Site response to earthquakes with reference to the application of microtremor measurements.

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sIrE

^RESP2NSE

r0

EAEIH?UAKES, WITH REFTRENCE

T0

THE APPLICATION OF MICROTREICIR I'{EASAREMENTS

Thesis presented for the degree of

Doetor of Philosophy

-atthe-

Sehool of Engineering

Ilniuersity of Auektotd

-by -

IAN M. PAHI)N, B.E. Hons. (Cilltl)

MaA,

L972

rlriar :l i

!loT!-lroN

CIIAP1ER

1

II{TRODUCTION CI{APIER

2

E.TRffQUAKES

2.1

Earthquake Occurrcnce aod

l{agalttde

2.2

Causee

of

Earthquakeg

2.1

Elaetlc l,Iave tlodel

2.4

^ElaetLc Body lJaves

2.5 Elaatlc

Surfgce Wavee 2. 5,

1

Raylei.g[ Ifavee

2.5.2

Love ard Dlaperalve Raylelglt llaves

2.5,3

Dlsperaion

2.5,4

Dlaperrlon Curveg

CUAPTER

3

^{SITE NESPONSE TO} EARTIIqUAKE EXCIATTION

3.1

Introductlon

3,2

Eurplrtcal Studlea

3.3

l,iatheuatlcsl Analyeia

of

^Ground

BeaPoaae

3.3.f

^Steady Steto Anelyelr

3.3.2

Transt.ent Aoalyate

3.3.21 Dlecrete

l{rra

Sheer Besa Hodel 3.1.22

Flnlte EleDlt

llodelr

3.3.23 ^Ttre Coutialoua Sheer Bera Model

3.4

Cooparleo

of Et4lrlcal

^aad

Theorettcel l{rttoala

CHAPTER

4

}TICRSIREHOR HEASUNSUENTS

4.1

Introductton

4.2

^Rewlen

of

Hlcrotrenor Inveatlgaclona

4.3

^The Appllcatlon

of

lllcrotrenor lleasur€rDtB

CIIAPTER

5

DEVELOPMEIM OF }fICROTRE}0R NBCORD-

DIG TECt{ilrqUES 5.

I

lot.oductlon

5,2

Developurent

of

the FrequencY

l{odulated ^}tethod

5.3

^Datr converaLoo

for

Dt8,ltal FrequencY AnalYals

5.4

C6l1bratloD

of

the FrequeacY

tlodulated SyBten

5.5

Developnent

of

the Dlrect Racotdltrg liethod

CIIAPTER

6

DBWLOPMENT OF UICROTREI,IOR ANALYSTS TECENIQUES

6.L

IntroductloD

6.2

D1g1t8l FrequencY AnalYsle

6.2.L

^Data Transfer ^{Prograt! PAIAf}

6.2.2

Sesponae Spectruu Progran ^BSPEC

6.7.3

Porer Spectruu ProSrsr PGPE

6.7.4

Fourlct Spectra

TABTE

OF

CONTENTS

Page

3 4 4 6 7 7

I

5.2.5

Slgnal Averaglng

6.3

^Analog lrcquancy Analyale

6.4

Test

of

Recordlng and Aoalyele Syatena

CBAPTER

?

UICROTNEU)R RECORI}INGS

7.L

Introductlotr

7.2

l{eadonbank Stte

7.3

Takantnl Slte

7.4

Tanakl Rhrer ^SLte

7.5 Slte

^Recordlnga

7.5.1

^tGadqrbank

7.5.2

laLanlnl

7.5.3

^Tauakl

7.6

Diacuealon

of

^SPectrs

7 .6.

