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Introduction to Earthquake Engineering

Seismology

Prof. Dr.-Ing. Uwe E. Dorka

published: October 2014

Plate tectonics

Prof. Dr.-Ing. Dorka | Seismology 2

normal fault

right lateral fault

left lateral fault

Plate tectonics

3 Prof. Dr.-Ing. Dorka | Seismology

reverse fault

Tectonics and seismicity


From Wakabayashi (1)

Epicentres for all earthquakes of 7 or larger that occurred between 1900 and 1980

San Andreas fault

Mid-Atlantic Ridge

Tectonics and seismicity


Ground surface

Epicentral distance ∆

Epicenter Intensity I0

Sediment layer

Fault Hyp

ocen

tral

dept

h h

Hypocenter Magnitude M

Building Intensity I

From Müller, Keintzel (2)

Definitions


Seismic waves

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 comparison with the 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)


t

Arrival of S-wave Arrival of P-wave Arrival of L-wave


Arrivalof P-wave Arrivalof S-wave

TSP

Vs Vp

1

1

s

∆

Determination of Hypocentre


−

=∆

PS

SP

VV

T11

2

S13

S12 3

S23

TSP2

∆2

TSP3

∆3

1 ∆3

∆1

∆2

Hypocentre

Epicentre

TSP1

∆1

Determination of Hypocentre


From Petersen (3)

Wave propagation in an elastic solid

It is satisfied in general by the following solution:

Waves in elastic solids are described by the following partial differential equation, which is called the „wave-equation“:


( ) ( )tcxftcxfy ⋅++⋅−= 21

The functions f1 and f2 define the form of the wave, which propagates with velocity c. Choosing: and f2=0, the figure to the right shows the propagation of its wave form in x-direction versus time t

02 =′′⋅− ycy

Wave propagation in layered bodies

Reflection and refraction on layers

Reflection and refraction between layers

1θ


Refraction in layers towards the surface



11

sinsin θθ ⋅=ccn

n

2

2

1

1 sinsincc

θθ=

Reflection on a free or ground surface

12

Thus, we find for the displacement yg on the surface:

With this solution, the wave in an arbitrary point in the ground is given by:

y


Prof. Dr.-Ing. Dorka | Seismology

At the surface (x=0), the shear stress is zero, thus . Applying this boundary condition to the general solution of the wave equation, we obtain: which gives f1 = f2 = f, and therefore

0=∂∂

⋅xyG

tf

tf

∂∂

=∂∂ 21

( ) ( )tcxftcxfy ⋅++⋅−=

( )tfyg ⋅= 2

( )

++

−⋅=

cxty

cxtyxty gg2

1,

Reflection and transmission between two layers

13



A part of the incident wave passes through the boundary surface into the upper layer, while the rest is reflected at the interface: The compatibility conditions at the boundary between both layers are:

14


Reflection and transmission between two layers


where α, β and γ are the wave-propagation impedances:

Wave propagation in a surface layer on bedrock

15



The solutions for the free surface and between two layers must be combined. The solution for the surface layer is: The solution for the bedrock is: The compatibility conditions at the boundary between both layers are These three equations lead to the expression on the right:

16


Wave propagation in a surface layer on bedrock


Assuming that the waveform vg at the surface is Ageiωt and the incident wave f1(t) is a eiωt, a is given by

The amplitude ratio Ag to 2a at the boundary between surface layer and bedrock is:

( ) ( )

⋅⋅+⋅=

⋅−+⋅+⋅=

−

22

sincos2

11422

cHi

cHA

eeAa

g

cHi

cHi

g

ωαω

ααωω

21

2

22

2

2 sincos2

−

⋅+=

cH

cH

aAg ωαω

Amplification characteristics of multi-layers

17



Earthquake motions on ground surface

18

viscously damped SDOF oscillator

From Clough, Penzien (4)

free body equilibrium

m

The seismometer


The seismometer

19

The general solution is:

2nd order differential equation for a SDOF system under sinusoidal base excitation:

Homogeneous plus particular solution


with the following definitions:

The seismometer

20

damped frequency:

logarithmic decrement:

Homogeneous solution: free vibration response

damped free vibration

t


21

The seismometer

tωθ

sρ

cρ

ρ t

Particular solution: steady-state response (free vibration has damped out)


( ) ( ) ( )( )[ ]tt

vtv g ωξβωξ

ξβξωcos2sin1

211 2

22220 −−⋅

+−⋅

−=

sine amplitude: cosine amplitude: phase angle: amplitude:

tGtGvp ωω cossin 21 ⋅+⋅=

The seismometer

22


Accelerometer: • high tuned SDOF

• damping ratio ξ ~ 0,7

dynamic magnification:

amplitude:

