POLITEKNIK
POLITEKNIK TUANKU TUANKU SULTSULTANAH ANAH BAHIYAHBAHIYAH KEMENTERIAN PENGAJIAN TINGGI MALAYSIA KEMENTERIAN PENGAJIAN TINGGI MALAYSIA
KULIM HI-TECH PARK KULIM HI-TECH PARK
09000 KULIM KEDAH DARUL AMAN 09000 KULIM KEDAH DARUL AMAN
GEOTECHNIC LABORATORY
GEOTECHNIC LABORATORY
DEPARTMENT OF CIVIL
DEPARTMENT OF CIVIL
ENGINEERING
ENGINEERING
EXPERIMENT TITLE:
EXPERIMENT TITLE:
CONSOLIDATION (OEDOMETER TEST)
CONSOLIDATION (OEDOMETER TEST)
GROUP NO:
GROUP NO:
3
3
LECTURER’S NAME:
LECTURER’S NAME:
PN. NADHIRAH
PN. NADHIRAH BT.
BT. NOR ZELAN
NOR ZELAN
N
NA
AM
MA
A
N
NO
O.
.
M
MA
AT
TR
RIIX
X
AHMAD FA
AHMAD FAHMI BIN GHAZALI
HMI BIN GHAZALI
16DKA13F1049
16DKA13F1049
M
MO
OH
HA
AM
MA
AD
D F
FA
AK
KH
HR
RI
I B
BIIN
N M
MO
OH
HD
D R
RO
OD
DZ
ZII
1
16
6D
DK
KA
A1
13
3F
F1
10
0
1
1
M
MU
UH
HA
AM
MM
MA
AD
D F
FA
AIIZ
ZU
UA
AN
N B
BIIN
N R
RA
AM
ML
LII
1
16
6D
DK
KA
A1
13
3F
F1
10
0!
!
ALE" RAO A
ALE" RAO A#L FRANCIS
#L FRANCIS
16DKA13F1043
16DKA13F1043
M
MU
UH
HA
AM
MM
MA
AD
D A
AZ
ZR
RI
I B
BIIN
N N
NO
OO
OR
R S
SH
HA
AH
H H
HIIZ
ZA
AL
L
1
16
6D
DK
KA
A1
13
3F
F1
10
03
39
9
ABDULLAH BIN A
ABDULLAH BIN ABDUL RAHMAN
BDUL RAHMAN
16DKA13F1061
16DKA13F1061
MO
MOHA
HAMM
MMAD
AD SH
SHAH
AHRU
RUL
L HA
HAZR
ZRIN
IN BI
BIN M
N MAH
AHAD
AD HA
HAMD
MDII
16DK
16
DKA1
A13F
3F1
11
11
19
9
N
NU
UR
RU
UL
L S
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A B
BIIN
NT
TI
I S
SA
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L A
AZ
ZH
HA
AR
R
1
16
6D
DK
KA
A1
13
3F
F1
10
0!
!0
0
%
%A
AN
NN
N S
SH
HA
AR
RF
FR
RIIN
NA
A B
BIIN
NT
TI
I A
AB
BD
DU
UL
L H
HA
AL
LIIM
M
1
16
6D
DK
KA
A1
13
3F
F1
10
0
TABLE OF CONTENTS TABLE OF CONTENTS
1.0
1.0 OBJOBJECTECTIVEIVESS 2.0
2.0 THEOTHEORY BARY BACKGROUCKGROUNDND 3.0
3.0 EUEUIPMIPMENTENTSS !.0
!.0 PROPROCEDCEDUREURESS ".0
".0 RESULTRESULTS AND SAMPLE CALCS AND SAMPLE CALCULATULATIONSIONS #.0
#.0 DISDISCUSCUSSIOSIONN $.0
$.0 CONCONCLUCLUSIOSIONN %.0
%.0 REFREFEREERENCENCESS
1.0
1.0 OBJOBJECTECTIVEIVESS
1.
