Deepankar- Strong Motion Charcteristics

Geotechnical Earthquake

Engineering

by

Dr. Deepankar Choudhury

Professor

Department of Civil Engineering

IIT Bombay, Powai, Mumbai 400 076, India.

Email: [email protected]

URL: http://www.civil.iitb.ac.in/~dc/

Lecture – 9b

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Module – 4

Strong Ground Motion

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Size of Earthquakes

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Magnitude and Intensity Intensity

• How Strong Earthquake Feels to Observer

– Qualitative assessment of the kinds of damage done by an earthquake

– Depends on distance to earthquake & strength of earthquake

– Determined from the intensity of shaking and damage from the earthquake

Magnitude

• Related to Energy Release.

– Quantitative measurement of the amount of energy released by an earthquake

– Depends on the size of the fault that breaks

– Determined from Seismic Records

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Measuring Earthquakes • Seismogram is visual record of arrival time and

magnitude of shaking associated with seismic wave. Analysis of seismogram allows measurement of size of earthquake.

• Mercalli Intensity scale Measured by the amount of damage caused in human

terms- I (low) to XII (high); drawback: inefficient in uninhabited area

• Richter Scale- (logarithmic scale) Magnitude- based on amplitude of the waves

Related to earthquake total energy

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Intensity

How Strong Earthquake Feels to Observer

Depends On:

• Distance to hypocenter/epicenter

• Geology of site

• Type of building /structure

• Observer’s feeling

Value varies from Place to Place

• Modified Mercalli Scale - I to XII

IIT Bombay, DC 7 Ref: Wikipedia

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Modified Mercalli Intensity Scale

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Earthquake Magnitude

ML - Local (Richter) magnitude

MW - Seismic Moment magnitude

MS - Surface wave magnitude

m

b- Body wave magnitude

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Richter Scale

• Richter Scale

– Amplitude scale is logarithmic (10-fold increase for every whole number increase)

– Scale 0 ---- 0.001 mm; 1---- 0.01 mm; 4---- 10mm; 6---- 1 meter

– Earthquake Energy: Each whole number represents a 33-fold increase in Energy; Energy difference between 3 & 6 means ~1000 times

– Drawbacks:

• Based on Antiquated Wood-Anderson Seismographs

• Measurement Past Magnitude 7.0 ineffective – Requires Estimates

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Local Magnitude of Earthquake

• Magnitude

– Richter scale measures the magnitude of an earthquake,

based on seismogram independent of intensity

– Amplitude of the largest wave produced by an event is

corrected for distance and assigned a value on an open-

ended logarithmic scale

– The equation for Richter Magnitude is:

ML = log

10A(mm) + (Distance correction factor)

Here A is the amplitude, in millimeters, measured directly from

the photographic paper record of the Wood-Anderson

seismograph, a special type of instrument. The distance factor

comes from a table given by Richter (1958).

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Right side diagram (nomogram)

demonstrates how to use Richter's

original method to measure a

seismogram for a magnitude

estimate After you measure the wave

amplitude you have to take its

logarithm and scale it according to

the distance of the seismometer from

the earthquake, estimated by the S-P

time difference. The S-P time, in

seconds, makes t. The equation

behind this nomogram, used by

Richter in Southern California, is:

ML = log10A(mm) +3 log10[8 t (sec)]-2.93

Richter’s Local Magnitude

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Richter Scale: Related to intensity

– M=1 to 3: Recorded on local seismographs, but generally not felt

– M= 3 to 4: Often felt, no damage

– M=5: Felt widely, slight damage near epicenter

– M=6: Damage to poorly constructed buildings and other structures within 10's km

– M=7: "Major" earthquake, causes serious damage up to ~100 km (Gujarat 2001 earthquake).

– M=8: "Great" earthquake, great destruction, loss of life over several 100 km

– M=9: Rare great earthquake, major damage over a large region over 1000 km

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Correlations

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Surface Wave Magnitude Richter’s local magnitude does not distinguish between

different types of waves.

At large distances from epicenter, ground motion is dominated

by surface waves.

