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Unformatted text preview: 11/17 The Relationship between Limit Equilibrium Slope Stabilitv Methods
La Relation des Méthodes de Limite d’EquiIibre de Pente Stable D.G. FREDLUND
.J. KRAHN
D.E. PUFAHL SYNOPSIS. Dept. of Civil Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada Some of the methods commonly used for analyzing slopes utilizing the principles of limit equilibrium are the Ordinary or Fellenius method, the simplified Bishop method, the Corps of Engineers method, the Janbu simplified and the Janbu generalized methods, the Spencer method, and the MorgensternPrice method. these methods have been obscure, largely because of: The similarities and differences in 1) the lack of uniformity in formulating the equations of equil~ ibrium, 2) the ambiguity concerning interslice forces and 3) the unknown limitations imposed by non—circular failure surfaces. Theoretical studies have shown that a common formulation of the equilibrium equations can be used for all of the methods.
The factor of safety equations have been derived with respect to moment equilibrium and with respect to force equilib— rium, and all methods use either or both of these equations. In addition, the use of an interslice force, functional relationship (i.e., lambda, A) has been used to relate and compare the factors of safety computed for the various meth ods. This approach has provided a clear and concise assessment of the variation in factors of safety that are computed
by the different methods for typical cross—sections, pore—water pressures and soil profiles. INTRODUCTION During the past three decades, numerous methods have been
proposed for performing the two—dimensional limit equili'
brium method of slices (Wright, 1969). The methods most
commonly used are: i) The Ordinary method. Other names given to this
method are the Fellenius, Swedish Circle and
Conventional method. ii) The simplified Bishop method.
iii) The Spencer method.
iv) The Janbu simplified and the Janbu generalized
methods. v) Force equilibrium methods such as the Lowe and
Karafiath method, the Corps of Engineers method,
and the Taylor modified Swedish method. vi) The MorgensternPrice method. The similarities and differences in these methods have
been obscure, largely because of the lack of uniformity
in formulating the factor of safety equations, the ambi
guity concerning interslice forces and the unknown limi
tations imposed by noncircular failure surfaces. Some
attempts have been made to assess the quantitative dif
ferences in factors of safety obtained from the various
methods (Bishop, 1955; Wright, 1969; Duncan and Wright,
1980). In general, the quantitative differences in fac
tors of safety obtained by the various methods, are not
substantial with the exception of the Ordinary method
which can differ by more than 60 percent from the other
methods (Whitman and Bailey, 1967). Some attempts have
also been made to show the relationship between the var
ious methods from a theoretical standpoint (Wright, 1969;
Fredlund and Krahn, 1977; Naderi, 1977; Popescu, 1978;
Janbu, 1980). The object of this paper is to present a general limit
equilibrium method of slices formulation in two
dimensions and to show how each of the methods listed
above is a special case of the general formulation.
(Hereafter, the general limit equilibrium method of slices is simply referred to as the GLE method). The
Ordinary method becomes an exception which cannot be re
lated to the general formulation since it does not sat
isfy Newtonian force principles at the interslices
(Fredlund and Krahn, 1977). The paper also shows how
the various methods of slices can be extended to non— circularslip surfaces. Example problems are used to
demonstrate the relationship between the factors of
safety. GENERAL LIMIT EQUILIBRIUM METHOD OF SLICES (GLE METHOD) The elements of statics that can be used to derive the
factor of safety are the summation of forces in two di—
rections and the summation of moments about a chosen
point of rotation. These elements of statics, along
with the failure criteria, are insufficient to make the
slope stability problem determinate. Either additional
elements of physics or an assumption regarding the di
rection or magnitude of some of the forces is re
quired to render the problem determinate. All methods
considered in this paper use the latter procedure and
make an assumption concerning the interslice forces. Theoretical studies have shown that factor of safety
equations can be independently derived to satisfy moment
equilibrium and force equilibrium of the slices contained
above an assumed slip surface (Fredlund and Krahn, 1977).
