laporan resmi fisika batuan

8/17/2019 Laporan Resmi Fisika Batuan

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PHYSICAL PROPERTIES OF ROCK EXPERIMENT

Author:

M.Irsyad Hibatullah 3714100020

TEKNIK GEOFISIKA

INSTITUT TEKNOLOGI SEPULUH NOPEMBER

SURABAYA

2014



TABLE OF O!TE!T"

#$EFAE.................................................................................................................2

CHAPTER I.............................................................................................................5

PRELIMINARY........................................................................................................5

1.1 Backgr!"#......................................................................................................5

1.2 Pr$%&'( Fr'!%a)*"(.......................................................................................6

1.+ O$,&c)*-&(........................................................................................................ 6

1.4 B&"&*)(............................................................................................................6

CHAPTER II............................................................................................................7

LITERATURE RE/IE............................................................................................7

2.1 E%a()*c Pr&r)*&(...............................................................................................7

2.2G&'&ca"*ca% Pr&r)*&(....................................................................................8

2.2.1 Fuda%&'tal Laboratory T&(h'i)u&s....................................................................8

2.2.2 *&+or%atio' #ro,&rti&s...................................................................................9

2.+ Pr*"c*%&( O La$ra)r3 M&a(!r&'&")(..............................................................10

2.4 &"(*)3 a"# Pr(*)3.........................................................................................11

2.4.1 #orosity.................................................................................................... 11

2.4.2 *&'sity..................................................................................................... 12

2.5 /&%c*)3 R&%a)*" ) Rck Carac)&r*()*c..............................................................13

2.6 A"#&(*)& Rck .................................................................................................15

CHAPTER III........................................................................................................ 17

METHOOLOGY..................................................................................................17

+.1 T*'& a"# P%ac&...........................................................................................17

+.2 T%( a"# Ma)&r*a%(.....................................................................................17

3.3.1 Elasti( #ro,&rti&s...................................................................................17

3.3.2 *&'sity o+ $o(-s....................................................................................17

+.+ E7&r*'&")a% Prc&#!r&...............................................................................17

3.3.1 M&asur&%&'t Elasti( #ro,&rti&s.................................................................17

3.3.2 M&asur&%&'t *&'sity o+ $o(-s..................................................................18

CHAPTER I/.........................................................................................................19

ATA ANALYSIS....................................................................................................19

4.1 M&a(!r&'&") a)a...........................................................................................19

4.2 A"a%3(*( a)a.............................................................................................19

4.+ a)a R&&r&"c& r' %*)&ra)!r&...........................................................................20

4.4 *(c!((*"...................................................................................................... 20



CHAPTER /..........................................................................................................22

CLOSING REMARKS.............................................................................................22

5.1 C"c%!(*"..................................................................................................... 22

5.2 R&c''&"#a)*".............................................................................................22

B*$%*gra3...........................................................................................................23



CHAPTER I

PRELIMINARY

1.1 BACKGROUN

&o,hysi(s is bra'(h s(i&'(& o+ &os(i&'(&/&o,hysi(s +o(us&d i' ,hysi(al

,ro,&rti&s o+ &arth. It also ,hysi(al ,ro,&rti&s o+ ro(-/ b&(aus& ro(- is ,art o+ &arth. $o(- or

&arth had %a'y ,hysi(al ,ro,&rti&s li-& d&'sity/%a'&tiity/radioa(tiity/a'd &t(. ,hysi(al

,ro,&rti&s o+ ro(- (a' b& us&d +or &sti%at& or i't&r,r&tati' subsur+a(& o+ &arth. "o ith

,hysi(al ,ro,&rti&s o+ ro(- & (a' -'o hat i'sid& th& &arth.

#hysi(al ,ro,&rti&s o+ ro(- is &ry i%,orta't s(i&'(& +or a &o,hysi(ist. B&(aus& ith

usi' ,hysi(al ,ro,&rti&s o+ ro(-/ a &o,hysi(ist (a' ,r&di(t hat ty,& ro(-/hat ty,& o+

+or%atio' i' sub sur+a(&. For su,,orti' i' l&ar'i' #hysi(al ,ro,&rti&s o+ ro(-/ & ar& doi'

this &,&ri%&'t. This &,&ri%&'t +o(us&d i' ultraso'i( a& ,ro,aatio' ro(-/str&ss a'd

strai' ro(-/,orosity a'd d&'sity.

1.2 PROBLEMS FORMULATIONS

This &,&ri%&'t ha& so%& ,robl&% to &,lor& :

1. Ho to %&asur& th& a& ,ro,&rti&s 5,65s usi' os(illos(o,&8

2. Ho th& r&latio' b&t&&' 5, ith d&'sity a'd ,orosity8

3. Ho to %&asur& you'9s %odulus8

4. Ho to %&asur& sh&ar %odulus8

. Ho to %&asur& ,oisso'9s ratio8

;. Ho to -'o th& ty,& o+ th& ro(- sa%,l&8

1.+ OB8ECTI/ES

This &,&ri%&'t had +i& %ai' ob<&(ti& as out,ut :

1. =s& os(illos(o,& to %&asur& a& ,ro,&rti&s usi' ,ara%&t&r o+ ti%& a'd sa%,l&

di%&'sio'

