Bài tập lớn thiết kế nền mặt đường oto, đường cấp 3, vùng núi, số liệu thiết kế đã cho như trên

 !"#
$%&'


 !"#$%&'() *'+, /0*1+
234/3- 56/-*7'8. 9/9 !: ;#<%
*=. >+?$9. ? ;* !+#&@A?. 5*1*A /@A?
 "B *& *&CDA*2<6%(*=3 *13EF /0#8(GGD!: ;#A
<&D +0<H* =<(GGD;? I*&+H A* ?J/0$A 2 *1+K+G
 7 /*1 *=H=/!"#$%?,. G*;L?#&+,+5(G$-*
"#M
N. G*2 +C/;*DO**8D*&DO*,<
 /0*1+E(*8+ >K+AH GP B;*(*=$; Q4<(*=$;L<
(*=$;$R$ >+HSJ+B T$ *13<U *. G*2@64 >+
%??$9. ? ;*('DT@A!:3C B((0< B;/= )(?
!:E/ *& *&F5VA3/64 >+%#. G*W A#X* :*'+
H*1 **=<H W 0+<4. G*$/0#7+Y/0*1+/ 
$;('DTDT. G*;*'+H*1 ? A -DAH Z*. ,!: ;#[
N\T. G*(GGD;L3(). Q 7> 8*GD64G
P<*GD62H *!: ;#$2"ALB3!: ;#<*GD*&+ A *&
*1+/HS$*+X* ]/?. 9^F"#D3#&+,+/D3. 5 -
K+A]8 ;*?  /0G*F22*&K+A T _/-*3?/
=+3 7. DT$`(>(*=$;"#U*aD<((0<Xb
8(GGD3(). QH * *=H=. G* *&4+ ]H=7+,DT W
L.C 7? ('DTE/ Yc-=?(*1. ?.Hd +0/ 1
 *F
Ne'DT?. G*2@3 ?D 7> C 7H **DAE8"
A 16B(?D*VA(? !:/DT;*'+H*1B !: ;#A/-*B
3A/ L., *=2 8$f!: A  2Fg&+,+#h
 @#=+. 9 +3/*1 ] &DT@AH=7+?/2 H 
2D"+ +i/-*#&+,+/'3(). Q< *hj* Z*. G* ?-

DT 0 A [
N6G6* W(9*BFe9*$!:3. ? ;*<(DjDT
[(9*D*GD,D <"#?$9!7+=  H ? /  2A<?(3
. 0D?#D2@A!:/D(kD*F
(l
 !"#
 . G*Yhj* Z*?2,#@. kD 7?.4?
#&+,+2*&D3? B 7</ /0#6_7BHSD< 7H *3/0
G*j 7.Fm2* *=H=. G*!+7. ?f#&+,+ %=<c nA!"#$%
b8AA VH=7+DT W  L. aADR?D43H ?
 A+?#&+,+2*&F

No G*+" :+#&p *=H=X 8'?<4D]*
 L.. G* Y]?(*1. ?."A3/6%X> 3
@AH +/%?$98;*'+H*1 '7 AD*A >+%^/-*?
=D4B*A<f2*GDL('$#?/ ;*?  !"#$%F
U *<j. G*6q$9?(*1. ?.X L.H ? A+C(*1. ?.6q$9/0
*1+/X L.?  . ,/0*1+<(*1. ?. ?- ? 2H GP(>
-!"D 0.bE8 ; =??$9@AkD/ *1=3/3('
@ADO*,< H=7+?/T(*1(*1. ?. ; =? *1
L. ? ;*('DTB*/-* DT&^$!: ;#"#AF
No G* ]/(BWY?,< /0*1+H=7+?6A 
. ^ L./-* 4P@ADO*,< /(GGDGH=7+?.4L V
#&+,+5(G :D9lFrFlU *. ^ L./-*H GP+4/0*1+<H G
P */H GPH A* ?$+#+<6qA VA<(G6A+#F
No G*6q$9B*A?/0*1+/. = G* *1.;* OC6q$9%
*=. T2*AB Y() 7H=$W /5 T V+5EF*A<. G* Y
]/0$9?H*  *1D/'!"#$%/H A* ??*'+H*19
 8@A>A. 5*K+AF
N,'!+7fs=r. 5?7+;H=7+?F *'!+7?

. 5? *=H=,. G* Y]=#&+,+(G/1D*<#&+,+(G
GDA*A /G#&+,+/'(G/164H t<(GGDA *
 *F
N,!S=. 5?. "Hu,+ *=H=7+;H=7+?
F&56v. 5? K+# ; 5A*,$%W (*1. ?.P
('$#8PH GP. 9/9@A?. ^ L./-*#&+,+!: ;#
P$, : **AFw*&B*/-*?AB/7. T7. 
H &!S=. 5?. "Hu!"#$%?F
NB*/-*?;2,DT;*7.Axl K+A/^7
#=+2H GP. ?6* 3Y-/HS$* 2 8 *=H=H=7+'?
 :+#&p. "Hu!"#$%&56vGD(G ,DT7.Axl
(s
 !"#
v&H (>  ;*$YFyY *=H=/i. G*$%A/L*A v+B*
 * ; *=H=8 *=H=H=7+/('$# H * *2 8*GD(-('
$#,DT54/-* **A. "Hu<L*6A+H *'*/X> 
D-*G**=. DT(& %A7.Axl T? ;. Q<; ?D&
^F
 !"#$%!&#
 !"#
D'DLW ? *=H= :K+#  *=H=?D'D
sssllNz{F
'%!&#
(G*]9W ?*&+ +kC95EMlzzCHEF
(.%W ?&DTM.|zF{C\.AEF
(HW /1(? !:Mm|rrCDEF
)*+,-$.
}
#
|DA!C}

D*
[}
!
E
)*+,-$./0
,

\+ U*B* *8+@A. ,!: ;#C'*ABE. 9 +3/7.
/7.?<L!?>  :)*+,-./011&122,345
 !"#$%&'()*
y;*/7.
y;*,DT@AH=7+? *=H=
7.Axl 7. 7.xs
lF ~
N7.
l{zCl•zE lzz
)*+,-$.12230
224
M
\+ U*#&+,+ :+L9!:W ?. 9 +3/G*
]!:W ?<7.?/+L9!:W ?&D3!:
D3#&D;*PD *=H=F
€?> +L9!:W ?&D3!:

