earthquakes mechanics and effects - university of · pdf fileinstructional material...

Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 1

Earthquakes Mechanics and Effects


Earthquakes: Cause and Effect

• Why earthquakes occur• How earthquakes are measured• Earthquake effects• Mitigation strategy• Earthquake time histories


Seismic Activity: 1961-1967


Plate Boundaries


Plate Tectonics: Driving Mechanism


Plate Tectonics: Details in Subduction Zone


Seismicity of North America

Pacific Plate

North AmericanPlate


Seismicity of Alaska

Pacific Plate

North American Plate


Faults and Fault Rupture

Fault plane

Hypocenter(focus)

Rupture surface

Epicenter


Types of Faults

Strike slip(left lateral)

Strike slip(right lateral)

Normal Reverse (thrust)


New fence

Time = 0 Years

Elastic Rebound Theory


Old fence

New road

Time = 40 Years


Old fence

Time = 41 Years

New road


Seismic Wave Forms(Body Waves)

Compression wave(P wave)

Shear wave(S wave)

Direction of

propagation

Direction of

propagation


Love wave Rayleigh wave

Seismic Wave Forms(Surface Waves)

Direction of

propagation

Direction of

propagation


Love wavesP waves S waves

Arrival of Seismic Waves


Relationship Between Reservoir Leveland Seismic Activity at Koyna Dam, India

Inflow

Reservoir level

Earthquake frequency


Effects of Seismic Waves

• Fault rupture• Ground shaking• Landslides• Liquefaction• Tsunamis• Seiches


Surface Fault Rupture, 1971 Earthquake in San Fernando, California


“If a saturated sand is subjected to groundvibrations, it tends to compact and decrease in volume.

If drainage is unable to occur, the tendency todecrease in volume results in an increase inpore pressure.

If the pore water pressure builds up to the point atwhich it is equal to the overburden pressure, theeffective stress becomes zero, the sand loses itsstrength completely, and liquefaction occurs.”

Cause of Liquefaction

Seed and Idriss (1971)


Liquefaction Damage, Niigata, Japan, 1964


Liquefaction and Lateral Spreading, 1993 Earthquake in Kobe, Japan


Landslide on Coastal Bluff,1989 Earthquake in Loma Prieta, California


Cause of Tsunamis

Tsunamis are created by a sudden vertical movement of the sea floor.

These movements usually occur insubduction zones.

Tsunamis move at great speeds, often 600to 800 km/hr.


Tsunami Damage, Seward, Alaska, 1964


Result of Ground Shaking, 1994 Earthquake in Northridge, California


Earthquake effect Strategy Fault rupture AvoidTsunami/seiche AvoidLandslide AvoidLiquefaction Avoid/resistGround shaking Resist

Mitigation Strategies


Measuring Earthquakes

INTENSITY• Subjective• Used where instruments are not available• Very useful in historical seismicity

MAGNITUDE• Measured with seismometers• Direct measure of energy released• Possible confusion due to different measures


Modified Mercalli IntensityDeveloped by G. Mercalli in 1902 (after a previous

version of M. S. De Rossi in the 1880s)

Subjective measure of human reaction and damage

Modified by Wood and Neuman to fitCalifornia construction conditions

Intensity range I (lowest) to XII (most severe)


Modified Mercalli Intensity

Not felt except by a few under especiallyfavorable circumstances.

Felt only by a few persons at rest, especially onupper floors if buildings. Suspended objects may swing.

Felt quite noticeably indoors, especially onupper floors of buildings. Standing automobiles mayrock slightly. Vibration like passing truck.

I.

II.

III.


Modified Mercalli IntensityDuring the day, felt indoors by many, outdoors byfew. At night, some awakened. Dishes, windows,doors disturbed; walls make creaking sound. Sensationlike heavy truck striking building. Standing automobilesrocked noticeably. [0.015 to 0.02g]

Felt by nearly everyone, many awakened. Somedishes and windows broken. Cracked plaster.Unstable objects overturned. Disturbance of trees, polesand other tall objects. [0.03 to 0.04g]

Felt by all. Many frightened and run outdoors.Some heavy furniture moved. Fallen plaster anddamaged chimneys. Damage slight. [0.06 to 0.07g]

IV.

