NPTEL- GEOTECHNICAL EARTHQUAKE ENGINEERING
Module 4
GROUND RESPONSE ANALYSIS
(Lectures 17 to 22)
PROBLEMS
1. For the case of uniform layer of undamped soil overlying rigid bedrock, develop a transfer function
that relates shear stress,
to the bedrock acceleration, ̈
. Plot the modulus of the
transfer function from
.
2. An acceleration reduction factor can be defined as the ratio of the peak acceleration at depth,
peak ground surface acceleration, i.e.,
to the
̈
̈
For the case of a uniform layer of undamped soil overlying rigid bedrock, develop an expression for
the reduction factor as a function of the thickness and shear wave velocity of the soil layer, and the
frequency of the input motion.
3. Plot the reduction factor determined in problem 2 with depth for a 15 m thick soil deposit with a
shear wave velocity of 300 m/sec at input motion frequencies of
.
4. Derive a transfer function that relates the displacement of the ground surface to the displacement of
bedrock for the site illustrated below.
(a) Define the complex wave numbers,
(b) Define the complex impedance ratio, .
(c) Express the transfer function in terms of
.
.
5. The shear modulus of the soil within the earth dam shown below increases linearly with depth. The
shear wave velocity of the soil just above the base of the dam is 800m/sec. compute the first two
natural frequencies of the dam.
Dept. of Civil Engg. Indian Institute of Technology, Kanpur
1
NPTEL- GEOTECHNICAL EARTHQUAKE ENGINEERING
Figure P-5
6. The SDOF system shown below is supported by 10 ft diameter circular footings. The mass of the
footing is small compared to the mass of the structure. Compute the damped natural period of the
soil-structure system:
(a) Assuming fixed base conditions.
(b) Assuming that the footing can translate horizontally (but not rotate), and
(c) Assuming that the footing can both translate and rotate.
Dept. of Civil Engg. Indian Institute of Technology, Kanpur
2