Civil Engineering Reference
In-Depth Information
compared with the regional seismicity on which
the codes are based.
The three steps in this analysis are first, to
establish the location and style of faulting of all
potential sources, and assign each a representative
earthquake magnitude. Second, an appropriate
attenuation relationship is selected as a function
of magnitude, fault mechanism, site-to-source
distance and site conditions. Third, the capable
sources are screened based on magnitude and
ground motion intensity at the site to determine
the governing source.
Attenuation.
Attenuation equations, discussed
in the previous paragraph, define the relationship
between the source moment magnitude
(M
w
)
and
peak ground acceleration (PGA) at the site. The
equations are based upon either statistical ana-
lysis of values observed in previous earthquakes,
or from theoretical models of the propagation of
strong ground motions, depending on the amount
of observed data available. For example, for sub-
duction zones and in the eastern United States the
PGA on rock at a hypocentral distance
R
is given
by (Youngs
et al
., 1988):
geology, PGA, frequency content, duration and
energy content.
6.5.4 Pseudo-static stability analysis
The limit equilibrium method of determining the
factor of safety of a sliding block as described in
Section 6.3 can be modified to incorporate the
effect on stability of seismic ground motions. The
analysis procedure, known as the pseudo-static
method, involves simulating the ground motions
as a static horizontal force acting in a direction
out of the face. The magnitude of this force is
the product of a seismic coefficient
k
H
(dimen-
sionless) and the weight of the sliding block
W
.
The value of
k
H
may be taken as equal to the
design PGA, which is expressed as a fraction of
the gravity acceleration (i.e.
k
H
=
0.1 if the PGA
is 10% of gravity). However, this is a conservat-
ive assumption since the actual transient ground
motion with a duration of a few seconds is being
replaced by a constant force acting over the entire
design life of the slope.
In the design of soil slopes and earth dams, it is
common that
k
H
is fraction of the PGA, provided
that there is no loss of shear strength during cyc-
lic loading (Seed, 1979; Pyke, 1999). Study of
slopes using Newmark analysis (see Section 6.5.5)
with a yield acceleration
k
y
equal to 50% of the
PGA (i.e.
k
y
ln
(
PGA
)
=
19.16
+
1.045
M
w
−
4.738 ln
[
R
+
154.7 exp
(
0.1323
M
w
)
]
(6.29)
for 20
<R
40 km, and
M
w
>
8. The moment
magnitude is a measure of the kinetic energy
released by the earthquake, and the hypocenter
is the point from which the seismic waves first
emanate.
Time histories.
If deformation analyses are
to be carried out, it is necessary to use a rep-
resentative time history of the ground motions.
Time histories can be selected from previously
recorded motions, or by simulation techniques
to generate a project-specific synthetic time his-
tory. In selecting a representative time history
from the catalogue of available records, the relev-
ant characteristics of the project and source sites
should be matched as closely as possible. Some of
the characteristics that are important in matching
time histories include magnitude, source mech-
anism, focal depth, site-to-source distance, site
≤
a
max
/g
) showed that per-
manent seismic displacement would be less than
1 m (Hynes and Franklin, 1984). Based on these
studies, the California Department of Mines and
Geology (CDMG, 1997) suggests that it is reas-
onable to use a value of
k
H
equal to 50% of
the design PGA, in combination with a pseudo-
static factor of safety of 1.0-1.2. With respect
to soil slopes, and rock slopes where the rock
mass contains no distinct sliding surface and some
movement can be tolerated, it may be reason-
able to use the CDMG procedure to determine
a value for
k
H
. However, for rock slopes there
are two conditions for which it may be advisable
to use
k
H
values somewhat greater than 0.5 times
the PGA. First, where the slope contains a dis-
tinct sliding surface for which there is likely to
be a significant decrease in shear strength with
=
0.5
·