2. M&asur& a'isotro,y o+ &lo(ity usi' +& %od&l o+ (al(ulatio'

3. *&t&r%i'& th& r&latio' b&t&&' 5, ith d&'sity a'd ,orosity

4. M&asur& th& bul- %odulus/ sh&ar %odulus/ a'd ,oisso' ratio +ro% th& ro(- sa%,l&

. *&t&r%i'& th& ty,& o+ ro(- sa%,l& bas& o' th& &,&ri%&'t

1.4 BENEFITSFro% this &,&ri%&'t/ th& stud&'t &t so%& b&'&+its su(h as :

1. "tud&'ts (a' %&asur& th& a& ,ro,&rti&s usi' os(illos(o,&

2. "tud&'ts (a' a'aly>& +& %od&l o+ (al(ulatio' to d&t&r%i'& a'isotro,y o+ a&

,ro,&rti&s

3. "tud&'t -'o th& r&latio' b&t&&' 5, ith d&'sity a'd ,orosity

4. "tud&'t -'o ho to %&asur& bul- %odulus/ sh&ar %odulus/ a'd ,oisso'9s ratio

. "tud&'t (a' id&'ti+y th& ty,& o+ ro(- bas& o' th&ir ,hysi(al ,ro,&rti&s

CHAPTER IILITERATURE RE/IE



2.1 ELASTIC PROPERTIES

Hoo-&9s la d&s(rib&s th& r&latio'shi, b&t&&' str&ss a'd strai' o+ a'&lasti( %at&rial.

I' a&'&ral +or%ulatio'/ th& str&ss?strai' r&latio'shi, is at&'sorial &)uatio':

h&r&

@ik is th& str&ss t&'sor

ik is th& strai' t&'sor

iklm is th& &lasti( %odulus or sti++'&ss t&'sor.

I+ strai' is &,r&ss&d as a +u'(tio' o+ str&ss/ th& r&sulti' strai'?str&ssr&latio'shi, is

h&r&

*iklm is th& &lasti( (o%,lia'(& t&'sor.

B&sid&s th& La%& ,ara%&t&rs /C/ a'y ,air o+ to o+ th& +olloi' %oduli(a' b& us&d+or a d&s(ri,tio'o+ th& &lasti( ,ro,&rti&s o+ a' isotro,i(%at&rial:

• Dou'9s %odulus E/ d&+i'&d as ratio o+ str&ss to strai' i' a u'iaial str&ssstat&

• o%,r&ssio'al a& %odulus M/ d&+i'&d as ratio o+ str&ss to strai' i' au'iaial strai'

stat&

• Bul- (o%,r&ssio'al %odulus -/ d&+i'&d as ratio o+ hydrostati( str&ss toolu%&tri(

strai'

• "h&ar %odulus C/ d&+i'&d as ratio o+ sh&ar str&ss to sh&ar strai'

• #oisso'9s ratio / d&+i'&d as th& '&ati& ratio o+ lat&ral strai' to aialstrai' i' a

u'iaial str&ss stat&.

orr&s,o'di' to th& to %oduli ar& to i'd&,&'d&'t body a&s:

o%,r&ssio'al/ lo'itudi'al/ or #a& ith th& &lo(ity:



"h&ar/ tra's&rsal/ or "a& ith th& &lo(ity:

h&r& G is th& bul- d&'sity.

Ho&&r/ i+ &lasti( a& &lo(iti&s a'd bul- d&'sity ar& -'o' +ro%%&asur&%&'ts/ th&

&lasti( ,ara%&t&rs (a' b& (al(ulat&d:

"(ho' . H./ 2011

2.2GEOMECHANICAL EFORMATION PROPERTIES

*&+or%atio' ,ro,&rti&s ar& d&ri&d +ro% a stati( (o%,r&ssio' t&st. Dou'9s%odulus is

d&+i'&d as ratio o+ a' aial str&ss a'd th& r&sulti' aial strai':

Th& str&ssstrai' diara% i' %ost (as&s shos a 'o'li'&ar sha,&.Th&r&+or&/ i' &'&ral/

th& %odulus is str&ssd&,&'d&'t a'd d&+i'&d as:

I' &'i'&&ri' a,,li(atio's/ Dou'9s %odulus %odulus o+ &lasti(ity iso+t&' d&ri&d

+ro% th& li'&ar ,ortio' o+ th& str&ssstrai' (ur&.



#oisso'9s ratio is d&+i'&d as th& r&lati& (ha'& o+ th& radius diid&d byth& r&lati&

(ha'& o+ aial l&'th i' str&ss dir&(tio':

"(ho' . H./ 201

2.4 ENSITY AN POROSITY

2.4.1 P OROSITY

#orosity is th& +ra(tio' o+ ro(- bul- olu%& o((u,i&d by ,or& s,a(&Jord&' 6

a%,b&ll/ 1K4.Thus/ ,orosity is d&+i'&d as th& su%%ari>&d olu%& o+ all ,or&s/

+ra(tur&s/(ra(-s/ &t(./ or &'&rali>&d all +luid&../ as/ at&r/ hydro(arbo's or

'o'solidJ(o'tai'i' ,arts o+ a sa%,l& r&lat&d to th& total olu%& o+ th&sa%,l&Fiur& 2.1:

#orosity is i&' as a olu%& +ra(tio' di%&'sio'l&ss or as ,&r(&'ta&.Th& d&+i'itio' abo&

d&s(rib&s th& total ,orosityJ. I+ th& ro(- (o'tai's a,art o+ 'o'(o''&(t&d or s&,arat&d ,or&s

us/ %oldi( ,or&s/ &t(./ th&' this,art do&s 'ot (o'tribut& to a'y +luid tra's,ort ithi' th&

ro(- a'd is 'o'&++&(ti&.JThus/ &++&(ti& ori't&r(o''&(t&d ,orosity is th& ratio o+ th&

(o''&(t&d,or& olu%& a'd th& total ro(- olu%&.