Gutenberg and Richter (1956) developed a magnitude scale

based on the amplitude of Rayleigh waves.

Surface wave magnitude Ms = log10A + 1.66 log10 +2.0

A = Maximum ground displacement in micrometers

= Distance of seismograph from the epicenter, in degrees.

Surface wave magnitude is used for shallow earthquakes

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Body Wave Magnitude

For deep focus earthquakes, reliable measurement of amplitude

of surface waves is difficult.

Amplitudes of P-waves are not strongly affected by focal depth.

Gutenberg (1945) developed a magnitude scale based on the

amplitude of the first few cycles of P- waves, which is useful

for measuring the size of deep earthquakes.

Body wave magnitude mb = log10A – log10T +0.01 + 5.9

A = Amplitude of P-waves in micrometers

T = period of P-wave

= Distance of seismograph from the epicenter, in degrees.

19

Source: Richter (1958)

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Limitations of Ms and mb due to Magnitude

Saturation

20

Magnitude saturation, is a general

phenomenon for approximately Mb >

6.2 and Ms > 8.3.

As Mb approaches 6.2 or MS

approaches 8.3, there is an abrupt

change in the rate at which

frequency of occurrence decreases

with magnitude.

Though the rupture area on the fault

is large, the predictions will saturate

at these magnitudes.

Because of this magnitude

saturation, estimation of magnitude

for large earthquakes through Mb

and Ms becomes erroneous. IIT Bombay, DC

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Seismic - Moment Magnitude

A Seismograph Measures Ground Motion at One Instant But --

• A Really Great Earthquake Lasts Minutes

• Releases Energy over Hundreds of Kilometers

• Need to Sum Energy of Entire Record

• Moment magnitude scale based on seismic moment (Kanamori, 1977) and doesn’t depend upon ground shaking levels.

• It’s the only magnitude scale efficient for any size of earthquake.

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Moment Magnitude • Moment-Magnitude Scale

– Seismic Moment = Strength of Rock x Fault Area x Total amount of Slip along Rupture

M0 = A D (in N.m) [Idriss, 1985]

Where, = shear modulus of material along the fault plane in

N/m2 (= 3x1010 N/m2 for surface crust and 7x1012 N/m2 for

mantle)

A = area of fault plane undergoing slip (m2)

D = average displacement of ruptured segment of fault (m)

Moment Magnitude, Mw = 2/3 x [log10M0(dyne-cm) –16]

Moment Magnitude, Mw = - 6.0 + 0.67 log10M0(N.m)

[Hanks and Kanamori (1979)]

– Measurement Analysis requires Time

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Seismic - Moment Magnitude

• Most magnitude scales saturate towards large earthquakes

with m b > 6.0, M L > 6.5, and M S > 8.0. The moment

magnitude M w (Kanamori 1977) represents true size of

earthquakes, as it is based on seismic moment, which in

turn is proportional to the product of the rupture area and

dislocation of an earthquake fault (Aki 1966). M W is

defined as,

MW = 2/3log10M0− 6.05

where M 0 is the scalar seismic moment in Nm. MW does

not saturate, this is the most reliable magnitude for

describing the size of an earthquake (Scordilis 2006).

Rigidity of Crust and Mantle for

Seismic Moment Estimation

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Correlation between Mw and ML • The distribution of M W versus M L is shown Fig. and the

correlation is given by Kolathayar et al. (2012) for India by

considering 69 earthquake data,

MW=0.815(±0.04)ML+0.767(±0.174), 3.3≤ML≤7, R2=0.884

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Correlations between various

magnitude scales

Heaton et al.

(1982)

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Seismic Energy

Both the magnitude and the seismic moment are related to the

amount of energy that is radiated by an earthquake. Gutenberg

and Richter (1956), developed a relationship between magnitude

and energy. Their relationship is:

logES = 11.8 + 1.5Ms

Energy ES in ergs from the surface wave magnitude Ms. ES is not

the total “intrinsic” energy of the earthquake, transferred from

sources such as gravitational energy or to sinks such as heat

energy. It is only the amount radiated from the earthquake as

seismic waves, which ought to be a small fraction of the total

energy transferred during the earthquake process.

