Civil Engineering Reference
In-Depth Information
Consequently, the return period is about 475 years, which can be computed from equation (3.4.1) . For
a facility lifetime larger than 80-90 years, the probability of the estimate being exceeded
P
can be
assumed approximately equal to the period of interest divided by the return period. For example, for
100 years and 1,000 years as the return period, the probability
P
is about 10%. The current discussion
ties in with Table 2.1 .
Problem 3.1
A long-span suspension bridge is going to be built in an active seismic region in Japan. The structural
earthquake engineer can choose the design ground-motion parameter with respect to three return
periods: 475, 950 and 2,500 years. Which is the most suitable return period to select and why? What
is the associated probability of the peak ground acceleration for the return period being exceeded?
3.3 Ground - Motion Models (Attenuation Relationships)
The 'attenuation' of earthquake ground motions is an important consideration in estimating ground-
motion parameters for assessment and design purposes. Ground-motion models (or attenuation relation-
ships) are analytical expressions describing ground-motion variation with magnitude, source distance
and site condition, which account for the mechanisms of energy loss of seismic waves during their
travel through a path as discussed in Sections 1.1 through 1.3. Attenuation relationships permit the
estimation of both the ground motion at a site from a specifi ed event and the uncertainty associated
with the prediction. This estimation is a key step in probabilistic and deterministic seismic hazard
analysis (Cornell, 1968). There are a number of ground-motion models that have been developed by
various researchers. Relationships based on peak ground-motion parameters (peak ground acceleration,
PGA; peak ground velocity, PGV; peak ground displacement, PGD) and spectral acceleration, velocity
and displacement parameters (
S
a
,
S
v
and
S
d
), presented in Section 3.4.3, are generally employed in
structural earthquake engineering.
The proliferation of strong-motion recording equipment over the past 50 years has provided large
databanks of earthquake records. The most basic ground-motion models express PGA as a function of
magnitude and epicentral distance. Several formulae include other parameters to allow for different site
types (e.g. rock versus soft soil) and fault mechanisms. These are developed by fi tting analytical expres-
sions to either observational or synthetic data, depending on the availability of strong- motion records
for the region under investigation. Ground-motion attenuation relationships are derived either empiri-
cally, utilizing natural earthquake records, or theoretically, employing seismological models to generate
synthetic ground motions that account for source, path and site effects. These approaches may overlap.
Empirical approaches generally match the data to a functional form derived from the theory; in turn,
theoretical approaches often use empirical data to determine values of parameters. The functional form
for ground-motion attenuation relationships is as follows:
()
=
()
+
[
()
]
+
[
()
]
+
[
(
)
]
+
[
()
]
+
()
log
Y
log
b
log
f
M f
log
R
log
f
,
R
log
4i
f
E
log
ε
(3.5)
1
1
2
3
where
Y
is the ground-motion parameter to be computed, for example PGA, PGV, PGD,
S
a
S
v
or
S
d
,
and
b
1
is a scaling factor. The second- to - fourth terms on the right -hand side are functions
f
i
of the
magnitude
M
, source - to - site distance
R
, and possible source, site and geologic and geotechnical
structure effects
E
i
. Uncertainty and errors are represented by the parameter
ε
. Equation (3.5) is an
additive function based on the model for ground-motion regression equations defi ned by Campbell
(1985). The logarithm can be expressed either a natural 'ln' or in a different base, e.g. ' log ' , depending
on the formulation. The above equation also accounts for the statistical log-normal distribution of the
ground - motion parameter
Y
. Peak ground -motion parameters decrease as the epicentral distance
