Environmental Engineering Reference
In-Depth Information
V
= horizontal water force
in tension crack
V
=
L
1
w
z
w
/2
2
3
θ
Positive
4
5
Negative
6
7
8
d
b
i
(a)
∆
x
W
i
FIGURE 9.79
Nomenclature for Janbu's simplified
method of analysis for noncircular
failure surfaces: (a) failure mass
geometry; (b) slice force system; (c) slice
parameters for analysis; and (d)
determination of pore pressure
u
. Useful
for cases where the failure surface is
known or assumed.
W
S
h
w
∆ + ∆
S
h
i
E
+
∆
E
δ
E
i
h
i
N
i
Equipotential line
N
θ
T
u
=
w
h
w
c
i
∆
L
i
U
U
i
δ =
line of thrust
(b)
(c)
(d)
possible positions for the line of action of the resultant forces between slices, and the line
of action must be checked to determine if it is a possible one.
Spencer's method
: This method (Spencer, 1967, 1973) is similar to the Morganstern and
Price method.
Friction Circle method
: See Taylor (1948).
Charts based on total stresses are used to find FS in terms of slope height and angle, and
of soil parameters
c
,
, and unit weight. The direction of the resultant normal stress for the
entire free body is slightly in error because the resultant is not really tangent to the friction
circle, but the analysis provides a lower bound for safety and is therefore conservative.
The Taylor charts are strictly valid only for homogeneous slopes with no seepage. They
consider that shear strength is mobilized simultaneously along the entire failure surface
and that there is no tension crack. They are used for rough approximations and prelimi-
nary solutions of more complex cases. If the strength values vary along the failure surface
they are averaged to obtain working values. This must be done with judgment and cau-
tion. For the foregoing conditions of validity, solutions using the charts are in close agree-
ment with the method of slices described below.
φ
Earthquake Forces
Pseudostatic methods
have been the conventional approach in the past (Terzaghi, 1950). The
stability of a potential sliding mass is determined for static loading conditions, and the
effects of earthquake forces are accounted for by including equivalent horizontal forces
acting on the mass. The horizontal force is expressed as the product of the weight of the
sliding mass and a seismic coefficient that is expressed as a fraction of the acceleration due
to gravity (see
Section 11.3.4).
Dynamic analysis
techniques provide for much more realistic results but also have
limited validity. These techniques are described by Newmark (1965) and Seed (1968).
The Newmark sliding block analyses are widely used for estimating the permanent
displacements of slopes during earthquakes (Kramer and Smith, 1997; Wartman et al.,
2003).