1. TT& & '*'*+, +, /&+/&+*,*,2,, 2,, .. 5.
2.0 THEORY BACKGROUND 2.0 THEORY BACKGROUND
C&&,',& , *'8 *'8/,& , :&8+ &7 78 8*' &, &7 &; C&&,',& , *'8 *'8/,& , :&8+ &7 78 8*' &, &7 &; *+2,, '8 & '*, &7 &+ &7 &* ;* 8'* ,/,& *+2,, '8 & '*, &7 &+ &7 &* ;* 8'* ,/,& &7 /& :*,/ &'< &* *+&: &7 *&8' ;* ;,/ /8 &7 /& :*,/ &'< &* *+&: &7 *&8' ;* ;,/ /8 ;* 2 & &;*. T, &7 &//8* , / * &* ;* ;, ;* 2 & &;*. T, &7 &//8* , / * &* ;* ;, *
77/,: *. T *&/ &7 /&&,',& /&,8 8, ?/ &* 77/,: *. T *&/ &7 /&&,',& /&,8 8, ?/ &* ;* *8* 8 2 ,/* , & * /&+ ',,'. ;* *8* 8 2 ,/* , & * /&+ ',,'. T ,+ / , &7 &-',+,& /&&,',&< , ;,/ >*& * T ,+ / , &7 &-',+,& /&&,',&< , ;,/ >*& * *, , 8+'.
*, , 8+'.
C
C&&&&,,'',,&& ++ , , ::**,/,/ '',,//++ &7 &7 8*8*77// /&**&', & :&8+ / &7 /&&,',& *&/. /&**&', & :&8+ / &7 /&&,',& *&/. C&&,',& + + 2 *8'< 7&* ?+< ,7 *8/8* , 28, &:* C&&,',& + + 2 *8'< 7&* ?+< ,7 *8/8* , 28, &:* * &7 8*' / &* ,7 ;* 2 , &;*' *+ , *8+ * &7 8*' / &* ,7 ;* 2 , &;*' *+ , *8+ &:*, / *. I / , ;,/ ,,7,/ * *, @
&:*, / *. I / , ;,/ ,,7,/ * *, @ /< */< * ;, 2 ,++', + '8 & '7&*+,& &7 &, 8'* 8'*,' ;, 2 ,++', + '8 & '7&*+,& &7 &, 8'* 8'*,' /&',,&< , '',,& & /&&,',& +. T *',/,& &7 2& /&',,&< , '',,& & /&&,',& +. T *',/,& &7 2& +
+,,8'8' ' ' ** &7 &7 /&/&&&,',',&,& ++ ** &7 &7 ** ,,** '' ,+&*/ & &/,/ ,* & & 8* *:,/2,, ,+, ,+&*/ & &/,/ ,* & & 8* *:,/2,, ,+, &7 *8/8* 2, 28, *
&7 *8/8* 2, 28, * ,7,'.,7,'.
U8< /&&,',& *&/ 7&* &, * / 2 ',:,'' ,& 3 +, U8< /&&,',& *&/ 7&* &, * / 2 ',:,'' ,& 3 +,
Primary Primary Settlement Settlement Secondary Secondary Settlement Settlement Initial Initial Settlement Settlement Time Time Settlement Settlement •
• T ,/ *,,& &7 S+ ;, T,+T ,/ *,,& &7 S+ ;, T,+
1.
1. II,,,, S S++
T, /&**&' & / , ,/@ &7 &, * &+ &7 T, /&**&' & / , ,/@ &7 &, * &+ &7 &/@ *' , &, * =8>' &8 ,++', 8& &/@ *' , &, * =8>' &8 ,++', 8& '',,& &7 &' 8, &, 2/&+ 8*'. A , &* ;* '',,& &7 &' 8, &, 2/&+ 8*'. A , &* ;* , & =8
, & =8>' &8. >' &8. H/H/< '',,< '',,& && &' , @ 8 2 &*' , @ 8 2 &* ;* *8*.
;* *8*. 5.