M
∑
=
×××=
+





,
,
/-
l
•<•
sl
EC
2M
N5M16B!S=6B!:
•-*•!:<H 2$G*. "? *VA7#‚|zFrƒF
N6

M16B!S=6B9!:M
l
l lFs C lE. = + × −
(r
 !"#
„DM6B9@A9D9F
N6

M16B!S=6B(? !:l9D(? F
„9D(? !:2l(? !:
s
|{F•
„9D(? !:2s(? !:
s
|lFz

„9D(? !:2•(? !:
s
|zFr…
NM†B;*!: ;#&F
N7

MG*]9@A;*!:F
N7

MG*]9@A;*!:W ?Fo

|lzCE
N

My+L@A;*!: :Gs *'+v **8D(p,+,+M


0 ElC +×=
„

My+L!: O L.;* **8DF
„KC‡EM16BP!:+(  PDFK|lz‡
„
szlƒ
My+L!:v,+PDA /H A* ?szlƒF

szlƒ
|•zzzC!KˆFE
‰+#X*+L!:K+#X*/'!: X L.M
•zzz|

!
ŠCzFlŠl„zFs•Šs„zFr‹ŠsFƒ„zFsŒŠrFƒE
•0#<
szlƒ
|l{zzC! ˆFE
„
*
My+L@A;*!: :Gs *'+v **8D(p,+,+M

) ×=
)

M  . ,;*!:
f?$V*1+&A0.(GW ?Ly+L9!:W ?

F
=K+GW ?LX L.(G6A+M
123456789:234-

PD
W
?
y;*
!:
9


C! ˆFE
)


C‡E

*
C!:ˆ
FE
o
*
CE
D 
l

s


ƒ
€:
-
sƒŒŒ
lz sƒ…
zFƒƒ N N N N
6A+ zFΠN N N N
€:G*
 •
-
s• {l…
sFz N N N N
6A+ { l l l ssF…ƒ
€:G*
+
-

r‹ lzzƒ
rFƒ l l {F• ssFsz
6A+ ŒFƒ l l l ‹‹Fsz
€:G*
T
-
sŒ {‹{
ƒFƒ l l {F• llsFrs
6A+ lz s sFs zFr… szrF{ƒ
(•
 !"#
•{zFss
lƒ
€:
-
{{…•
lz {{…
zFƒƒ N N N N
6A+ zFΠN N N N
€:G*
 •
-
s• l{z•
sFz N N N N
6A+ { l l l ƒ‹Frl
€:G*
+
-
r‹ s{zŒ
rFƒ l l {F• ƒŒFƒ…

6A+ ŒFƒ l l l sŒƒFrs
€:G*
T
-
sŒ l…zƒ
ƒFƒ l l {F• s‹lFs‹
6A+ lz s sFs zFr… ƒs…Fl•
lsllF{•
f+L9!:W ?<A)*+56./011&122,34<AL
\+ U* :+L!: ;#F}
!
C\.AE
;7)+<0=(!"#$%&>
$
PDW
?
}
D*
}
!
}
#
|DA!C}
D*
<}
!
E
xl xs xl xs xl xs
ƒ lzz lƒzF{l lƒzF{l
lƒ l{z l‹ƒFl… l‹ƒFl…

8'
8 9:,
(€?> &+X*/6p.!=. 4%&<$-*@A? /0*1+?
. 5?H=7+?&56v 4P/ *1D/9@ADO* 8GD
(GGH=7+? GDR5(G?#&+,+ +F
No G*+" :+#&p *=H=X 8'DT<;*'+H*18'
7 AD*A >+%^/-*H=7+?=D4B*AF
N7+; DT/D36B L.j2 (G/1& DT
 )D ; =? ;*@A;*%=  >+% @#=+@A,DTF
No G* Yc6q$9B*A?/0*1+;* O<. = G* *1.F
No G*. ^ L./-*H GP * %=<P A B3$"# +#' *
<5*-* 2A< *&. 2AK+? !"#$%?<2.. ,*GD
*?  !"#$%F
N.$9+#&p. "Hu,+ *=H=7+;?<$%W
(*1. ?.P('$#< A#X*H=7+8"7.?8. ^ L./-*
+L!: ;#P$, : **AF
N=7+&L. " *A   *'+, 8. ^ L./-**'+H*1 >+
%/0$9/0*1+t*'8D $-*F
(ƒ
 !"#
N *'+$#@ADO* /0*1+H  Z 5 *'+$#B* *8+8 *$8
$//0*1+H (>R#/Ž9(3K+? +•/ >+G*]6A+
#F
8;/4<=
87=,>2?0

@A8BC<9D
 ,?4@
zN7'‹…
lN7.. B*?$PD;*m

DA!
|rŒ<ƒDD$#sƒDCssrr•Nz{E
sN7.. B*?$PD;*m
DA!
|sƒDD$#szDCssrr•Nz{E
rNe T ;+;*m
DA!
|sƒDD$#…DCsss•‹N‹…E
•Ne T ;+;*m
DA!
|szDD$#{DCsss•‹N‹…E
AB.CD343)?4@
E ,?4@E
zN7'‹…
lN7.. B* *& *&;*x$#sƒDCssrz•NzrE
sN?/??*AB!*DP$#srDCssrr•Nz{E
rNe& %A T ;+;*m
DA!
|szDD$#ŒD
•Ne& %A T ;D>;*m
DA!
|lƒDD$#ƒD
AB1.CD343)?4@E
 ,?4@
({
 !"#
zJ7'‹…
lJ€Ij 7LU'+3k7?$#sƒDCssrz•NzrE
sJ7.. B*?$PDm
DA!