28

Size of an earthquake using the Richter’s Local Magnitude Scale is shown on the left

hand side of the figure above. The larger the number, the bigger the earthquake. The scale

on the right hand side of the figure represents the amount of high explosive required to

produce the energy released by the earthquake.

Local Magnitude - Seismic Energy correlation

Gujarat (2001)

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Frequency of earthquakes

Frequency of earthquakes

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Example Problem

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Ground Motion

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Strong Ground Motion

Evaluation of the effects of earthquakes requires the

study of ground motion.

Engineering Seismology deals with vibrations related to

earthquakes, which are strong enough to cause damage

to people and environment.

The ground motions produced by earthquakes at any

particular point have 3 translational and 3 rotational

components.

In practice, generally translational components of

ground motion are measured and the rotational

components are ignored.

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Strong motion seismographs

• Designed to pickup

strong, high-amplitude

shaking close to quake

source

• Most common type is

the accelerometer

• Directly records ground

acceleration

• Recording is triggered

by first waves

• Difficult to differentiate

S and surface waves

Seismographs in

India

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Seismogram interpretation

• Seismograms can provide information on

– epicenter location

– Magnitude of earthquake

– source properties

• Most seismograms will record P, S & surface waves

• First arrival is P wave

• After a pause of several seconds/10s seconds the higher amplitude S wave arrives

• Defines S-P interval

- surface waves follow and may

continue for tens of seconds

- surface waves are slower but

persist to greater distances than

P & S waves

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Wave terminology • Wave amplitude

– height of a wave above its zero position

• Wave period

– time taken to complete one cycle of motion

• Frequency

– number of cycles per second (Hertz)

– felt shaking during quake has frequencies from 20 down to 1 Hertz Human ear can detect frequencies

down to 15 Hz

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Ground Motion Recording The actual ground motion at a given

location is derived from

instrumentally recorded motions. The

most commonly used instruments for

engineering purposes are strong

motion accelerographs/

accelerometers. These instruments

record the acceleration time history

of ground motion at a site, called an

accelerogram.

By proper analysis of a recorded accelerogram to account for instrument

distortion and base line correction, the resulting corrected acceleration

record can be used by engineers to obtain ground velocity and ground

displacement by appropriate integration.

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Accelerometer Types of Accelerometers:

Electronic : transducers

produce voltage output

Servo controlled: use

suspended mass with

displacement transducer

Piezoelectric: Mass attached

to a piezoelectric material,

which develops electric charge

on surface.

Generally accelerometers are placed in three orthogonal directions to

measure accelerations in three directions at any time. Sometimes

geophones (velocity transducers) are attached to accelerometers to

measure the seismic wave velocities.

Principle: An acceleration a will cause the

mass to be displaced by ma/k or

alternatively, if we observe a displacement

of x, we know that the mass has undergone

an acceleration of kx/m.

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An earthquake history can be described using amplitude, frequency

content, and duration.

Amplitude: The most common measures of amplitude are

PGA: Peak ground acceleration (Horizontal- PHA & Vertical- PVA)

EPA: Effective peak acceleration

PGV: Peak ground velocity ( PHV & PVV)

EPV: Effective peak velocity

PGD: Peak ground displacement

Frequency Content: The frequency content of an earthquake history is

often described using Fourier Spectra, Power spectra and response spectra.

Duration: The duration of an earthquake history is somewhat dependent on

the magnitude of the earthquake.

Ground Motion Parameters

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Measurement of ground acceleration

A seismograph can be illustrated by a mass-spring-dashpot single

degree of freedom system.

2

g2

u um c k u m u 0

tt

where u is the trace displacement (relative displacement between

seismograph and ground), ug is the ground displacement, c is the

damping coefficient, k is the stiffness coefficient.

