1
Lecture#15
CE-312
Engineering Geology and Seismology
Instructor:
Dr Amjad Naseer
Department of Civil Engineering
N-W.F.P University of Engineering and Technology, Peshawar
2
Outlines of the Presentation
•
Ground Motion Parameters
•
Amplitude, Frequency and Duration
3
Ground Motion Parameters
•
Ground motion parameters are essential for describing the
important
characteristics
of
strong
ground
motion
in
compact, quantitative form.
•
Amplitude, Frequency and Duration
4
(A) Amplitude Parameters
•
Amplitude
Parameters:
The most common way of
describing a ground
motion is with a time
history. The motion
parameter may be
acceleration, velocity,
or displacement, or all
three
may
be
displayed.
Typically,
only one of these
quantities is measured
directly
with
the
others computed form
it
by
integration
and/or differentiation.
5
(a) Peak Acceleration
•
The most commonly used measure of the amplitude of a
particular ground motion is the peak horizontal acceleration
(PHA). The PHA for a given component of motion is simply
the largest (absolute) value of horizontal acceleration
obtained from the accelerogram of that component.
6
(a) Peak Acceleration
Horizontal accelerations have
commonly
describe
because
been
used
ground
of
relationship
to
motions
their
natural
to
inertial
forces; indeed, the largest
dynamic forces induced in
certain
type
of
structures
(that is very stiff structures)
are closely related to the
PHA.
7
(a) Peak Acceleration
•
The PHA can also be correlated to earthquake intensity.
Although this correlation is far from precise, it can be very
useful for estimation of PHA when only intensity information
is available, as in the cases of earthquakes that occurred
before strong motion instruments were available (preinstrumental
earthquakes).
A
number
of
intensity-
acceleration relationships have been proposed.
•
8
(a) Peak Acceleration
•
Vertical
acceleration
have
received
less
attention
in
earthquake engineering than the horizontal acceleration,
primarily because the margins of safety against gravityinduced static vertical forces in constructed works usually
provide adequate resistance to dynamic forces induced by
vertical accelation during earthquakes. For engineering
purposes, the peak vertical acceleration (PVA) is often
assumed to be two third of PHA.
•
9
(a) Peak Acceleration
•
Ground motions with high peak accelerations are usually,
but not always, more destructive than motions with lower
peak accelerations. Very high peak accelerations that last
for only a very short period of time may cause little damage
to many types of structures. A number of earthquakes have
produced peak acceleration in excess of 0.5 g but caused no
significant
damage
to
structures
because
the
peak
accelerations occurred at very high frequency and the
duration of the earthquake was not long. Although peak
acceleration is a very useful parameter, it provides no
information on the frequency content or duration of the
motion;
consequently,
it
must
be
supplemented
by
additional information to characterize a ground motion
accurately.
10
(b) Peak Velocity
Peak Velocity:
The peak horizontal velocity (PHV) is another useful parameters
for characterizations of ground motion amplitude. Since the
velocity
is
less
sensitive
to
the
higher-frequency
components of the ground motion, the PHV is more likely
than the PHA to characterize ground motion amplitude
accurately at intermediate-frequencies. For structures or
facilities that are sensitive to loading in this intermediate
frequency range (for example, tall or flexible buildings,
bridges, etc), the PHV may provide a much more accurate
indication of the potential for damage than the PHA.
11
(c) Peak Displacement
Peak Displacement:
Peak displacements are generally associated with the lowerfequency components of an earthquake motion. They are,
often
difficult
processing
to
errors
determine
in
the
accurately
filtering
and
due
to
signal
integration
of
accelerograms and due to long-period noise. As a result,
peak displacement is less commonly used as a measure of
ground motion than is peak acceleration or peak velocity.
12
(B) Frequency Content
Frequency Content Parameters:
Dynamic response of buildings, bridges, slopes or soil deposit is
very sensitive to the frequency at which they are loaded.
