probabilistic approach for seismic microzonation ...civil.iisc.ernet.in/anbuseminar.pdf ·...
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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
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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
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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
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• 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.
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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
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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
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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.
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Final hazard map of Jabalpur
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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.
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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
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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
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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.
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Geomorphologic attributes
Geohazard map by integrating geomorphologic attributes
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Probabilistic seismic microzonation index map? has been generated for central frequency
Final hazard map of Sikkim
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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
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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
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Final hazard Index map of Guwahati
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Preliminary seismic population risk map Risk map is generated by integrating microzonation map with demography (population) distribution map
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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".
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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
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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
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SourcesUncertainty in the Distance/source
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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( +−=
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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
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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.
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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 −== −
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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
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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
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Combining uncertainties - probability computations
Mean annual rate of exceedance
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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.
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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
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Seismotectonic of region• EQ data are
homogenized• Data are
Declustered• Seismic sources
are considered from seismo-Atlas (2002) and literature
Hazard Estimation -Probabilistic approach
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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
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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
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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
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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
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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
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Hazard zonation map PGA at 10% probability in 50Years
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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?
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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
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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
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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
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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
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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
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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
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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
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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 =
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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=
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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
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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
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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
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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
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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).
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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
=∑
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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
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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
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Corrected N Value Required to Prevent Liquefaction for 475 Years
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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)( >=
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Liquefaction potential map
Very high0<LI<2
High0<LI<2
Moderate2<LI<5
Low0<LI<2
Non-liquefiable0
Liquefaction potentialcategory
LI
Liquefaction potential classification
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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)( >=
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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
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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
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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 /
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Hazard map based on probabilistic approach
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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
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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
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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
![Page 68: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/68.jpg)
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.
![Page 69: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/69.jpg)
Bangalore site class using SPT-N
Site class using 30m SPT-N
Site class using H m SPT-N
![Page 70: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/70.jpg)
Bangalore site class using Vs
Site class using 30m Vs
Site class using H Vs
![Page 71: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/71.jpg)
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
![Page 72: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/72.jpg)
Spectral acceleration comparison
Sa at 1s for site class C
Sa at 1s for site class D
![Page 73: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/73.jpg)
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
![Page 74: Probabilistic Approach for Seismic Microzonation ...civil.iisc.ernet.in/anbuseminar.pdf · Probabilistic Approach for Seismic Microzonation ... • Gumbel’s method ... the value](https://reader031.vdocument.in/reader031/viewer/2022011800/5aba47b47f8b9ab1118baad2/html5/thumbnails/74.jpg)
Special Thanks to Prof T. G. SitharamMr. K.S. VipinMr. S.PatilMr. Narendra Kumar JN