basics for seismic risk managementquake.enveng.titech.ac.jp/lecture/tsunami2013/morikawa_1.pdfbasics...

Basics for Seismic Risk Management

—Evaluation of Seismic Risk—

Hitoshi Morikawa

[email protected]

Tokyo Institute of Technology

Basics for Seismic Risk Management – p.1/65

This document is used in the lecture “Earthquake andTsunami Disaster Reduction” at Tokyo Institute of Technology,Japan, Churalongkorn University, Thailand, National CentralUniversity, Taiwan, and Universiti Sains Malaysia, Malaysia.Thus, only the students relating this course can access thisdocument.

Ver. 1.00 (Jan. 02, 2006)Ver. 1.01 (Nov. 24, 2006)Ver. 1.02 (Nov. 14, 2007)Ver. 1.03 (Nov. 12, 2008)Ver. 1.10 (Nov. 13, 2009)Ver. 1.11 (Nov. 12, 2010)


First of All...

I would like to emphasize the following points:• “Stochastic” method is NOT for “Ambiguity.”

The probability theory deals with the mathematics of the“uncertainty.” “Uncertainty” is completely different from“ambiguity.” The probability theory requires the completeinformation about stochastic properties, that is, “uncertainty.”Some people may try to use the stochastic method if theydo not have enough information about the consideringphenomena. Most of them is in the misuse of probability.

• “Statistics” is NOT “Probability.”Of course, they are related mutually, but it is important to

distinguish strictly the probability theory from the statisticaltechnique. Probability is the absolute mathematics, thoughstatistics sometimes includes subjective judgment. Somepeople confuses them.


Introduction

To reduce the total loss by the earthquake (and tsunami), thetechnique of risk management may be useful. In this lecture, Iwill discuss what is the risk and the basic idea and theprocedure for the risk management is introduced.

Risk Management: A method to find “risk” for consideringobject(s) and a process to reduce the “risk” under aneconomical and/or technical reasonableness.


Contents

• What’s risk?• How to represent risk• Strategy for risk management• Evaluation of risk

◦ Damage assessment◦ Seismic Hazard Analysis◦ Some functions to represent risk

• Homework• Appendix: Hazard map


Absolute Safe?

If you design a structure very safely against earthquakes,floods, and so on, can you say that the structure is safeabsolutely?

There is much ambiguity in the natural phenomena. Forexample, we do not have enough information of the locationwhere earthquakes occur in future.


Uncertainties in Seismic and Relating Phenomena

• Uncertainties about the earthquake ground motion• Uncertainties about the dynamic response of structures• Uncertainties about miscellaneous factors



• Uncertainties about the earthquake ground motion◦ Where and when does earthquake occur?◦ Source parameters such as magnitude.◦ Path effect from the source to the site.◦ Local site effect such as the amplification at the site.

Fault

Base rock

Subsurface structure

Source effect Path effect Local site effect



• Uncertainties about the dynamic response of structures◦ Properties of the materials.◦ Differences between the structural design and

constructed structure.◦ Safety ratio?



• Uncertainties about miscellaneous factors◦ Weather condition such as wind.◦ Indirect influence.

1923 Kanto 1948 Fukui

2007 Niigata ???? Tokyo?Basics for Seismic Risk Management – p.10/65

Absolute Safe?




Absolute Safe?



⇓Generally speaking, it is impossible to confirm “absolute safe.”

⇓To deal with this type of “ambiguity,” we will introduce theprobability.

I do not agree this concept, though it is true that there is noalternative way. Thus, I will accept this...(I’m so weak...).


Loss!

What kind of loss is occurred by earthquakes?• Direct Loss

◦ Structural loss◦ Loss by functional failure and/or degradation

1995 Kobe 2004 Niigata 1999 Chi-Chi


Loss!

What kind of loss is occurred by earthquakes?• Indirect Loss

◦ Loss by derivative/secondary matters◦ Human loss (life or psychological matter)

1993 Hokkaido SW Offshore 1994 Hokkaido E Offshore


Loss!

What kind of loss is occurred by earthquakes?• Direct Loss

◦ Structural loss◦ Loss by functional failure and/or degradation

• Indirect Loss◦ Loss by derivative/secondary matters◦ Human loss (life or psychological matter)

The Loss is caused by the damage.⇓

Probability of the Damage ≈ Probability of the Loss


What’s the risk?