In addition, an assumed functional relationship is used
to specify the direction of the interslice forces. Later
in this paper, the various limit equilibrium methods of
slices are viewed as special cases of the GLE formula—
tron. Circular Slip Surface
Figure 1 shows the forces involved in the derivation of moment and force equilibrium factor of safety equations
for a circular slip surface. 11/17 CENTER OF ROTATION s——n 7mm caucus
wrm wares 1"” Fig. I Forces Acting For The Method Of Slices (Circular
Slip Surface) The definition of each variable is as follows: W = the total vertical force due to the mass of a
slice of width 'b' and height 'h'. P I the total normal force on the base of a slice.
Sm  the shear force mobilized on the base of each
slice.
E  the horizontal interslice normal forces.
X = the vertical interslice shear forces.
R = the radius or the moment arm associated with the mobilized shear force, Sm. x = the horizontal distance from the centroid of
each slice to the center of rotation. a = the perpendicular distance from the resultant external water force to the center of rotation. = the width of a slice. the resultant external water forces. a = the angle between the tangent to the center of
the base of each slice and the horizontal. {>7
(I The 'L' and 'R' subscripts on the 'E‘, 'X' 'a' and 'A'
variables designate the left and right sides, respective
1y. The magnitude of the shear force mobilized at the base of a slice can be written in terms of the MohrCoulomb fail
ure criterion. Sm  § {c' + (an — u)tan ¢'1 [11 = effective cohesion intercept ¢'  effective angle of internal friction.
o  PIE 2  length of the failure surface at the base of
each slice. F ‘ factor of safety. A moment equilibrium equation for the GLE method is des
cribed for all slices by summing moments about the center
of rotation. zwx  2st : Aa a 0 [2] The interslice shear and normal forces (i.e., X and E) do not appear directly in equation [2] since their summation
over the overall slope must cancel. The mobilized shear force, 5 , is written in terms of the
shear strength criterion [1]? and equation [2] can be
solved for the factor of safety with respect to moment
equilibrium, Fm. 410  Z[c‘l + (P  u2)tan ¢']R
Fm {ﬁx 1 Aa [3] The force equilibrium equation for the GLE method is writ ten by summing forces in the horizontal direction for the
overall slope. 2? Sin a  23m cos a 1 A  0 [4] Once again the interslice forces must cancel. The
mobilized shear force is again written in terms of the failure criterion [1], and equation [4) can be solved for
the force equilibrium factor of safety, Ff. _ [[c'l + (P — u2)tan '] cos o
F: D sin ala [5] The normal force, F, for equations [3] and [5] can be
evaluated by summing forces vertically on each slice. _ _ _ c'l Sin a ul tan @' Sin a
P_” (KR XL) F 4' F [6]
no
where: Sin o tan ¢'
m  cos a +
o F The factor of safety, F, in [6] can be either with res
pect to moment or force equilibrium depending upon the
factor of safety equation being solved. Any one of a
number of possible assumptions can be made in order to
compute the interslice shear forces. The various methods
of slices that are commonly used can be categorized in
terms of the assumption that is made regarding the inter
slice shear forces, and whether the computed factors of
safety satisfy moment or force equilibrium, or both. NonCircular Slip Surface Figure 2 shows the forces that are used in the derivation
of the moment and force equilibrium factor of safety
equations in the GLE method for a noncircular slip sur
face. The slip surface that is shown starts and ends
with a circular portion, and has a central linear portion
The noncircular portion is assumed to be the result of a
geological discontinuity which does not allow the slip
surface to penetrate deeper. This type of non circular surface is termed a composite slip surface
(Fredlund, 1975), and it attempts to model typical ob
served modes of failure (Krahn et a1, 1979). From a
theoretical standpoint there are two changes in the moment
equilibrium equation. The moment arm associated with the
mobilized shear force becomes a variable distance, R, and
the normal force, P, has an offset arm, f. #1 norm c NTER
‘1 or WATISN 0L TENSJON CRACKS
WITH WATER Fig. 2 Forces Acting For The Method Of Slices (Composite
Slip Surface) The factor of safety equation for moment equilibrium be—
comes, F I Z[c'l + (P  u2) tan Q']R [7]
m EWx  ZPf I As The factor of safety equation for force equilibrium [5]
and the equation for the normal force [6] remain unchan
ged. The center for moment equilibrium is the center of
rotation for the circular portion of the slip surface. COMPARISON OF THE GLE FORMULATION AND COMMONLY USED
METHODS OF SLICES Morgenstern—Price Method Horgenstern and Price (1965) solved for the factor of
safety using the summation of forces tangential and norm—
al to the base of a slice and the summation of moments
about the center of the base of each slice. The equat—
ions were written for a slice of infinitesimal thickness.
