Dr. P.Anbazhagan M.E, PhD.Lecturer

Department of Civil EngineeringIndian Institute of Science, Bangalore

http://www.civil.iisc.ernet.in/~anbazhagan/

Probabilistic Approach for Seismic Microzonation –

Geotechnical Issues

Objective of MicrozonationMicrozonation practice in IndiaProbabilistic based Microzonation maps• Rock level hazard• Surface level hazard considering site effects• Liquefaction hazard

Probabilistic Hazard map using GIS -case studyGeotechnical issues on site classSummary

Contents

Providing useful information for land use planning .Providing basic seismic hazard information for regional damage potential estimatesLifelines:• Identification of areas where lifeline systems (e.g., water, sewer,

gas, electricity) are most vulnerable to seismic hazards;• Selection of routes for linear structures (e.g., transportation

corridors); and• Setting priorities for seismic upgrading or remediation work

Community Planning:• Selection of sites for essential facilities (e.g., hospitals, fire

stations) or for high hazard structures (e.g., toxic waste containment facilities)

Objective of Microzonation

• Providing a basis for restrictions on development in high seismic hazard areas; and

• Identification of areas requiring special study before development is allowed to proceed

Building Codes:• Providing information on site effects to be accounted for, in

design of new structures; and• Establishing more rigorous design requirements for certain types

of structures on sites with high seismic hazard levelsInsurance and Financial:• Assessment of the relative seismic hazard-related risks of a

project, which is to be insured or financedSeismic microzonation main goals are:• To define seismic actions for designing or improving the

resistance of structures such as buildings, bridges and plants and• To plan land-use so as to reduce the level of hazard.

Jabalpur urban area –Pilot project in India, Level 1 and Level 2 maps

Sikkim Himalaya- Hazard maps using GIS integration

Guwahati region- Hazard maps and vulnerability of buildings

Microzonation Practice in India

A detailed study on seismotectonic of region has been carried out and seismic source map is prepared for JabalpurHazard values are estimated using deterministic approach considering Scenario earthquake (Maximum Credible Earthquake)• M 6.5, Depth 30 km, Epicenter at Lat 23.08o N, Long. 80.06o E on Son

Narmada South Fault (SNSF)• Past Earthquake- 22 May, 1997, Epicenter at Lat 23.08o N, Long. 80.06o E, • Focal Depth: 35 km, Magnitude: 6.

• The attenuation relation used for DSHA is proposed by Joyner andBoore, (1981)

• Maximum PGA estimated at rock level is 0.1g (BIS 1893-2002-0.2g) Site response studies have been conducted using Nakamura receiver function technique • Predominant frequency has been estimated• Amplification map is generated based on noise survey

Microzonation of Jabalpur Urban Area-2004

Liquefaction susceptibility map is generated• Factor of safety of site estimated using SPT data using method proposed

by Seed and Idriss (1982)• Surface acceleration (0.15 to 0.40g) is estimated using amplification

curve suggested by Seed and Idriss (1982)• Liquefaction induced surface deformation is estimated using

methodology proposed by Ishihara (1986)Earthquake induced slope instability is estimated using terrain slope map.Shear wave velocity maps are generated using Multichannel analysis of surface wave (MASW). Level II map:• The first level maps are further improved incorporating semi-

quantitative parameters of liquefaction susceptibility and response in GIS and level II map is generated• Hazard map, liquefaction map, site response based on noise curve

typologies, peak frequency map and peak amplification map.• Vs

30 shear wave velocity map.

Final hazard map of Jabalpur

Vulnerability & Risk Map for Jabalpur Vulnerability Study • Quantitative assessment of Demand capacity approach• Qualitative assessment with rapid screening procedures

approach• Vulnerability of buildings are assessed based on MCE as per

IS1893-2002

Preliminary Seismic Risk map• The seismic hazard map has been integrated with

vulnerability analysis results• The integrated map has been reinterpreted to transform, “2nd

precision level hazard map” into preliminary risk map of Jabalpur urban area.

