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Geotechnical EarthquakeEngineering

by

Dr. Deepankar Choudhury Professor

Department of Civil EngineeringIIT Bombay, Powai, Mumbai 400 076, India.

Email: dc@civil.iitb.ac.inURL: http://www.civil.iitb.ac.in/~dc/

Lecture 1 5

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Module 4

Strong Ground Motion

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Other Spectral Parameters

RMS acceleration : This is the parameter that includes theeffects of amplitude and frequency, defined as

dT

0

2

d

dttaT1

rmsa

Where a(t) is the acceleration over the time domain and T d isthe duration of strong motion

AI - The Arias Intensity is a measure of the total energy at therecording station and is proportional to the sum of the squared

acceleration. It is defined as

dt t a g

AI 2

02

Ref: Kramer (1996)

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SI - The Spectrum Intensity is defined as the integral of the pseudo-Spectral velocity curve (also known as the velocity response spectrum),integrated between periods of 0.1 - 2.5 seconds. These quantities aremotivated by the need to examine the response of structures to groundmotion, as many structures have fundamental periods between 0.1 and2.5 sec. The SI can be calculated for any structural damping ratio.

Dominant frequency of ground motion (F d) is defined as thefrequency corresponding to the peak value in the amplitude spectrum.Thus, F d indicates the frequency for which the ground motion has themost energy. The amplitude spectrum has to be smoothed beforedetermining F d.

Other Spectral Parameters

Ref: Kramer (1996)

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Predominant Period (T p): Period of

vibration corresponding to the maximumvalue of the Fourier amplitude spectrum.This parameter represents the frequencycontent of the motion. The predominant

period for two different ground motions with

different frequency contents can be same,making the estimation of frequency contentcrude.

Bandwidth (BW) - of the dominant

frequency; measured where the amplitudefalls to 0.707 (1 /sq. root 2) of the amplitudeof the dominant frequency. Again, this is

based on a smoothed amplitude spectrum.

Other Spectral Parameters

T p

Period

F o u r i e r

A m p l

i t u d e GM1

GM2

T p is same for the twoground motions, though

the frequency content isdifferent

Ref: Kramer (1996)

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Central Frequency : Power spectral density function can be used to

estimate statistical properties of ground motion. The nth

spectralmoment and central frequency ( ) is given by,

Centr al frequency is used to calculate theoretical median peakacceleration as follows,

Shape Factor It indicates the dispersion of the power spectraldensity function about the central frequency,

Other Spectral Parametersn

d Gnn0

)(n

d Gnn0

)(

n

d Gnn0

)(0

2

28.2ln2 0max

d T u

20

211

It lies between 0 and 1, higher valueindicates larger bandwidth.

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Other Spectral Parameters

vmax /a max ratio : It is related to the frequency content of the motion.For SHM with period T, v max /amax = T/2 .

Seed and Idriss (1982) proposed average values of v max /amax fordifferent sites within 50 km of source.

Rock 0.056 sec., Stiff soils (200ft) 0.138 sec.

Ref: Kramer (1996)

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Spatial variability of ground motions

The ground motion parameters at any site depend upon themagnitude of earthquake and the distance of the site fromepicenter.

The ground motion parameters measured at a site have been usedto develop empirical relationships to predict the parameters asfunctions of earthquake magnitude and source-to-site distance. Butthese predictions are not accurate.

For structures that extend over considerable distance (such as bridges and pipelines), the ground motion parameters will bedifferent at different part of the structure, causing differentialmovement of the supports. Local variation of ground motion

parameters need to be considered for the design of such structures.

Ref: Kramer (1996)

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Amplitude Parameters - EstimationPredictive relationships for parameters (like peak acceleration,

peak velocity) which decrease with increase in distance are calledattenuation relationships.

Peak Acceleration

Campbell (1981) developed attenuation relationship for mean PHAfor sites within 50 km of fault rupture in magnitude 5.0 to 7.7earthquakes:

ln PHA(g) = - 4.141+0.868M 1.09 ln [R+0.0606 exp(0.7M)]

Where M = ML for magnitude < 6 or M

s for magnitude > 6, R is

the closest distance to fault rupture in km.

Latest mostly used relationship in western North America is given by Boore et al. (1993)

Ref: Kramer (1996)

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Amplitude Parameters - EstimationAttenuation relationship in western North America is given by

Boore et al. (1993)(From North American Earthquakes (magnitude 5-7.7) within 100 km of surface

projection of fault)

Log PHA(g) = b 1+b 2(M w-6)+b 3(M w-6) 2+b 4R+b 5logR+b 6G b+b 7G c

R = (d 2+h2)1/2 , d = closest distance to the surface projection of the fault in km.