The force and moment equilibrium equations were combined
and a modified NewtonRaphson numerical technique was
used to solve for the factor of safety satisfying force
and moment equilibrium. The solution required an arbi—
trary assumption regarding the direction of the result
ant of the interslice shear and normal forces. Figure 3
shows typical functional forms which can be written as x/E = Af(x)
where: f(x)  a function that describes the manner in which
X/E varies across the slope, and
A x a constant representing the percentage (i.e.,
portion of the function used when solving for
the factor of safety. f(x) CONSTANT ﬁx)  HALF— SI NE
I l
12 ..
v K
" 3':
1 o O L x R L x ‘ f (x)CLPPED—SINE I ﬁx)  TRAPEZOID
22
O L x R I f1x) SPECIFIED L LEFT
R RIGHT L x R Fig. 3 Typical Functional Variations For The Direction
Of The lnterslice Force With Respect To The X
Direction The moment and force factor of safety equations (i.e.,
equations [3] and [5] for the OLE method can be solved
independently for a given function, f(x). by assuming
various trial values of "X" (Fredlund, 1974). A bestfit
regression line through the factors of safety associated
with the "K" values indicates the factor of safety satis
fying both moment and force equilibrium. The factor of
safety satisfying both force and moment equilibrium can 11/17 also be obtained by using a NewtonRaphson numerical sol
ver . The assumption regarding the interslice forces and the
elements of statics used in the MorgensternPrice formu—
lation are the same as those used in the CLE formulation.
However, there is a light difference in the way the norm—
al force is applied to the base of the slice (Figure A).
The MorgensternPrice method uses integration across the
slope, and this results in a linear variation of the nornr
31 force across the base of the slice. As a result, the
resultant normal force, F, can have a slight offset from
the center of the slice. The GLE formulation assumes that
the resultant normal force acts through the center of the
slice. Fredlund and Krahn (1977) used a 12,2 m high, 2:1 slope
to study the difference in factor of safety and "A" be—
tween the MorgensternPrice formulation and the GLE form
ulation. The first example considered a circular slip
surface passing through a homogeneous soil with an ef
fective angle of internal friction of 20 degrees and an
effective cohesion intercept of 28.7 kPa. The example
problem was then modified to form a composite slip sur
face by introducing a hard layer at a depth of 1.52 m be
low the toe of the slope. A thin, soft layer with an ef
fective angle of internal friction of 10 degrees and zero
effective cohesion was located immediately above the hard
layer. Two pore pressure coefficients were used for each
case. The computed factors of safety and "A" values are
presented in Table 1. The MorgensternPrice method was
solved using the University of Alberta computer program
(Krahn et a1, 1971) and the OLE formulation was solved
using the SLOPE computer program (Fredlund, 1974). MORGEN STERN  PRICE
FORMULATION C / ¢ GENERAL LIMIT
/ EQUILIBRIUM
FORMULATION Fig. h Point of Application of Normal Force For
MorgensternPrice Formulation and General
Formulation 411 11/17 Table I. Comparison of Factors of Safety and "A" Using the MorgensternPrice Method and the GLE Method __..._________..._____..___________.__.__________________ Shape of Side Force Morgenstern—Price GLE
Failure r Function Method Method