Seismic source for the region is considered from Bhatia et al (1999) map MCE with specified probability of exceedance is estimated using• Gumbel’s method (1958)• b value approach using

Gutenberg and Richter, (1954)

Attenuation model for the region has been developed

Microzonation of Sikkim Himalaya

Assam

Different theme layers are generated using Geomorphologic attributes and seismological attributes Geomorphologic attributes• Surface geological map from Survey of India • Soil site classification map using soil taxonomy map from

National Bureau of soil survey report (1994)• Rock outcrop map• Land slide spot out using FCC of IRS-IC, LISS III imagesSeismological attributes• Site response in terms of amplification using strong motion

station data• Peak ground acceleration for scenario earthquake of MCE 8.3

• This earthquake is assumed to be nucleating from the hypocenter of magnitude 5.6 which was the largest earthquake observed in the duration of acquisition time.

• Predominant frequency (PF) distribution from observed accelerogram data

Geomorphologic attributes

(a)

(c)(b)

(a) Slope coverage map, (b) Rock outcrop coverage of the Sikkim Himalaya, (c) Landslide coverage of the Sikkim Himalaya on IRS LISS III image. Larger circle represents high landslide.

Geomorphologic attributes

Geohazard map by integrating geomorphologic attributes

Probabilistic seismic microzonation index map? has been generated for central frequency

Final hazard map of Sikkim

PGA is estimated using spectral strong motion synthesis for a scenario earthquake magnitude (SEM) of Mw 8.7 • Seismic source is assumed great Shillong Earthquake (Mw of

8.7, 1897) location

Site response is estimated using noise survey and geotechnical data by empirical equationsVs30 is calculated using standard penetration test data of 200Ground response spectra is computed using WESHAKE91 software by considering the synthesized earthquake of MCE and borehole data

Microzonation of Guwahati Region

Geology and geomorphology –base mapEffective shear wave velocity of 30m (calculated from SPT data)Liquefaction potential/ factor of safetyLand use mapBasement configuration and thickness of valley fillLandslide hazard zonation Site response (considering at predominant frequency)Predominant frequencyPeak ground acceleration

All these layers are formed in GIS and integrated to obtain the hazard index map

Themes considered

Final hazard Index map of Guwahati

Preliminary seismic population risk map Risk map is generated by integrating microzonation map with demography (population) distribution map

Seismic Microzonation

Hazard Mapping

Vulnerability Assessment

Risk Mapping

Hazard: Hi|T, can be understood as the probability of occurrence of an event with an intensity greater than or equal to i during an exposition period T.

Vulnerability, Ve, is the intrinsic predisposition (inherent tendency) of the exposed element e to be affected or of being susceptible to suffer a loss as a result of the occurrence of an event with intensity i.

Risk,Risk, Rie|T, can be defined as the probability of loss in an exposed element e as a consequence of the occurrence of an event with intensity larger than or equal to i during an exposition period T

Microzonation is an efficient tool to mitigate the earthquake risk byhazard-related land use management.

"Earthquake Risk = Earthquake Hazard*Vulnerability*Value at Risk".

Probabilistic based seismic Microzonation

Evaluation of seismic hazard

Deterministic Seismic hazard

Analysis (DSHA)

Probabilistic Seismic hazard Analysis (PSHA)

Relatively simpleuncertainties should not be taken

Relatively complicateduncertainties are taken in to account

Uncertainties in seismic hazard

uncertainty in location, size, frequency, and effects of earthquakes, and combines all of them to compute probabilities of different levelsof ground shaking

SourcesUncertainty in the Distance/source

Uncertainty is probabilistically estimated by assuming equal likelihood of occurrence at any point of sourceProbabilistic distribution function (PDF) is

Approach

Site

h

d

D

ro

L0

L

X

Rupture

Source

r0)|( ==< mMrRP for 2/12

02 )( LDR +<

)()(

)|( 02/122

mXLLdr

mMrRP−

−−==< for

[ ]{ } 2/120

220

2 )()( mXLLDRLD −++<≤+

1)|( ==< mMrRP for [ ]{ } 2/120

2 )(mXLLDR −++>

Where X(m) is the rupture length in kilometers for the event of magnitude m is estimated

using the Wells and Coppersmith (1994) equation, which is as given below:

[ ]lengthfaultmX im ,10min)( ))(59.044.2( +−=

Given source can produce different earthquakes• Low magnitude - often• Large magnitude - rare

