Climate change and Urban
Vulnerability in Africa
Assessing vulnerability of urban systems,
population and goods in relation to natural and
man-made disasters in Africa
“Training on the job” Course on Hazards, Risk and
(Bayesian) multi-risk assessement
Napoli, 24.10.2011 – 11.11.2011
08/04/2015
Fatemeh Jalayer
1
Outline
1. ALTERNATIVE PROBABILISTIC REPRESENTATIONS OF EARTHQUAKE GROUND MOTION
2. PROBABILISTIC SEISMIC HAZARD ANALYSIS
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Fatemeh Jalayer
Slide 2
Earthquake Ground Motion the
Major Source of Uncertainty
THE UNCERTAINTY IN THE PREDICTION OF EARTHQUAKE
GROUND MOTION SIGNIFICANTLY CONTRIBUTES TO
THE UNCERTAINTY IN DEMAND AND CAPACITY.
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Fatemeh Jalayer
Slide 3
Alternative Probabilistic Representations
of Earthquake Ground Motion
A
Direct Probabilistic Representation of the
Ground Motion
B
Implicit Probabilistic Representation of the
Ground Motion
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Fatemeh Jalayer
Slide 4
Alternative Direct Probabilistic
Representations
of Ground Motion Uncertainties
A
Probabilistic Representation of Ground Motion using
Intensity Measures (IM-Based, FEMA-SAC Guidelines,
PEER Methodology)
B
Complete Probabilistic Representation of the Ground
Motion Time History
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Fatemeh Jalayer
Slide 5
Direct Probabilistic Representations
of Ground Motion
Using Intensity Measure (IM)
It is assumed that the spectral acceleration is a sufficient intensity
measure.
A sufficient intensity measure renders the structural response
(e.g., qmax) independent of ground motion parameters such as M
and R.
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Fatemeh Jalayer
Slide 6
Direct Probabilistic Representations
of Ground Motion
Using Intensity Measure (IM)
– IM Hazard Curve A probabilistic representation of the ground motion intensity measure be stated in terms of the mean
annual frequency of exceeding a given ground motion intensity level. This quantity is also known as
the IM hazard curve.
 ( IM  x)
IM  x
Spectral acceleration hazard curve for: T=0.85sec - Van Nuys, CA Attenuation law: Abrahamson and Silva, horizontal
motion on soil .
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Fatemeh Jalayer
Slide 7
Implicit Probabilistic Representation
of Ground Motion
in Current Seismic Design
and Assessment Procedures
Current seismic design procedures (FEMA 356, ATC-40) take into account the uncertainty in the ground
motion implicitly by defining “design earthquakes” with prescribed probabilities of exceeding given
peak ground acceleration (PGA) values in a given time period (e.g., Po=10% probability in 50 years).
 ( PGA  0.4) 
10% in 50 years
PGA=0.40g
Mean Annual Frequency of Exceeding PGA Also Known as PGA Hazard Curve
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Fatemeh Jalayer
Slide 8
Choice of IM
The spectral acceleration at the small-amplitude fundamental period of the structure
denoted byS a (T1 ) or simply, Sa is adopted as the intensity measure (IM).
u (t )
M ,r
c
k
T1  period of the oscillator
m 1
  dam ping coefficient
u (t )
t
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Sa(T1,ξ ) 
Fatemeh Jalayer
4 2
T
2
max[abs(u(t))]
Slide 9
Probabilistic model for the
occurrence of earthquakes
It is assumed that the occurrence of earthquakes can be
modeled by a Poisson distribution
P(at least onesignificant EQ in timeT )  1  exp(T )
 is the mean annual rate of occurrence of earthquakes
T is a given time interval
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Fatemeh Jalayer
Slide 10
Seismic zoning
Point source: this typology of modeling it’s used for fault very far from the site
Linear source (linear fault): all the point of the line can be the epicenter with
the same probability.
Areal source: all the points within an area can be the epicenter of an earthquakes
with the same probability.
Planar source: all the point on the plane can be the epicenter with the same
probability, Finite rupture area.