V.

VI.


Modified Mercalli IntensityEverybody runs outdoors. Damage negligible inbuildings of good design and construction, slight tomoderate in well built ordinary structures, considerablein poorly built or badly designed structures. Noticedby persons driving cars. [0.10 to 0. 15g]

Damage slight in specially designed structures,considerable in ordinary construction, great inpoorly built structures. Fall of chimneys, stacks,monuments. Sand and mud ejected is smallamounts. Changes in well water. Persons drivingcars disturbed. [0.25 to 0.30g]

VII.

VIII.


Modified Mercalli IntensityDamage considerable in specially designedstructures, well designed frame structures thrownout of plumb, damage great in substantial buildingswith partial collapse. Buildings shifted off foundations.Ground cracked conspicuously. Underground pipesbroken. [0.50 to 0.55g]

Some well built wooden structures destroyed. Mostmasonry and frame structures destroyed withfoundations badly cracked. Rails bent. Landslidesconsiderable from river banks and steep slopes.Shifted sand and mud. Water splashed over banks.[More than 0.60g]

IX.

X.


Modified Mercalli Intensity

Few, if any, (masonry) structures left standing. Bridges destroyed. Broad fissures in ground. Underground pipelines completely out of service.Earth slumps and land slips in soft ground.Rails bent greatly.

Damage total. Waves seen on ground surface. Linesof sight and level distorted. Objects thrown into air.

XI.

XII.


Isoseismal Map for the Giles County, Virginia,Earthquake of May 31, 1897.


Isoseismal MapFor New MadridEarthquake ofDecember 16, 1811


Isoseismal Mapfor 1886 CharlestonEarthquake


Isoseismal Map for February 9, 1971,San Fernando Earthquake


Comparison of Isosiesmal Intensity for Four Earthquakes


Comparisons of Various Intensity Scales

MMI = Modified MercalliRF = Rossi-ForelJMA = Japan Meteorological AgencyMSK =Medvedez-Spoonheur-Karnik


Instrumental Seismicity

ML = Log [Maxumum Wave Amplitude (in mm/1000)]

Recorded Wood-Anderson seismograph

100 km from epicenter

Magnitude (Richter, 1935)

Also called local magnitude


M = Log A +f(d,h) +CS + CR

A is wave amplitude

F(d,h) accounts for focal distance and depth

CS and CR, are station and regional corrections

Magnitude (in general)


MS Surface-wave magnitude (Rayleigh waves)

mb Body-wave magnitude (P waves)

MB Body-wave magnitude (P and other waves)

mbLg (Higher order Love and Rayleigh waves)

MJMA (Japanese, long period)

Other Wave-Based Magnitudes


Moment Magnitude

Seismic moment = MO = μAD

Where:μ = modulus of rigidityA = fault rupture areaD = fault dislocation or slip

Moment magnitude = MW = (Log MO-16.05)/1.5

[Units = force times distance]

(Units = dyne-cm)


Moment Magnitude vs Other Magnitude Scales(Magnitude Saturation)


0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12

Intensity

Mag

nitu

de

Richter (Local)MbLg

Approximate RelationshipBetween Magnitude and Intensity

0ˆ 0.67 1LM I= +

66.149.0ˆ 0 += ImbLg


Seismic Energy ReleaseLog E = 1.5 MS + 11.8

1E+12

1E+14

1E+16

1E+18

1E+20

1E+22

1E+24

1E+26

1E+28

0 2 4 6 8 10

Magnitude, Ms

Ener

gy, E

rgs

..

31 1000


Seismic Energy Release

1E+12

1E+14

1E+16

1E+18

1E+20

1E+22

1E+24

1E+26

1E+28

0 2 4 6 8 10

Magnitude, Ms

Ener

gy, E

rgs

..