For r&s&roird&s(ri,tio' it is i%,orta't to disti'uish b&t&&':

• Total ,orosity/ th& +ra(tio' o+ bul- olu%& o((u,i&d by total ,or& s,a(&

• E++&(ti& ,orosity/ th& +ra(tio' o+ bul- olu%& o((u,i&d by i't&r(o''&(t&d

,or& s,a(&.

Th& +olloi' ar& a,,li&d i' ord&r to d&t&r%i'& ,orosity:

• dir&(t %&asur&%&'ts laboratory bas&d o' d&t&r%i'atio' o+ bul- a'dsolid olu%&/

as &,a'sio'/ or dis,la(&%&'t t&(h'i)u&s

• i'dir&(t %&asur&%&'ts loi' %&thods/ s&is%i( %&thods bas&d o' (orr&latio'

b&t&&' ,orosity a'd ,ro,&rti&s li-& d&'sity/ '&utro' r&s,o's&/a'd s&is%i( a&

&lo(ity. #orosity (a' also b& d&ri&d +ro% !M$ %&asur&%&'ts

2.4.2 D ENSITY

*&'sity G is d&+i'&d as th& )uoti&'t o+ %ass % a'd olu%& 5 o+ a %at&rial:

*u& to th& h&t&ro&'&ity o+ ro(-s/ it is '&(&ssary to disti'uish b&t&&'di++&r&'t d&'siti&s

that ar& r&lat&d todi++&r&'t ro(- (o%,o'&'ts:

• G bul- d&'sity: th& %&a' d&'sity o+ th& (o'sid&r&d ro(- olu%& i'(ludi',or&s/

&t(. +or &a%,l&/ d&'sity o+ sa'dsto'&.



• ρi d&'sity o+ a'y i'diidual %i'&ral ro(- (o%,o'&'t i +or &a%,l&/d&'sity o+

)uart>.

• G%a %&a' d&'sity o+ th& solid %atri %at&rial %i'&ral or %itur& o+%i'&rals/ also

(all&d rai' d&'sity +or &a%,l&/ d&'sity o+ a (arbo'at&%atri ithout ,or& +luid.

• G+l %&a' d&'sity o+ th& ,or& or +ra(tur& +luid +or &a%,l&/ d&'sity o+at&r G.

Bul- d&'sity o+ a (o%,osit& %at&rial ro(- (o'sisti' o+ ' (o%,o'&'ts is

h&r& ρi is th& d&'sity a'd 5i is th& olu%& +ra(tio' o+ (o%,o'&'t i.

Bul- d&'sity o+ ro(-s +ollos &a(tly &)uatio' abo&a'd d&,&'ds o':

• th& %i'&ral (o%,ositio' %i'&ral d&'siti&s a'd olu%& +ra(tio's

• ,orosity ,or&s/ +ra(tur&s a'd d&'sity o+ ,or& +luids.

This &,lai's th& &'&ral rul& o+ d&'sity ariatio':

• I'&ous ro(-s sho a' i'(r&as& o+ d&'sity +ro% +&lsi( a(id to %a+i(basi( ty,&s

• #orous ro(-s sho a d&'sity d&(r&as& ith i'(r&asi' ,orosity a'dd&(r&asi' at&r

saturatio'.

2.5 /ELOCITY R ELATION TO R OCK CHARACTERISTIC

ra'& o+ th& (o%,r&ssio'al a'd sh&ar a& &lo(iti&s +or (o%%o'ly o((urri' ro(-

ty,&s a'd i'di(at&s so%& ty,i(al t&'d&'(i&s a'd (hara(t&risti(s:

- Th& &lo(ity o+ i'&ous ro(-s i'(r&as&s +ro% a(idi(N+&lsi( ra'it& to basi(N%a+i(

,&ridodit& %&%b&rs th& ra'& +or a' i'diidual ro(- ty,& is th& r&sult o+ ariatio' o+

ro(- (o%,ositio' %i'&ral (o't&'t a'di+ ,r&s&'t+ra(turi'.

- A%o' th& %&ta%or,hi( ro(-s/ '&iss a'd s(hist i' ,arti(ular sho a' a'isotro,yith &lo(ity ,arall&l s(histosity.&lo(ity ,&r,&'di(ular s(histosity.

- "&di%&'tary ,orous ro(-s sho a broad ra'& o+ &lo(ity/ h&r& hih &lo(iti&s ar&

ty,i(al +or thos& that ar& r&lati&ly d&'s& lo ,orosity a'd lo &lo(iti&s ar& ty,i(al

+or ,orous asb&ari' %&%b&rs.

- Th& lo&st &lo(iti&s ha& dry u'(o'solidat&d ro(-s as a r&sult o+ th& s,&(i+i( rai'

- rai' (o'ta(t a'd hih ,orosity. Th&r& is a broad s(att&r +or ,orous ro(-s i'+lu&'(& o+

,orosity/ ,or& +luid/ a'd %i'&ral (o%,ositio' i' ,arti(ular a'd a (o%,arabl& s%all

ra'& +or a d&'s& ro(- ith &lld&+i'&d (o%,ositio' a'hydrit&.

Th& ratio o+ th& to a& &lo(iti&s 5#N5" or th& #oisso'9s ratio is (o'troll&d %ai'ly byro(- ty,& a'd ,or& +luid.