= 0 for site class A = 0 for site class A

G b = 1 for site class B G c = 0 for site class B= 0 for site class C = 1 for site class C

(Site classes are defined next slide on the basis of the avg. V s in the upper 30 m).

Ref: Kramer (1996)

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Definitions of Site Classes for Boore et al. (1993) Attenuation Relationship

Coefficients for Attenuation Relationships of Boore et al. (1993)

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Attenuation Relationship for peak horizontal rock acceleration by Toroet al., 1994 (for mid continent of North Amer ica)

ln PHA (g) = 2.2+0.81(M w-6)-1.27 lnR m+0.11 max[ln (R m /100), 0]-0.0021R m

lnPHA = ( m 2+ r 2)1/2

Where R m = (R 2+9.3 2)1/2 , R being closest horizontal distance to earthquake rupture (inkm), m = 0.36 + 0.07(M w-6), and

= 0.54 for R < 5 km

r = 0.54-0.0227(R-5) for 5 km

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Peak Velocity Attenuation Relationships (Joyner and Boore, 1988)

(for earthquake magnitudes 5-7.7)

log PHV (cm/sec) = j 1+j 2(M-6)+j 3(M-6)2+j 4logR+j 5R+j 6

Where PHV can be selected as randomly oriented or larger horizontal component

R = (r 02+j72)1/2 , and r 0 is the shortest distance (km) from the site to the vertical projection of the EQ fault rupture on the surface of the earth.

The coefficients j i are given in the table below:

Coefficients after Joyner & Boore (1988) for PHV Attenuation Relationship

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Amplitude Parameters - EstimationA.Patwardhan et al. (1978):

ln y= ln A+B Ms +E ln [R + d exp(f Ms)]Where, y in cm/s 2, d=0.864 and f = 0.463

Path A: Shallow focus earthquakes (California, Japan, Nicaragua andIndia), 63 records

Path B: Subduction (Benioff) zone earthquakes (Japan & SouthAmerica) 23 earthquakes, 5.3Ms7.8, 32 records

Path A(for median) A( for mean) B E

Path A (rock) 157 186 1.04 -1.90Path A(stiff soil) 191 224 0.823 -1.56

Path B (stiff soil) 284 363 0.587 -1.05

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Considered:

For Path A:1. Rock sites = 21 records and 2. Stiff soil = 42 recordsUse only stiff soil records for deriving subduction zone equation

Most earthquakes for path A have 5 Ms 6.7

All data corrected. PGA for corrected Japanese and South Americanrecords much higher than uncorrected PGA.

IIT Bombay, DC

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Aptikaev & Kopnichev (1980)

log Ae = a 1M + a 2logR+a 3

PGA corresponds to S-wave

Used five source mechanism categories (about 70 records, 59earthquakes from W. N. America including Hawaii, Guatemala,

Nicaragua, Chile, Peru, Argentina, Italy, Greece, Romania, centralAsia, India and Japan):

1. Contraction faulting (uplift and thrust), about 16 earthquakes

2. Contraction faulting with strike-slip component, about 6earthquakes

Ae ( cm/s2

) a 1 a 2 a 3

160 0.28 -0.8 1.70

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3. Strike-slip, about 17 earthquakes

4. Strike-slip with dip-slip component, about 6 earthquakes

5. Dip-slip, about 9 earthquakesUse these approximately 70 records to derive ratios of meanmeasured, A0, to predicted PGA, Ae, log(A0/Ae), and for ratios ofmean horizontal to vertical PGA, logAh/Av, for each type of faulting.Use every earthquake with equal weight independent of number ofrecords for each earthquake.

IIT Bombay, DC

Aptikaev, F., & Kopnichev, J. (1980). Correlation between seismic vibration parameters andtype of faulting. Proceedings of Seventh World Conference on Earthquake Engineering, Vol.1, pp. 107-110.

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PML (1982)

ln(a) = C 1 + C 2M + C 3 ln[R + C 4 exp(C 5M)]

Where a is in g, C 1 = 1.17, C 2 = 0.587, C 3 = 1.26, C 4 = 2.13, C 5 = 0.25

and = 0.543

Used data from Italy (6 records, 6 earthquakes), USA (18 records, earthquakes),

Greece (13 records, 9 earthquakes), Iran (3 records, 3 earthquakes), Pakistan (3

records, 1 earthquake), Yugoslavia (3 records, 1 earthquake), USSR (1 record, 1

earthquake), Nicaragua (1 record, 1 earthquake), India (1 record, 1 earthquake)

and Atlantic Ocean (1 record, 1 earthquake).

IIT Bombay, DC

PML. 1982. British earthquakes. Tech. rept. 115/82. Principia Mechanica Ltd., London. Not seen. Reported in Ambraseys et al. (1992)