In DSHA, one magnitude (MCE) is Considered, irrespective of source zone.In PSHA as possible range of magnitudes from M0 to Mu

(MCE)Maximum magnitude can be determined using available data (complete or incomplete) Earthquake events in region should follow trend called as Regional Recurrence law• Counted number of earthquakes exceeding different magnitude

levels over period of many years

Magnitude Uncertainty

The maximum magnitude is an important variable in the seismic hazard estimation as it reflects maximum potential of strain released in larger earthquakes.The instrumental and historical records of earthquakes are often too short to reflect the full potential of faults or thrusts.The maximum regional magnitude, Mmax, is defined as the upper limit of magnitude for a given region or it is magnitude of largest possible earthquake.The maximum regional magnitude Mmax can be estimated using Kijko and Graham (1998 and 2001) approach

Estimation of Maximum magnitude

1/ 2

max maxexp[ /(1 ) ( 1/ , ) ( 1/ , )

q q qobs qnr rm m q r qδ δ δ

β

+ − ⎡ ⎤= + Γ − − Γ −⎣ ⎦

Where ( )22/( ) , /p qβ ββ σ β σ= = , β =2.303 b, β denotes the mean value of β , βσ is the

standard deviation of β and Cβ is a normalizing coefficient and which is equal to 1

max min{1 [ /( )] }qp p m m −− + − , max min/( )r p p m m= + − , 1 exp[ (1 )]c n Cβ= − − , nCβδ = and

( , )Γ ⋅ ⋅ is the Incomplete Gamma Function.

Recurrence law for region or source zones

Regional Recurrence

Gutenberg-Richter Recurrence Law

bMam −=λlog Implies that earthquake magnitudes areexponentially distributed (exponential pdf)

Can also be written as

Mm βαλ −=lnThen

]exp[10 MbMam βαλ −== −

Approach Magnitude probability

Where

- Minimum magnitude for the given source- Maximum magnitude for the given source

0mum

Deaggregation

regiontheinearthquakeofnumberTotalsourcethetocloseearthquakeofNumber

i =χ

0 0

00

( ) ( )

( )( ) ( )

1

u

u

m m m m

i m m

e eN m N me

β β

β

− − − −

− −

−=

−

β =b ln (10) and Ni (m0) weightage factor for a particular source based on deaggregation

)(5.0 iifactorWeighting χα +=

∑=i

ii L

LαThe weighting factor for length Li is the length of the fault i

The earthquake event weighting factor (χi) has been taken as the ratio of the past events associated with source i to the total number of events in the region

Standard error - use to evaluate conditional probability

• The normal cumulative distribution function has a value which ismost efficiently expressed in terms of the standard normal variables (z) which can be computed for any random variables using transformation

Uncertainty in Predictive relationships

PGA

PGAPGAzln

lnlnσ

−=

Where PGA is the various targeted peak acceleration levels which will be exceeded. PGAln is the value calculated using attenuation relationship equation and PGAlnσ is the uncertainty in the attenuation relation expressed by the standard deviation

Combining uncertainties - probability computations

Mean annual rate of exceedance

Poisson process - describes number of occurrences of an event during a given time interval or spatial region.• The number of occurrences in one time interval are independent

of the number that occur in any other time interval.• Probability of occurrence in a very short time interval is

proportional to length of interval.• Probability of more than one occurrence in a very short time

interval is negligible.

Temporal uncertainty

Poisson process

!][

nenNP

n µµ −

== TzezZP Tz )(1)( )( νν ≤−=> −

where n is the number of occurrences and µ is the average number of occurrences in the time interval of interest.Where )(zν is (mean annual rate of exceedance) the average frequency during time period T at which the level of ground motion parameters, Z, exceed level z at a given site.

Consider an event that occurs, on average, every 1,000 yrs.• What is the probability it will occur at least once in a 100 yr period?