5&lo(ity o+ i'&ous ro(-s shos a' i'(r&as& +ro% a(idN+&lsi( to basi(N%a+i( ro(- ty,&s. Th&

sa%& t&'d&'(y shos th& d&'sity. This i&s th& ba(-rou'd +or a' &%,iri(al (orr&latio'

b&t&&' d&'sity a'd &lo(ity/

I+ i'&ous or %&ta%or,hi( ro(-s ar& +ra(tur&d/ th&':

- &lo(ity d&(r&as&s (o%,ar&d ith th& (o%,&t&'t ro(-

- +ra(turi' (r&at&s a hih&r ,r&ssur& s&'sitiity/ thus &lo(ity shos a disti'(t ,r&ssur&d&,&'d&'(&

- i' (as& o+ ,r&+&rr&d ori&'tatio' o+ +ra(tur&s/ a'isotro,y r&sults.

5&lo(ity d&(r&as& ith i'(r&asi' +ra(turi' is 'ot alo'& a olu%&tri( +ra(tur&/ ,orosity

&++&(t it is %or& a' &++&(t o+ th& i'(r&asi' d&+&(tsJ i' th& (o%,&t&'t ro(- %at&rial a'd

th&r&+or& it '&&ds s,&(ial ty,&s o+ %od&ls to d&s(rib& su(h &++&(ts

B&lu% ada ra+i- a&, &rsus ,orositasN+ra(tur&



F*g!r& 2.6.1 $a'& o+ (o%,r&ssio'alHih&r 5alu& a'd "h&ar a& lo&r alu&s 5&lo(iti&s +or

(o%%o'ly o((urri' ro(-

"(ho' . H./ 201

2.6 ANESITE R OCK

A'd&sit& is th& 'a%& us&d +or a +a%ily o+ +i'&rai'&d/ &trusi& i'&ous ro(-s that

ar& usually liht to dar- ray i' (olor. Th&y o+t&' &ath&r to arious shad&s o+ bro' a'd

th&s& s,&(i%&'s %ust b& bro-&' +or ,ro,&r &a%i'atio'. A'd&sit& is ri(h i' ,laio(las&

+&lds,ar %i'&rals a'd %ay (o'tai' biotit&/ ,yro&'&/ or a%,hibol&. A'd&sit& usually do&s 'ot

(o'tai' )uart> or olii'&. A'd&sit& is ty,i(ally +ou'd i' laa +los ,rodu(&d by



stratool(a'o&s. B&(aus& th&s& laas (ool&d ra,idly at th& sur+a(& th&y ar& &'&rally

(o%,os&d o+ s%all (rystals. Th& %i'&ral rai's ar& usually so s%all that th&y (a''ot b& s&&'

ithout th& us& o+ a %a'i+yi' d&i(&. "o%& s,&(i%&'s that (ool&d ra,idly (o'tai' a

si'i+i(a't a%ou't o+ lass/ hil& oth&rs +or%&d +ro% as(har&d laas ha& a &si(ular or

a%ydaloidal t&tur&.

A'd&sit& a'd diorit& ar& (o%%o' ro(-s o+ th& (o'ti'&'tal (rust abo& subdu(tio'

>o'&s. Th&y &'&rally +or% a+t&r a' o(&a'i( ,lat& %&lts duri' its d&s(&'t i'to th& subdu(tio'

>o'& to ,rodu(& a sour(& o+ %a%a. *iorit& is a (oars&rai'&d i'&ous ro(- that +or%s h&'

th& %a%a did 'ot &ru,t/ but i'st&ad sloly (rystalli>&d ithi' EarthPs (rust. A'd&sit& is a

+i'&rai'&d ro(- that +or%&d h&' th& %a%a &ru,t&d o'to th& sur+a(& a'd (rystalli>&d

)ui(-ly. Th& (o%,ositio' o+ a'd&sit& a'd diorit& ha& a (o%,ositio' that is i't&r%&diat&

b&t&&' basalt a'd ra'it&. This is b&(aus& th&ir ,ar&'t %a%as +or%&d +ro% th& ,artial

%&lti' o+ a basalti( o(&a'i( ,lat&. This %a%a %ay ha& r&(&i&d a ra'iti( (o'tributio' by

%&lti' ra'iti( ro(-s as it as(&'d&d or %i&d ith ra'iti( %a%a.

A'd&sit& d&ri&s its 'a%& +ro% th& A'd&s Mou'tai's o+ "outh A%&ri(a. I' th& A'd&s

it o((urs as laa +los i't&rb&dd&d ith ash a'd tu++ d&,osits o' th& st&&, +la'-s o+

stratool(a'o&s. A'd&sit& stratool(a'o&s ar& +ou'd abo& subdu(tio' >o'&s i' &'tral

A%&ri(a/ M&i(o/ Qashi'to'/ Or&o'/ th& Al&utia' Ar(/ a,a'/ I'do'&sia/ th& #hili,,i'&s/

th& aribb&a' a'd !& R&ala'd/ a%o' oth&r lo(atio's. A'd&sit& (a' also +or% aay +ro%

th& subdu(tio' >o'& &'iro'%&'t. For &a%,l&/ it (a' +or% at o(&a' rid&s a'd o(&a'i( hot

s,ots +ro% ,artial %&lti' o+ basalti( ro(-s. It (a' also +or% duri' &ru,tio's at (o'ti'&'tal

,lat& i't&riors h&r& d&&, sour(& %a%a %&lts (o'ti'&'tal (rust or %i&s ith (o'ti'&'tal

%a%as. Th&r& ar& %a'y oth&r &'iro'%&'ts h&r& a'd&sit& %iht +or%.

