Civil Engineering Reference
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graphs that can be thought of as damped single-degree-of-freedom oscilla-
tors. When an earthquake occurs, these oscillators respond to the shaking
that they experience and we can record their response. The act of respond-
ing to the input excitation has the same effect as fi ltering the original excita-
tion that the oscillator was subjected to. Under the assumption that we
know the response characteristics of the oscillator, and that it responds in
a linear manner, we can remove the response of the oscillator from the
recording in order to recover the original input excitation. This excitation
consists of a series of acceleration values recorded at discrete time
increments.
For a seismic risk application, we are interested in determining the
response of structural or geotechnical systems to earthquake-induced
ground-motions and in doing so in as effi cient a manner as possible. It is
therefore common to characterise the ground-motion by a representative
scalar quantity and to then relate this quantity to some measure of the
response of the system we are analysing. So, when we refer to 'ground-
motion' herein, we are talking about this scalar quantity that is chosen to
represent the features of the acceleration time-history that we deem to be
most relevant for a given application. The discussions that follow in the rest
of this chapter are applicable to any scalar quantity that is used to represent
the earthquake-induced ground shaking. However, it is the 5% damped
spectral acceleration (or pseudo-spectral acceleration) that is far and away
the most commonly used scalar quantity within seismic hazard and risk
applications.
2.2.1 The role of GMPEs within seismic hazard and
risk applications
Ground-motion models provide the connection between the occurrence of
earthquakes and the shaking that might be experienced by a structure at a
given location. While many people believe that ground-motion models
attempt to
predict
values of ground motion, and that these predictions have
an associated error, it is better to not view GMPEs in this way. In order for
a ground-motion model to be useful within the context of seismic risk
analyses, it is crucial that the model be able to provide a prediction of both
the expected value of the ground-motion for a given scenario, as well as a
prediction of the dispersion of ground-motion values about this expected
value. These two parameters, when coupled with the assumption that
ground-motion values can be described by a lognormal distribution, fully
defi ne the likelihoods that a ground-motion value takes on a particular level
given the occurrence of an earthquake.
This is a very important point. Within the context of seismic hazard and
risk analysis, the role of a ground-motion model is to defi ne the distribution
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