Introduction Introduction to to Earthquake Earthquake Engineering Engineering Seismology Seismology
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Plate Tectonics
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reverse faultnormal fault
Right lateral fault
Left lateral fault
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Tectonics and Seismicity
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55From Wakabayashi (1)
Tectonics and SeismicityEpicenters for all earthquakes of 7 or larger occured between 1900 and 1980
San Andreas fault
Mid-Atlantic Ridge
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The functions f1 and f2 define the form
of the wave, propagating with a
velocity c.
Chosing
and f2=0, the following figure shows
the propagation of the wave in x-
direction versus time t:
( ) ( )⋅ π− ⋅ = ⋅ ⋅ − ⋅λ1
2ˆf x c t y sin x c t
Wave Propagation in a One-Dimensional Body
′′− ⋅ =&& 2y c y 0
is satisfied by the following solution: ( ) ( )= − ⋅ + + ⋅1 2y f x c t f x c t
The partial differential equation,
which is called the „wave-equation“:
From Petersen (3)
Seismic Waves
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Seismic Waves
( ) ( )− ν= ⋅ −
ρ + ν ⋅ − ⋅ νP
E 1V Velocity of P Wave
1 1 2
( )= = ⋅ −ρ ρ ⋅ + νS
G E 1V Velocity of S Wave
2 1
E =Young‘s modulus
G =shear modulus
ρ =mass density
ν =Poisson ratio
i.e.: VP = 260 to 690 m/s and
VS = 150 to 400 m/s
In comparision with atmospheric speed of sound: V = 360 m/s ~ 0,36 km/s
Body waves
P-Wave
S-Wave
homogeneous body
From Grundbau-Taschenbuch (10)
Surface waves
Love-Wave
Rayleigh-Wave
From Grundbau-Taschenbuch (10)
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Ground surface
HypocenterMagnitude M
Hypoce
ntral
distance
s
BuildingIntensity I
Epicentraldistance ∆
EpicenterIntensity I0
Sedimental layer
FaultHyp
ocen
tral
deap
thh
From Müller, Keintzel (2)
Definitions
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t
Arrival of S-waveArrival of P-wave Arrival of L-wave
∆ =
−
SP
S P
T
1 1
V V
Arrival of P-wave Arrival of S-wave
TSP
P-W
ave
S-Wave
VsVp
1
1
s
∆∆∆∆
From Wakabayashi (1)
Determination of Hypocentre
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2
S13
S12 3
S23TTSP1SP1
∆∆∆∆∆∆∆∆11
TTSP2SP2
∆∆∆∆∆∆∆∆22
TTSP3SP3
∆∆∆∆∆∆∆∆33
1∆∆∆∆∆∆∆∆33
∆∆∆∆∆∆∆∆11
∆∆∆∆∆∆∆∆22
HypocentreHypocentre
EpicentreEpicentre
Determination of Hypocentre
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Wave Propagation in layered Bodies
θ θ=1 2
1 2
sin sin
c c
θ = ⋅ θnn 1
1
csin sin
c
Reflection and refraction on layers
Reflection and refraction of waves
1θθθθ
From Wakabayashi (1)
Refraction of waves in the surface of layers
From Wakabayashi (1)
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Amplification characteristics of multilayers
From Wakabayashi (1)
Wave Propagation in layered Bodies
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Earthquake motions on ground surface
( ) ( ) ( ) ( )⋅ + ⋅ + ⋅ = − ⋅&& & &&gm v t c v t k v t m v t
viscously damped SDOF oscillator
From Clough, Penzien (4)
Free body equilibrium
m
cFvc =⋅ &
kFvk =⋅
mFvm =⋅ &&
∑ =++⇒= 00!