5. P*P*,+,+* * SS++ A
A , , < < &* &* ;* ;* *8* *8* , , *'8 *'8 ',,' ',,' ;* ;* ,, =8>' &8< *8, , *'8/,& , ,/@ ; :&,' *,& =8>' &8< *8, , *'8/,& , ,/@ ; :&,' *,& &7 &,
&7 &, /,+. /,+. T '',,&T '',,& &' ;, 2 &' ;, 2 *'8 2 *'8 2&* 2 &* 2 &, *,/.
&, *,/.
3.
3. SS/&/&''* S* S++
T, , /&=8/ &7 /* &2 ,* ; , &*,+ &7 ,+. T, , /&=8/ &7 /* &2 ,* ; , &*,+ &7 ,+.
Vo
Void rid ratio,atio, ee
Increasing applied pressure Increasing applied pressure
Log
Log1010 (Load) (Load)
•
• A A * &7 :&,' *,&* &7 :&,' *,& ee , & , &1010 (&'). (&').
T :,*, /&+*,& /8*: 7&* &, + , */,/ *, , T :,*, /&+*,& /8*: 7&* &, + , */,/ *, , ;,/ /&**&' & &', /8*: 7&* / &, *. I7 &' , ;,/ /&**&' & &', /8*: 7&* / &, *. I7 &' , &;' & *'< /8*: ;& */ 2/@ & &*,, /8*: 28 ;, */ &;' & *'< /8*: ;& */ 2/@ & &*,, /8*: 28 ;, */ &* /8*: ;, * &. T, /8*: , @&; 8&', /8*: &* /8*: ;, * &. T, /8*: , @&; 8&', /8*: ' &, + , ,' & 2 &:*-/&&,''. T 77/,: * ' &, + , ,' & 2 &:*-/&&,''. T 77/,: * ,
,**//,,& & 22;; :,:,**, , ' ' 88&&'',, /8/8*:*: , , @@&;&; **- -/&+*,& *.
/&+*,& *.
I7 + + , &'' ,< /8*: ;, 7&&; 8&', /8*: ' I7 + + , &'' ,< /8*: ;, 7&&; 8&', /8*: ' & 2/@ & :,*, /8*: ,' * ,/*. T '* &7 & 2/@ & :,*, /8*: ,' * ,/*. T '* &7 /&
/&&&,',',&,& 7&7&* * &:&:**-/-/&&&&,,''' ' &&, , , , +8+8/ / &7 &7 8
8',',8*8*22' ' &&,, // , , , , 77* * 7&7&* * 8 8 & & 2828,,' ' *8*8//8*8* &:&:* * &:&:* *--/&&,'' &,.
/&&,'' &,.
T& =8,7 /&+*,2,, &7 &,< ;& /&77,/, * ,*&'8/'< + T& =8,7 /&+*,2,, &7 &,< ;& /&77,/, * ,*&'8/'< +
/&/&777,7,/,/, &7 &7 :&:&88+ + // mmv v ' ' /&/&++**,&,& ,,''?? C C c c . . TT
/&77,/, &7 :&8+ / , '7,' * &7 / &7 :&,' *,& ;, /&77,/, &7 :&8+ / , '7,' * &7 / &7 :&,' *,& ;, */ & / , 77/,: * ;, /&+*,& ,'? *7* & */ & / , 77/,: * ;, /&+*,& ,'? *7* & * &7 / &7 :&,' *,& ;, */ & / , &*,+,/ :8 &7 * &7 / &7 :&,' *,& ;, */ & / , &*,+,/ :8 &7 77/,: *.
:8 7&* :8 &7
:8 7&* :8 &7 77/,: *.77/,: *.
T *&* &7 /&&,',& ,-,8 / 2 +&,&*' 2 ,, ,>&+* T *&* &7 /&&,',& ,-,8 / 2 +&,&*' 2 ,, ,>&+* & */&*' / , &* ;* *8* ;, ,+ ;, +,8' &7 & */&*' / , &* ;* *8* ;, ,+ ;, +,8' &7 + / 2 +8*' 2 */&*', : &7 8,2 *7*/ &, + / 2 +8*' 2 */&*', : &7 8,2 *7*/ &, & *8/8*. T /&+*,2,, /*/*,,/ &7 &, *, 2& & & *8/8*. T /&+*,2,, /*/*,,/ &7 &, *, 2& & +&8 ' * &7 + '8*, &-',+,& /&&,',& / & +&8 ' * &7 + '8*, &-',+,& /&&,',& / & 2 '*+,' , 2&*&* 2
2 '*+,' , 2&*&* 2 &'&+* .&'&+* .
