Geotechnical Earthquake
Engineering
by
Dr. Deepankar Choudhury
Professor
Department of Civil Engineering
IIT Bombay, Powai, Mumbai 400 076, India.
Email: [email protected]
URL: http://www.civil.iitb.ac.in/~dc/
Lecture – 11
Module – 4
Strong Ground Motion
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Size of Earthquakes
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Magnitude and Intensity
Intensity
• How Strong Earthquake Feels to Observer
– Qualitative assessment of the kinds of damage done by an
earthquake
– Depends on distance to earthquake & strength of
earthquake
– Determined from the intensity of shaking and damage
from the earthquake
Magnitude
• Related to Energy Release.
– Quantitative measurement of the amount of energy
released by an earthquake
– Depends on the size of the fault that breaks
– Determined from Seismic Records
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Measuring Earthquakes
• Seismogram is visual record of arrival time and
magnitude of shaking associated with seismic wave.
Analysis of seismogram allows measurement of size of
earthquake.
• Mercalli Intensity scale
Measured by the amount of damage caused in human
terms- I (low) to XII (high); drawback: inefficient in
uninhabited area
• Richter Scale- (logarithmic scale)
Magnitude- based on amplitude of the waves
Related to earthquake total energy
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Intensity
How Strong Earthquake Feels to Observer
Depends On:
• Distance to hypocenter/epicenter
• Geology of site
• Type of building /structure
• Observer’s feeling
Value varies from Place to Place
• Modified Mercalli Scale - I to XII
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Ref: Wikipedia
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Modified Mercalli Intensity Scale
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Earthquake Magnitude


ML - Local (Richter) magnitude
MW - Seismic Moment magnitude

MS - Surface wave magnitude
 mb-
Body wave magnitude
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Local Magnitude of Earthquake
• Magnitude
– Richter scale measures the magnitude of an earthquake,
based on seismogram independent of intensity
– Amplitude of the largest wave produced by an event is
corrected for distance and assigned a value on an openended logarithmic scale
– The equation for Richter Magnitude is:
ML = log10A(mm) + (Distance correction factor)
Here A is the amplitude, in millimeters, measured directly from
the photographic paper record of the Wood-Anderson
seismograph, a special type of instrument. The distance factor
comes from a table given by Richter (1958).
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Richter’s Local Magnitude
Right side diagram (nomogram)
demonstrates how to use Richter's
original method to measure a
seismogram for a magnitude
estimate After you measure the wave
amplitude you have to take its
logarithm and scale it according to
the distance of the seismometer from
the earthquake, estimated by the S-P
time difference. The S-P time, in
seconds, makes t. The equation
behind this nomogram, used by
Richter in Southern California, is:
ML = log10A(mm) +3 log10[8 t (sec)]-2.93
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Richter Scale: Related to intensity
– M=1 to 3: Recorded on local seismographs, but generally
not felt
– M= 3 to 4: Often felt, no damage
– M=5: Felt widely, slight damage near epicenter
– M=6: Damage to poorly constructed buildings and other
structures within 10's km
– M=7: "Major" earthquake, causes serious damage up to
~100 km (Gujarat 2001 earthquake).
– M=8: "Great" earthquake, great destruction, loss of life
over several 100 km
– M=9: Rare great earthquake, major damage over a large
region over 1000 km
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Correlations
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Surface Wave Magnitude
Richter’s local magnitude does not distinguish between
different types of waves.
At large distances from epicenter, ground motion is dominated
by surface waves.
Gutenberg and Richter (1956) developed a magnitude scale
based on the amplitude of Rayleigh waves.
Surface wave magnitude Ms = log10A + 1.66 log10 +2.0
A = Maximum ground displacement in micrometers
= Distance of seismograph from the epicenter, in degrees.
Surface wave magnitude is used for shallow earthquakes
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Body Wave Magnitude
For deep focus earthquakes, reliable measurement of amplitude
of surface waves is difficult.
Amplitudes of P-waves are not strongly affected by focal depth.