sƒDD*AB!*DPƒ‡$#szD
rJe& %A T ;+;*m
DA!
|szDD$#ŒDCsss•‹N
‹…E
•Je& %A T ;D>;*m
DA!
|lƒDD$#ƒDCsss•‹N‹…E
AB;.CD343)?4@
87=<EF
m+U/B,+ ? !"#$%5(Gj ; •.&/*10.
+/BD3Y7H 2H PF80$9 =H GPD/*1@A/0*1+/
H p. 9L ; =&<A2 8!S. "Hu,+  :f*A*
]AF•*1,+!"#$%. "Hu :f*A*;6_?.4L3!:
 ;#&+#=P$, : **A/H GP !:h }
#
@AH=7+
? *Hu6q$9F
m%A/+L!: ;#/?PD5A*/ **A++<;*+
@A?;*,DT?<A'!+7. "Hu 6A+M
N*A*;…PD,+ ]7.?xs<}
#
|l•lFz{\oAF
N*A*;ŒPD*=. : ]7.?xl<}
#
|l…rF•r\oA
,?4
F3DGH &'I3C)J1*
G
l

|•D< 7D 0. %A
G
s
|l•D<7.. B*?$PD;*lmDA!sƒ
G
r
|l…D<7.. B* *& *&F
G7'‹…$#ƒzCDE2}|•ƒ\.AF
1F3DKH <):3'I3C)J*
"7.f?7.xs&7.xl()?  &D&DTh
D3 My (& %A T;*C?$PD•ƒz‡E |{D
E,?41
EF3DGH &'I3C)J1*
(Œ
 !"#
„
l
|{D 7D 0. %A
„
s
|l{D<7.. B*?$PD;*CmDA!sƒEF
„
r
|szD<7.. B*?$PD;*CmDA!rŒFƒE
G7'‹…$#ƒzCDE2}|•ƒ\.AF
E1F3DKH <):3'I3C)J*
"7.f?7.xs&7.xl()?  &D&DTh
D3 M\3 (& %A T;*C?$PD•rƒ‡E |ƒD/l e&
 %A T;*lC?$PD•ƒz‡E |ŒDF
,?4;

F3DGH &'I3C)J1*
G
l
|rDM 7D 0. %AF
L
s
|lƒD<?$PD-F
G
r
|l…D<7*AB 7*&H=/5F
G7'‹…$#ƒzCDE2}|•ƒ\.AF
1F3DKH <):3'I3C)J*
"7.f?7.xs&7.xl()?  &D&DTh
D3 My (& %A T;*C?$PD•ƒz‡E |{D
MN34=)?4
‘o 5?lM
„o 5?# DT6q$9(&7.xs 7D 0. %A$#•DF
GD(GDT@6q$9ƒPD
„y sl 7.. B*?$PD;*l< r7.. B* *& *&F+#*=
H*1D 86q$9  **A6A+#,;*'B 5
‘o 5?sM
„o 5?# DT6q$9(&7.xs 7D 0. %A$#{DF
GD(GDT@6q$9…PD
„s *=. :7.. B*?$PDF2 80$9B  K+? 6q
$96A+#
‘o 5?rM
„o 5?# DT6q$9(&7.xs 7D 0. %A$#rDF
GD(GDT@6q$9ƒPD
„y DT6q$9?$PD-<? *H 2H PH *5/> *
H @*'+H*1!:D?#/?*'+3!:D?#&>A  Y*

7H 2H P<K+? +7.-. 9/9 *&+#=hH 
 +0L*F
(…
 !"#
„y D26q$9/0*1+7*AB 7*&H=/5&. G*, *
*A8 D2@3<DP **A */? *. WH 
, *=K+?  *F
‘O<6P‰+A. "W + L*8D@A?. 5?'AA ]. 5?
sD7+;H=7+?F
(‹
 !"#
$%&''
’“
*+-H#
N3*0#/16B3

M
2 8 ]3*0# *=H=B*/-*?;*/7. ; v
E;@;%Q11 1@RS< :+#&p2B3A< *
*A *=H=$*  ]3*0#A H L Z 5>6B
 Z 7v(GF
•-*7.A ]3*0#Mz<‹ƒF
f3*0#$%A/E;@1";@K%Q11 1@RSA2? 1
6B3M
$
/
|l<lz[
$

|l[

$
H+
|lF
N? 6B/''7M
„m%A/E1@T%Q11 1@RS<3 T@A'‹…
„*G *=7' +37;*CkD/fAE<76S< ADH G)8
68%Q11 1@RS<A2? 6B'7 6A+M
}|{z\oA[|zFzr…\oA[
ϕ
|sŒ

[
N? 6B@A? /0*1+M
 * *=H=H=7+?2,DT;*7.Axl<xs A#
*A*; *=H=56v0.$%?,+R. G* % *1?/*16A+"#M
„ *=H=  . , O L./0*1+ DO* H=7+C”1. B* L.?
  . , ;<”13/0*1+ ;H ?/-* 7*&H=E B*/-* (&
 %A< 7?*AB*&H=< 7.. B*?$PD T7.. B* *& *&b&
56v?/0*1+ %=$%H*=6_6q$9$]+#=< :2 =(>?Di+/0*1+
54/-*  . ,R *=&+&<*=  ? W *1D. j 
?  I$iv. 998!?> D+ U*@A YF
„†6? ?6B*1+ W *1D. j-*?>6BA(Gv. 99
8K+#=> >6BD+ U*$^8W ?/-*DO* H=7+F
•"#AH *=   *=H=  . ,/ W *1DD7#?*?>
 ADH Gv!787/./011&122,345
7=,>2
 ,?4@';@*
† y H=7+f$-*&&
e'$#
CDE

}C\oAE w
H+
C\oA
E

C\oAE
ϕ
C

E
W /'
]/a
W /'
L
W /'
HS+B
z 7'‹… {z zFzr… sŒ
l 7.. B*?$PDA* sƒ szz szz szz
(lz
 !"#
mDA!|rŒ<ƒ
s
7.. B*?$PD;*
mDA!|sƒ
sz rzz rzz rzz
r e Tm
DA!
|sƒDD … •sz rzz l…zz sF•
• e Tm
DA!

|l‹DD { •sz rzz l…zz sF…
1 ,?4@E';@1*
†
y H=7+f$-*&
&
e'
$#
CDE
}C\oAE
w
H+
C\oAE

C\oAE
ϕ
C

E
W /'
]/a
W /'
L
W /'
HS+B
z 7'‹… {z zFzr… sŒ
l
7.. B* *& *&
;*x
sƒ szz szz szz zFzƒ •z
s