Surface u * * F X F X Circular 0.0 Constant 2.085 0.257 2.076 0.254 Circular 0.0 Half Sine 2.085 0.314 2.076 0.318 Circular 0.25 Constant 1.772 0.351 1.765 0.244 Circular 0.25 Half Sine 1.770 0.434 1.764 0.304 Composite 0.0 Constant 1.394 0.182 1.378 0.159 Composite 0.0 Half Sine 1.386 0.218 1.370 0.187 Composite 0.25 Constant 1.137 0.334 1.124 0.116 Composite 0.25 Half Sine 1.117 0.4A1 1.118 0.130 * The tolerance is 0.001 The average difference in the factors of safety obtained
from the MorgensternPrice method and the GLE method was
negligible (i.e., less than 0.01). The average difference
in the "A" values was in the order of 0.1 with the
Morgenstern—Price formulation being higher. The differ
ence in "A" value is attributed to the procedure used to handle the normal force at the base of the slice. The
results indicate that there is a small difference in the computations due to the manner in which this force is
handled. The Spencer Method The Spencer method assumes a constant relationship be
tween the magnitude of the interslice shear and normal
forces (Spencer, 1967). x/E = tan 6 [9] where: 6  angle of the resultant interslice force from the
horizontal. Equation [9] is the same as equation [8} if the inter
slice force function, f(x), is equal to 1; then "X" is
equal to tan 8. Spencer (1967) summed forces perpendicu
lar to the interslice forces to derive the normal force
equation. However, the same equation can be derived by
sunning forces in a vertical and horizontal direction
(i.e., equation [6]. Spencer (1967) derived two factor of safety equations;
one satisfying force equilibrium. These equations are
essentially the same as those proposed in the GLE form—
ulation when the interslice force function, f(x), is as
sumed to be a constant. Two example problems were selected to demonstrate the re— lationship between the Spencer method and the GLE formu
lation (Figure 5). Example No. 1 considers a circular slip surface while example No. 2 is forced into a composite mode by a bed
rock layer. The examples ate similar to those described
previously in this paper (Fredlund and Krahn, 1977) with
the exception that a 3.05 m tension crack zone with no water is assumed and the pore pressure coefficient is
0.2. The results for example No. 1 (Figure 6) show that the
Spencer method and the OLE formulation give the same
results. Likewise, the results for example No. 2 (Fig— ure 7) show agreement between the Spencer method and the
GLE formulation. The interslice force directions on Figures 6 and 7 are presented in terms of tan 9 (i.e., A). 412 °(56£,2741 18
E
5 12
E P: 1.92 Mq/m3
I
a ¢= 20°
5,1 6 c‘=2e.75 kPa
(u: 0.2
6 12 1e 24 30 36 42
DISTANCE (m)
o (36.6.2141
P=1.92 Mq/m3
A '8 ¢‘=10°
E _____ 6:0
5 12 P=1.92 Mg/m3
E 49: 20"
a c'=28.75ch1
d 6 ru=o_2 BEDROCK [2 18 24 30 36 42
WSTANCE [NU Fig. 5 Example Problems with Circular And Composite Slip
Surfaces 220
215
210 205 ',_ 200
E
< 195
U)
3 1.90
K
.9 '35 SIMPLIFIED
g BISHOP
u 1.80
175
1.70 +SPENCER METHOD
0 GENERAL LIMIT EQUILIBRIUM
155 1111)  CONSTANT ISO JANBU'S SIMPLIFIED
(WITHOUT CORRECTION FACTOR) O Q! 02 Q3 Q4 Q5 03 I Fig. 6 Comparison of Factors 0f Safety For Example No. 1
(Circular Slip Surface) l25 [20 [15 110
SIMFHJFIED '// mSHOP FACTOR OF'SAFETY JANBU'S SIMPLIFIED
(WITHOUT CORRECTION FACTOR) +SPENCER
0 GENERAL LIMIT EQUILIBRIUM
f(x)CONSTANT I00 0 0,1 (12 0.3 0.4 0.5 0.6
I Fig. 7 Comparison Of Factors Of Safety For Example No. 2
(Composite Slip Surface) Simplified Bishop Method The simplified Bishop method neglects the interslice
shear forces (Bishop, 1955). The normal force equation
is the same as equation [6] with the interslice shear
forces set to zero. The factor of safety equation is
derived by taking moments about the center of rotation.