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Fatemeh Jalayer
Slide 11
Hypocenter and Epicenter
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Fatemeh Jalayer
Slide 12
Probabilistic model for the
occurrence of earthquakes
With IM>x
Under certain ergodicity assumptions, it can be asumed that the occurrenceof
earthqaukes with IM>x is a filtered Possion probability distribution:
IM  x
is the mean annual rate of occurrence of earthquakes with
IM >x
T is a given time interval
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Fatemeh Jalayer
Slide 13
Probabilistic model for the
occurrence of earthquakes
With IM>x
The mean annual rate of occurrence of earthqaukes with IM>x can be calculated as
the sum of the mean annual rate of occurrence of EQ’s with IM>x on all the
possible seismogenetic zones around the site:
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Fatemeh Jalayer
Slide 14
The San Andreas Seismic Zones:
Los Angeles Area
source i: San Andreas Fault
site: Van Nuys
(M,R)
Faults of Los Angeles region
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Fatemeh Jalayer
Slide 15
Probabilistic model for the
occurrence of earthquakes
With IM>x for seismic zone i
The mean annual rate of occurrence of earthqaukes with IM>x can from
seismic zone i be calculated as the product of the rate of EQ’s with M>mo
on the seismic zone i and the probability of EQ’s with IM>x given that an
earthquake with M>mo has taken place:
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Fatemeh Jalayer
Slide 16
Probabilistic model for the
occurrence of earthquakes
With IM>x for seismic zone i given M>m0
The probability of earthquakes with IM>x from a given seismic zone can be
calculated using the Total Probability Theorem by summing up the probabilities
of having EQ’s with IM>x for all the possible combinations of magnitude and
distance from the given seismic zone:
probability distribution for distance
i  M m ,i   P(IM  x | m, r ) p(m) p(r )
o
m
r
ground motion prediction relation
magnitude relation
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Fatemeh Jalayer
Slide 17
Probabilistic Representation of
IM for a given M and r
The relation between IM and ground motion parameters, such as magnitude and distance,
can be expressed in the following generic form:
ln IM  f (M , r )     ln IM |M ,r
The spectral acceleration for a given magnitude and distance can be described by a lognormal distribution. The parameters of this distribution, namely, mean and standard
deviation, are predicted by the attenuation relation:
P[ Sa  x | M , r ]  1  (
08/04/2015
ln x  f ( M , r )
Fatemeh Jalayer
 ln Sa |M ,r
)
Slide 18
Ground Motion
prediction relations
State-of-the-art estimates of expected ground motion at a given distance from an earthquake of a
given magnitude are the second element of earthquake hazard assessments. These estimates are
usually equations, called attenuation relationships, which express ground motion as a function of
magnitude and distance (and occasionally other variables, such as type of faulting). Commonly
assessed ground motions are maximum intensity, peak ground acceleration (PGA), peak ground
velocity (PGV), and several spectral accelerations (SA). Each ground motion mapped
corresponds to a portion of the bandwidth of energy radiated from an earthquake. PGA and 0.2s
SA correspond to short-period energy that will have the greatest effect on short-period structures
(one-to two story). PGA values are directly related to the lateral forces that damage short period.
Longer-period SA (1.0s, 2.0s, etc.) depict the level of shaking that will have the greatest effect on
longer-period structures (10+ story buildings, bridges, etc.). Ground motion attenuation
relationships may be determined in two different ways: empirically, using previously recorded
ground motions, or theoretically, using seismological models to generate synthetic ground
motions which account for the source, site, and path effects. There is overlap in these approaches,
however, since empirical approaches fit the data to a functional form suggested by theory and
theoretical approaches often use empirical data to determine some parameters.
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Fatemeh Jalayer
Slide 19
Ground Motion
prediction relations
The ground motion at a site, for example Peak Ground Acceleration depends on the earthquake
source, the seismic wave propagation and the site response. Earthquake source signifies the
earthquake magnitude, the depth and the focal mechanism, the propagation depends mainly on
the distance to the site. The site response deals with the local geology (site classification); it is the
subject of microzonation.