I

^lGedorbank

7.6.2

^Takanlal

7

.6.3

^Taoaki

7.7

Concluelotrs

$UTTER

8

THE FRSE VIBRATIOT{ TOR^SIO}{ TEST

8.1

Introductlon

8.2

Ao Outllne

of

Teetlng technlquea

8.3

Slr€aor Straln iad !q41ng RelatloarhlPe

8.4

Co4arl'aon

of D't!d€

Teatlog Technlquee

8.5

Revien

of

Hethodr foa DeterDlnlng thc ProPertlea

of

^SolLe

ln

^Shear

8.6

Davelopoelt

of

the Free Vlbratl'on

Teat EqulPeot

8.6.1

Inttoductl'on

8.6.2

Deecrlptlon

of

the ^CoEponenta

8.7

Free Vlbratton Teat Relatlonahlpe

8.8

Teet Prograu

8.S.1

^EqulPcat Callbratlon

8.8.2 llaterlale

^Teated

8.9

llYrad'c Test ^Reaultg

8.9.1

^{Genaral Procedure}

8.9.2

Dlgcusslol

of

Teet Rasulta

8.9'3

Coryarlsou

of

Teet ^{Reeulte bY} Varlow ^Methoda

8.9.31 rstandardr _{Seed and}

Idrlsa

^Curvet 8.9.12 Dyoaoil.c Stress and Straln-Cont-

rolled

^Teets

8.10 SumarY and Conclueiona

CHAPTER

9

SIUIJLATED EART$QUAKE UOTIONS

Pa8e

9.1 Introductlon

¹¹⁵

9,2

^Progra.c

to

Calculate th€ ^{Re.PotBa 115}

of

florlaontal So11 LaYeEs

9.3

SlEuhted Earthqueke IDPUt l{ot1@8

9.4

Co4uted Eartlrquekc S,urface

Hotlons

at

the Tanekl Stte

9.4.1

^SelectLon

of

^Bedrock Hotto!

Characterloticg

52 53 53

9 9

57 57 57 57 57 61 61 52 62 62 62 62 63

8t

81 81 83 84 87 87 88 95 98 98 99 101 101 108 108 11

11

LA 14 15

I8

23 23 24

25 25 29

34 34 40 42 42

108 109 110

118 123 4s 123

45 45 46 48 51

g.4.2

Detcrd.aatlon

of

Dyaadc

Sotl

^L24

ProPertLca

9.4.3

Surface ^{uotLou Relponae}

Spectra

L26

PaBe 120

Page

44.5

Rcrpmre Spectrun

Averaglng

163

Progr.s ^(RPL0T)

A4.6 Pocr

^Spectrun Progran

(PO8PB)

163

A4,7

Pcrrer Spectrrn Averaglug

Progran

^L67

(PPIOT)

9.5

ConcLuelooa and Dlecugeloo of Curreat Deelgo llethode

CHAPTER 10 SIuI'IATED I{ICN(}[BEI,0R UYTIONS

10.1

lDtroducttoa

10.2

Tatlakl RLver Site

10.3 lakanlnl

Stte

10.4

Conclueloos

CIIAPTER 11 SIJUHANX AI{D CONCLUSIONS

APPENDIX

1

II{DI'STRIAL APPLICATIONS OF lTE lficRoTlgloR EQITTPITEM APPET{DIX

2

ELBCTBICAL CIRCUITS APPENDIX

3

lBE DECIBEL SCALE APPENDI,X

4

^{COUPUIER PROGNAH!}

A4.l

Introduct{on

A4.2

Paper Tape Readtng ProPan

(PATAP)

A4.3

Reaponee

of llorizontal

Leyera Progran

A4.4

Reaponee Spectnru ProSraa (RSPEC)

t37 L17 L37 140

A4.8

AFPEilDIX 5

45.1 A5.2 A5.3

APPENDIX 6 A6.1 L6.2 APPENDIX 7

A7.1 A7.2 A7.3

APPEI{DIX

8

^RBFERENCES

Torsion Tegt Reeult

Program

^L67

(sloD)

}TICROTRBUOR RECORDINC ^PROCEDURS

Frequeacy l,todulatloa

Equl.prnent

^L7L

Dlrect

Recordlng

Eqrdpunt

¹⁷¹

IDdustrlsl vlbratloo Recording

L7l

EquLpcot

UICK}TREIOR AI{ALYSIS PROCEDI'RE

Frequency Hodulatlon t{ethod Dl.rect Becordlng liethod

TORSI,OTI TEST PROCEDTNE

ScttlDg ^Up

ad

Coagolidatlon Te8t Procedure

Analyala Procedure 143

144 151

L73 L73

L52 L52 152 154

L74 L74 L75 176

trtr

a 6

ll

la l6

20

a!

38 48

{9

57 82 86 92 9?

CORRIGEIIIDIJI.I

Carl.ctloq tor Evcnoa rced Errkoa

rqt!.2.19b, L.E.s. to t."a o t'!

at.

Gol. 2 9rrr. ³ ll,m 2. for t! r.rd I

l(ot - t.z.)

Sccond tcn ol cqtn 3.4 to rced brc ^{J J}

Col. 2 pare. 3 llne 12. for eqtn 2.lil ^end 2.19 rcad 2.20 rod 2.21.

Col. 2 1st ^para llne 9' ^for Ernt read DoveEclt

Col. 2 ltne 9, for Tukl resd Yarhrrr Col. 2 pan 2 llne 9, for uect rcad aet Eqta 5.23, lor dt rced df

Col. 2 para 2 ![ne 4, read as r...eould _have r.rco troct Col. 2 para 2, for plastocene tead plelstocenc

l1g. 8.1, for G read !

Col. 2 para 3 Lto. 2, deletc ifrcnl IDtcrchaote tltles for Figs Vl aod VII.