?/??*AB!*
DP
sr rƒz rƒz rƒz
r e Tm
DA!
|ƒDD Œ •sz rzz l…zz sF•
• e Tm
DA!
|l‹DD ƒ •sz rzz l…zz sF…
; ,?4@';@;*
†
y H=7+f$-*&
&
e'
$#
CDE
}C\oAE
w
H+
C\oAE

C\oAE
ϕ
C

E
W /'
]/a
W /'
L

W /'
HS+B
z 7'‹… {z zFzr… sŒ
l
€Ij 7LU
'+3k7?
sƒ szz szz szz
s
7.. B*?$PD
mDA!|sƒ€\
sz •zz •zz •zz zFƒ
r e Tm
DA!
|sƒDD Œ •sz rzz l…zz sF•
• e Tm
DA!
|l‹DD ƒ •sz rzz l…zz sF…
FU.46V"$ +3)868.E.@W.@1"6VXY
7=<EF
'#1I>J$.
6-K#
$
>O> ×≤
ClE
2M
„}

M\+ U*@A? /0*1+F
„}
#M

\+ U*#&+,+F}
#
|l‹ƒFl…\.AF
„
$
/
M16333/aF
$
/
|lFl
'#$:,!9
7=,>2
(ll
 !"#
Z+V234 :*&+ +k#H=7+L!:D@3H *>6B
D+ U* +@AGH=7+'?C T@AH=7+?'2*ABE
}

- 5 T()>6BD+ U*#&+,+}# " &D/-*D3 16B$%
V3/'3/a
M
M
O
L!?> +u :3*0#DD+BF16B
M
M
O
L!?>  :D9rF•Fs@A**1+–l—<7.•<3*0# *=H=
zF‹ 
M

M
O
|lFlF
F
M
 M $
> O >≥
ClE
8!?> L}

 -*&A. G*K+*X* 1 *'+ /' 1 A* M
 %K+#X* 1 *'+ /' 1 A*  6A+MCX*f$-*&E
AB;@N?#6[)"6[)
 4!?* }
(
M
r
lˆr
˜
l
l
E
+
> >
+
 
+
=
 
+

 
F†A+H *K+#X* *'+ /'D3  ,
 " &D/-*}
(
D3 16B*'+ I 
C ˆ E/ A \
β
∈
!?>  :(GrN{@A*
*1+–l—< T : 4M
z<ls
l<ll•C ˆ EA \
β
=
H *ˆm•sF
˜
F
M
E E
> >
β
=
CsE
FU
LA6"M"$3"E+<C43\6"+2VE49:
\];; 
L7)2
M
E
>

:3'1*3+<06[? 3MM$"#6[
CP6V346[)+<C: 0B^6C$
M
E
>
E_ 3M$
"#6[C`
f
z
(


M
M
E
A
\ >
O3 >
>
>
>



+ ⇒ ⇒




11 ,?4@

eGrN•M=K+GW X*,s D3@A. 5?NAM
y H=7+ }
*
|}
s
ˆ}
l
*CDE H|
s
ˆ
l

(
}
(
(ls
 !"#
C\oAE
7.. B*?$PDA*

sƒz sƒ sƒ sƒz
7.. B*?$PD;*

rzz lFsz lƒ zF…zz •ƒ sŒlF•Œ
e T ;+
A*
•sz lFƒƒ … zFlŒ… ƒr s‹lFl…
e T ;+
;*
•sz lF•• { zFllr ƒ‹ rzsF…Œ

eGrNƒM=K+GW }

. 5?NAM
y H=7+ ˆm
β
M
E
>
z
ˆ
M
E
> >
ˆ
M
 E
> >
}

7'‹… {zFzz
7.. B*?$PDA*

zFŒ{ lFzŒ… s{‹Fƒz zFssr zF•{ lsrF‹Œ
7.. B*?$PD;* lFr{ lFlƒ{ rlrF…s zFl‹l zFƒ• l{‹F•{
e T ;+
A*
lF{l lFl…z r•rFƒ‹ zFlŒƒ zFƒ… l‹‹Fs…
e T ;+
;*
lFŒ‹ lFl‹ƒ r{lF‹r zFl{{ zF{ slŒFl{

 *1D;*(*8+ 4M
slŒFl{ F lFl l‹ƒFl… sl•FŒ
M
 M $
> O >= ≥ = × =
|•Y
=+0M=7+$%H*=. 5?NAGD(G#&+,+3 :*&+ +k3
/a U*F
111 ,?4@E
eGrN{M=K+GW X*,s D3@A. 5?N(M
y H=7+
}
*
C\oAE
|}
s
ˆ}
l
*CDE H|
s
ˆ
l

(
}
(
7.. B* *& *&
;*x
szz sƒ sƒ szz
?/??*AB!*

DP
rƒz lFŒƒ sr zF‹s •… s{•F‹•
e ;+A*
mDA!|szC?
$PD•ƒz‡E
•sz lFƒ… Œ zFl•{ ƒƒ s…sFz‹
e ; Z;*
mDA!|lƒC?
$PD•ƒz‡E
•sz lF•‹ ƒ zFz‹l {z s‹sFss
eGrNŒM=K+GW }

. 5?N(M
y H=7+ ˆm
β
M
E
>
z
ˆ
M
E
> >
ˆ
M
 E
> >
}

(lr

 !"#
7'‹… {z<zz
7.. B* *& *&
;*x
zFŒ{ lFzŒ… slƒF{z zFsŒ… zFƒz lzŒF…z
?/??*AB!*
DP
lF•ƒ lFl{ƒ rz…F{{ zFl‹• zFƒŒ lŒƒF‹r
e ;+A*
mDA!|szC?
$PD•ƒz‡E
lF{Œ lFl…• rrrF‹‹ zFl…z zFƒ‹ l‹ŒFz{
e ; Z;*
mDA!|lƒC?
$PD•ƒz‡E
lF…s lFl‹Œ r•‹FŒ‹ zFlŒs zF{s sl{F…Œ
 *1D;*(*8+ 4M
sl{F…Œ F lFl l‹ƒFl… sl•FŒ
M
 M $
> O >= ≥ = × =
|•Y
=+0M=7+$%H*=. 5?N(GD(G#&+,+3 :*&+ +k3
/a U*F
11; ,?4@
eGrN…M=K+GW X*,s D3@A. 5?NM
y H=7+
}
*
C\oAE

|}
s
ˆ}
l
*CDE H|
s
ˆ
l

(
}
(
€Ij 7LU
'+3k7?
szz sƒ sƒ szz
7.. B*?$PD
mDA!|sƒ€\
•zz sFzz sz zF…zz •ƒ sŒŒF{r
e ;+A*
mDA!|szC?
$PD•ƒz‡E
•sz lFƒl Œ zFlƒ{ ƒs s‹•Fƒƒ
e ; Z;*
mDA!|lƒC?
$PD•ƒz‡E
•sz lF•r ƒ zFz‹{ ƒŒ rz•Fr‹
eGrN‹M=K+GW }