Nuclear bomb

1964 Alaska earthquake

1906 San Francisco earthquake

1972 San Fernando earthquake

Atomic bomb

1978 Santa Barbara earthquake


Ground Motion Accelerograms

Sources:• NONLIN (more than 100 records)• Internet (e.g., National Strong Motion Data Center)• USGS CD ROM

Uses:• Evaluation of earthquake characteristics• Development of response spectra• Time history analysis


Sample Ground Motion Records


Ground Motion Characteristics

• Acceleration, velocity, displacement• Effective peak acceleration and velocity• Fourier amplitude spectra• Duration (bracketed duration)• Incremental velocity (killer pulse)• Response spectra• Other (see, for example, Naiem and Anderson 2002)


Corrected vs Uncorrected Motions

Corrections made primarily:

• To remove instrument response

• To account for base line shift


-500

-250

0

250

500

0 1 2 3 4 5 6 7 8 9 10

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10

0

200400

600

800

0 1 2 3 4 5 6 7 8 9 10

Time, sec

Acceleration, in/sec2

Velocity, in/sec

Displacement, in

Base Line Correction for Simple Ground Motion


-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45

-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45

-600

-400

-200

0

200

400

600

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

Tim e (s e c )

Horizontal acceleration (E-W), cm/sec2

Vertical acceleration (E-W), cm/sec2

Horizontal acceleration (N-S), cm/sec2

Typical Earthquake Accelerogram Set

Time, Seconds Loma Prieta Earthquake

-463 cm/sec2

-500 cm/sec2

-391 cm/sec2


-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45

Bracketed duration

0.05g

Definition of Bracketed Duration

Time, Seconds

Acceleration, cm/sec2


Definition of Incremental Velocity

Time, Seconds

-400

-300

-200

-100

0

100

200

300

400

8 9 10 11 12

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5


Time, Seconds



Concept of Fourier Amplitude Spectra

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5


N points at timestep dt

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Frequency (Hz)

N/2 points at frequency df

Normalized Fourier Coefficient

)2cos()2sin()2cos()(2/

100

2/

1

2/

1000 j

N

jj

N

j

N

jjjg jfAajfbjfaatv φπππ ∑∑ ∑

== =

++=++≅&&

22jjj baA +=Ndtdff /10 == ⎟

⎟⎠

⎞⎜⎜⎝

⎛−=

j

jj a

barctanφ


Concept of Fourier Amplitude Spectra

-50-40-30-20-10

01020304050

0.00 0.10 0 .20 0 .30 0 .40 0.50 0.60 0 .70 0 .80 0 .90 1.00

T im e, S econds

Am

plitu

de

0

2

4

6

8

1 0

1 2

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

F r e q u e n c y , H z .

Four

ier A

mpl

itude


Ground Motion Frequency Content (1)

-600

-400

-200

0

200

400

600

0 10 20 30 40 50

-600

-400

-200

0

200

400

600

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30

Frequency (Hz)

Four

ier A

mpl

itude

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30

Frequency (Hz)Fo

urie

r Am

plitu

de

Horizontal acceleration (E-W), cm/sec2

Vertical acceleration (E-W), cm/sec2

Time, Seconds


-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Frequency (Hz)

Four

ier A

mpl

itude

- 4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Frequency (Hz)

Four

ier A

mpl

itude

-1 5

-1 0

-5

0

5

1 0

1 5

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 50.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Frequency (Hz)

Four

ier A

mpl

itude

`

Horizontal acceleration, cm/sec2

Horizontal velocity, cm/sec

Horizontal displacement, cm

Ground Motion Frequency Content (2)

Time, Seconds

-463 cm/sec2

-30.7 cm/sec

11.0 cm


-0.40

-0.20

0.00

0.20

0.40

0.00 1.00 2.00 3.00 4.00 5.00 6.00

TIME, SECONDS

GR

OU

ND

AC

C, g

T=2.0 Seconds

T=0.6 Seconds

El Centro Earthquake Record

Maximum Displacement Response Spectrum

Development of an Elastic DisplacementResponse Spectrum

-4.00

-2.00

0.00

2.00

4.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

DIS

PLA

CEM

ENT,

in.

-8.00

-4.00

0.00

4.00

8.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

DIS

PLA

CEM

ENT,

In.

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

PERIOD, Seconds

DIS

PLA

CEM

ENT,

inch

es

earthquakes mechanics and effects - university of · pdf fileinstructional material...

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