The response of such system for shaking is given by

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Measurement of ground acceleration

If the ground displacement is simple harmonic at a circular

frequency g , the ground acceleration amplitude is calculated

from the trace displacement amplitude using the equation of

acceleration response ratio:

22222

02

2

41

1

t

u

u

g

where 0 is the undamped natural circular frequency

is tuning ratio, given by g/ 0

Is damping ratio, given by km

c

2

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Amplitude Parameters

From the time histories of acceleration, velocity and displacement

are obtained by integrating the acceleration records. All other

amplitude parameters are calculated from these time histories.

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Peak Acceleration

Most commonly used measure of amplitude of a ground motion is the

Peak horizontal acceleration (PHA). It is the absolute maximum value

obtained from accelerogram.

Maximum resultant PHA is the vector sum of two orthogonal

components. Estimation of PHA is most important for any design. PHA

and MMI relationship (Trifunac and Brady, 1975) are often used.

PVA is not that important and PVA = (2/3)PHA is commonly assumed

for design (Newmark and Hall, 1982).

Peak acceleration data with frequency content/duration of earthquake is

important. Because for e.g. 0.5g PHA may not cause significant damage

to structures if earthquake duration is very small.

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Peak Acceleration

Proposed relationships between PHA & MMI (Trifunac & Brady, 1975).

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Peak Velocity and Displacement

Peak horizontal velocity (PHV) is also used to characterize ground

motion. PHV is better than PHA for intermediate frequencies as velocity

is less sensitive to higher frequency.

For above reason, many times PHV may provide better indication for

damage than PHA. PHV and MMI relationship (Trifunac and Brady,

1975) are also used.

Peak displacements are associated with low frequency components of

earthquake motion. Hence signaling and filtering error of data is common

and hence not recommended for practical uses over PHA or PHV.

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Other Amplitude Parameters Sustained Maximum Acceleration: The absolute values of

highest accelerations that sustained for 3 and 5 cycles in

acceleration time history are defined as 3-cycle sustained and 5-

cycle sustained accelerations respectively.

Effective Design Acceleration: The acceleration which is

effective in causing structural damage. This depends on size of

loaded area, weight, damping and stiffness properties of structure

and its location with respect to epicenter.

Kennedy (1980) proposed EDA as 25% higher than 3-cycle PHA

recorded in filtered time history.

Benjamin and Associates (1988) proposed EDA as the PHA after

filtering out accelerations above 8-9 Hz.

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Frequency Content Parameters

The frequency content of an earthquake history is often

described using Fourier Spectra, Power spectra and

response spectra.

Ground Motion Spectra - Fourier Spectra

A periodic function (for which an earthquake history is an

approximation) can be written as

where cn and n are the amplitude and phase angle

respectively of the nth harmonic in the Fourier series.

)sin()(1

0 nnn

n tcctx

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The Fourier amplitude spectrum is a plot of cn versus n

Shows how the amplitude of the motion varies with

frequency.

Expresses the frequency content of a motion

The Fourier phase spectrum is a plot of n versus n

Phase angles control the times at which the peaks of

harmonic motion occur.

Fourier phase spectrum is influenced by the variation of

ground motion with time.

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Fourier Amplitude Spectrum

fc fmax

Frequency (log)

Fou

rier

Am

pli

tud

e (l

og)

The Fourier amplitude spectra of actual

earthquakes are often plotted on

logarithmic scales, so that their

characteristic shapes can be clearly

distinguished from the smoothed curves.

Two frequencies that mark the range of

frequencies for largest Fourier

acceleration amplitude are corner

frequency (fc) and cutoff frequency (fmax)

fc is a very important parameter because it is inversely proportional to

the cube root of seismic moment, thus indicating that large earthquakes

produce greater low-frequency motions.

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Power Spectra

The power spectrum is a plot of G( ) versus n . The power

spectrum density (PSD) function is defined by the following

equation and is closely related to the Fourier amplitude

spectrum:

where G( ) is the PSD, Td is the duration of the ground

motion, and cn is the amplitude of the nth harmonic in the

Fourier series. PSD function is used to characterize an

earthquake history as a random process.

2

dT π

1)(

ncG

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Response Spectra

Response spectra are widely

used in earthquake

engineering. The response

spectrum describes the

maximum response of a

SDOF oscillator to a

particular input motion as a

function of frequency and

damping ratio. The response

spectra from two sites (one

rock and the other soil) are

shown in figure.