cmk FFFF
The seismometer
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( ) ( ) ( ) tvtvtvtv g ωωξω sin2 02 ⋅−=⋅+⋅+ &&&&& amplitudeonaccelerati ground0 −gv&&
frequency2 −=mKω
ratio damping2
1 2
−⋅
=mK
cξ
Solution (e.g. Clough, Penzien): pc vv +
Solution for sine base excitation
Homogeneous and particular solution
The seismometer
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( )tBtAev DDt
c ωωξω cossin ⋅+⋅⋅= −
damped frequency:
21 ξωω −=D
logarithmic decrement:
21 1
2ln
ξπξδ−
==+n
n
vv
The seismometer
Homogeneous Solution: free vibration response
damped free vibration.
te ξωρ −⋅
Dωπ2
1v2v
t
Dωπ4
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tGtGv p ωω cossin 21 ⋅+⋅=
( ) ( ) ( )( )[ ]tt
vtv g ωξβωξ
ξβξωcos2sin1
21
1 2
22220 −−⋅
+−⋅
−=
&&
ωωβ =
Particular Solution: Steady state response (free vibration has damped out)
tωθ
sρ
cρ
ρ t
The seismometer
( )( ) ( ) 2
0
222
2
21
1ωξβξ
ξρ gs
v&&⋅
+−−= ( ) ( ) 2
0
222 21
2ωξβξ
ξβρ gs
v&&⋅
+−=
sine amplitude: cosine amplitude:
( ) ( )22220 21 ξββ
ωρ +−= gv&&
phase angle:
( )21
1
2tan
βξβθ
−= −
amplitude:
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From Clough, Penzien (4)
ξ=0.7
Accelerometer:• high tuned SDOF
• damping ratio ξ ξ ξ ξ ~ 0,7
spD
ρ=
dynamic magnification:
responsestatic - 20
ωg
s
vp
&&
=
( ) ( )22 21
1
ξββ +−=D
The seismometer
Dvg ⋅= 2
0
ωρ
&&
amplitude:
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From Clough, Penzien (4)
ξ=0.5
Displacement meter:• low tuned SDOF
• damping ratio ξ ξ ξ ξ ~ 0,5
( ) tvtv gg ωω sin02 ⋅⋅−=
harmonic base displacemnet:
( )DvDv gg ⋅=⋅⋅= 2002
2
βωωρ
amplitude:
The seismometer
Vorlesung Earthquake EngineeringVorlesung Earthquake EngineeringProf. Dr.Prof. Dr.--Ing. Uwe E. DorkaIng. Uwe E. Dorka Stand: 29.06.2006
1919
Data Processing of measured acceleration
i.e. Measurement of the east-west acceleration-component of
Montenegro earthquake, 1979
Measured ground acceleration, time-domain
Base line
correction
Filtering
raw data
numerical
Integration
numerical
Integration
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2020
Fourier Spectrum
Fourier Spectrum:
Function a(t) in Time-Domain
FourierTransformation ( ) ( )
∞− ⋅ω⋅
−∞
ω = ⋅ ⋅∫i tU a t e dt
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Power Spectrum
Power Spectrum:
Correlation-Function Φ(τ) in Time-Domain
FourierTransformation ( ) ( )
∞− ⋅ω⋅
−∞
ω = Φ τ ⋅ ⋅∫i tS e dt
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Generation of artificial Accelerograms
Random Process
Intensity Function
i. e. Kanai-Tajimi-Filter:( )
ω+ ⋅ ξ ⋅ ω ω = ω ω− + ⋅ ξ ⋅ ω ω
2
2
gg
22 2
2
gg g
1 4
H
1 4
From Flesch (6)
Generated Accelerogram; equivalent to measured Accelerograms
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Empirical Green‘s functions
Earthquake process simulation
From DGEB (9)
Empirical Green‘s functions
location
Hypocentre
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FEM-simulation
three-dimensional Model
From DGEB (9)
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Earthquake scales
There is an empirical relationship between the energy of the seismic wave and the magnitude M. ( )= ÷ + ⋅logE 4,8 11,8 1,5 M
Also the length of earthquake fault [km] is related to the magnitude M by the following Equation: ( )= ⋅ +M 0,98 logL 5,65
Furthermore the magnitude M depends on the slip U [m] of the fault ( )= ⋅ +M 1,32 logU 4,27
MM=Modified-Mercalli-Scale