Various definitions for the “risk.”• Peril (dangerous events such as accident, disaster etc.).• Hazard such as earthquake, typhoon, traffic accident etc.• Probability of the loss.• Loss without considering its occurrence probability.• Differences from an expected result.• Loss with its occurrence probability.• Expected loss.

To deal with the loss, it is useful to introduce the monetary value.Of course, we should consider the difficult problem such as thevalue of human life.


What’s the risk?


It is easy to understand qualitatively the concept of “risk.”


What’s the risk?


If the loss is always same, it is enough to consider theprobability. This is not bad idea to deal with the risk.


What’s the risk?


If the probability of the loss is always same, this is enough toconsider the risk.


What’s the risk?


This definition is used in the financial field. It is effective todiscuss the accuracy of an estimation.


What’s the risk?


Hereafter, we will use these definitions for the “risk.” Expectedloss can be used for a kind of indicator of risk. These are goodto evaluate quantitatively the risk, but...


What’s the risk?


If we can estimate reasonably the probability of the loss, themathematics is very simple (too easy!) for the quantitativediscussion of the risk. It is noted that we have hardly the way toget the reasonable probability of events under less informations.


Quantitative Representation of Risk

� Expected Risk

Basic representation of the risk as the expected value.

R = PC,

R : RiskP : Probability of the lossC : Loss



� Expected Risk

In a case where we consider various losses which depend onthe different types of damage.

R =n∑

i=1

Ri =n∑

i=1

PiCi

R : Risk (expected loss)Ri : Risk by i-th damagePi : probability of the loss by i-th damageCi : loss by i-th damage



� An Example

Probability Loss Riski Damage Pi Ci Ri = PiCi

(×1000$) (×1000$)

1 No 0.7 0 02 Slight 0.25 5 1.253 Moderate 0.04 50 24 Severe 0.01 200 2

∑5.25

Note:Pi depends on the intensity of the earthquake ground motion.



� An Example

0

0.2

0.4

0.6

0.8

1

0 10 100 1000

Pro

babi

lity

Loss (x 1000$)

R=5.25 (x 1000$)

0

0.2

0.4

0.6

0.8

1

0 10 100 1000

Pro

babi

lity

Loss (x 1000$)

R=32 (x 1000$)

small intensity large intensity


Objective of Risk Management

Risk Management:A method to find risk for considering object(s) and a process

to reduce the risk under an economical and/or technicalreasonableness.

Procedure of Risk Management:• To evaluate quantitatively risk• To study reasonable provision against the risk• To execute the provision


Method of Risk Management

• Risk Retention (リスクの保有)

• Risk Avoidance (リスクの回避)

• Risk Optimization/Mitigation (リスクの最適化/低減)

• Risk Transfer (リスクの移転)



• Risk Retention• Risk Avoidance• Risk Optimization/Mitigation• Risk Transfer

I know the risk, but accept it.

ex.: A cash card (ATM card) may be risky, but it is very useful.So, I will continue to use it. If someone use my card illegally, I donot care because I have lots of money in another bank account.




I understand the risk. I will give up to do it.

ex.: A cash card (ATM card) may be risky. To avoid any riskregarding to the cash card, I will give up to use the cash card.So, I will hide all my money under the floor.




I understand the risk. I try to mitigate the risk.

ex.: A cash card (ATM card) may be risky. To mitigate the riskregarding to the cash card, I will change the PIN numbereveryday and use the IC card with bio-identification instead ofthe conventional magnetic card.




I understand the risk. I will share the risk with other people.

ex.: A cash card (ATM card) may be risky. So, I will take outinsurance upon my cash card and bank account.



• Risk Retention◦ saving fund to recover the damage (self-insurance)◦ doing nothing

• Risk Avoidance• Risk Optimization/Mitigation

◦ prevention (retrofitting/improving structures, ground etc.)◦ mitigation (education, redundant network etc.)

• Risk Transfer◦ insurance


Quantitative Evaluation of Risk

To manage the risk, we should evaluate quantitatively the risk forthe considering objects such as structures. This process is mostimportant, but most difficult in the process of risk management.

