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Assignment 1: Introduction to Seismic Hazard Assessment / Probability Review
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Describe the difference between a deterministic seismic hazard analysis and a probabilistic seismic
hazard analysis.
Why don’t we design for the worst case ground motion in most projects?
Assume that the earthquake magnitudes on a fault follow a truncated exponential distribution with a
minimum magnitude of 5.0 and a maximum magnitude of 7.0 with a b-value of 1.0. Note: the
parameter, , in the exponential model is given by ln(10) times the b-value. If an earthquake greater
than 5.0 occurs on the fault, what is the probability that the magnitude of the earthquake is between 6.0
and 6.5? (You can compute this either analytically or numerically)
Consider a fault that is 70 km long and 12 km wide (down-dip). Assume that the model for the mean
characteristic magnitude on this fault is given by:
M = log(A) + 4.0
and that the characteristic magnitude is normally distributed with a standard deviation of 0.2 magnitude
units.
a. What is the mean value of the characteristic magnitude?
b. What is the probability that the magnitude of the characteristic earthquake is between 6.9 and
7.0? (You can compute this numerically or using standard calls in MathCAD or excel.)
5.
Consider the peak acceleration from a magnitude 6.5 earthquake at a distance of 10 km. Assume that
the peak acceleration (PGA) follows a lognormal distribution and that the median value is 0.3g and the
standard deviation is 0.6 natural log units. What is the probability that the PGA from this earthquake is
greater than 0.5g? (You can compute this numerically or using standard calls in MathCAD or excel.)
6.
The soil site A is located in a seismic region. It is estimated that an earthquake in the region might be
strong (S), moderate (M) and weak (W) with probabilities P(S)=0.03, P(M)=0.25 and P(W)= 0.72. The
probabilities of liquefaction of the 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.
7.
Calculate the peak ground acceleration (PGA) values that have 2%, 5%, and 10% chances of
exceedance in 50 years using the hazard curve given below. (Hint: Use Poisson process!)
Annual Prob. Of Exceedence
1
0.1
0.01
0.001
0.0001
0.01
0.1
1
10
PGA (g)
Figure 1: PGA Hazard Curve for Berkeley City Center, CA (After Gülerce and Abrahamson, 2011)
CE 5603 SEISMIC HAZARD ASSESSMENT |
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8.
What is the difference between aleatory variability and epistemic uncertainty in PSHA?
9.
Classify the following as either aleatory variability or epistemic uncertainty and comment on the
classification.
Aleatory
Epistemic
Item
Comment
Variability Uncertainty
Length of the fault
Length of a rupture for a given
earthquake magnitude
Mmax in the truncated exponential
pdf for earthquake magnitude
Mean earthquake magnitude given
the rupture area
Value of the standard deviation of
log(area) of a given earthquake
magnitude
Slope (c1) of the magnitude scaling
(i.e., M= c1 log(A) +c2)
b‐value in the Y&C characteristic
earthquake model for magnitude
pdf
Location of the rupture on a fault
Slip‐rate on a fault
Due: Monday, March 21, 2016
CE 5603 SEISMIC HAZARD ASSESSMENT |
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