ξ=0.7


The seismometer

23


ξ=0.5

Displacement meter: • low tuned SDOF

• damping ratio ξ ~ 0,5

harmonic base displacemnet:

amplitude:


24

Data processing of measured acceleration

Measurement of the east-west acceleration component of the Montenegro earthquake, 1979

Base line correction

Filtering raw data

numerical integration

numerical integration


Fourier spectrum

25

Function a(t) in the time domain

Fourier transformation


Power spectrum

26

Correlation function Φ(τ) in the time domain

Fourier Transformation


From Flesch (6)

Generation of artificial accelerograms

27

Random process

i. e. Kanai-Tajimi-Filter:

Generated accelerogram; statistically equivalent to measured accelerograms

Intensity function


Earthquake process simulation

28

Empirical Green‘s functions

From DGEB (9)

empirical Green‘s functions

location

Hypocentre


29


FEM simulation

two-dimensional model

From DGEB (9)


30


FEM-simulation

From DGEB (9)

three-dimensional model


31

Seismic moment and moment magnitude

The length of the fault rupture L [km] is related to Mw :

Richter established an empirical relationship between the energy of the surface wave Es and the surface magnitude Ms:


with: d - average displacement of ruptured surface A - area of ruptured surface µ - shear strength of rock

KANAMORI gives the following relationship between seismic moment M0 and moment magnitude Mw:

Mw and Ms are almost identical up to 7,5 with 1 dyn = 10-8 kN

Today, the Magnitude is based on the seismic moment M0, which is a mechanical measure of the rupture process:

with Es in erg, 1 erg = 10-4 kNm

Magnitude and intensities

One earthquake has only one magnitude but the intensity differs with the hypocentral distance r:

The relationship between hypocentral depth h, Magnitude M and the epicentral Intensity I0 for European conditions is given by the following equation:



33

Intensity scales

Abridged Modified Mercalli Intensity Scale Intensity Descripton

I Not felt except under exceptionally favorable circumstances

II Felt by persons at rest

III Felt indoors; may not be recognized as an earthquake

IV Windows, dishes, and doors disturbed; standing motor cars rock noticeably

V Felt outdoors; sleepers wakened; doors swing

VI Felt by all; walking unsteady; windows and dishes broken

VII Difficult to stand; noticed by drivers; fall of plaster

VIII Steering of motor cars affected; damage to ordinary masonry

IX General panic; weak masonry destroyed, ordinary masonry heavily damaged

X Most masonry and frame structures destroyed with foundations; rails bent slightly

XI Rails bent greatly; underground pipes brocken

XII Damage total; objects thrown into the air


34

Intensity scales

MM = Modified-Mercalli-Scale

MSK = Medvedev-Sponheuer-Karnik Scale

JMA = Japanese Meteorological Agency



35

European earthquake intensities

Maximum observed intensities in Europe



36

Earthquake as statistical process

Generalized Gumbel distribution:

Parameters

Input rate

Observed data

Inaccuracies

Seismicity model

Location: Cologne

Site intensity

From DGEB (11)

From DGEB (11)


37

Magnitude input rate

From DGEB (11)



38



39

Probabilistic seismic hazard in Germany for the 1000-year return period

From DGEB (11) From DGEB (11)



Probabilistic seismic hazard in Germany for the 10000-year return period

40

Paleo-Seismology

Earthquakes and gradual motions in active faults in the Lower Rhine embankment

From DGEB (7)


41

Paleo-Seismology

from DGEB (7)


42

Paleo-Seismology

Erft fault at the 66-m floor of an open-pit mine near Cologne

From DGEB (7)


43

Paleo-Seismology

Ancient dislocation of layers at the Erft fault:

Evidence for a single earthquake with more than 6.0 Mw? From DGEB (7)


44

Paleo-Seismology

From DGEB (7) Three types of typical motion pattern in tectonic zones


45

Paleo-Seismology

From DGEB (7)

Gradual motions in active faults in California


46

Paleo-Seismology

From DGEB (7)


References

49

(1) Wakabayashi – Design of Earthquake-Resistant Buildings McGraw-Hill Book Company

(2) Müller, Keintzel – Erdbebensicherung von Hochbauten Verlag Ernst &Sohn

(3) Petersen – DynamikderBaukonstruktionen Vieweg

(4) Clough, Penzien – Dynamics of Structures McGraw-Hill

(5) Meskouris – Baudynamik Ernst &Sohn

(6) Flesch – Baudynamik Bauverlag

(7) Deutsche Gesellschaft für Erdbebeningenieurwesen - DGEB Schriftenreiheder DGEB, Heft 9 Elsevier



(10) Ulrich Smoltczyk Grundbau-Taschenbuch Ernst und Sohn



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