Procedure for Risk Evaluation:

Damage Assesment

Seismic Hazard Analysis

Seismic Loss Function

Seismic Hazard Curve

Annual Seismic Risk Density

Seismic Risk Curve

Life Cycle Cost

Loss by EarthquakeCost for Risk Mitigation

Total CostStrategy for dealing with Risk- Risk Retention- Risk Avoidance- Risk Mitigation- Risk Transfer



� Damage Assessment Damage Assesment





Seismic Risk Curve

Life Cycle Cost



Detailed Procedure:

Probability of Damage(Determining Fragility)

Loss by Damage(Event Tree)

Modeling Damage by EarthquakeSeismic Loss Function


Damage Assessment

� Determining FragilityProbability of Damage(Determining Fragility)



• Analytical Method◦ mathematically accurate◦ accuracy of model for the physics◦ setting the criteria of damage

• Statistical Data◦ based on the fact◦ population is not clear◦ less data for severe damage


Damage Assessment

� Determining FragilityProbability of Damage(Determining Fragility)



PGA

Fai

lure

Pro

babi

lity


Damage Assessment

� Determining LossProbability of Damage(Determining Fragility)



• Listing up the probable damage• Estimating the loss by damage

◦ direct loss◦ indirect loss


Damage Assessment

� Determining LossProbability of Damage(Determining Fragility)



An Example

Lossi Damage Ci

(×1000$)

1 No 02 Slight 53 Moderate 504 Severe 200


Damage Assessment

� Modeling DamageProbability of Damage(Determining Fragility)



Damage byVibration Failure Collapse

ColumnDamage

No

Slight

Moderate

Severe

Probability

Loss Risk

No

Yes

0.7

0.3

0.83

0.17

0.8

0.2

0.7

0.25

0.04

0.01

Pi

Ci Ri

5

50

200

0 0

1.25

2.0

2.0

(x 1000$)

Σ 5.25Ri

This event tree is available for a PGA (ex. 300 Gal). For otherPGAs, the event trees must be different.


Damage Assessment

� Probability Function of Loss

Probability function of seismic loss can be obtained through theevent tree: for example...

0

0.2

0.4

0.6

0.8

1

0 10 100 1000

Pro

babi

lity

Loss (x 1000$)

R=5.25 (x 1000$)


Damage Assessment

� Probability Function of Loss

Probability function of seismic loss can be obtained through theevent tree. In a case where the value of loss is continuous, theprobability function can be replaced by the probability densityfunction.

0

0.2

0.4

0.6

0.8

1

0 10 100 1000

Pro

babi

lity

Loss (x 1000$)Basics for Seismic Risk Management – p.42/65

Damage Assessment

� Seismic Loss Function Probability of Damage(Determining Fragility)



Seismic loss function represents the relationship between PGAand loss.

PGA (Gal)

Sei

smic

Los

s(x

100

0$)

Slight

Moderate

Severe

2.0

2.0

1.25

300

5.25


Damage Assessment

� Seismic Loss Function Probability of Damage(Determining Fragility)



From the comparison of the seismic loss function and the PDF ofseismic loss, we can observe that seismic loss function passesthrough the center of gravity for the PDF of loss at each PGA.

PGA (Gal)

Sei

smic

Los

s Seismic Loss Function

Probability Density Function of Loss



� Seismic Hazard Analysis Damage Assesment





Seismic Risk Curve

Life Cycle Cost



Objective:To estimate stochastically the intensity of earthquake groundmotion at the considering site. For this, we have to consider thefollows:

• probability of earthquake occurrence(frequency / number per year),

• intensity of ground motions at the considering site.



� Seismic Hazard Analysis Damage Assesment





Seismic Risk Curve

Life Cycle Cost



Detailed Procedure:

Ground Condtion

Seismic Hazard CurveEstimation of Earthquake

Ground Motion

Selecting Indicator for Intensity of Earthquake Ground Motion(PGA, PGV, SI, Response Spectra etc.)

Seismic Environment(Location of Fault etc.)



� Probability of Earthquake Occurrence

Gutenberg and Richter’s Equation:

log N(M) = a − bM

N(M) : # of earthquake whose magnitude is larger than M

M : Magnitudea, b : constant values

Note:• a and b depend on seismic source area / zone.• G-R equation does not consider the upper limit of

magnitude.



� Probability of Earthquake Occurrence

Gutenberg and Richter’s Equation:

M

log

N(M

)



� Intensity of Earthquake Ground Motion at a Site

Regression equations for attenuation and/or results of numericalcalculation of earthquake ground motion are used.

Distance from Fault

PG

A M=7.5

M=7.0

M=6.5



� A Simple Example

Hereafter, I will show a simple example to explain how to get ahazard curve (Dan and Kaneko, 2001).

This example denotes only the basic procedure to understandthe concept of the seismic hazard analysis. Thus, it should benoted that more complicated techniques are applied to realproblems.


