Given:   , H, , cu Required: min Fs

m = 0.195

1. Get m from chart

2. Calculate cd from
cd   H m
3. Calculate Fs
cu
Fs 
cd

88
 How to use the previous chart?

Given:  , H, , cu, HD (depth to hard stratum) Required: min. Fs

D = Distance from the top surface of slope to firm base

Height of the slope

m = 0.178

1. Calculate D = HD/H
2. Get m from the chart
3. Calculate cd from
cd   H m
cu
4. Calculate Fs Fs 
cd

Note that recent investigation put angle  at 58o instead of the 53o value. 89
EXAMPLE

90
Rock layer
SOLUTION

D=1.5m
91
SOLUTION

92
 Slopes in Homogeneous clay Soil with c  0 ,  = 0

 The results of analytical solution to obtain critical circles was represented

graphically as the variation of stability number, m , with slope angle 

Toe slope Toe, Midpoint or slope circles

Firm Stratum

m is obtained from this chart depending on angle 

93
 Method of Slice

Geometry of Ordinary Method of Slices. Example of dividing the failure mass in slices
 Method of Slope Stability Analysis

Method of Slices
• Non-homogenous soils (mass procedure is not accurate)
• Soil mass is divided into several vertical Parallel slices
• The width of each slice need not be the same
• It is sometimes called the Swedish method

112
 Method of Slices

• It is a general method that can be used for analyzing irregular slopes in

non-homogeneous slopes in which the values of c’ and  ’ are not
constant.

• Because the SWEDISH GEOTECHNCIAL COMMISION used this method

extensively, it is sometimes referred to as the SWEDISH Method.

• In mass procedure only the moment equilibrium is satisfied. Here attempt

is made to satisfy force equilibrium.

1, c’1,

’1
2, c’2, , c’, ’
’2 
3, c’3,
’3
Irregular Slope 113
Non-homogeneous Slope
 Method of Slices

• The soil mass above the trial slip surface is divided into several vertical parallel
slices. The width of the slices need not to be the same (better to have it equal).
• The accuracy of calculation increases if the number of slices is increased.
• The base of each slice is assumed to be a straight line.
• The inclination of the base to the horizontal is .
• The height measured in the center line is h.
• The height measured in the center line is h.
• The procedure requires that a
series of trial circles are chosen
and analyzed in the quest for
the circle with the minimum
factor of safety.

Tr

114
 Method of Slices

• Forces acting on each slice

• Total weight wi=hb
• Total normal force at the base Nr = *L
• Shear force at the base Tr=*L
• Total normal forces on the sides, Pn and Pn+1
• Shear forces on the sides, Tn and Tn+1
• 5 unknowns Tr ,Pn ,Pn+1 ,Tn ,Tn+1
• 3 equations Fx=0 , Fy=0 ,M=0
• System is statically indeterminate
• Assumptions must be made to solve the
problem
• Different assumptions yield different methods
• Two Methods:
• Ordinary Method of Slices (Fellenius Method)
• Bishop’s Simplified Method of Slices

115
 Method of Slices

For the whole sliding mass

 Mo  0
W *r*sin  - T *r  0
W *sin  T
f
T   d *l  *l
F
s

W *sin  f *l
Fs
 f *l
Fs 
W *sin
(c*l  *tan *l)
Fs  n
W *sin 116
 Method of Slices

(c*l  *tan *l)

Fs  n
W *sin
  n *l  N
Fs  c*l  tan *N
W *sin
Equation is exact but approximations are introduced in finding
the value of force N

Two Methods:
• Ordinary Method of Slices
• Bishop's Simplified Method of Slices

84
 Ordinary Method of Slices

Fellenius’ Method
Assumption
 For each slice, the resultant of the interslice forces is
zero.
 The resultants of Pn and Tn are equal to the resultants
of Pn+1 and Tn+1, also their lines of actions coincide.