• λ = 1/1000 = 0.001• P = 1 - exp[-(0.001)(100)] = 0.0952

• What is the probability it will occur at least once in a 1,000 yr period?• P = 1 - exp[-(0.001)(1000)] = 0.632

Then, the annual rate of exceedance for an eventwith a 10% probability of exceedance in 50 yrs is

The corresponding return period is TR = 1/λ = 475 yrs.For 2% in 50 yrs, λ = 0.000404/yr TR = 2475 yrsFor 50% in 50 yrs, λ = 0.01386/yr TR = 72 yrs

0021.050

)1.01ln(=

−−=λ

Seismotectonic of region• EQ data are

homogenized• Data are

Declustered• Seismic sources

are considered from seismo-Atlas (2002) and literature

Hazard Estimation -Probabilistic approach

Among 48 seismic sources about 6 sources given the PGA values of 0.035g and above

Seismogenic sources

14150261305.3L22

50104581115.2L20

1277181095.2L16

251045.21055.1L15

2088511254.7F47

1511697384.6F19

No of EQ close to Source

Longer Distance

(km)

Shorter Distance

(km)

Length (km)(Mw)Source

14150261305.3L22

50104581115.2L20

1277181095.2L16

251045.21055.1L15

2088511254.7F47

1511697384.6F19

No of EQ close to Source

Longer Distance

(km)

Shorter Distance

(km)

Length (km)(Mw)Source

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500

Hypocentral Distance

Cum

ulat

ive

Dis

tanc

e Pr

obab

ility

Earthquake data are classified as two parts, recurrence relation is calculated • Historic data –before 1960• Instrumented data-After 1960

Regional Recurrence relation

3

3.5

4

4.5

5

5.5

6

6.5

1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960Period (Year)

Earth

quak

e M

agni

tude

(Mw

)

Log(N) = -0.62M + 2.14R2 = 0.95

-2-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

3 3.5 4 4.5 5 5.5 6 6.5Magnitude (Mw)

Log

(Cum

ulat

ive.

no

of e

vent

s/yre

ar)

1

Historic data with corresponding frequency magnitude distribution

Instrumented data with corresponding frequency magnitude distribution

3

3.5

4

4.5

5

5.5

6

6.5

1960 1970 1980 1990 2000 2010Period (Year)

Earth

quak

e M

agni

tude

(Mw

)Log(N) = -0.98M + 4.56

R2 = 0.94

-1.5

-1

-0.5

0

0.5

1

1.5

2

3 3.5 4 4.5 5 5.5 6 6.5Magnitude (Mw)

Log

(Cum

ulat

ive.

no

of e

vent

s/yre

ar)

3

3.5

4

4.5

5

5.5

6

6.5

1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000Period (Year)

Earth

quak

e M

agni

tude

(Mw

)

Log(N) = -0.86M + 3.53R2 = 0.97

-2

-1.5

-1

-0.5

0

0.5

1

1.5

3 3.5 4 4.5 5 5.5 6 6.5Magnitude (Mw)

Log

(Cum

ulat

ive.

no

of e

vent

s/yre

ar)

Total data with corresponding frequency magnitude distribution

Magnitude Uncertainty

0.00

0.01

0.02

0.03

0.04

0.05

0.06

4.00 4.50 5.00 5.50 6.00 6.50 7.00

Magnitude

Cum

ulat

ive

Mag

nitu

de P

roba

bilit

y

Recurrence relation and Mmax using maximum likelihood method by Kijko and Sellevoll (1989, 1992)• Mmax = 6 ± 0.5 and • b value 0.87 ± 0.03

MN 87.052.3)log( −=

Attenuation relationThe attenuation relation (for peak ground acceleration and spectral acceleration) for rock site in Peninsular India developed by Iyengar and RaghuKanth(2004) and RaghuKanth and Iyengar(2007) has been used

( ) ( ) )ln(ln66ln 42

321 ∈+−−−+−+= RcRMcMccyWhere y, M, R and ∈ refer to PGA/spectral acceleration (g), moment magnitude,

hypocentral distance and error associated with the regression respectively

Study area is divided in to 0.005o x 0.005o grid, hazard values for center each grid point is calculated

Hazard Curves

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6Peak Ground Acceleration (g)

Mea

n A

nnua

l rat

e of

Exc

eeda

nce

L15F47F19L16L20L22Cumulative

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 0.1 0.2 0.3 0.4 0.5 0.6

Spectral Aceeleration (g)

Mea

n A

nuua

l rat

e of

Exc

eeda

nce F47

L15L16F19L20L22Cumulative

Hazard zonation map PGA at 10% probability in 50Years

PGA at 2% in 50Y

PGA From DSHA

PGA at 50% in 50Y

PGA from Scenario earthquake is not matching with PGA 2% &10% in 50YUse of DSHA or Scenario earthquake for seismic microzonation is reliable?