. 5?NM
y H=7+ ˆm

β
M
E
>
z
ˆ
M
E
> >
ˆ
M
 E
> >
}

7'‹… {zFzz
€Ij 7LU
'+3k7?
zFŒ{ lFzŒ… slƒF{z zFsŒ… zFƒl lz‹F‹{
7.. B*?$PD
mDA!|sƒ€\
lFr{ lFlƒ{ rszF‹• zFl…Œ zFƒ• lŒrFrl
e ;+A*
mDA!|szC?
$PD•ƒz‡E
lFƒ… lFlŒŒ r•{F{‹ zFlŒr zFƒ‹ sz•Fƒ•
e ; Z;* lFŒr lFl…‹ r{lF‹s zFl{{ zF{z slŒFlƒ
(l•
 !"#
mDA!|lƒC?

$PD•ƒz‡E
 *1D;*(*8+ 4M
slŒFlƒ lFl l‹ƒFl… sl•FŒ
M
 M $
> O >= ≥ × = × =
|•Y
=+0M=7+$%H*=. 5?NGD(G#&+,+3 :*&+ +k3
/a U*F
7=<EF
'#1IELM!3
W ?/-* '7F
6-K#
2M
„
9
τ
M™6+7p ;3- 7!+7 *1'7 T
? /0*1+HSD$W $G*]!: ;#"#AF
„

τ
M™6+7p ;3!+7 *1'7 T? 
/0*1+HSDW $?]L(G "@A? /0*1+v. WA
&"#AF
„

M
O
M16B3 >+pCLEF

„

.
My%$W W ?@A'7 T@A? /0*1+HSD$W 
v; ?*W ?F
'#$:,!9
7=,>2
D
E
ch
p
h
2
h
3
E
3
E
o
h
1
E
2
E
1
AB1N?#234:3Q[D743
a4.


.+++.


×××=
rsl
2M
„My%$W W ?@A 7'M|zFzr…\.A
„H
l
M16B!S=6%*GDH GP Bp$-*?$9@AG*
]^. 9F
•-*. ,!: ;#MH
l
|zF{
„H
s
M16BA!S=*'+H*1D/*1H U 7@AH=
7+< 16B#. 9 +3+L!: ;#M
•-*|lsllF{•C9ˆFF&DE<A)*+,9./011&122,
34
(lƒ
9

M
.O
≤+×
EC
ττ
 !"#
H
s
|zF{ƒ

„H
r
M16B!S=6%*AP64 BL@A7 T/0*1+
HSD$W H *D/*1H=7+/*'+H*1*=.!Y%*=.*VA
? H=7+?/-*'7F
B*/-*7$W MH
s
|lFƒ
l s r
zF{ zF{ƒ lFƒ zFzr… zFzsssr

. + + + . ()→ = × × × = × × × =
Ea4
9
τ

9
9

E
)
!34
>
>
\
A
τ
τ
ϕ
→→→










FFFFFF
2M
LbM23*DA6?@A'7F
z
sŒ
φ
=
„MX *'+$#@A? ?W =/>WW ?F
|sƒ„sz„…„{|ƒ‹DF
„}
 D
M\+ U*@A'7/? /0*1+. WA$-*/>W
W ?F}
 D
|}
z
|{z\.AF
„}
(
M\+ U*@A? ?. WA&/>WW ?F
o 5?NAM

z
sŒ
ƒ‹
lFŒ…… FFF FFF zFzlƒ zFzlƒ zF{ zFzz‹
rr
r{lF‹r
{Fzr
{z
9
9
E

A
 34!
\ )
>
>
φ
τ
τ


=


→ = = → → = → = × =



= =



o 5?N(M
z
sŒ
{z
lF…l… FFF FFF zFzlƒ zFzlƒ zF{ zFzz‹
rr
r•‹FŒ‹
ƒF…r
{z
9
9
E

A
 34!
\ )
>
>
φ
τ
τ


=


→ = = → → = → = × =




= =


o 5?NM
z
sŒ
ƒŒ
lFŒsŒ FFF FFF zFzlƒ zFzlƒ zF{ zFzz‹
rr
r{lF‹s
{Fzr
{z
9
9
E

A
 34!
\ )
>
>
φ
τ
τ


=



→ = = → → = → = × =



= =


a4
9
τ

,?4@
(l{
 !"#
z
sŒ
FFF FFF zFzzl…
ƒ‹
9
 34!
A
φ
τ

=
→ → = −

=


,?4@
z
sŒ
FFF FFF zFzzl…
{z
9
 34!
A
φ
τ

=
→ → = −

=

,?4@
z
sŒ
FFF FFF zFzzlŒ
ƒŒ
9
 34!
A
φ
τ

=
→ → = −


=

7)2347)?4@

$



9
τ
9
τ
l
 
l
H
s
H
r
b  m }
 D
}
(
b 
zFzr… zF{ zF{ƒ lFƒ sŒ ƒ‹ rr {z r{lF‹r sŒ ƒ‹
zFzsssr zFzz‹ NzFzzl…
7)2347)?4@E

$




9
τ
9
τ
l
 
l
H
s
H
r
b  m }
 D
}
(
b 
zFzr… zF{ zF{ƒ lFƒ sŒ {z rr {z r•‹FŒ‹ sŒ {z
zFzsssr zFzz‹ NzFzzl…
7)2347)?4@

