CE 5603 Seismic Hazard Assessment
Middle East Technical University, Ankara,Turkey
Department of Civil Engineering
Prof. Dr. K. Önder Çetin
ASSIGNMENT 1 – Review of Probabilistic Concepts
1. Earthquakes on a 150 km long fault occur as ruptures of length S, where S is anywhere
between zero and half the length of the fault. A dam is located in the vicinity of the
fault as shown in the figure given below.
(a) In a two-dimensional coordinate system show the sample space of the rupture
length S and the coordinate X of the center of the rupture (i.e.: x-axis shows the
coordinate of the ruptured fault segment’s midpoint, X, y-axis shows the rupture
length, S). Assume the rupture may not extend beyond the ends of the fault.
(b) Show the event that the center of rupture is within 30 km of the dam.
(c) Show the event that the shortest distance from the rupture to the dam is less than
30 km.
150 km
X
Fault
Rupture
S
20 km
50 km
Dam
2. Two soil sites A and B are located in a seismic region. It is estimated that an
earthquake in the region might be strong (S), moderate (M), or weak (W) with
probabilities P(S) = 0.03, P(M) = 0.25 , and P(W) = 0.72. The probabilities of
liquefaction of each soil site if these earthquakes occur are 0.30, 0.15, and 0.08,
respectively.
(a) Determine the probability of liquefaction of site A if the earthquake occurs.
(b) If site A is liquefied, what is the probability that the earthquake was of weak
strength?
Assignment 1 : Review of probabilistic concepts
CE 5603 Seismic Hazard Assessment
Middle East Technical University, Ankara,Turkey
Department of Civil Engineering
Prof. Dr. K. Önder Çetin
(c) Due to proximity of the sites to each other and similarities in the soil profile
characteristics, it is estimated that if site A liquefies the probability that site B will also
liquefy is 0.55, 0.16, and 0.04 for the three types of earthquakes. Determine the
probability that both sites will liquefy in an earthquake.
(d) If site A has liquefied and site B has not, what is the probability that the
earthquake was not strong?
3. The highway system for transportation between Ankara and Istanbul includes two
parallel bridges A and B that are crossed by a North Anatolian Fault system. In the
event of an earthquake on NAF, each bridge will fail if the fault rupture crosses it.
Assuming that the other parts of the highway system are not vulnerable to
earthquakes,
(a) Determine the probability of failure of the highway system, i.e., the probability
that transportation between Ankara and Istanbul will be interrupted, if an earthquake
caused by a 120 km long rupture occurs on the fault. Assume the rupture is equally
likely to occur anywhere along the fault, but not extending beyond its ends.
(b) Suppose bridge B is known to have failed, what is the probability that bridge A has
survived?
(c) If transportation between cities Ankara and Istanbul is known to be possible after
the earthquake, what is the probability that both bridges survived?
İstanbul
200 km
140 km
A
an 60 km
bu
l
Assignment 1 : Review of probabilistic concepts
B
an
bu
l
Ankara