A
A &, /,+ , 7&*+ &7 ',/< &, /,+ , 7&*+ &7 ',/< /&' , + /&7,, *,/&' , + /&7,, *, ;,/ ;,/ +&& &,' 8*7/ & *'8/ ,' 7*,/,&< , ';,/' 2; 5 +&& &,' 8*7/ & *'8/ ,' 7*,/,&< , ';,/' 2; 5 &*&8 & ',/. T &;* &*&8 & ',+* , ** &*&8 & ',/. T &;* &*&8 & ',+* , ** &7 + *,< ;, 8* & , +* ' / / +&: &7 + *,< ;, 8* & , +* ' / / +&: ,,'
,,' *, ;, *, ;, + /*+ /*//. A + &',. A + &', / , / , 7,?7,?' ' & & & & &7 &7 8* &*&8 &. T ;& +2 , /' , & / &7 ;* & 8* &*&8 &. T ;& +2 , /' , & / &7 ;* & ;,/ &* ;* , /,+ 7* //. A :*,/ ,/ &' , ;,/ &* ;* , /,+ 7* //. A :*,/ ,/ &' , ,' *&8 :* + , &', 7*+. U'* /&',,& &7 ,' *&8 :* + , &', 7*+. U'* /&',,& &7 >*& * *, (,+&' 2 + /&7,, *,)< /&+*,& &7 >*& * *, (,+&' 2 + /&7,, *,)< /&+*,& &7 &, /,+ 8'* *8* , +8*' 2 + &7 ',/+ ', &, /,+ 8'* *8* , +8*' 2 + &7 ',/+ ', 8 &*, & &', /.
8 &*, & &', /.
T *&/'8* , '*',>' , BS 13!! (P* ) 4. T ,,, *8* T *&/'8* , '*',>' , BS 13!! (P* ) 4. T ,,, *8* ,' ;, '' & &7 &,. T =8/ &7 *8* , ,' ;, '' & &7 &,. T =8/ &7 *8* , ,' & /,+< / 2, '&82 *:,&8 :8. I ,
,' & /,+< / 2, '&82 *:,&8 :8. I , &' 7&* &' 7&*
,, &,&, ++ &2&2,,' ' 7*&7*&+ + ,,< < 8+8+2* 2* ' :8 ' :8 &7 &7 &' &' ,/*+ ;, '' & &7 &, ; & * &7 * ,/*+ ;, '' & &7 &, ; & * &7 *
,/,' & ,. T *8* ,' 7&* 7,* &8' &*+ 2 ,/,' & ,. T *8* ,' 7&* 7,* &8' &*+ 2 =8 & ,-,8 :*,/ * ' 7*&+ ;,/ + ; =8 & ,-,8 :*,/ * ' 7*&+ ;,/ + ; &2,'. U8< / *8* , +,,' 7&* *,&' &7 54 &8*< ' , &2,'. U8< / *8* , +,,' 7&* *,&' &7 54 &8*< ' , &+ ?/,& / *,&' &7 4 &8* + 2 *=8,*'< & &+ ?/,& / *,&' &7 4 &8* + 2 *=8,*'< & /,+ , 78 /&&,''. C&+*,& *', * &2*:' 8,2 /,+ , 78 /&&,''. C&+*,& *', * &2*:' 8,2 ,*: '8*, *,&'.
,*: '8*, *,&'.