$



9
τ
9
τ

l
 
l
H
s
H
r
b  m }
 D
}
(
b 
zFzr… zF{ zF{ƒ lFƒ sŒ ƒŒ rr {z r{lF‹s sŒ ƒŒ
zFzsssr zFzz‹ NzFzzlŒ
MO +V
,?4@
C E l CzFzz‹ zFzzl…E zFzzŒs zFzsssr

M 9  
O () . ()
τ τ
× + = × − = ≤ =
 aADRF
,?4@E
C E l CzFzz‹ zFzzl…E zFzzŒs zFzsssr

M 9  
O () . ()
τ τ
× + = × − = ≤ =

 aADRF
,?4@
C E l CzFzz‹ zFzzlŒE zFzzŒr zFzsssr

M 9  
O () . ()
τ τ
× + = × − = ≤ =
()
 aADRF
7=<EF
)'#1I+N
)6-K#
W ?/-* DT(& %A TF
™6+7HS+B!+7 *1v?#? /0*1+H B*$G*]!: ;#
"#AH L/LK+?46+7HS+B . S.@A? /0*1+2F
+
+
+
M
cO ≤×
σ
(lŒ
 !"#
2M
„
+
σ
M™6+7HS+B- 7!+7 *1? /0*1+
H B*$G*]!: ;#"#AF

„
+

c
M3 >+HS+BW ?@A/0*1+F
„
+
M
O
M16B3/' >+HS+BF
)'#$:,!9
)7=,>2
.UdO234:3%Q+e3+ !"#6[)E%
!fg6C$hVR@T
R
.>
T
]1RRR()
E12
E4
E5
h1+h2
h4
h5
D
Ech
p
E3
h3
ABGN?#234:3%Q+e3+

a4
+E+
)+
σσ
××=
2M
„)M.%(? !:W ??$9&DTF)|zF{\.A
„H
(
M16B!S=T*8D. "(B46+7H=7+?
$-*?$9@AG*]W ?F
 *H*8DA/-*9D(? *F
(
|zF…ƒF
„
+
σ
M™6+7HS+B5/>F
AA!?> /-* DTF
}
lsr•
|sŒlF•Œ\oAF

y H=7+
}
*
C\oAE
|}
s
ˆ}

l
*CDE H|
s
ˆ
l

(
}
(
7.. B*?$PDA*

sƒz sƒ sƒ sƒz
7.. B*?$PD;*

rzz lFsz lƒ zF…zz •ƒ sŒlF•Œ
e T ;+
A*
•sz lFƒƒ … zFlŒ… ƒr s‹lFl…
e T ;+
;*
•sz lF•• { zFllr ƒ‹ rzsF…Œ
(l…
 !"#
•
lsr
l…zz
{F{r
sŒlF•Œ
>


>
= = =
[
•
lsr
…
zFlŒ…
•ƒ

O

= = =

zFls zFls
ƒr
lFll• lFll• lFl…
rr
A
\
β
   
= × = × =
 ÷  ÷
   
r r
l l
r r
lsr• lsr
l l zFlŒ… {F{r
lFl… sŒlF•Œ r‹•F•ƒ

l l zFlŒ…
E
O 
> > ()
O
β
   
+ × + ×
 ÷  ÷
= × × = × × =
 ÷  ÷
+ +
 ÷  ÷
   
z
lsr•
lsr•
ƒr
lF{l
rr
FFF FFF FFF zFƒƒ
{z
zFlƒs
r‹•F•ƒ

E
E
A
\
>

 34! O3
>
>
>

= =


→ → =


= =


•0#<}
 D
|sl{F‹ƒ\oAF
ƒ
ƒ
{
zFl…s
rr
rF… FFF FFF lFƒ
l…zz
…Fr
sl{F‹ƒ
+


\

 34!
>
>
σ

= =


→ → → =


= =


zF…ƒ zF{ lFƒ zFŒ{ƒ
+ E +
+ ) ()
σ σ
→ = × × = × × =
Ea4
+

c

+
+

c++c ××=
sl
2M

„w
H+
M3 >+HS+B*-* ;@A /0*1+W ?F
w
H+
|sF…\.A
„H
l
M16B!S=6%*GD3$/0*1+ >+G*]^
. 9F
•-* /0*1+(& %AM
l
zFss
llFll
:
+
-
=
2
:
6B9!:W ?W h#K+? H A* ?F
lƒ
{
lƒ
l lƒ l
Cl E l Cl zFlE l
r{ƒ r{ƒ lsllF{• rFŒ lz
Cl E zFl Cl zFlE

:


0
- -
0 0
− −
   
+ − + −
   
= × × = × × = ×
× + × +
l
z<ss { zFss
llFll llFll
zFr‹‹
CrFΠlz E
:
+
-
→ = = =
×
„H
s
M16B!S=6%6+#*GD3 : **A$?? "
/'H W 0+ **="#AF
•-*(& %A TMH
s
|lFzF
l s
lFz zFr‹‹ sF… lFllŒs
+

 +
c + + c ()→ = × × = × × =
S7)234+e3)?4 6&
+
M
O
+
σ
+

c
l
+
)
)
+
σ
+

+
1
+
c
zF…ƒ zF{ lFƒ zFr‹‹ lFz sF…
(l‹
 !"#
zFŒ{ƒ lFllŒs
O :3+V+e3+
l zFŒ{ƒ zFŒ{ƒ lFllŒs
+ +

M + 
O () c ()
σ
× = × = ≤ =
→
 aADRF
)7=<EF
8O2P
87=,>2
 ZADR?*'+H*1 B. ? ;*<2 86q$9D. 5?,+
!"#$%F
87=<EF
 ZADR?*'+H*1 B. ? ;*<2 86q$9D. 5?,+
!"#$%F
$%&'''
yš™††›oœ
'#<#P<!Q9R<=
'S3<=
†q$95*?€"#$%I \A+PDszls
7)?4)?4& 6&
\R *1+ y H=7+? 5/> •0*1+
 "

\?# 5*?
xmFslss…
yDDT7.. B*$-*
 *'+$#DTR•S.
lzzD
s
lFs…ƒFszz ƒŒŒFll… lF…{sF{•• rFŒs•F‹{s