O((asio'ally/ a'd&sit&s (o'tai' lar&/ isibl& rai's o+ ,laio(las&/ a%,hibol&/ or

,yro&'&. Th&s& lar& (rystals ar& -'o' as S,h&'o(rystsS. Th&y b&i' +or%i' h&' a

%a%a/ hi(h is (ooli' at d&,th/ a,,roa(h&s th& (rystalli>atio' t&%,&ratur& o+ so%& o+ its

%i'&rals. Th&s& hih (rystalli>atio' t&%,&ratur& %i'&rals b&i' +or%i' b&lo th& sur+a(&

a'd ro to isibl& si>&s b&+or& th& %a%a &ru,ts. Qh&' th& %a%a &ru,ts o'to th& EarthPs

sur+a(& th& r&st o+ th& %&lt (rystalli>&s )ui(-ly. This ,rodu(&s a ro(- ith to di++&r&'t

(rystal si>&s/ lar& (rystals that +or%&d sloly at d&,th -'o' as S,h&'o(rystsS/ a'd s%all

(rystals that +or%&d )ui(-ly at th& sur+a(& -'o' as Srou'd%assS. SA'd&sit& ,or,hyryS is

th& 'a%& us&d +or th&s& ro(-s ith to (rystal si>&s.



"o%& %a%as that ,rodu(& ol(a'i( &ru,tio's abo& subdu(tio' >o'&s (o'tai'

&'or%ous a%ou'ts o+ dissol&d as. Th&s& %a%as (a' (o'tai' s&&ral ,&r(&'t dissol&d as

by &iht. This as (a' ha& s&&ral orii's/ &a%,l&s o+ hi(h i'(lud& th& +olloi'

• Qat&r a,or ,rodu(&d h&' o(&a'+loor s&di%&'ts o' a' o(&a'i( ,lat& ar& h&at&d i' a

subdu(tio' >o'&.

• Qat&r a,or ,rodu(&d h&' hydrous %i'&rals d&hydrat& i' th& h&at o+ a subdu(tio'

>o'&.

• arbo' dioid& ,rodu(&d h&' risi' %a%a &'(ou't&rs (arbo'at& ro(-s/ su(h as

li%&sto'&/ %arbl& or dolo%it&.

• Qat&r a,or ,rodu(&d h&' a risi' %a%a (ha%b&r &'(ou't&rs rou'dat&r.

At d&,th th&s& as&s (a' b& dissol&d i' th& %a%a li-& (arbo' dioid& dissol&d i' a(a' o+ (old b&&r. I+ that (a' o+ b&&r is sha-&' a'd sudd&'ly d&,r&ssuri>&d by o,&'i' th& (a'/

th& as a'd th& b&&r ill &ru,t +ro% th& o,&'i'. A ol(a'o b&ha&s i' a si%ilar %a''&r. A

risi' %a%a (ha%b&r i'sta'tly d&,r&ssuri>&d by a la'dslid&/ +aulti'/ or oth&r &&'t (a'

,rodu(& a si%ilar but %u(h lar&r &,losi& &ru,tio'. Ma'y ol(a'i( ,lu%&s a'd ash

&ru,tio's o((ur h&' as(har&d a'd&siti( %a%as &ru,t. Th& as ,r&ssur& that (aus&s th&

&ru,tio' blos lar& a%ou'ts o+ ti'y ro(- a'd %a%a ,arti(l&s i'to th& at%os,h&r&. Th&s&

,arti(l&s (a' b& blo' hih i'to th& at%os,h&r& a'd (arri&d lo' dista'(&s by th& i'd. Th&y

o+t&' (aus& ,robl&%s +or air(ra+t o,&rati' do'i'd +ro% th& ol(a'o.

&oloy.(o%/ 201

B&lu% ada r&+&r&'si ,orositas disi'i/



CHAPTER III

METHOOLOGY

+.1 TIME AN PLACE

Os(illos(o,9s &,&ri%&'t ha& do'& o' Thursday/ 2;th !o&%b&r 201 i' laboratory o+

&o,hysi(al E'i'&&ri'

+.2 TOOLS AN MATERIALS

3.3.1 E LASTIC P ROPERTIES

Tools that us& i' this &,&ri%&'t ar& *iital "tora& Os(illos(o,& *"O BU

242N242B o'& s&t/ ArbitaryN Fu'(tio' &'&rators BU40;AQ o'& s&t/ *iital Multi

M&t&r BU270KB o'& s&t/ Br&ad Board V &,&ri%&'t (o%,o'&' U?# V (abl& o'& s&t/ o'&

o%,ut&rN la,to,/ *atash&&t Tools o'& s&t/ ="B/ a'd th& %at&rials ar& a ra'it& sto'& a'd

so'i( &ll.

3.3.2 D ENSITY OF ROCKS

Tools that us& to +i'd th& d&'sity o+ ro(-s is a olu%& lass ith %l or (( s(al&/ a

at&r a'd a &iht. Th& %at&rial +or this %&asur&%&'t is at&r a'd ra'it& ro(-s

+.+ EXPERIMENTAL PROCEURE

3.3.1 M EASUREMENT E LASTIC P ROPERTIES

"t&,s i' this &,&ri%&'t ar&/ b&+or& th& %&asur&%&'t/ b&+or& obs&r&d ro(- sa%,l&s

& %ust (ori' S th& ro(- ith a dia%&t&r o+ ; (% a'd th&' do ri'di' to s%ooth th&

sur+a(& o+ ro(-s. B&+or& &,&ri%&'t/ ,r&,ar&d os(illos(o,& a'd oth&r su,,ort &)ui,%&'t su(has ultraso'i( tools a'd ibrators. B&+or& usi' os(illos(o,&/ & %ust (alibrat& th&

os(illos(o,&/ a'd th&' th& os(illos(o,& (o''&(t&d to ultraso'i( a&. A+t&r that/ th& &%itt&r

a'd r&(&i&r a++i&d to th& s&(o'd a& o' a +lat sur+a(& ro(- sa%,l&s. Th&' do th& s&tti's

o' s(hal& ,lay&d i' th& > dir&(tio'/ th&' s&t th& ,uls& rat& so it ill b& s&&' th& 'u%b&r o+