The basic functional (logarithmic) form for ground motion attenuation relationship is defined as
(Reiter 1990)
ln Y = ln b1 + ln f1(M) + ln f2(R) + ln f3(M,R) + ln f4(P) + ln 
Where: Y is the strong motion parameter to be estimated (dependant variable), it is lognormal
distributed; f1(M) is a function of the independent variable M, earthquake source size generally
magnitude; f2(R) depends on the variable R, the seismogenic area source to site distance;
f3(M,R) is a possible joint function between M and R (for example for an earthquake with big
magnitude the seismogenic area is large and the source to site distance may be different);
f4(P) are functions representing possible source and site effects (for example different style of
faulting in the near field may generate different ground motions values Abrahamson and
Shedlock (1997));  is an error term representing the uncertainty in Y
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Fatemeh Jalayer
Slide 20
Ground Motion
prediction relations
Sabetta e Pugliese (attenuation law for Italy)
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Fatemeh Jalayer
Slide 21
Seismogenetic source
Distance probability distribution
PUNCTUAL SEISMIC SOURCE
Site
r
H
LINEAR SEISMIC SOURCE (CASE 1)
d
Site
l
r
H
L1
L-L1
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Fatemeh Jalayer
Slide 22
Seismogenetic source
Distance probability distribution
LINEAR SEISMIC SOURCE (CASE 1)
d
Site
l
r
H
L1
L-L1
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Fatemeh Jalayer
Slide 23
Seismogenetic source
Distance probability distribution
LINEAR SEISMIC SOURCE (CASE 2)
d
Site
r
l
H
L1
L
𝑟 2 = 𝑑2 + 𝑙 + 𝐿1
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2
Fatemeh Jalayer
Slide 24
Seismogenetic source
Distance probability distribution
LINEAR SEISMIC SOURCE (CASE 2)
d
Site
r
l
H
L1
L
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Fatemeh Jalayer
Slide 25
Seismogenetic source
Distance Probability Distribution
AREAL SEISMIC SOURCE: ITALIAN CASE
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Fatemeh Jalayer
Slide 26
Seismogenetic source
Distance Probability Distribution
GENERIC PLANAR SEISMIC SOURCE: REAL FAULT
𝜆 𝐼𝑀 > 𝑥 𝑖 =
𝛼𝑖 ∙
𝑖
𝑃(𝐼𝑀 > 𝑥|𝑚, 𝑟 𝑊, 𝑅𝐴, 𝑥, 𝑦 ) ∙ 𝑃(𝑚) ∙ 𝑃(𝑤|𝑚) ∙ 𝑃(𝑅𝐴|𝑚) ∙ 𝑃(𝑥) ∙ 𝑃(𝑦) ∙ 𝑑𝑚 ∙ 𝑑𝑥 ∙ 𝑑𝑦 ∙ 𝑑𝑅𝐴 ∙ 𝑑𝑤
𝑊 𝑅𝐴 𝐸𝑥 𝐸𝑦 𝑚
GROUND MOTION PREDICTION EQUATION (GMPE)
GUTTENBERG-RICHTER
WELLS AND COPPERSMITH (1985)
WELLS AND COPPERSMITH (1985)
UNIFORM DISTRIBUTION
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Fatemeh Jalayer
Slide 27
Seismic hazard for IM
The mean annual rate of exceeding a given spectral acceleration value, also known as spectral
acceleration hazard can be calculated as follows:
attenuation relation




Sa ( x)   i ( S a  x)   i ( M  m0 )  P( S a  x | M , r ) p( M , r )dMdr


i 1
i 1
m , r

N
N
summation over all
the
surrounding
seismic zones
mean annual rate that an
earthquake event of interest
takes place at seismic zone i
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Fatemeh Jalayer
all the possible earthquake event scenarios
that can take place on seismic zone i and
which produce spectral acceleration larger
than x.
Slide 28
The Return Period
The return period is defined as the inverse of the mean annual frequency of exceeding a
given IM level:
T
1
 IM  x
e.g., L=0.002, or 10% in 50 years, T=475 years
What is the probability that IM>x in the return period?
1
P(IM  x)  1  exp(  T )  1  e 1  0.63
T
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Fatemeh Jalayer
Slide 29
Deaggregation of Hazard
The hazard curve gives the combined effect of all magnitudes and distances on the probability of
exceeding a given ground motion level. Since all of the sources, magnitudes, and distances are
mixed together, it is difficult to get an intuitive understanding of what is controlling the hazard
from the hazard curve by itself. A common practice is to break the hazard back down into its
contributions from different magnitude and distance pairs to provide insight into what events are
the most important for the hazard.
  (M  m ) p( IM | m, r ) p(m, r )
p(m, r | IM ) 
  (M  m )  p( IM | m, r ) p(m, r )
i
0
zone
i
zone
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0
m,r
Fatemeh Jalayer
Slide 30
Deaggregation of Seismic Hazard
Contribute of magnitude and distance to the seismic hazard of site of interest.
Distance 0÷20 km
Magnitude 4÷6
Mean Distance: 8.54 km
Mean Magnitude: 4.98
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Fatemeh Jalayer
Slide 31