Hazard at surface using Probabilistic Much of damages and induced effects such as liquefaction and land slides are influenced by the ground surface hazard values.Estimation of surface level hazard/acceleration considering site specific study is essence of microzonationProbabilistic based surface acceleration requires the site classifications based on site specific geotechnical properties of soilUniversally followed site classifications are based on 30 m equivalent/average soil strength, in terms of • Standard Penetration Resistance -N• Soil undrained shear strength –Su• Shear wave velocity -Vs

Site classification methods for seismic microzonation

Geotechnical Methods Geophysical methods Description Geology and

Geomorphology SPT SCPT SASW MASW

Strain - Lager Large Small Small

Drilling - Essential Essential No No

Cost Small high high Small Moderate

Time Large Lager Moderate Less Less

Quality of data Poor Good Very Good Fair Very Good

Detection of variability of soil deposits

Poor Good Very Good Good Very Good

Suitable soil type All Non

Gravel

Non Gravel All All

Depth of information suitable for Microzonation

Poor Good Fair – Vs is

available up to 20m

Good Very Good

Measurement of dynamic properties Poor Fair Good Good Very Good

Success full cases used Small Large Medium Medium –

Lager Very Lager

Measure the layer strength (N, Cu or Vs) and its thicknessEstimate equivalent values by using

Site classification procedures

∑

∑

=

=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

n

i iii

i

n

ii

SuorVsorNd

dSuorsVorN

1

1

Where ∑=

n

iid

1

is summation of total depth, for 30m average (⎯N30 ) ∑=

n

iid

1

= 30m, di and Ni denote

the thickness (in meters) and Standard Penetration Resistance not to exceed 100 blows/0.3m as directly measured in the field without corrections of the ith formation or layer respectively, in a total of n layers, existing in the top 30 m. vi denote the shear-wave velocity (at a shear strain level of 10−5 or less, m/s) of the ith formation or layer in a total of n layers within the depth of 30m

NEHRP -National Earthquake Hazards Reduction Program site classes.• Site class A -Vs30 > 1.5 km/s -• Site class B -0.76 km/s < Vs30 ≤ 1.5 km/s -• Site class C -0.36 km/s < Vs30 ≤ 0.76 km/s >50• Site class D -0.18 km/s < Vs30 ≤ 0.36 km/s 50< <15• Site class E - Vs30 < 0.180 km/s <15Attenuation relation is modified to account the site effects and

calculate spectral accelerations.The value of spectral acceleration for different site classes can be

obtained using equation .

Site class as per NEHRP

N

N

N

1 2ln lns br sF a y a= + + δWhere 1a and 2a are regression coefficients, bry is the spectral acceleration at rock level and

sδ is the error term.

s br sy y F=Where sy is the spectral acceleration at the ground surface for a given site class

SPT N values and shear wave velocity values are used to classify Bangalore as per NEHRP classification

Case study of Bangalore

Site class using SPT-N

Site class using Vs

PGA at ground surface considering site class C has been estimated for 50%, 10% and 2% probability in 50years- 50% probability map is presented

PGA at surface considering site C

PGA at surface for site class CPGA at surface from site response

study using shake2000

The earthquake amplitudes are represented usually by the peak ground acceleration; however for the structural designs and building code the most widely used parameter is spectral acceleration andcorresponding period/frequency.Design spectrum needs the spectral acceleration values, which can be produced easily in probabilistic approach

Response Spectrum

Find spectral acceleration values for different periods at constant λ (mean annual rate of exceedance)

All spectral acceleration values have same λ-value and same probability of exceedance is used to develop the Uniform hazard spectrum

Site Coefficients and Adjusted Maximum Considered Earthquake Spectral Response Acceleration Parameters• The maximum considered earthquake spectral response acceleration for short

periods, SMS, and at 1 second, SM1, adjusted for site class effects, shall be determined