In other words, the simplified Bishop method corresponds
to the moment equilibrium factor of safety equation [3]
when "X" is equal to zero or the Spencer moment equilib
rium equation when 9 is equal to zero (See Figure 6 and
7). The simplified Bishop method bears the same rela
tionship to the GLE formulation (or the Spencer equat
ions) regardless of whether the slip surface is circular
or composite. In general, the difference between the
simplified Bishop factor of safety and the factor of
safety satisfying both force and moment equilibrium, de—
creases as a particular slip surface has an increasing
planar portion. Janbu Simplified Method In the derivation of the Janbu simplified method the
interslice shear forces are assumed to be zero (Janbu et
a1, 1956). The normal force equation is the same as
equation [6] with the interslice shear forces set to zero
The factor of safety is computed from the horizontal
force equilibrium equation (i.e., equation [5]). Then an empirical correction factor is multiplied by the com
puted factor of safety in an attempt to account for the
effect of the interslice shear forces. ‘The empirical
correction factor is related to the shear strength prop—
erties and the shape of the slip surface. Moment equili—
brium is not satisfied. The uncorrected factors of safe
ty correspond to the force equilibrium factor of safety,
[5], when "A" equals zero. For examples No. 1 and No. 2,
the uncorrected factors of safety for the Janbu simpli—
fied method are 1.609 and 1.005, respectively, (See Fig—
ures 6 and 7). The empirical correction factor generally 11/17 increases the factor of safety by up to approximately 10
percent. Janbu Generalized Method The Janbu generalized method includes the effect of inter
slice forces by making an assumption regarding the point
at which the interslice forces act (i.e., the line of
thrust; Janbu, 1954; Janbu et al, 1956). The normal force
equation is derived from the summation of vertical forces
equation [6]. The factor of safety equation is derived from the horizon—
tal force equilibrium equation (equation [5]). In order
to solve for the factor of safety, the interslice shear
forces are computed from the summation of the moments
about the center of the base of each slice. XR = ER tan at — (ER  EL) tR/b [10]
where:
at = angle between the line of thrust on the right
side of a slice and the horizontal.
tR = vertical distance from the base of the slice to the line of thrust on the right side of the
slice. The horizontal interslice forces required for equation
[10], are obtained by summing forces in the horizontal
direction on each slice. EL — ER Sm cos a ~ P sxn a [11] Once the Janbu generalized factor of safety equation, [5),
has been solved, it is possible to plot the computed in
terslice shear and normal forces and determine a corres
ponding side force function. It was not possible to ob
tain a side force function for examples No. 1 and No. 2
since convergence difficulty was encountered because of the geometry that was arbitrarily chosen in these two
cases. Example No. 3 (Figure 8) is used to demonstrate the rela—
tionship between the Janbu generalized method and the GLE formulation. The factor of safety by the Janbu general
