introduction to earthquake engineering - universität · pdf filevorlesung earthquake...

IntroductionIntroduction to to

EarthquakeEarthquake EngineeringEngineering

SeismologySeismology

Vorlesung Earthquake EngineeringVorlesung Earthquake EngineeringProf. Dr.Prof. Dr.--Ing. Uwe E. DorkaIng. Uwe E. Dorka Stand: 29.06.2006

22

Plate Tectonics


33

reverse faultnormal fault

Right lateral fault

Left lateral fault


44

Tectonics and Seismicity


55From Wakabayashi (1)

Tectonics and SeismicityEpicenters for all earthquakes of 7 or larger occured between 1900 and 1980

San Andreas fault

Mid-Atlantic Ridge


66

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


77

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)


88

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


99

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


1010

2

S13

S12 3

S23TTSP1SP1

∆∆∆∆∆∆∆∆11

TTSP2SP2

∆∆∆∆∆∆∆∆22

TTSP3SP3

∆∆∆∆∆∆∆∆33

1∆∆∆∆∆∆∆∆33

∆∆∆∆∆∆∆∆11

∆∆∆∆∆∆∆∆22

HypocentreHypocentre

EpicentreEpicentre

Determination of Hypocentre


1111

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


Refraction of waves in the surface of layers



1212

Amplification characteristics of multilayers


Wave Propagation in layered Bodies


1313

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


1414

( ) ( ) ( ) 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


1515

( )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


1616

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:


1717


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:


1818


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


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


2020

Fourier Spectrum

Fourier Spectrum:

Function a(t) in Time-Domain

FourierTransformation ( ) ( )

∞− ⋅ω⋅

−∞

ω = ⋅ ⋅∫i tU a t e dt


2121

Power Spectrum

Power Spectrum:

Correlation-Function Φ(τ) in Time-Domain

FourierTransformation ( ) ( )

∞− ⋅ω⋅

−∞

ω = Φ τ ⋅ ⋅∫i tS e dt


2222

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


2323

Empirical Green‘s functions

Earthquake process simulation

From DGEB (9)

Empirical Green‘s functions

location

Hypocentre


2424

FEM-simulation

three-dimensional Model

From DGEB (9)


2525

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)



2626

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



2727

Maximum-observed-intensity map of Europe



2828

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


2929

Generalized Gumbel distribution:

Parameters

Input rate

Observed data

Inaccuracies

Seismicitymodel

Location: Cologne

Site intensity

Earthquake as statistical process

From DGEB (11)From DGEB (11)


3030

Magnitude input rate

From DGEB (11)



3131

Surveyed area

Source regionB and C

Source regionA

Magnitudefrequency

Damping relation

Location to investigate



3232

Probabilistic map of seismic hazard

Probabilistic mapof seismic hazard

From DGEB (11)From DGEB (11)

Probabilistic seismic hazard of Germany


3333

Active faults in Lower Rhine EmbaymentFrom DGEB (7)

Earthquakes in Germany


3434

Erft fault at the 66-m floorbrown coal opencast mining

All pictures from DGEB (7)

Earthquakes in Germany


3535

Dislocation of layers

Paleoseismologie

From DGEB (7)


3636

From DGEB (7)

Paleoseismologie


3737

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





(10) Ulrich Smoltczyk

GrundbauGrundbau--TaschenbuchTaschenbuchErnst und Sohn



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