+r&)u&'(i&s assi'&d to th& sto'&/ a'd s&t th& r&(&i& ai' to d&t&r%i'& th& 'u%b&r o+ r&(&i&

si'als (a,tur&d a%%a. Hai' obtai'&d th& a&+or%/ ,aus&d a'd sa&d to a ="B dri& to

&t a s(r&&'shot o+ th& os(illos(o,& s(r&&'. *&tail st&,s th& us& o+ osilos-o, as +ollos:

1. Butto's o'o++ i' a ,ositio' o++

2. #ut all a butto' that hai' thr&& ,ositio' o' a %iddl& ,ositio'3. Tur' th& -&y i't&'sity i' a %iddl& ,ositio'

4. Thrust butto's ,ull %a i'to to obtai' th& 'or%al ,ositio'

. #ush a butto' tri&ri' th& l&&l at th& auto

;. &t o' th& ir& (abl& ,o&r li'&s (o%%uti' b&t&&' to ada,t&r a(

7. Tur' th& -&y o'o++ i' a ,ositio' o'. A,,roi%at&ly 20 s&(o'ds lat&r o'& li'& o+ th&

li'& shall d&,i(t&d i' (rt s(r&&'. I+ this li'& has 'ot b&&' obs&r&d/ tur' th& -&y

i't&'sity (lo(-is&.

. "&t th& +o(us a'd i't&'sity to (lari+y th& li'&

K. Ma-& arra'&%&'ts ,ositio' r&,&at&d &rti(al a'd hori>o'tal i' a((orda'(& ith th&ir

'&&ds



10. &t ,rob& to th& i',ut (ha''&la N (ha''&l a (ha or to i',ut (ha''&lb N (ha''&l b

(hb as '&&d&d

11. &t o' th& ir& ,rob&s i'to th& t&r%i'al (al to obtai' th& (alibratio' 0/,,

12. Tur' lo&ri' &rti(ally &rti(al sy'(hro'i>atio' att&'uator / sit(h olts N di i'

10th % / a'd tur' th& -&y ariabl& (lo(-is& .Tur' tri&ri' sour(& to (ha / a&s

s)uar& +our s)uar&a& ill sho o' th& s(r&&'

13. I+ dis,lay a&s s)uar& +our l&ss tha' ,&r+&(t/ s&t tri%%&r hi(h is ith ,rob& to

%a-& sha,& a&s s&&'.

14. Mo& ,rob& +ro% t&r%i'al (al 0/,, .Os(illos(o,& ar& r&ady to us&

Th& data obtai'&d ar& th&' ,ro(&ss&d usi' so+tar& a,,li(atio's S &'au& diiti>&r S that

(o'&rts i%a&s .<,& i'to th& (oordi'at&s o+ th& (ur& .%l / a'd th&' (o'&rt&d to

E(&l data obtai'&d +urth&r (oordi'at& ra,h is ,lott&d i' (oordi'at& a'd y.

3.3.2 M EASUREMENT D ENSITY OF ROCKS

Q& (ould su%%ari>& this st&,s b&lo :

1. Q&iht th& %ass o+ th& ro(- a'd 'ot& th& r&sult

2. #our at&r i'to th& lass u'til r&a(h 200%l

3. #ut th& ro(-s i' th& lass a'd rit& th& (ha'& o+ th&

total olu%&

4. ou't th& d&'sity usi' &'&ral +or%ula

CHAPTER I/

ATA ANALYSIS



4.1 MEASUREMENT ATA

Fro% th& os(illos(o,& %&asur&%&'t & had so%& i'+or%atio' about +r&)u&'(y/ ti%&

,&riod/ l&'th o+ th& a& :

4.1 Tabl& *ata =ltraso'i( M&asur&%&'t

Qa& L % T, us F-H>

1 0/04 320

;17

2 0/04 420

3 0/04 32

4 0/04 40

0/04 420

; 0/04 400

7 0/04 400

Figur 4.1 O!"ill#!"#$ r!ul%

Fro% th& d&'sity %&asur&%&'t & a()uir&d that :

1.

M

ass o+ th& ro(- is : 27; ra%

2. 5olu%& o+ th& ro(- is : 100 %l

This %&asur&%&'t ar& usi' $T# # W 10at%/ T W 20 sta'dard

4.2 ANALYSIS ATA

Fro% th& data abo&/ & (ould +i'& a'oth&r ,hysi(al ,ro,&rti&s that i'+lu&'(& th&

(hara(t&ri>& o+ ro(- usi' this +or%ula:



1. V p=

L(m)

T ( s ) Qa&# 5&lo(ity

2. ρ=

m(gram)V (ml) *&'sity

3. λ=

V p (m /s)

f ( Hz) Qa&

l&'th

4. M = ρ (V p )2 o%,r&ssio'al

Qa& Modulus

. μ=( M − λ)

2 "h&ar

Qa& Modulus

;. K = λ+(

2

3 μ)

Bul- Modulus

7. υ=

λ

2( λ+ μ)

#oisso'9s $atio

. Vs=V p

υ Qa&" 5&lo(ity

4.2.1 D ENSITY C ALCULATION

K"9":

m=0.276kg

v=10−6

m3

A(k&#:

ρ=…?

A"(9&r&#:

ρ=m

v

ρ=0.276

10−6 =276000 Kgm

−3



4.2.2 P WAVE V ELOCITY C ALCULATION

K"9":

L=0.04 m

tp=0.000395 s

A(k&#:

Vp=… ?