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Duration of an earthquake is very important parameter that influences the

amount of damage due to earthquake. A strong motion of very high

amplitude of short duration may not cause as much damage to a structure

as a motion with moderate amplitude with long duration can cause. This

is because the ground motion with long duration causes more load

reversals, which is important in the degradation of stiffness of the

structures and in building up pore pressures in loose saturated soils.

Duration represents the time required for the release of accumulated

strain energy along a fault, thus increases with increase in magnitude of

earthquake.

Relative duration does not depend on the peak values. It is the time

interval between the points at which 5% and 95% of the total energy has

been recorded.

Duration

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Bracketed duration is the measure of time between the first and

last exceedence of a threshold acceleration 0.05 g.

Duration

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Other Spectral Parameters

RMS acceleration : This is the parameter that includes the

effects of amplitude and frequency, defined as

dT

0

2

d

dttaT

1rms

a

Where a(t) is the acceleration over the time domain and Td is

the duration of strong motion

AI - The Arias Intensity is a measure of the total energy at the

recording station and is proportional to the sum of the squared

acceleration. It is defined as

dttag

AI2

02

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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 are

motivated by the need to examine the response of structures to ground

motion, as many structures have fundamental periods between 0.1 and

2.5 sec. The SI can be calculated for any structural damping ratio.

Dominant frequency of ground motion (Fd) is defined as the

frequency corresponding to the peak value in the amplitude spectrum.

Thus, Fd indicates the frequency for which the ground motion has the

most energy. The amplitude spectrum has to be smoothed before

determining Fd.


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Predominant Period (Tp): Period of

vibration corresponding to the maximum

value of the Fourier amplitude spectrum.

This parameter represents the frequency

content of the motion. The predominant

period for two different ground motions with

different frequency contents can be same,

making the estimation of frequency content

crude.

Bandwidth (BW) - of the dominant

frequency; measured where the amplitude

falls to 0.707 (1 /sq. root 2) of the amplitude

of the dominant frequency. Again, this is

based on a smoothed amplitude spectrum.


Tp

Period

Fou

rier

Am

pli

tud

e

GM1

GM2

Tp is same for the two

ground motions, though

the frequency content is

different

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Central Frequency: Power spectral density function can be used to

estimate statistical properties of ground motion. The nth spectral

moment and central frequency ( ) is given by,

Central frequency is used to calculate theoretical median peak

acceleration as follows,

Shape Factor – It indicates the dispersion of the power spectral

density function about the central frequency,


n

dGn

n

0

)(n

dGn

n

0

)(

n

dGn

n

0

)(0

2

28.2ln2 0max

dTu

20

2

11It lies between 0 and 1, higher value

indicates larger bandwidth.

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vmax/amax ratio: It is related to the frequency content of the motion.

For SHM with period T, vmax/amax = T/2 .

Seed and Idriss (1982) proposed average values of vmax/amax for

different sites within 50 km of source.

Rock – 0.056 sec., Stiff soils (<200ft) – 0.112 sec., Deep stiff soil

(>200ft) – 0.138 sec.

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Spatial variability of ground motions

The ground motion parameters at any site depend upon the

magnitude of earthquake and the distance of the site from

epicenter.

The ground motion parameters measured at a site have been used

to develop empirical relationships to predict the parameters as

functions of earthquake magnitude and source-to-site distance. But

these predictions are not accurate.

For structures that extend over considerable distance (such as

bridges and pipelines), the ground motion parameters will be

different at different part of the structure, causing differential

movement of the supports. Local variation of ground motion

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

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Amplitude Parameters - Estimation

Predictive relationships for parameters (like peak acceleration,

peak velocity) which decrease with increase in distance are called

attenuation relationships.

Peak Acceleration

Campbell (1981) developed attenuation relationship for mean PHA

for sites within 50 km of fault rupture in magnitude 5.0 to 7.7

earthquakes:

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

Where M = ML for magnitude < 6 or Ms 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)

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Amplitude Parameters - Estimation

Attenuation 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) = b1+b2(Mw-6)+b3(Mw-6)2+b4R+b5logR+b6Gb+b7Gc

R = (d2+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

Gb = 1 for site class B Gc = 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. Vs in the upper 30 m).