Design Spectral Response Acceleration Parameters• Design earthquake spectral response acceleration at short periods, SDS ,

and at 1 second period, SD1, shall be determined from

Developing response spectrum

SsFaSMS =11 SFvSM =

where site coefficients Fa and Fv are defined for different site class in Tables 4.1.2 4a and 4.1.2 4b in NEHRP guide (BSSC,2000)

MSDS SS32

= 11 32

MD SS =

General Procedure Response Spectrum• Where a design response spectrum is required by the Provisions and site-

specific procedures are not used, the design response spectrum curve shall be developed as indicated in Figure and as follows

• For periods less than or equal to To, the design spectral response acceleration, Sa, shall be taken Eq-1

• For periods greater than or equal to To and less than or equal to TS, the design spectral response acceleration, Sa, shall be taken as equal to SDS• For periods greater than TS, the design spectral response acceleration, Sa, shall be taken as given Eq-2

• where:• SDS = The design spectral response acceleration at short periods,• SD1 = The design spectral response acceleration at 1 second period,• T = the fundamental period of the structure (sec),• To = 0.2SD1/SDS, and• TS = SD1/SDS.

DSo

DSa ST

TS

S 4.06.0 +=

TS

S Da

1=

Spectral acceleration at 10% probability in 50years calculated and mapped for short periods and long periods (1s)

Spectral acceleration maps

Spectral Acceleration at 0.01s

Spectral Acceleration at 1s

Design spectrum as per NEHRP for Bangalore for return period of 475 years

Response spectrum A

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 0.5 1 1.5 2 2.5 3 3.5 4

Time Period (s)

Spec

tral

Acc

eler

atio

n Sa

(g)

Site_C

Site_D

Liquefaction Estimations Conventional MethodCyclic Stress Ratio (CSR)-Due to earthquake

The capacity of the soil to resist liquefaction, expressed in terms of CRR.(CSR required to cause liquefaction)• CRR is depends on several factors, the best way to estimate

CRR is the field testing• Several field tests have gained common usage for evaluation of

liquefaction resistance- widely used is SPT test • Corrected SPT N values are calculated and used to estimate

CRR

Where, 0.65 g

amax represents 65 % of the peak cyclic shear stress, maxa is peak ground

surface acceleration, g is the acceleration due gravity, voσ and 'voσ are the total and effective vertical stresses and dr = stress reduction coefficient.

dvo

vo rg

aCSRσσ

′= max65.0

Factor of safety against liquefaction• The cyclic stress ratio caused by the earthquake is greater than

the cyclic resistance ratio of in situ soil then liquefaction could occur during an earthquake. The factor of safety against liquefaction is defined as follows:

• Here subscript 7.5 for CRR denotes that CRR values calculated for the earthquake moment magnitude of 7.5. MSF is the magnitude scaling factor

• Considers only single ground motion hazard level• Results are not for required probability in project period

MSFCSR

CRRFS ⎟⎠⎞

⎜⎝⎛= 5.7

Drawback

Factor of safety assessment • Mean annual rate of exceedance of engineering damage

parameter

• The above equation modified for FS

Probabilistic Evaluation of Factor of Safety Against Liquefaction

* *i

1im

IM

i

N

EDP imi

P EDP EDPλ λ=

⎡ ⎤= > ⏐ΙΜ = ∆⎣ ⎦∑Where EDP – Engineering damage parameter like factor of safety etc.; IM – intensity measure which is used to characterize the earthquake loading like peak ground acceleration etc. *

EDPλ - mean annual rate of exceedance of EDP*; iimλ∆ - incremental mean annual rate of

exceedance of intensity measure imi.

*

iL L1 1

[FS FS a , ] ,aM

iL

NN

j a jFSj i

P m mλ∗

= =

Λ = < | ∆∑∑

Where *LFS

Λ - annual rate at which factor of safety will be less than LFS∗ ; FSL – factor of

safety against liquefaction; LFS∗ - targeted value of factor of safety against liquefaction; MN -Number of magnitude increments; aN - number of peak acceleration increments; ,

ia jmλ∆ - incremental annual frequency of exceedance for acceleration ai and magnitude mj (this value is obtained from the deaggregated seismic hazard curve with respect to magnitude).