MSK=Medvedev-Sponheuer-Karnik Scale
JMA=Japanese Meteorological Agency
Intensity ScalesFrom Wakabayashi (1)
From Wakabayashi (1)
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Earthquake scales
One earthquake has only one Magnitude but the Intensity differs with
the hypocentral distance r.= + ⋅ − ⋅I 8,16 1,46 M 2,46 ln r
The relationship between hypocentraldepth h, Magnitude M and the epicentral
Intensity I0 for European conditions is given by the following equation:
= ⋅ + +0M 0,5 I logh 0,35
From Wakabayashi (1)
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Maximum-observed-intensity map of Europe
From Wakabayashi (1)
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Seismic Moment and Moment Magnitude
The seismic Moment M0 is given by: = µ ⋅ ⋅0M D A
Where: D=average displacement of rupture surface
A=area of rupture surface
µ=strength of ruptured rock
KANAMORI gives the following Relationship between seismic moment M0 and moment magnitude Mw:
= ⋅ − ⋅ W 0
2M logM 10,73 dyn cm
3
With: 1dyn=10-8 kN
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Generalized Gumbel distribution:
Parameters
Input rate
Observed data
Inaccuracies
Seismicitymodel
Location: Cologne
Site intensity
Earthquake as statistical process
From DGEB (11)From DGEB (11)
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Magnitude input rate
From DGEB (11)
Earthquake as statistical process
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Surveyed area
Source regionB and C
Source regionA
Magnitudefrequency
Damping relation
Location to investigate
Earthquake as statistical process
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Probabilistic map of seismic hazard
Probabilistic mapof seismic hazard
From DGEB (11)From DGEB (11)
Probabilistic seismic hazard of Germany
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Active faults in Lower Rhine EmbaymentFrom DGEB (7)
Earthquakes in Germany
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3434
Erft fault at the 66-m floorbrown coal opencast mining
All pictures from DGEB (7)
Earthquakes in Germany
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3535
Dislocation of layers
Paleoseismologie
From DGEB (7)
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From DGEB (7)
Paleoseismologie
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References
(1) Wakabayashi –
Design of EarthquakeDesign of Earthquake--Resistant BuildingsResistant BuildingsMcGraw-Hill Book Company
(2) Müller, Keintzel –
ErdbebensicherungErdbebensicherung von von HochbautenHochbautenVerlag Ernst & Sohn
(3) Petersen –
DynamikDynamik derder BaukonstruktionenBaukonstruktionenVieweg
(4) Clough, Penzien –
Dynamics of StructuresDynamics of StructuresMcGraw-Hill
(5) Meskouris –
BaudynamikBaudynamikErnst & Sohn
(6) Flesch –
BaudynamikBaudynamikBauverlag
(7) Deutsche Gesellschaft fürErdbebeningenieurwesen - DGEB
SchriftenreiheSchriftenreihe derder DGEB, Heft 9DGEB, Heft 9Elsevier
(8) Deutsche Gesellschaft fürErdbebeningenieurwesen - DGEB
SchriftenreiheSchriftenreihe derder DGEB, Heft 2DGEB, Heft 2Elsevier
(9) Deutsche Gesellschaft fürErdbebeningenieurwesen - DGEB
SchriftenreiheSchriftenreihe derder DGEB, Heft 10DGEB, Heft 10Elsevier
(10) Ulrich Smoltczyk
GrundbauGrundbau--TaschenbuchTaschenbuchErnst und Sohn
(11) Deutsche Gesellschaft fürErdbebeningenieurwesen - DGEB
SchriftenreiheSchriftenreihe derder DGEB, Heft 6DGEB, Heft 6Elsevier