A
A ' ' &7 &7 ,/*+ ,/*+ *,&'< *,&'< ; ; ?/ ?/ &* &* ;* ;* *8* *8* /&+ ',,'< ,' *8* ;, =8 & 77/,: :*,/ /&+ ',,'< ,' *8* ;, =8 & 77/,: :*,/ *
* , /,+ , /,+. . A7A7* 78 /&&* 78 /&&,',&,',& , , */*/' 8'* 7,' 8'* 7, &'< &'< &' , *+&:'< ,* , & &* , :* < ' + , &;' &' , *+&:'< ,* , & &* , :* < ' + , &;' & ;. T ?,& &7 /,+ '8 & *+&: &7 7, *8* & ;. T ?,& &7 /,+ '8 & *+&: &7 7, *8* , +8*'. T ,- ;, *,&' ,+ 2 /,+ & , +8*'. T ,- ;, *,&' ,+ 2 /,+ & 2,,> 27&* 7, ;* /& , '*+,'. O*;,< ;, +, 2,,> 27&* 7, ;* /& , '*+,'. O*;,< ;, +, &//8* /,+ , 2, *+&:' 7*&+ &'&+* ' 8 ' & &//8* /,+ , 2, *+&:' 7*&+ &'&+* ' 8 ' & **&*.
**&*.
T *8 7*&+ / ,* 2 *' 2 &, ,/@ (&* T *8 7*&+ / ,* 2 *' 2 &, ,/@ (&* */ / , ,/@) &7 /,+ &* :&,' *,& ' &7 */ / , ,/@) &7 /,+ &* :&,' *,& ' &7
/ / ,/,/*+*+ *,&*,&' ' ,, /&*/&***&&',', 7777//,: ,: ** , , ,,* * 8* &* &*,+,/ /. T :&,' *,& ' &7 / ,/*+ *,&' 8* &* &*,+,/ /. T :&,' *,& ' &7 / ,/*+ *,&' / 2 //8' 7*&+ ', 8 *', ' ,* ;* /& &* / 2 //8' 7*&+ ', 8 *', ' ,* ;* /& &* '* ;, &7 /,+ ' &7 7&&;
'* ;, &7 /,+ ' &7 7&&;
h h s s Soilds Soilds h h o o ∆ ∆hh h h 1 1 Water Water
P D,*+ P D,*+
(1
(1)) %%* * /&/& + +88**' ' ' ' &7 &7 w w f f
&
&,' *,& ,' *,& ' &7 (8+,' &7 (8+, S S r r 110000)) eef f w w f f GGss
T
T,/,/@@ &7 &7 /,/,++ * * &7 &7 hh0 0
C
C ,, ,,//@@ ''88**,, ∆∆hh
&&,,' ' **,,& & ** &&7 7 eeii eeff++ ∆∆ee
;* ;* s s s s o o ii h h h h h h ee == −− s s s s f f h h h h h h ee == 11 −− s s s s o o s s s s s s s s o o f f ii h h h h h h h h h h h h h h h h h h h h h h ee ee ee== −− == −− −− −− == −− == ∆∆ ∆ ∆ 11 11 o o ii h h ee h h ee ++ = = ∆ ∆ ∆ ∆ 11 I + ;<
I + ;< ∆∆ee / 2 //8' 8 & / 2 //8' 8 & ' &7 ,/*+ *,&'. ' &7 ,/*+ *,&'.