The conditional probability (Kramer and Mayfield, 2007)

i

*1 60 1 2 , 3 4 0 5 6

L L

( ) (1 ) ln( ) ln( ) (ln( / )P[FS FS a , ] eq i L j v a

j

N FC CSR FS m P FCm

ε

θ θ θ θ σ θ θσ

′∗

⎡ ⎤+ − − − + +< | = Φ −⎢ ⎥

⎢ ⎥⎣ ⎦Where Ф – standard normal cumulative distribution; 0vσ ′ - effective over burden pressure; Pa – atmospheric pressure in the same unit as 0vσ ′ .

, 0.65 i vo

eq i dvo

aCSR rg ′

σ=

σCSReq,i, the CSR value calculated without using the MSF for an acceleration ai, will be calculated for all the acceleration levels.

*,12

*,12

*,12

0.341( 0.0785 7.586)*,12 *

,120.341(0.0785 7.586)

23.013 2.949 0.999 0.05251

16.258 0.201( , , , )23.013 2.949 0.999 0.0525

116.258 0.201

s

rd

s

i j sd V

d j i si j s

V

a m V

er d m a Va m V

e

εσ− + +

+

⎡ ⎤− − + ++⎢ ⎥

+⎢ ⎥⎣ ⎦= ±⎡ ⎤− − + +

+⎢ ⎥+⎢ ⎥⎣ ⎦

Where ai and mj correspond to the discretized acceleration and magnitude values

*,12

12

i

si

s

V dV

=∑

Factor of Safety Against Liquefaction for a Period of 475 Years

FS at 3 m Depth

FS at 6 m Depth

Least FS using DSHA

In a similar way the liquefaction potential can be characterized by liquefaction resistance required at a site for a given return periodAnnual frequency of exceedance Nreq

• Where

SPT N values required to prevent liquefaction

*ireq req

1 1[N N a , ] ,

aM

ireq

NN

j a jNj i

P m mλ λ∗

= =

= > | ∆∑∑

i

req 1 2 , 3 4 0 5 6req req

N (1 ) ln( ) ln( ) (ln( / )P[N N a , ] eq i j v a

j

FC CSR m P FCm

ε

θ θ θ θ σ θ θσ

∗ ′∗

⎡ ⎤+ − − − + +> | = Φ −⎢ ⎥

⎢ ⎥⎣ ⎦

The value of reqN∗ is the corrected N value required to prevent the liquefaction with an annual frequency of exceedance of *

reqNλ

Corrected N Value Required to Prevent Liquefaction for 475 Years

Factor of safety values are not considered depth/thickness of layers Factor of safety values are further used to estimate Liquefaction potential index (LI) considering depth

• Where FL is factor of safety against liquefaction

Liquefaction hazard map

∫=20

0

)()( dzzWzFLI

2.10)( ≥= LFforzF

95.01)( ≤= LL FforFzF

95.02.1102)( 427.186 ><Χ= −L

F FforezF L

mzforzzW 205.010)( <−=

mzforzW 200)( >=

Liquefaction potential map

Very high0<LI<2

High0<LI<2

Moderate2<LI<5

Low0<LI<2

Non-liquefiable0

Liquefaction potentialcategory

LI

Liquefaction potential classification

Probability of liquefaction can also be assessed for given magnitude and acceleration Liquefaction severity is calculated and using this, probability of liquefaction can be determined Liquefaction severity index

• Where PL is probability of liquefaction

Liquefaction severity index map

mzforzzW 205.010)( <−=mzforzW 200)( >=

dzzWzPL LS )()(20

0∫=

411.1)96.0(1

1)( 5.4 ≤+

= LL

L FforF

zP

layerseliquefiablnonorFforzP LL 411.10)( >=

Liquefaction severity map

Very low0<LS<15

Non liquefiable0

Low15<LS<35

Moderate35<LS<65

High65<LS<85

Very high85<LS<100

DescriptionLS

Liquefaction severity classification

A GIS approach comprises of three distinct phases (Sander, 1998):• (1) data acquisition, • (2) data processing and • (3) data analysis.

There are several ways of digitizing the map data for its incorporation in a GIS. The data can be directly digitized from the map using a digitizing table or the outline of the required classes may be traced on a transparent overlay in an image processing software.

The GIS can be used for hazard management at different levels of development planning.