Rn

Rn+1

85
 Ordinary Method of Slices

Fn  0 (to stay away from Tr )

N r  Wn * cos  n n
 ( c* l  W * cos tan )
Fs  n n n
Wn * sinn
For undrained condition:
c  cu  0
cul
Fs 
Wn * sinn
86
 Ordinary Method of Slices

Steps for Ordinary Method of Slices

• Draw the slope to a scale
• Divide the sliding wedge to various slices
• Calculate wn and n for each slice
• n is taken at the middle of the slice wn
wn
• Calculate the terms in the equation

 ( c* l W * cos tan )
Fs  n n n
n
Wn* sinn n
+ve
-ve

• Fill the following table

Slice# wn n sin n cos n ln wn sin n wn cos n

87
 EXAMPLE

Find Fs against sliding

Use the ordinary method of slices

88
 Bishop’s Simplified Method of Slices

Assumption
For each slice, the resultant of the interslice forces is
Horizontal.

i.e. Tn =Tn+1

89
 Bishop’s Simplified Method of Slices

Fy  0 (to stay away from Pn and Pn1 )

y
Wn  N r * cos  n  Tr * sin n
 c   n tan 
Tr   d * ln   ln
 Fs 
cl n  n  l n tan
Tr  
Fs Fs
cl n N r tan
Tr  
Fs Fs
cln N tan
Wn  N r * cos n  sin n  r sin n
Fs Fs

90
 Bishop’s Simplified Method of Slices

cln
Wn  sin  n
Fs
Nr 
tan  sin  n
cos  n 
Fs
 cln 
 sin  n
 Wn Fs 
 cl n  tan   
 cos   tan  sin  n 
 n
Fs  bn
Fs  but l n 
tan  sin  n cos  n
cos  n 
Fs

Fs 
1
 W n sin  n
 cb n  W n tan 
tan  sin  n
cos  n 
Fs
Trail and error procedure
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 Bishop’s Simplified Method of Slices

Steps for Bishop’s Simplified Method of Slices

• Draw the slope to a scale
• Divide the sliding wedge to various slices
• Calculate wn and n for each slice
• n is taken at the middle of the slice
• Calculate the terms in the equation

cb n  W n tan 
Fs 
1
 W n sin  n
 tan  sin  n
cos  n 
Fs
• Fill the following table
Slice# wn n sin n cos n bn wn sin n
• Assume Fs and plug it in the right-hand term of the equation
then calculate Fs
• Repeat the previous step until the assumed Fs = the
calculated Fs.
92
 Bishop’s Simplified Method of Slices

tan  sin  n
m ( n )  cos  n 
Fs
1
( cb n  W n tan  )
Fs    W n sin  n
m ( n )

c' bn Wn tan 

Fs 
1
( )
Wn sin  n cos  n 
sin  n tan  
Fs

93
 Bishop’s Simplified Method of Slices

• Example of specialized software:

– Geo-Slope,
– Geo5,
– SVSlope
– Many others

94
 Final Exam Fall 36-37 QUESTION #4

Determine the safety factor for the given trial rupture surface shown in
Figure 3. Use Bishop's simplified method of slices with first trial factor of
safety Fs = 1.8 and make only one iteration. The following table can be
prepared; however, only needed cells can be generated “filled”.

95
 SOLUTION
Fs = 1.8
Table 1. “Fill only necessary cell for this particular problem”
Width Height Height Area Weight
Slice Wn sin 
bn hl h2 A Wn α(n) mα(n)
No. (kN/m)
(m) (m) (m) (m2) (kN/m) (7) (8)
(1) (9)
(2) (3) (4) (5) (6)

1 22.4 70
2 294.4 54
3 ? 38
4 435.2 24
5 390 12
6 268.8 0.0
7 66.58 -8

96
 Remarks on Method of Slices

o Bishop’s simplified method is probably the most widely used (but it has
to be incorporated into computer programs).

o It yields satisfactory results in most cases.

o The Fs determined by this method is an underestimate (conservative) but

the error is unlikely to exceed 7% and in most cases is less than 2%.

o The ordinary method of slices is presented in this chapter as a learning

tool only. It is used rarely now because it is too conservative.

o The Bishop Simplified Method yields factors of safety which are higher
than those obtained with the Ordinary Method of Slices.

o The two methods do not lead to the same critical circle.

o Analyses by more refined methods involving consideration of the forces acting
on the sides of slices show that the Simplified Bishop Method yields answers
for factors of safety which are very close to the correct answer. 130
 Remarks on Method of Slices

Two Methods:
Ordinary Method of Slices
• Underestimate Fs (too conservative)
• Error compared to accurate methods (5-20%)
• Rarely used

Bishop’s Simplified Method of Slices

• The most widely used method
• Yields satisfactory results when applying computer
program

131