(5
(5)) DD* * ;;,, + +8*8*' ' ' &' &7 7 W W (,.. ;, &7 &,')
(,.. ;, &7 &,') T
T,/,/@@ ' &' &7 7 ,,/*/*++ **,&,&'' hh11
A* &7 /,+
A* &7 /,+ A A E
E==88,,:: ,,//@@ &&7 7 &&,,''
w w s s A A W W h h ργ ργ = =
II,,,, ::&&,,' ' **,,&& s s s s o o ii h h h h h h ee == −− F
F,, ::&&,,' ' **,,&& == 11−− == 11 −−11
s s s s s s f f h h h h h h h h h h ee G*
G* &7 &7 :&:&,' *,' *,&,& ee 77* * /&/&&&,',',&,& ,, 7777//,: *,: * σ σ ’’ 7&* 7&*
8*' / / 2 &'. T * &; ,,, /&+*,& 7&&;' 8*' / / 2 &'. T * &; ,,, /&+*,& 7&&;' 2 ?,& ' */&+*,&. T &7 /8*: * *' & 2 ?,& ' */&+*,&. T &7 /8*: * *' & * ,&* &7 /. T
* ,&* &7 /. T ee - &- & σ σ ’’ *,&, 7&* &*+ /&&,'' *,&, 7&* &*+ /&&,''
/ , ,* ' , /' :,*, /&+*,& ,. T */&+*,& /8*: / , ,* ' , /' :,*, /&+*,& ,. T */&+*,& /8*: 8,+
8,+ J&, J&, :,*, /&+*:,*, /&+*,& , ,& , 78*78** * /&+/&+*,*,& & &//8* &//8* & :,*, ,. D8*, /&+*,&< / , &, *8/8* /&,8&8 & :,*, ,. D8*, /&+*,&< / , &, *8/8* /&,8&8 @ / ' / '& & *
@ / ' / '& & *:* & &*,, :* & &*,, *8/8* '8*, ?,&.*8/8* '8*, ?,&.
T /&+*,2,, &7 / / 2 **' 2 /&+*,& ,'? T /&+*,2,, &7 / / 2 **' 2 /&+*,& ,'? C C c c <<
;
;,,/ / , , && &7 &7 ,,* * &*&*,,& & &7 &7 ee - - && σ σ ’’ && ' ' ,,
',+,&. F&* ;& &, & ,*
',+,&. F&* ;& &, & ,* &*,& &7 &<&*,& &7 &<
T ?,& * &7
T ?,& * &7 ee - &- & σ σ ’’ & / 2 *&?,+' & *, ,< & / 2 *&?,+' & *, ,<
& &7 ;,/ ,
& &7 ;,/ , *7**' & ?,& ,'?*7**' & ?,& ,'? C C ee..
T :8 &7 /&77,/, &7 /&&,',&<
T :8 &7 /&77,/, &7 /&&,',&< C C V V ,,7&* *,/8* *8* ,/*+ ,7&* *,/8* *8* ,/*+ ,
&'&+* / 2 '*+,' 2 /&+*, /*/*,,/ &7 &'&+* / 2 '*+,' 2 /&+*, /*/*,,/ &7 ?*,+ ' &*,/ /&&,',& /8*:< *&/'8* 2, *7**' ?*,+ ' &*,/ /&&,',& /8*:< *&/'8* 2, *7**'
)) // log( log(σ σ 11'' σ σ 00'' f f ii C C ee ee C C == −−
& /8*: 7,,.
& /8*: 7,,. O +&' & '*+, /&77,/, &7 /&&,',& , *O +&' & '*+, /&77,/, &7 /&&,',& , * &&&& ,+
,+ ++&' &' '8'8 & & TT&*&*. . T T ',', 88 **',', * * &&' ' ,, =8* *&& &7 ,+ , +,8 ' :* '* &7 /&&,',& , =8* *&& &7 ,+ , +,8 ' :* '* &7 /&&,',& , =8* *&& &7 ,+
=8* *&& &7 ,+ 7/&*.7/&*.
T
T &&**,,// /8/8*:*: , , ,,* * 8 8 & & 22&8&8 6060 /&/&&&,',',&,& ' ' 9090 /&&,',& 2/, , 1.1 ,+ 2/, &7 *&'8/,& &7 /&&,',& 2/, , 1.1 ,+ 2/, &7 *&'8/,& &7 ,* * &7 /8*:. T, /*/*,,/ , 8' & '*+, &, & ,* * &7 /8*:. T, /*/*,,/ , 8' & '*+, &, & ?*,+ /8*: /&**&', &
?*,+ /8*: /&**&', & U U 90. 90.