Eqtn 8.32, to rrad ⁰ - ^oo.eoaot Eqtu t.35 lnd 6.36 ?- should read T^Z

Llne precldilg aqto 8l'39, for equatlEa 8.3 rerd 8.!E Elto 8.45, R.H.S. to t""a f, ⁺

ffi

table 9.1 rcad H7.l for El centro

Col. I pare 2 llne 6, for ^{rT^} hasr read 'T^ k!

trEahlr! f,. (1970) ref. should rcad Vol. ld. llo. I' lderdr.

9'

9E

lul

r23 136 180

A

dtaplacecnt

ratlo

C

wave group

veloclty,

danpLn8i

mtrit(r

auto- covarlnrce

C

_o ^varLsnce

D

dlarcter

E

eoerry,

straln

derrl.ator tenaor, Young8 uodulue

F

frequency

ratlo

R

thlckneea

of goil layerr transfer

fuqctiorr

I

^polar DoERt

of l|rertis

J co4llatrce,

[aaa

nocnt of lnettia K etlffneaa natrLr,

coogtant tern

L

length

H

eattlrquske uagol,ttder ^naqa Datrlx

Ul,t

eerthqueke lntenst

ty

P

prlncLpal

stresa,

co4rcsal.on r8$e8t spectral denrtty

R

load

vectot,

radlue

S

^{shear rraveg}

I perlod, tlne,

torque

U dlgplacerot

W straln

energy, pouet

X

dtaplacemat vectoEr ^bodY force t'an€ propagatlm

conetent trt"'

trave propagatlon

drinbteotl. -,'-.''. r'r

save

celet{ty,

^dauptng coefflcl'eot

crltl.cal da4lng

coefflcLent

equlvaleot vlecoua ilanprirb'

cJefflqiett

_-:

dlotttter

frequency, force, Esro

g

acceleratLon

of gtavltY ' :,

^'

h

trangfer fuactl.on,

redlal

cLearance, conetint

tern

k

bulk nodulus, tt.nte ProPagatl.cr.cooetaoti stlffnegg

m

nesa, gradlcnt

P

Pregsurer atfeaa

q

constant ^teEa

t tlE

u

illaplacemnt

i

veloclty

O

acceleratl,otr

x

coordLoate dl.rectlon

NOTATION

ahear streee,

constand,

:.

y

coordlaate dlrect{oa

z

coordl,nate dlrectlon

a

coqreaalso ualt€

teloclty,

l4edance

ratlot daqlng

conatait,

B

^{ghear wave} nelocl,ty, daqLag conBtantr

1 rmlt

^{reLglrt, shear}

etraln

€ atrein

teu3or

4

^vlecoelty

g dflatatlon, rotatl6,

angulardl.eplacernent

K

save

trrder

I

navelength, daql.ng factot

I--

equl-valent vlecoug darptug factor

eq

u

^{theer uodulttg}

v

Poleeonlg

ratlo I

^vlccoalty

p ff84

de!8lty

:r' '

lag

0

scalsr quanttty, ^phase angler autocorrelatlon

S

vectof'potbntLal

0I

rotetlorir'angular frequeneY

a b c cc

".q

d f,

I

ACKNOWTEDGEMENTS

the york _dcecrlbcd

lu thlr thcglr rar crtrlcd

out

!t

the Ita|.rGsalry

of

Aucklanil, Sdrool

of

Elghccrl.ag, undct the eupervleloo

of

Asrochtc Profacaor

P.tl. trylor.

^Ttrc euthor

c4rrallcl hir

apprcc-

latlon

to Amoclrtc Profereor Teylor

for

hl.rr

mfetltng

enthueiral,

rncouregcEnt end

edrrlce. lte

ruthor alro

slehcr to thel, ttc folblng,

wlrose arelatrDcc

ia

epprccletcd.

Dr.

G.R.

llartit

nbo rtrpcrvlacd thc

rott rhllo Alloelrta

Profeesor

faylor sls

^oD eabbatlcel

brve.

l{y

rlfc for

ber prtlctrcc md uldcratendlug drri"ng the coursc

of thls uott.

l,lr8. G.

lfirgetts for bcr

cerc

ud

ttororq[acre

ln

scttl.ng out rnd

typtrg

th€

tcxt.

Mr.

B.

Fled.og snd thc tlorkehop

8taff, for thelr

cxcellcnt sork

lo

conrtructlng eqrdpunt.

l{rarr8.

G. Du8k

,

^R.F.

lcrco,

^{B.R. hrthd8G, C.}

Colllna for

^the

varlous

perts

thcy bave pleyed.

Profemot H.A.

llhrle, Dlrcctor of

thc 8rdl.o leacardr Centre

of

Auckland UDlveralty,

for

the help

rrd

edvlce ^gl,ven duriug

thc

^couree

of thtr

ctrdy.