A"(9&r&#:

Vp= L

tp

Vp= 0.04

0.000395=101.2658 ms

−1

Fro% th& data/ -'o' that +r&)u&'(y o+ th& a& is 5617000 Hz / so & (a' (al(ulat& th&

l&'th o+ a& ith:

¿ v

f

¿101.2658

5617000=1.808125 x10

−5m(s Hz)−1

4.2.3 C OMPRESSIONAL M ODULI C ALCULATION

K"9":

ρ=276000 Kg m−3

Vp=101.2658 ms−1

A(k&#:

M =… ?

A"(9&r&#:



Vp¿¿

M = ρ ¿

M =276000 x101.26582

=28303156155 Kg /m s2

4.2.4 S &EAR M ODULI C ALCULATION

K"9":

M =28303156155 Kg/m s2

¿ 1.808125 x 10−5

m(s Hz)−1

A(k&#:

μ=…?

A"(9&r&#:

μ=( M − λ)

2

μ=(28303156155−1.808125 x 10−5)2

=1415157827 Kg/s m2

4.2.' (ULK M ODULI C ALCULATION

K"9":

¿1.808125 x 10−5m(s Hz)−1

μ=1415157827 Kg/s m2

A(k&#:

k =… ?

A"(9&r&#:

k = λ+(2

3 μ)



k =1.808125 x 10−5+

2(1415157827 )3

=943438551.5 Kg/m s2

4.2.) P OISSON R ATIO C ALCULATION

K"9":

¿1.808125 x 10−5m(s Hz)−1

μ=1415157827 Kg/s m

2

A(k&#:

v=… ?

A"(9&r&#:

υ= λ

2( λ+ μ)

v= 1.808125 x10

−5

2(1.808125 x10−5+1415157827 )

=6.36977 x10−15

4.2.* S+A,E

, ELOCITY

C ALCULATION

K"9":

v=6.36977 x10−15

Vp=101.2658 ms−1

A(k&#:

Vs=…?

A"(9&r&#:

Vs=V p

υ

Vs= 101.2658

6.36977 x10−15

=1.58979 x1016

ms−1

All th& (o%,utatio' (ould b& r&ad at th& list&d tabl& b&lo



Tabl& 4.2 o%,utatio' *ata I

Qa& L % T, us T,s 5,%Ns + H>

1 0/04 320 0/00032 12

;17000

2 0/04 420 0/00042 K/231

3 0/04 32 0/00032

123/07;

K

4 0/04 40 0/0004 3/3333

3

0/04 420 0/00042 K/231

; 0/04 400 0/0004 100

7 0/04 400 0/0004 100

Total A&ra& 0/0003K

101/2;

Tabl& 4.3 o%,utatio' *ata II

V p (ms−1 ρ

-N%3

λ M

Kg/m s2¿

μ

Kg/m s2¿

K

Kg/m s2¿

υ Vs

ms−1¿

101/2; 0/00000027; 1/0E

0

23031; 1411727 K43431/ ;/3;K77E

1

0/;40K70

4.+ ATA R EFERENCE FROM LITERATUREdata a'isotro,y

r&+&r&'si ,orositas

ra+i- -or&lasi a'tara 5, d&'a' ,orositas da' d&'sitas

4.4 ISCUSSION O' this &,&ri%&'t th&r& th&r& ar& thr&& -i'd &,&ri%&'t. Elasti(

,ro,&rti&s/&o%&(ha'i(al/*&'sity.a(tually th&r& ar& 4 -i'd &,&ri%&'t but & ot li%it&d tool +or

%&asuri' ,orosity. "o & o'ly do thr&& -i'd o+ &,&ri%&'t. This &,&ri%&'t had +i& %ai'

ob<&(ti& as out,ut th&r& ar&/U! #!"ill#!"#$ %# m-!ur -/ $r#$r%i! u!i0g $-r-m%r #

%im -0 !-m$l im0!i#0M-!ur -0i!#%r#$ # /l#"i% u!i0g m#l # "-l"ul-%i#0D%rmi0 %5 rl-%i#0 6%0 ,$ i%5 0!i% -0 $#r#!i% M-!ur %5 6ulk

m#ulu! !5-r m#ulu! -0 $#i!!#0 r-%i# r#m %5 r#"k !-m$l D%rmi0 %5 %$ # r#"k

!-m$l 6-! #0 %5 7$rim0%.

Fu'da%&'tal %&asuri' th&ory +or this &,&ri%&'t is usi' &lo(ity o+ ultraso'i(

a& ,ro,aatio' i' ro(- %&diu%. =si' os(illos(o,& a'd ultraso'i( a&& had so%&

i'+or%atio' about +r&)u&'(y/ ti%& ,&riod/ l&'th o+ th& a& sho by Tabl& 4.1

4.1 Tabl& *ata =ltraso'i( M&asur&%&'t

Qa& L % T, us F-H>1 0/04 320 ;17



2 0/04 420

3 0/04 32

4 0/04 40

0/04 420

; 0/04 400

7 0/04 400

A'd +ro% th& d&'sity %&asur&%&'t & a()uir&d that :

1. Mass o+ th& ro(- is : 27; ra%

2. 5olu%& o+ th& ro(- is : 100 %l

This %&asur&%&'t ar& usi' $T# # W 10at%/ T W 20 sta'dard

A'd +or a's&ri' th& ,robl&% at ha,t&r 1 & us& di++&r&'t &)uatio' +or %&asuri' ,$ ,!