Earthquake produces complicated loading with components
of motion that span a broad range of frequencies. The
frequency content describes how the amplitude of a ground
motion is distributed among different frequencies. Since the
frequency content of an earthquake motion will strongly
influence the effects of that motion, characterization of the
motion cannot be complete without consideration of its
frequency content.
13
(C) Duration
Duration:
The duration of strong ground motion can have a strong
influence on earthquake damage. Many physical processes,
such as the degradation of stiffness and strength of certain
types of structure and the buildup of porewater pressures in
loose, saturated sands, are sensitive to the number of load
or stress reversals that occure during an earthquake. A
motion of short duration may not produce enough load
reversals for damaging response to build up in a structure,
even if the amplitude of the motion is high. On the other
hand, a motion with moderate amplitude but long duration
can produce enough load reversals to cause substantial
14
damage.
(C) Duration
The duration of a strong ground motion is related to the time required
for release of accumlagted strain energy by rupture along the
fault. As the length or area of fault rupture increase, the time
required for rupture increase. As a result, the duration of strong
motion increases with increasing earthquake magnitude. While
this relationship has been supported empirical evidence for many
years, advances in source mjuechanism modeling, have provided
theoretical support indicated that
15
Response Spectra
RESPONSE SPECTRA
The response spectrum is the most important characterisation
of seismic ground-motion in earthquake engineering and
forms the basis for most design. This chapter introduces the
concept of the response spectrum and the particular
influence that certain features of the earthquake can have
on have on its shape and amplitude.
16
Response Spectra
Definition of the elastic response spectrum
A single-degree-of-freedom (SDOF) system is a mechanical
system with mass, m, that provides inertia, and stiff, k, that
provides a restoring force, whose deformation can be fully
described by a single coordinate. The natural period of
vibration of such an SDOF system, T, is given by the
following equation:
T  2
m
k
Real systems do not vibrate indefinitely when they are
perturbed because of the dissipation of energy by damping.
The damping is usually expressed as a proportion of critical
damping, which is the level of damping that will restore a
system to its at rest position without vibrations. For
reinforced concrete structures it is usually assumed that the
damping can be taken as 5% of critical.
17
Response Spectra
Real systems do not vibrate indefinitely when they are perturbed
because of the dissipation of energy by damping. The damping is
usually expressed as a proportion of critical damping, which is the
level of damping that will restore a system to its at rest position
without vibrations. For reinforced concrete structures it is usually
assumed that the damping can be taken as 5% of critical.
18
Response Spectra
If a series of SDOF systems with a given level of structural
damping are all subjected to an acceleration time-history
acting at their base, each mass will respond differently
according to its natural period and the relationship between
this period and the frequency content of the ground motion.
The maximum absolute value of the response of each SDOF
oscillator can be calculated and plotted against the
corresponding value of period, T. The resulting plot, called a
response spectrum, shows the maximum response that an
SDOF system will experience when subjected to the ground
motion represented by that particular accelerogram. This is
illustrated in figure on the last slide. The response spectrum
reflects the characteristics of the earthquake that generated
the motion and the nature of the recording site.
19
Response Spectra
Figure 2. Elastic response spectra of absolute acceleration of the four
accelerograms shown in Figure 9.8. 1 – Peru 1974, 2 – Yugoslavia
20
1979, 3 – Romania 1977, 4 – Mexico 1985
Response Spectra
Three different spectra can be defined according to how the
response of each SDOF is measured: relative displacement,
relative velocity or absolute acceleration. At zero period the
spectra of relative displacement and relative velocity are
equal to zero since for an infinitely rigid SDOF there is no
vibration. At zero period the relative acceleration is also
zero and the absolute acceleration is equal to the maximum
acceleration of the ground. This is a very important point to
grasp: the response spectrum of absolute acceleration
anchors at PGA, as can be appreciated from fig.2: despite
their very significant differences, all of the spectra converge
to 0.18g at the period T=0.
21