Example to Get A Seismic Hazard Analysis

Let us consider three seismic source areas where are locatedat 10 and 20 kms from the considering site.

20 km

20 km10 km

Source Area

Source Area

Source Area

A

B

C

Considering Site



Using the G-R equation, the occurrence number ofearthquakes for 10,000 years is estimated as follows:

Source Area CumulativeA B C

∑# of Earthquake

M7.5 1 1 1 3 3M7.0 3 3 3 9 12M6.5 13 13 13 39 51

Distance [km] 10 20 20



Using attenuation of PGA, values of PGA at the site areestimated as follows:

Distance [km] 10 20

M7.5 480 370M7.0 410 290M6.5 330 210

Units in [cm/s2]



From the above results, we can obtain the maximum PGAsand their occurrence number for next 10,000 years are listed as:

10 [km] # 20 [km] #

M7.5 480 [cm/s2] 1 370 [cm/s2] 2M7.0 410 [cm/s2] 3 290 [cm/s2] 6M6.5 330 [cm/s2] 13 210 [cm/s2] 26



Then, we can get the maximum PGAs and their occurrencenumbers.

maximum PGA # per Cumulative # per(cm/s2) 10,0000 years 10,000 years

480 1 1410 3 4370 2 6330 13 19290 6 25210 26 51



From the occurrence number for 10,000 years, we can obtainthe “annual probability of exceedance.”

max. PGA # per #/year Annual Prob. ofy (cm/s2) 10,000 years ν(y) Exceedance; p(y)over 480 0 0 0

over 410 to 479.9 1 1/10000 1/10000over 370 to 409.9 4 4/10000 4/10000over 330 to 369.9 6 6/10000 6/10000over 290 to 329.9 19 19/10000 19/10000over 210 to 289.9 25 25/10000 25/10000

over 0 to 209.9 51 51/10000 51/10000



Hazard curve at the considering site can be drawn as follows:

0

0.001

0.002

0.003

0.004

0.005

0.006

0 100 200 300 400 500

Ann

ual P

rob.

of E

xcee

danc

e

Maximum PGA [cm/s2]

Return Period

200 years

500 years

1000 years

2000 years

5000 years

10000 years

Return period T (y) = 5000 means that we may experienceonce the earthquake ground motion larger than 409.9 cm/s2 asexpected value. In this case, the values will be 410 or 480 cm/s2.



From the hazard curve, we can obtain the cumulativedistribution function of the maximum PGA as

q(y) = 1 − p(y)

Furthermore, the probability (density) function is obtained bythe derivative of q(y):

f(y) =d

dyq(y) = − d

dyp(y)



0.99

0.992

0.994

0.996

0.998

1

0 100 200 300 400 500

Cum

ulat

ive

Pro

b.

Maximum PGA [cm/s2]

0

0.002

0.004

0.006

0.008

0 100 200 300 400 500

Pro

babi

lity

Maximum PGA [cm/s2]

0.995

Cumulative probability function Probability (density) functionq(y) f(y)



� Annual Seismic Risk Density Damage Assesment





Seismic Risk Curve

Life Cycle Cost



PGA (Gal)

Sei

smic

Los

s

Seismic Loss Function×

PGA (Gal)

PD

F o

f PG

A

PDF of PGA

⇒ PGA (Gal)

Ris

k D

ensi

ty

Annual Seismic Risk DensityThe area of this function cor-

responds to the annual expectedloss.



� Seismic Risk Curve Damage Assesment





Seismic Risk Curve

Life Cycle Cost



PGA (Gal)

Seismic Loss

Probability of Exceedance

Seismic Loss

Hazard Curve


Seismic Risk Curve


Application to Determination of a Design Level

� Earthquake Occurence Models

Area-sourcemodels

Inter-plateearthquakemodels

Active faultsmodels


Application to Determination of a Design Level

� Seismic risk map using yield strength

(a) Pf/year = 10−3 (b) Pf/year = 10−4

If we introduce the risk analysis, we may determine appropriatedesign levels for each site.


Appendix: Hazard Map

You can find a global hazard map at the web site of GSHAP(Global Seismic Hazard Assessment Program whose address ishttp://www.seismo.ethz.ch/GSHAP/).

As an example, I will show the seismic hazard map of Asiadepicting peak ground acceleration (PGA), given in units ofm/s2, with a 10% chance of exceedance in 50 years. The siteclassification is rock.


Appendix: Hazard Map


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