Geoscience Reference
In-Depth Information
The primary issue in calculating
k
y
is estimating the dynamic strength of the critical
stratawithintheslope.Severalpublicationsincludeextensivediscussionsofthedynamic
strengthofsoil(e.g.,Blakeetal.,2002;DuncanandWright,2005;Chenetal.,2006),and
a satisfactory discussion of this important topic is beyond the scope of this paper. Need-
lesstosay,theengineershoulddevoteconsiderableresourcesandattentiontodeveloping
realistic estimates of the dynamic strengths of key slope materials. In this paper, it is
assumed that
k
y
is constant, so consequently, the earth materials do not undergo severe
strength loss as aresult of earthquake shaking (e.g.,no liquefaction).
Duncan (1996) found that consistent (and assumed to be reasonable) estimates of a
slope's static factor of safety (
FS
) are calculated if a slope stability procedure that sat-
isfies all three conditions of equilibrium is employed. Computer programs that utilize
such methods as Spencer, Generalized Janbu, and Morgenstern and Price may be used
to develop sound estimates of the static
FS
. Most programs also allow the horizontal
seismic coefficient that results in a
FS
0 in a pseudostatic slope stability analysis
to be calculated, and if a method that satisfied full equilibrium is used, the estimates of
k
y
are fairly consistent. With the wide availability of these computer programs and their
easeofuse,thereisnoreasontouseacomputerprogramthatincorporatesamethodthat
does not satisfy full equilibrium. Simplified equations for calculating
k
y
as a function
of slope geometry, weight, and strength are found in Bray et al. (1998) among several
other works. The equations provided in Figure 14.1 may be used to estimate
k
y
for the
simplified procedures presented inthispaper.
=
1
.
The potential sliding mass that has the lowest static
FS
may not be the most critical for
dynamic analysis. A search should be made to find sliding surfaces that produce low
k
y
values as well. The most important parameter for identifying critical potential sliding
masses for dynamic problems is
k
y
/
k
max
, where
k
max
is the maximum seismic coeffi-
cient, which represents the maximum seismic loading considering the dynamic response
of the potential slidingmassas described next.
S
2
1
1
H
c = cohesion
φ = friction angle
S
1
q
1
= tan
−1
(1
/
S
1
)
β
L
f
.
(
S
1
.
H
/
2
.
cos
2
q
1
+
L
+
S
2
.
H
/
2)
tan
FS
static
=
c
cos
q
1
.
sin
q
1
.
S
1
.
H
/
2
k
y
=
tan (
f
−
b
) +
γ
.
H
.
cos
2
b
.
(1+tan
f
.
tan
b
)
q
1
.
S
1
.
H
/
2
H
.
(
S
1
+S
2
)
/
2+
L
1
)
.
cos
q
1
.
sin
(
FS
static
−
k
y
=
(a) (b)
Fig. 14.1. Simplified estimates of the yieldcoefficient: (a) shallow sliding
and (b) deep sliding