T
T ??*,*,++ /8*/8*: : 8888 /&/&,, &7 &7 &&* * /8*/8*: : ****, , ,,,,,, /&+*,&< ,* * ' /&' /8*:. T &, /&**&', &
/&+*,&< ,* * ' /&' /8*:. T &, /&**&', & U U 00 , &2,' 2 *&'8/, 2/@ ,* * &7 /8*: & &*', >*& , &2,' 2 *&'8/, 2/@ ,* * &7 /8*: & &*', >*& ,+. A *, , , '*; :, 2/, 1.1 ,+ /&**&', ,+. A *, , , '*; :, 2/, 1.1 ,+ /&**&', 2/, & ,* * &7
2/, & ,* * &7 ?*,+ /8*:. T ,*/,& &7 ,?*,+ /8*:. T ,*/,& &7 , DE ;, ?*,+ /8*: &/ &, /&**&', &
DE ;, ?*,+ /8*: &/ &, /&**&', & U U 90 ' 90 ' /&**&', :8
/&**&', :8 t t 9090 / 2 &2,'. T :8 / 2 &2,'. T :8 T T 90 90 /&**&', & /&**&', & U U
90 ,
90 , 0.848 0.848 ' /&77,/, &7 /&&,',& , ,: 2 ' /&77,/, &7 /&&,',& , ,: 2
90 90 !"! !"! ## 0 0 t t d d C C vv == ;* ;* d d L &7 '*, L &7 '*, t
t 90 90 T, T,+ 7&* 90 /&+ 7&* 90 /&&,',& 7&* / &,',& 7&* / &' ,/*+&' ,/*+
3.0 APPARATUS 3.0 APPARATUS
1.
1. C&C&&&,',',&,& CC
I , & @&; &'&+*. I /&, &7 + *, , ;,/ &, I , & @&; &'&+*. I /&, &7 + *, , ;,/ &, /,+ , 7&*+ &7
/,+ , 7&*+ &7 ',/ , /&'. T /,+ , /' 2; 5',/ , /&'. T /,+ , /' 2; 5 &*&8 & ',/< ;, 8* & :, ',+* , +* &*&8 & ',/< ;, 8* & :, ',+* , +* &7 + *, ' &;* & , **. A &', / , /' &7 + *, ' &;* & , **. A &', / , /' & &. T ;& +2 , /' , & / &7 ;* & ;,/ & &. T ;& +2 , /' , & / &7 ;* & ;,/ &* ;* ,
&* ;* , /,+ 7* // '8*, ./,+ 7* // '8*, .
5.
5. 0.00.005+05++#'+#',:,:. . D,D, G G88
I , 8' & +8* / , ,/@ (&* /&+*,&) &7 &, I , 8' & +8* / , ,/@ (&* /&+*,&) &7 &, +. I , /&/' & /&+8* ' *', * @ , *8* ,+ +. I , /&/' & /&+8* ' *', * @ , *8* ,+ ,*:.
,*:.
3.
3. L&L&'',, F*F*++
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!.0 PROCEDURE !.0 PROCEDURE
1.
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5. F, F, *, *, ;, ;, *+& *+&8'' 8'' &, &, ' *-' *-;,;,.. 3.
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N& PP& & 88 **'',, ;;* * ,, ==88* * *&*&& & &7 &7 ,,+ + *&/'.
*&/'. 6.
6. A7* A7* &' 2 &' 2 & 7& & 7&* &8* &8*< @ *< @ 7, 7, 8 *8 *',',<< /&' &' ,/*+ ' @ *', 27&*.
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!. RR ' ' 6 6 88,, 7&7&&&;,;, & &' :' : 22 ,,' & ' & +
+
5< 0< 100 ' 500@P. 5< 0< 100 ' 500@P.
N& 102. & * *
N& 102. & * * =8,: & 100@P & +.=8,: & 100@P & +. .
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&7 + ;, 7,* * ' *-;,. 9.