(sz
 !"#
xmFslss…
yDDT7.. B*$-*
 *'+$#DTR•S.
lzzD
s
lFs…ƒFszz ƒŒŒFll… lF…{sF{•• rFŒs•F‹{s
xmFsrssƒ
wG* GDDT(&
 %A ;+ *'+$#R•
S.ŒDF
lzzD
s
ssF‹{rFzsr ƒrsF{…z {{sFl{Œ s•FlƒŒF…Œz
xmFsrsrr
wG* GDDT(&
 %A ;D> *'+$#R•
S.ƒDF
lzzD
s
lŒF‹…ƒF…lr r…{F•ƒ• ƒ{ŒF…Œ• l…F‹•zFl•l
17)?4)?4&)i+j3DGH &
17)?4)?4&)i+j3DKH 
'#<#P<!
W ?H B*L?;+#=$*lDF
•-*7.<('3DTlƒD<'*AB()7F
„m*1W DTM
s
lƒ lzzz lƒzzz × =

„ ]H B*L*&@A?$PDMlF{ˆD
r
„ ]H B*L*&@Ae& %A ;+MsFsƒˆD
r
„ 8W /0*1+H=7+?M
lƒzzzk 
= ×
CD
r
E
„ B*L/0*1+H=7+?M
7.. B*?$PDM
lƒzzz lF{ llszzl  = × × = ×
CE
e& %AM
lƒzzz sFsƒ rrŒƒzl  = × × = ×
CE
•-* *'+$# H=7+?W ?F
 *. W;*+<++. 9 +3/;*,DT?F
A)*-,2:;/<=>?@A65
„\T(& %AM
z
‡•s OO

=
<
z
‡l<ƒ OO

=

„\T?$PDM
z
‡l<ƒr OO

=
<
z
‡‹ OO

=
234)2)?4& 6&
\R *1+ y H=7+? 5/> 5*?
e'
$#
CDE
 B*
L
CE


CˆHDE
xmFslss…
yDDT7.. B*$-*
 *'+$#DTR•S.
lzzD
s
rFŒs•F‹{s sƒ s…zz ƒƒ…FŒ••Frzz
xmFslss…
yDDT7.. B*$-*
 *'+$#DTR•S.

lzzD
s
rFŒs•F‹{s sr sƒŒ{ ƒƒ…FŒ••Frzz
xmFsrssƒ
wG* GDDT(&
 %A ;+ *'+$#R•
S.ŒDF
lzzD
s
s•FlƒŒF…Œz Œ sr{sFƒ rF{srF{…zFƒzz
xmFsrsrr
wG* GDDT(&
 %A ;D> *'+$#R•
S.ƒDF
lzzD
s
l…F‹•zFl•l ƒ l{…ŒFƒ sF…•lFzslFlƒz
ŒFƒ…sFl‹zFsƒz
(sl
 !"#
zl
ŒFƒ…sFl‹zFsƒzO =
CˆDE[
z
•s‡ rFl…•Fƒl‹F‹zƒ

O O= =
CˆDE[
z
ƒFl‡ r…{F{‹lFŒzr


O O= =
CˆDE
T234)2)?4&)i+j3DGH &
S234)2)?4&)i+j3DTH &
K7)4)2P)
o 5?


CˆDE


CˆDE


CˆDE
,+D3, ŒFƒ…sFl‹zFsƒz rFl…•Fƒl‹F‹zƒ r…{F{‹lFŒzr
,+
. "
Hu
…PD
,+
sFŒr{Fss{F{‹
r
lF•ƒsF‹r{FƒŒ•
s•{Fs{zF•zs
ŒPD
*=. :
rFszzFr•zFlƒ
{

sF•‹rFrƒ…FzŒŒ
rzsFŒ{•F‹z‹<r
'#<#96

Q9R<=
6<#TL%TU$V,?6

T
D
 *. W$+#+<6qA VAK+Gc PD2 8!?> &56v
> D4@A?5K+AK+GcH A* ?C9(3•*1ADE[
 L.2 8<&!?> ^# +37. ;<;*DT/+L/0
 +#8 PDF
w*& L.. "W  *1+K+GH* =/66? ?. 5?H=7+
?  *. W;*+<++/$+#+ !+#&2 8 ADH G)*-,
2B;/<>?@A65
G7))2M$06d"H '.

M
*
o 5?
y;*,DT
?

CˆDE


$
CˆPDFDE
,+D3, e& %A

ŒFƒ…sFl‹zFsƒz


$
|zFƒƒ‡
z
|

•lFŒzsFz•{
,+
. "
Hu
…PD
,+
e& %A sFŒr{Fss{F{‹r 

$
|lF{‡
zl
|•rFŒŒ‹F{sŒ
ŒPD
*=. :
e& %A rFszzFr•zFlƒ{ 

$
|zFƒƒ‡C
zl
„
zs
E|


l{F…z‹F•r•<Œ
6<#P:LMW-?6


D
 *. W/0 +#8LW   PD!?> fH B*L  2A
/0 +#8/*?  /0 +#8@APD2F



Nl. ×=
2M
‰

MyL  2A/0 +#8vPD 4F
E
-Fl ××××=
βγ
r{ƒ
„

My+L!: O L.vPD 4F
l l
z
Cl E l{zz Cl zFllE
 

- - 0
− −

= × + = × +
„
γ
M16BL*$9G*]F
‹ƒ<z=
γ
„
β
M16BL*$9   F
{ƒ<z=
β
(ss
 !"#
„
E
F
MG*]+( @A?;*!: AD*A/0 +#8F
zF{ƒ
lzz
 
