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Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 1
Earthquakes Mechanics and Effects
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 2
Earthquakes: Cause and Effect
• Why earthquakes occur• How earthquakes are measured• Earthquake effects• Mitigation strategy• Earthquake time histories
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 3
Seismic Activity: 1961-1967
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 4
Plate Boundaries
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 5
Plate Tectonics: Driving Mechanism
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 6
Plate Tectonics: Details in Subduction Zone
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 7
Seismicity of North America
Pacific Plate
North AmericanPlate
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 8
Seismicity of Alaska
Pacific Plate
North American Plate
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 9
Faults and Fault Rupture
Fault plane
Hypocenter(focus)
Rupture surface
Epicenter
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 10
Types of Faults
Strike slip(left lateral)
Strike slip(right lateral)
Normal Reverse (thrust)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 11
New fence
Time = 0 Years
Elastic Rebound Theory
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 12
Old fence
New road
Time = 40 Years
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 13
Old fence
Time = 41 Years
New road
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 14
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 15
Seismic Wave Forms(Body Waves)
Compression wave(P wave)
Shear wave(S wave)
Direction of
propagation
Direction of
propagation
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 16
Love wave Rayleigh wave
Seismic Wave Forms(Surface Waves)
Direction of
propagation
Direction of
propagation
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 17
Love wavesP waves S waves
Arrival of Seismic Waves
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 18
Relationship Between Reservoir Leveland Seismic Activity at Koyna Dam, India
Inflow
Reservoir level
Earthquake frequency
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 19
Effects of Seismic Waves
• Fault rupture• Ground shaking• Landslides• Liquefaction• Tsunamis• Seiches
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 20
Surface Fault Rupture, 1971 Earthquake in San Fernando, California
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 21
“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)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 22
Liquefaction Damage, Niigata, Japan, 1964
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 23
Liquefaction and Lateral Spreading, 1993 Earthquake in Kobe, Japan
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 24
Landslide on Coastal Bluff,1989 Earthquake in Loma Prieta, California
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 25
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 26
Tsunami Damage, Seward, Alaska, 1964
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 27
Result of Ground Shaking, 1994 Earthquake in Northridge, California
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 28
Earthquake effect Strategy Fault rupture AvoidTsunami/seiche AvoidLandslide AvoidLiquefaction Avoid/resistGround shaking Resist
Mitigation Strategies
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 29
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 30
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)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 31
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 32
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 33
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 34
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 35
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.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 36
Isoseismal Map for the Giles County, Virginia,Earthquake of May 31, 1897.
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 37
Isoseismal MapFor New MadridEarthquake ofDecember 16, 1811
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 38
Isoseismal Mapfor 1886 CharlestonEarthquake
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 39
Isoseismal Map for February 9, 1971,San Fernando Earthquake
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 40
Comparison of Isosiesmal Intensity for Four Earthquakes
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 41
Comparisons of Various Intensity Scales
MMI = Modified MercalliRF = Rossi-ForelJMA = Japan Meteorological AgencyMSK =Medvedez-Spoonheur-Karnik
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 42
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 43
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)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 44
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 45
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)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 46
Moment Magnitude vs Other Magnitude Scales(Magnitude Saturation)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 47
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 48
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 49
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 50
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 51
Sample Ground Motion Records
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 52
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)
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 53
Corrected vs Uncorrected Motions
Corrections made primarily:
• To remove instrument response
• To account for base line shift
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 54
-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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 55
-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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 56
-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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 57
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
Acceleration, cm/sec2
Time, Seconds
Acceleration, cm/sec2
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 58
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
Acceleration, cm/sec2
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 59
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 60
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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 61
-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
Instructional Material Complementing FEMA 451, Design Examples Earthquake Mechanics 2 - 62
-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
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