9. P/P/ + + , &: , &: 7&* 7&* 54 &8* 54 &8*< *+&: 7*< *+&: 7*&+ ' *-;&+ ' *-;,.,.
".0 RESULT AND SAMPLE CALCULATION ".0 RESULT AND SAMPLE CALCULATION
II* D* D,,++* &* &7 R7 R,, ( (++)) 00..00!!6633 H
H,, &&7 7 RR,, ((++)) 00..0011 C*& S/,& A*
C*& S/,& A* A A (+ (+55)) 00..000044!!5533
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m
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;* ee :&,' *,& :&,' *,& S
S r r '* &7 8*,& '* &7 8*,&
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M
M &&7 7 '',,/ / ;; &&,, **,, (()) 3311!!..44 331166.. 331144..66 3311..99 M
M &&7 7 '',,/ / ''** &&,, **,, (()) 5566..44 5566!!..55 556633..44 556699..!! M
M &&7 7 **,, (()) 9911..99 9955..33 9955..99 9944..33 M
M &&7 7 ;;* * ,, &&,, (()) 4499..00 4499..33 11..55 4466..55 M
M &&7 7 ''** &&,, (()) 110066..11 110000..99 9944.. 110000..11 %* /&
%* /& w w 11(()) 4466..1133 44..6600 44..0000 4466..1144
F, :&,' *,&
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2.
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S++ AA BB CC DD
L
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D* %, &7 S+ W W ((NN)) 11..004400 00..999933 00..9955999999 00..991199 C*& S/,& A*
C*& S/,& A* A A (+ (+55)) 00..000044!!5533
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E=8,: H, hhss((++++)) ..!!6655 ..3355!!44 !!..554400 ..55661144
T
T2 3 T 2 3 T //8' =8,: , &7 //8' =8,: , &7 &, &,'. &, &,'.
S
S++ 11 55 33 44
L
L&&' ' ((@@PP)) 55 00 110000 550000 T,+
T,+ t t ( (++,,)) SS==88** **&&&& &&7 7 ,,++ t t
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9 9 33..00 --00..331155 --00..!!!! --11..!!!! --11..9955 1 155..55 33.. --00..331166 --00..99!! --11..4444 --11..9999 1 166 44..00 --00..335500 --00..661111 --11..00 --55..0011 5 500..55 44.. --00..335544 --00..665511 --11..990044 --55..003355 5 5 ..00 --00..3355 --00..663300 --11..991166 --55..004400 3 366 66..00 --00..333300 --00..663399 --11..995566 --55..0044 4 499 !!..00 --00..333355 --00..6644!! --11..993355 --55..0044 6 644 ..00 --00..333344 --00..6633 --11..993366 --55..006600 11 99..00 --00..334455 --00..66 --11..9933 --11..9955 1 10000 1100..00 --00..334455 --00..66!! --11..994400 --11..993355 F F,, ++ '' ** --00..334466 --00..666699 --11..9955 --11..9933 A7* *2&8' A7* *2&8' 0.0560.056 -0.5!5-0.5!5 -1.496-1.496 -1.595-1.595 T T2 4 T 2 4 T /8 ',/+ /8 ',/+ /&**&', ,+ '8*, ./&**&', ,+ '8*, .
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G* 5 T * &7 /&+*,& , =8* *&& &7
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G* 3 T * &7 /&+*,& , =8* *&& &7 ,+ 7&* + C.,+ 7&* + C.
G* 4 T * &7 /&+*,& , =8* *&& &7
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-I*/ &7 I,, S*, L, P&*,& (++)
(++)
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F
F,, CC&&++**,,&& 77* * RR22&&88' ' ((++++)) 00..005566 --00..55!!55 --11..449966 --11..559955 C&**/' C&+*,& 7* R2&8'
C&**/' C&+*,& 7* R2&8' hh0 0
(++) (++)
0
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+. +.
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T / , :&,' *,&
T / , :&,' *,&δ δ ee / 2 &2,' 2 / 2 &2,' 2 7&&;, ?*,&7&&;, ?*,&
s s o o ee h h h h δ δ δ δ == ;* ;* δ δ hhoo C , ,/@ &7 C , ,/@ &7 /,+/,+ h
hss H, &7 &,' , /,+ H, &7 &,' , /,+
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S++ AA BB CC DD
L
L&&'',, ((@@PP)) 55 00 110000 550000 C&**/' C&+*,& 7* R2&8'
C&**/' C&+*,& 7* R2&8' hh0 0
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I,, :&,' *,&
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L
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