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DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY
Geotechnical Earthquake
Engineering
Quiz
Full Marks – 100
Duration – One (1) Hour
Answer ALL Questions
Assume reasonable data if required
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1. The seismicity of a particular region is described
by the Gutenberg-Richter recurrence law as:
log λm = 4.0 – 0.72M
(a) What are the probabilities that at least one
and exactly one earthquake of magnitude
greater than 6.5 will occur in (i) 10 year period
(ii) 50 year period and (iii) 150 year period?
(b) Determine the
would have a 10%
at least once in a
nomenclature of
(10+20 = 30)
earthquake magnitude that
probability of being exceeded
50 year period. What is the
this level of earthquake?
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2. Using probabilistic seismic hazard curve, for
λm = 0.1, amax = 0.27g. Compute the probability of
exceeding this maximum seismic acceleration in
50 years and 150 years period and the
corresponding equivalent maximum value of the
earthquake magnitude using Gutenberg and
Richter Recurrence Law for worldwide data
(Circumpacific belt).
(20)
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3. In a field test, primary wave velocity of a sandy
soil with Poisson’s ratio = 0.3, unit weight = 17
kN/m3 is obtained as 400 m/s. Estimate shear wave
(S-wave) velocity propagating through that soil
layer. Calculate the maximum shear modulus of the
soil. If this soil layer with 8% damping and of 10 m
thickness is located between the ground surface and
rigid bed rock, compute the amplification of bed rock
spectral acceleration of an earthquake of 1.5 Hz
frequency which will be felt at the ground surface.
(30)
4. Among different types of body waves, which
one is having largest shadow zone and why?
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Distance between two seismographic stations X
and Y is 196 km on a level ground. A shallow
earthquake occurred with the epicenter Z, which is
estimated at 56 km from station X and Z is
located exactly on the line joining two stations X
and Y. The recorded difference in arrival time
between P and S wave was 20 seconds at station
Y. Estimate the difference in arrival time between
P and S waves at station X. If velocity of S wave is
half of the velocity of P wave. Estimate the crustal
velocities of P and S waves for this earthquake.
(5+15 = 20)
END
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