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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 Toro

et al., 1994 (for mid continent of North America)

ln PHA (g) = 2.2+0.81(Mw-6)-1.27 lnRm+0.11 max[ln (Rm/100), 0]-0.0021Rm

lnPHA = ( m2+ r

2)1/2

Where Rm = (R2+9.32)1/2, R being closest horizontal distance to earthquake rupture (in

km), m = 0.36 + 0.07(Mw-6), and

= 0.54 for R < 5 km

r = 0.54-0.0227(R-5) for 5 km <= R <= 20 km

= 0.2 for R > 20 km

Attenuation relationship for subduction zone (Youngs et al., 1988)

ln PHA (g) = 19.16 + 1.045Mw – 4.738 ln [R+205.5exp(0.0968Mw)] + 0.54 Zt

lnPHA = 1.55-0.125Mw, R = closest distance to the zone of rupture in km and Zt = 0 for

interface and 1 for intraslab events

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Peak Velocity Attenuation Relationships (Joyner and Boore, 1988)

(for earthquake magnitudes 5-7.7)

log PHV (cm/sec) = j1+j2(M-6)+j3(M-6)2+j4logR+j5R+j6

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

R = (r02+j7

2)1/2, and r0 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 ji are given in the table below:

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

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If fmax is assumed constant for a given geographic region (15 Hz and 20 Hz

are typical values for Western & Eastern North America respectively), then

the spectra for different quakes are functions of seismic moments M0 and fc

which can be related (Brune, 1970 & 1971) thus:

Where vs is in km/sec, M0 is in dyne-cm, and is referred to as stress

parameter or stress drop in bars. Values of 50 bars and 100 bars are common

for stress parameters of Western & Eastern North America respectively.

1/ 3

6

0

4.9 10c sf vM

Fourier Amplitude Spectra

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Ratio vmax/amax

This ratio is proportional to the magnitude and distance dependencies

proposed by McGuire (1978) as shown in the table below:

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RMS Acceleration

Hanks and McGuire (1981) used a database of California

earthquake of local magnitude 4.0 to 7.0 to develop an

attenuation relationship for RMS acceleration for hypocentral

distances between 10 and 100 km,

where fc is the corner frequency, fmax is the cutoff frequency, and

R is in kilometer.

max /0.119

crms

f fa

R

Estimation of other parameters

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Kavazanjian et al. (1985) used the definition of duration

proposed by Vanmarcke and Lai (1980) with a database of 83

strong motion records from 18 different earthquakes to obtain

where R is the distance to the closest point of rupture on the fault.

The database was restricted to Mw > 5, R < 110 km (68 mi),

rupture depths less than 30 km (19 mi), and soil thicknesses

greater than 10 m (33 ft).

2

0.966 0.2550.472 0.268 0.129log 0.1167rms wa M R

RR

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Arias Intensity

Campbell and Duke (1974) used data from California earthquakes to

predict the variation of Arias intensity within 15 to 110 km (9 to 68

mi) of magnitude 4.5 to 8.5 events.

0.33 1.47

3.79/ sec 313

s sM M

a

eI m S

R

where S

0.57R0.46 for basement rock

1.02R0.51 for sedimentary rock

0.37R0.81 for alluvium ≤ 60ft thick

0.65R0.74 for alluvium > 60ft thick

and R is the distance from the center of the energy release in kilometers.

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Wilson (1993) analyzed strong motion records from California to

develop an attenuation relation which, using the Arias intensity

definition of equation which can be expressed as

where

D is the minimum horizontal distance to the vertical projection of

the fault plane, h is a correction factor (with a default value of 7.5

km (4.7 mi)), k is a coefficient of inelastic absorption (with default

value of zero), and P is the exceedance probability.

log / sec 2log 3.990 0.365(1 )a wI m M R kR P

2 2R D h

D. Choudhury, IIT Bombay, India

Questions?

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