Hazard index map Using GIS

Hazard parameter layers• PGA from probabilistic approach• Site response parameters• Elevation levels to account topographical variation• Liquefaction

The matrix developed by pair wise comparisons between the factors can be used to derive the individual normalized weights and ranks of each factor

GIS integrations

minmax

jRRanks Normalized

RRRmim

−

−=

Where, RJ is the raw rank, Rmax and Rmin are the minimum and maximum scores of a particular layer.

( ) ∑+++++= WrwrwrWrWrWrW FSLFSLPFPFSASAPGAPGAAVsAVsOTOTHI /

Hazard map based on probabilistic approach

Hazard maps comparisonsDeterministic hazard maps are developed for Scenario earthquake Probabilistic hazard map for particular return periodFor disaster management and retrofitting the existing structures for desired probability level, PSH maps are more useful.PSH maps can produce the meaningful vulnerability and risk studies

Deterministic Microzonation (DSH) map

Calculation of surface level hazard and liquefaction potential using probabilistic approach is mainly depends on site class of regionSite class is based on 30m average strength of soil, but the site having engineering rock (Vs>760±60 m/s) at shallow (less than 30m) or deep (more than 35 m) depth, application of 30m site classification is questionable. • Pitilakis (2004) highlighted the problems associated with site

classes using exclusively the average S-wave velocity over the 30m for seismic site characterization

• The use of 30 m data as a basis for soil and seismic site characterization is misleading in many cases; hence, it has to be used with caution.

• The use of 30 m is only applicable when the actual site conditions are appropriate to that

Geotechnical Issues

Site class in International codes

<10Soft soil

< 183< 15< 180< 15E

10-30-NMediumsoil

< 180< 15183-36615-50180-36015-50D

180 – 36015-50366-762> 50360-760> 50C

360 – 800> 50762-1524-760-1500-B

> 800->1524->1500-A

VNVsNVsNVs N

BIS 1893-2002

Euro code 8IBCNEHRPSiteClass

Note- N and Vs are 30m average values, Vs in m/s

The soil overburden thickness in Bangalore varies from 1m to about 40mConsidering 30m concept will lead to higher equivalent soil strength values due to the shallow rock massEquivalent soil strength (SPT-N, Vs) for soil overburden thickness has been calculated for Bangalore The equivalent soil strength up to a depth of soil overburden thickness H (VH)

Site class based on overburden thickness

∑

∑

=

=

⎥⎦

⎤⎢⎣

⎡=

di

i ii

i

n

ii

H

VsorNd

dV

1

1Where idH ∑= = cumulative depth in m

di and Ni or vi denote the thickness (in meters) and SPT-N or shear-wave velocity (at a shear strain level of 10−5 or less, m/s) of the ith formation or layer respectively, in a total of n layers within the depth of H.

Bangalore site class using SPT-N

Site class using 30m SPT-N

Site class using H m SPT-N

Bangalore site class using Vs

Site class using 30m Vs

Site class using H Vs

Based on site class the design spectrum vary consideratelyConsidering the equivalent value for soil thickness is appropriate for seismic site characterization for microzonationSpectral acceleration is more for site class C at shorter periods and site class D at longer periods

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

Period (s)

Spec

tral A

ccel

erat

ion

(g)

Rock

Site Class-C

Site Class-D

Spectral acceleration comparison

Sa at 1s for site class C

Sa at 1s for site class D

Summary Probabilistic approach for seismic microzonation is meaningful for• Proper urban planning and disaster management • Retrofitting the existing structures for required level of probability • Fulfill the objective of microzonation studies• Vulnerability and risk studies

Site class based on 30m concept may not be applied directly for seismic microzonation Caution is needed to select proper site class for probabilistic approachFor shallow engineering rock depth region, site class based on equivalent strength of soil thickness ( up the engineering rock depth) is appropriate Guide line/road map for seismic microzonation in India need to bedrafted by highlighting the following• Procedures for different component microzonation maps• List of necessary maps produced in the study• List of maps to be integration to produce final hazard index map • Hazard map for required probability in specified period • PGA and Sa maps using probabilistic approach to develop design response

spectrum and future vulnerability and risk studies

Special Thanks to Prof T. G. SitharamMr. K.S. VipinMr. S.PatilMr. Narendra Kumar JN