Gutenberg (1945) developed a magnitude scale based on the
amplitude of the first few cycles of P- waves, which is useful
for measuring the size of deep earthquakes.
Body wave magnitude mb = log10A – log10T +0.01
+ 5.9
A = Amplitude of P-waves in micrometers
T = period of P-wave
= Distance of seismograph from the epicenter, in degrees.
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Source: Richter (1958)
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Limitations of Ms and mb due to Magnitude
Saturation
Magnitude saturation, is a general
phenomenon for approximately Mb >
6.2 and Ms > 8.3.
As Mb approaches 6.2 or MS
approaches 8.3, there is an abrupt
change in the rate at which
frequency of occurrence decreases
with magnitude.
Though the rupture area on the fault
is large, the predictions will saturate
at these magnitudes.
Because of this magnitude
saturation, estimation of magnitude
for large earthquakes through Mb
and Ms becomes erroneous.
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Seismic - Moment Magnitude
A Seismograph Measures Ground Motion at One
Instant But -• A Really Great Earthquake Lasts Minutes
• Releases Energy over Hundreds of Kilometers
• Need to Sum Energy of Entire Record
• Moment magnitude scale based on seismic moment
(Kanamori, 1977) and doesn’t depend upon ground
shaking levels.
• It’s the only magnitude scale efficient for any size
of earthquake.
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Moment Magnitude
• Moment-Magnitude Scale
– Seismic Moment = Strength of Rock x Fault Area x Total amount of Slip
along Rupture
M0 =
A D (in N.m)
[Idriss, 1985]
Where, = shear modulus of material along the fault plane in
N/m2 (= 3x1010 N/m2 for surface crust and 7x1012 N/m2 for
mantle)
A = area of fault plane undergoing slip (m2)
D = average displacement of ruptured segment of fault (m)
Moment Magnitude, Mw = 2/3 x [log10M0(dyne-cm) –16]
Moment Magnitude, Mw = - 6.0 + 0.67 log10M0(N.m)
[Hanks and Kanamori (1979)]
– Measurement Analysis requires Time
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Seismic - Moment Magnitude
• Most magnitude scales saturate towards large earthquakes
with m b > 6.0, M L > 6.5, and M S > 8.0. The moment
magnitude M w (Kanamori 1977) represents true size of
earthquakes, as it is based on seismic moment, which in
turn is proportional to the product of the rupture area and
dislocation of an earthquake fault (Aki 1966). M W is
defined as,
MW = 2/3log10M0− 6.05
where M 0 is the scalar seismic moment in Nm. MW does
not saturate, this is the most reliable magnitude for
describing the size of an earthquake (Scordilis 2006).
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Rigidity of Crust and Mantle for
Seismic Moment Estimation
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Correlation between Mw and ML
• The distribution of M W versus M L is shown Fig. and the
correlation is given by Kolathayar et al. (2012) for India by
considering 69 earthquake data,
MW=0.815(±0.04)ML+0.767(±0.174), 3.3≤ML≤7, R2=0.884
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Correlations between various
magnitude scales
Heaton et al.
(1982)
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Seismic Energy
Both the magnitude and the seismic moment are related to the
amount of energy that is radiated by an earthquake. Gutenberg
and Richter (1956), developed a relationship between magnitude
and energy. Their relationship is:
logES = 11.8 + 1.5Ms
Energy ES in ergs from the surface wave magnitude Ms. ES is not
the total “intrinsic” energy of the earthquake, transferred from
sources such as gravitational energy or to sinks such as heat
energy. It is only the amount radiated from the earthquake as
seismic waves, which ought to be a small fraction of the total
energy transferred during the earthquake process.
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Local Magnitude - Seismic Energy correlation
Gujarat (2001)
Size of an earthquake using the Richter’s Local Magnitude Scale is shown on the left
hand side of the figure above. The larger the number, the bigger the earthquake. The scale
on the right hand side of the figure represents the amount of high explosive required to
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produce the energy released by the earthquake.
Frequency of earthquakes
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Frequency of earthquakes
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Example Problem
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