M#ulu! (ulk M#ulu! S5-r8g!r P#i!!#0 R-%i# 0!i% 5alu&. A'd & ot th& r&sult

shoi' by Tabl& 4.2 a'd Tabl& 4.3

Tabl& 4.2 o%,utatio' *ata I

Qa& L % T, us T,s 5,%Ns + H>

1 0/04 320 0/00032 12

;17000

2 0/04 420 0/00042 K/231

3 0/04 32 0/00032

123/07;

K

4 0/04 40 0/0004 3/3333

3

0/04 420 0/00042 K/231; 0/04 400 0/0004 100

7 0/04 400 0/0004 100

Total A&ra& 0/0003K

101/2;

Tabl& 4.3 o%,utatio' *ata II

V p

ms−1¿

ρ

-N%3

λ M (

Kg

ms2) μ(

Kg

m s2) K Kg/m s

2¿ υ Vs

ms−1¿

101/2; 0/00000027

;

1/0E

0

0/00230

3

0/00140;1 0/000K 0/00;32K

1,58979E

+16

+ro% r&sult tabl& 4.2 a'd tabl& 4.3 & (a' s&& alu& o+ 5,/ ρ /M/ C/ K/a'd 5s but & (a't

d&t&r%i'& ori&'tatio' %i'&ral b&(aus& th& %i'&ral is Fa'&riti- or u'abl& to s&& ithour %i(ros(o,&/

a'd & (a't d&t&r%i'& a'isotro,hy or isotro,hy ori&'tatio' b&(aus& & did'9t %&asuri' ith

di++&r&'t a'l&/& o'ly %&asuri' ith 1 a'l&.Th& alu& o+ 5, is d&,&'d o+ i't&r'al ,ro,&rti&s o+ ro(- hi(h is a'isotro,y/,orosity/a'd



d&'sity. I' (ha,t&r 2 & +ou'd that 5&lo(ity o+ i'&ous ro(-s shos a' i'(r&as& +ro% a(idN+&lsi(

to basi(N%a+i( ro(- ty,&s/ a'd 5&lo(ity d&(r&as& ith i'(r&asi' +ra(turi' or i'(r&asi'

,orosity/b&(aus& h&' ,orosity i'(r&as&s it %&a' th& d&'sity ill d&(r&as&s a'd &lo(ity ill

d&(r&as&s too b&(aus& alu& o+ &lo(ity d&,&'ds to d&'sity.+ra(turi' (r&at&s a hih&r

,r&ssur& s&'sitiity/ thus &lo(ity shos a disti'(t ,r&ssur& d&,&'d&'(&. I' this &,&ri%&'t& ar& usi' a'd&sit& ro(- hi(h is (at&ori>&d as i't&r%&di&t& I'&ous $o(- hi(h %&a'

th& sa%,l& had 5, 5alu& b&t&&' +&lsi( a'd %a+i( 5, alu&

CHAPTER /

CLOSING REMARKS

5.1 CONCLUSION

Fro% this &,&ri%&'t/ & ha& a (o'(lusio's list&d as b&lo :

1. Q& (a' +i'd th& alu& o+ 5, a'd 5s o+ a' ob<&(t by usi' os(illos(o,&.

2. Th& a&ra& alu& o+ 5, is 101/2; %Ns

3. Th& a&ra& alu& o+ 5s is 1/K7KEV1; %Ns

4. Th& alu& o+ #oisso'9s $atio is 0/00;32K

. Th& alu& o+ Dou'9s Modulus is 0/002303 Kg/m s2

;. Th& alu& o+ "h&ar Modulus is 1411727 Kg/m s2

7. Th& alu& o+ Bul- Modulus is 943438551,5 Kg

/m s

2

. Th& alu& o+ *&'sity is 2.7; -N%3

K. Th& 5alu& o+ #orosity r&+&r to th& lit&ratur& is

10. B&sar'ya a&, t&rhada, ,orositas

11. B&sar'ya a&, t&rhada, d&'sity

5.2 R ECOMMENATION

For th& '&t &,&ri%&'t/ & ha& s&&ral r&((o%&'datio's su(h as :

1. Th& '&&d +or assista'(& +ro% th& l&(tur&r or l&(tur&r assita'(& duri' th& &,&ri%&'t

2. Mor& d&tail&d &,la'atio' about st&, o+ &,&ri%&'t a'd usability o+ tool

3. "(h&dul& o+ ,hysi(al ,ro,&rti&s &,&ri%&'t should b& +i&d a'd th& stud&'t ta-& th&&,&ri%&'t



BIBLIOGRAPHY

Hol%&s/ . Q. 1K7. *istributi' o+ "&l&(t&d El&%&'t i' "ur+i(ial Mari'& "&di%&'t o+ th& !orth&r'

ul+ o+ M&i(o o'ti'&'tal "h&l+ a'd "lo,& . 9#l#gi"-l Sur/ / 3.

5%%$:88.66"."#.uk8!"5##l!8g"!6i%!i;8!"i0"8-<-8-/!8g0r-l-/!r/1.!5%ml . 201.

htt,:NN&oloy.(o%Nro(-sNa'd&sit&.sht%l isit at d&s&%b&r 201 i' 7.30 ,%

"ari/ *. !. t.th'.. #E!=U=$A! UEE#ATA! ELOMBA! " #A*A "AM#EL BAT=A!.

"(ho'/ . H. 2011. P&YSICAL PROPERTIES OF ROCKS : A +ORK(OOK. O+ord: Els&i&r B.5.

"(ho'/ . H. 201. P&YSICAL PROPERTIES OF ROCKS : FUDAMENTALAND PRINCIPLES OF

PETROP&YISICS SECOND EDITION. O+ord: Els&i&r B.5.

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