ized method is 1.19. Px 208 Mq/m3
dxs7s7hPo
49245 so
995 P: 205 Mm!
c' 9.59 “’0 so 4’" “' ELEVATION (m) 30 SLIP SURFACE .J_ _L_ _L J 1.— .I
O 30 60 90 I20 I50 ISO 210
DISTANCE lm) Fig. 8 Example No. 3 To Demonstrate The Janbu General
ized Method The ratio of the computed interslice shear and nor—
mal force was plotted versus the distance along the slip
surface (Figure 9). The resulting plot was used as a
side force function, f(x), in the OLE equations with the
"A" value set to 1. The factor of safety from the GLE
(Force) equation, {5], yielded the same factor of safety 413 11/17 as that obtained by the Janbu generalized method. In
other words, the summation of forces on each slice can be
viewed as a means of obtaining a particular type of side
force function. In this way, moment equilibrium is im~
Dlicitlv satisfied. 20 L5 10 1(1) Th __+ _._.,L _1. I L—
30 60 90 IZO I50 I80
DISTANCE ( m 1 Fig. 9 Side Force Function For Example No. 3 Using The
Janbu Generalized Method Force Equilibrium Methods
— Lowe and Karafiath Method The Lowe and Karafiath method computes the factor of safe
ty from a force equilibrium equation. The direction of
the resultant of each interslice force is assumed to be
equal to the average of the surface and slip surface
slopes. The computed side force functions for examples
No. 1 and 2 (Figure 5) are shown in Figures 10 and 11,
respectively. These side force functions were then used
in the GLE formulation with "X" set to 1. 24 EXAMPLE N01 5 ELEVATION (m)
K) 6 I2 I8 24 30 36 42 48 DISTANCE (m) L0 11“ DISTANCE (m) Fig. 10 Side Force Function Using Lowe and Karafiath
Method (Example No. I) 414 N
b EXAMPLENQZ E ELEVATION (m)
E 6 12 I8 24 30 36 42 48 DISTANCE ("U DISTANCE (m) Fig. 11 Side Force Function Using Lowe And Karafiath
Method (Example No. 2) Table 2 shows the force and moment equilibrium factors of
safety from the GLE equations when using the Love and
Karafiath assumption regarding the interslice force dir
actions. Table II. Factors of Safety Using the Lowe and Karafiath
Interslice Force Assumption Example GLE Method
No. F F f m I 1.880 1.791 2 1.096 1.068 The force equilibrium factor of safety, [5], corresponds
to the Love and Karafiath factor of safety. These fac
tors of safety can be compared with those obtained by
other methods (See Figure 6 and 7). The Lowe and Kara
fiath assumption regarding the interslice forces can be
interpreted as a special side force function applied to
the CLE formulation. — Corps of Engineers Method The Corps of Engineers method (1970) computes the factor
of safety from the force equilibrium equation [5]. The
direction of the resultant interslice force is assumed to
be equal to the average surface slope. This appears to
be interpreted as either equal to the average slope be—
tween the extreme extrance and exit of the failure sur—
face, (Case 1) or the changing slope of the ground sur
face (Case 2). A side force function is computed for
Case I and 2, (Figure 12). 24 EXAMPLENQZ ELEVAWON (m) 4 BEDROCK *rauunrnm 6 I2 8 24 30 36 42 4B NSTANCE (m) LO 05 I'llIllllllllliiiillllllllllllllll mSTANCE (m) (CASEZ Fig. 12 Side Force Function Using the Corps 0f Engineers
Method (Example No. 1 and 2) The side force functions, f(x), are the same in both ex
amples No. 1 and 2. Table 3 summarizes the factors of
safety obtained using the OLE equations along with the
Corps of Engineers interslice force assumptions. The "A"
value is set equal to 1. Table III. Factors of Safety Using the Corps of Engineers
Interslice Force Assumptions Example Case GLE Method
No. No. F F f m 1 1 1.893 1.810 2 2.000 1.801 2 1 1.102 1.068 2 1.100 1.050 The force equilibrium factors of safety (GLE method) cor
respond to the Corps of Engineers factor of safety. Since
the function, f(x), is a constant, it can be set to 1 and
"A" can be used as before. The factors of safety for the
Case 1 assumption can be seen to correspond to a "K"
value of 0.364 in Figure 6 and 7. Again, the Corps of
Engineers assumption regarding the direction of the re
sultant interslice forces can be interpreted as a special
side force function applied to the GLE formulation. The Corps of Engineers factors of safety (as well as the
Lowe and Karafiath factors of safety) lie along a force
equilibrium factor of safety line. The magnitude of the
factor of safety may either be higher or lower than the
factor of safety satisfying both force and moment equilib
rium. It should be noted that the force equilibrium
factor of safety is more highly influenced by the side
force assumption than the moment equilibrium factor of
safety. 11/17 SUMMARY The factor of safety equations for all methods of slices
considered can be written in the same form if the moment
and/0r force equilibrium are explicity satisfied. This
applies for both circular and composite (noncircular)
slip surfaces. The normal force at the base of each slice can be solved using the same equation for all meth
ods, with the exception of the Ordinary method. The type
of side force function assumed or computed, results in a
variation in the normal force at the base of a slice. This also accounts for the difference in factors of safety
between various methods when force or moment equilibrium
are considered independently. The analytical aspects of
slope stability analysis can be viewed in terms of one
factor of safety equation satisfying overall moment equi
librium and another satisfying overall force equilibrium
for various "X/E” values. Each of the methods of slices
coneideredbecomes a special case of the proposed GLE fonr
ulation. LIST OF REFERENCES Bishop, A. W. (1955), "The Use of the Slip Circle in the
Stability Analysis of Slopes", Geotechnique, 5, pp. 7—17. Duncan, J. M. and Wright, S. G. (1980), "The Accuracy of
Equilibrium Methods of Slope Stability Analysis", Proceed—
ings of the International Symposium on Landslides, New
Delhi, Vol. 1, pp. 247—255. Fredlund, D. G. (1974), "Slope Stability Analysis", User's
Manual CDé, Dept. of Civil Engineering, University of
Saskatchewan, Saskatoon, Canada. Fredlund, D. G. (1975), "A Comprehensive and Flexible
Slope Stability Program", Presented at the Roads and
Transportation Association of Canada Meeting, Calgary,
Alberta, Canada. Fredlund, D. G. and Krahn, J. (1977), "Comparison of
Slope Stability Methods of Analysis", Canadian Geotechni
cal Journal, Vol. 1h, pp. 429A39. Janbu, N. (1980), "Critical Evaluation of the Approaches
to Stability Analysis of Landslides and Other Mass Move ments, Free. International Symposium on Landslides, New
Delhi, Vol. 2, pp. 109128. Janbu, N. (1954), "Application of Composite Slip Surfaces
for Stability Analysis", Proceedings of the European Con
ference on Stability of Earth Slopes, Stockholm, Vol. 3
pp. 43—49. Janbu, N.; Bjerrum, L. and Kjaernsli, B. (1956), "Stabil—
itetsberegning for fyllinger skjaeringer og naturlige
skraninger", Norwegian Geotechnical Publication No. 16,
Oslo, Norway. Krahn, J.: Johnson, R. P.; Fredlund, D. G. and Clifton,
A. W. (1979), "A Highway Cut Failure in Cretaceous Sedi—
ments at Maymont, Saskatchewan", Canadian Geotechnical
Journal, Vol. 16, No. 4, pp. 703715. Krahn, J.; Price, V. E. and Morgenstern, N. R. (1971),
"Slope Stability Computer Program for MorgensternPrice
Method of Analysis", User's Manual No. 14, University of
Alberta, Edmonton, Alberta. Lowe, J., III and Karafiath, L. (1960), "Stability of
Earth Dams Upon Drawdown”, Proceedings First PanAmerican Conference on Soil Mechanics and Foundation, Mexico City,
Vol. 2, pp. 537552. 415 11/17 Morgenstern, N. R. and Price, V. E. (1965), "The Analysis
of the Stability of General Slip Surfaces", Geotechnique,
15, pp. 7093. Naderi, F. (1977), "Examination of the 'SLOPE' Computer
Program", M.Sc. Thesis, University of Saskatchewan, Sask—
atoon, Canada. Popescu, M. (1978), "Analiza Comparative a Metodelor de
Calcul al Slabilitatic Taluzurilor”, Hidrotehnica, 23, A,
pp. 76—79. Spencer, E. (1967), "A Method of Analysis of the Stability
of Embankments Assuming Parallel Interslice Forces", Geo
technique, 17, pp. 11—26. U.S. Army Corps of Engineers (1970), "Engineering and
Design, Stability of Earth and Rock—Fill Dams", Depart—
ment of the Army, Corps of Engineers, Engineer Manual,
EM111021902, April. Whitman, R. V. and Bailey, W. A. (1967), “Use of Computers
for Slope Stability Analysis", ASCE Journal of the Soil
Mechanics and Foundation Division, 93(SM4). Wright, S. (1969), "A Study of Slope Stability and the Undrained Shear Strength of Clay Shales", Ph.D. Thesis,
University of California, Berkeley, Calfornia. 416 ...
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