E
F )
F
×
= ×
∑
m234=EB
y;*!:
  . ,
.*C‡E

9
-
CE
96A+
CE
†B9
6A+

∑
×
lzz

)F
zF{ƒ
lzz
 
F )×
∑

€: lz zFƒƒ zFŒ l zFlsƒ zFz…lr
€:G* • s• sFz {Fz l lF‹s lFzŒr
€:G*+ r‹ rFƒ ŒFƒ l •Fs‹ sFŒ……ƒ
€:G*T sŒ ƒFƒ lz s {F……ƒ •F•Œƒr

lrFss …Fƒ‹r
R2+67"`H n
PD


C!: ˆF&DE

γ
β

(
CE
‰

CE
l l{zz zF‹ƒ zF{ƒ …Fƒ‹r rz‹……z…
s lŒ{z zF‹ƒ zF{ƒ …Fƒ‹r r•z…{……
r l‹r{ zF‹ƒ zF{ƒ …Fƒ‹r rŒ•‹ƒƒŒ
• sls‹F{ zF‹ƒ zF{ƒ …Fƒ‹r •ls•ƒlr
ƒ sr•sFƒ{ zF‹ƒ zF{ƒ …Fƒ‹r •ƒr{‹{•
{ sƒŒ{F…s zF‹ƒ zF{ƒ …Fƒ‹r •‹‹z{{l
Œ s…r•Fƒ zF‹ƒ zF{ƒ …Fƒ‹r ƒ•…‹ŒsŒ
… rllŒF‹ƒ zF‹ƒ zF{ƒ …Fƒ‹r {zr…{‹‹
‹ r•s‹FŒ• zF‹ƒ zF{ƒ …Fƒ‹r {{•sƒ{‹
lz rŒŒsFŒs zF‹ƒ zF{ƒ …Fƒ‹r Œrz{…s{
ll •l•‹F‹‹ zF‹ƒ zF{ƒ …Fƒ‹r …zrŒƒz‹
ls •ƒ{•F‹‹ zF‹ƒ zF{ƒ …Fƒ‹r ……•ls{z
lr ƒzslF•‹ zF‹ƒ zF{ƒ …Fƒ‹r ‹Œsƒr…{
l• ƒƒsrF{r zF‹ƒ zF{ƒ …Fƒ‹r lz{‹Œ‹s•
lƒ {zŒ{ zF‹ƒ zF{ƒ …Fƒ‹r llŒ{ŒŒlŒ
†

M*?  /0 +#8+( ()~vPD 4F
E
E
E



F
,
kF
,
N
××
+
×××
=
γβ
γβ
„o

M *. WB> +(  l*6q$9!:?;*L
 + 0.v?!W *1./0G*!:CUˆ!:F*E[ . 9 +3/
  C +&!:H *h. G*G*'#E/(AUD?H G *
 /*1K+Gc. 5*1v?!W *1./0G*<?H GH 7+ A
!:D?#5?*!:b
o

|ŒzzzzCUˆ!:F*E
„
γ
M16BL*$9G*]F
zF‹ƒ
γ
=
„
β

M16BL*$9   F
zF{ƒ
β
=
„
k
MyB3!: ;#+( &CHDˆ E[ L. *=+
6B*1+ %=<B*/-*!:G*2 8W 
zFŒ
+
k k= ×
</-*•
H
B3Hd +0
(sr
 !"#
+( @A!:G*. 9 +37.K+Gc/?;*,DT?
F
A)*-,1;/<=>?@A65
94EB
7.K+Gc
 :
••zƒ•Nzƒ
y;*,DT
?
>A

B3Hd
 +0
•

H
CDˆ E
B3+
(
•|zFŒ•
H
CDˆ E

xl
U
()
lzz Œz
xs …z ƒ{
„
(
M]G*+( &? AD*A/0 +#8F
RW mM
…Fƒ‹r
lzz
 
E
F )
F
×
= =
∑

„o
(
M *. W(*=X*+(  D3   !:~CUˆ!:FHDE

λ
××= :,
E
:MyL*&+ A *&*1++( &+#=W  lDF

zF•ƒ:→ =
CWE
λ
M”1*VA *. W(*=X*6/-* *. W *&*1+F
sF…
λ
=
M*? *&*1+* **8D *1;*F
*?$,+m}•}yM|sz…zzCˆWE
zF•ƒ sF… sz…zz s{sz…
E
, : 
λ
→ = × × = × × =
CUˆ!:FHDE
1F4P$"`23O 
7.?

o
Cˆ!:F E
o(
Cˆ!:FHDE
•
CHDˆ E
β

γ
(
CE
†

CUˆFHDE
xl
Œzzzz s{sz…
Œz
zF{ƒ zF‹ƒ …Fƒ‹r
ƒls…
xs ƒ{ ƒlŒƒ
'#S<#4ETX$9YS/V,7

 R
<=
 *66?  ]. 5?H=7+?M
∑
=
+
+=
lƒ
l
ElC





>

.
O,
2M


MX *. W!"#$%0.+K+#/'PDBF
∑
=
+
lƒ
l
ElC




>
.
MX *. WH A* ?K+#X*/'PDBF
}

|lz‡F
'S<#4ETXP<!YS/V,
,?4& 6&
E,?4&)i+j
(s•
 !"#
0
4
8 13

15
K1
K1tr
K2
K2tr
K2d
AB1Mo&4)2P))?4&)i+j
l s
zl
ƒ lz lƒ
Cl E Cl E Cl E
 

  
O O O
O O
> > >
= + + +
+ + +
?*?> *. W0.+LX L.)*'''5C
;7)+<0234)2P)0$H 
o 5
?
 *. W
0.+

CPDE
Cl„}E

ˆCl„}E


,+
D3,

zl
ŒFƒ…sFl‹zFsƒz ŒFƒ…sFl‹zFsƒz

l

r…{F{‹lFŒzr
ƒ lF{ll s•zFzrsFz‹r

s

r…{F{‹lFŒzr
lz sFƒ‹• l‹•FzŒlFƒ…‹


rFl…•Fƒl‹F‹zƒ
lƒ •FlŒŒ Œ{sFr‹•Fz•z
…FŒŒ…F{…ŒF‹Œs
,+
. "
Hu

zl
sFŒr{Fss{F{‹r<z sFŒr{Fss{F{‹r<z

l


sr…FzƒlFŒss<r • lF•{• l{sF{zr<{

zs
rFszzFr•zFlƒ{<z … sFl•• lF•‹sF{‹{<z

s

sŒ…F•s‹Fƒ‹r<{ lr rF•ƒs …zF{ƒŒ<ƒ


lFƒ…ŒFr{…FŒlŒ<• lƒ •FlŒŒ r…zFzs{<z


| sFŒr…Fr•sF{Œ{<l
'S<#9YS/V,
∑∑∑
===
+
+
+
=
+
lƒ
l
lƒ
l
lƒ
l
ElCElCElC









M





>
.
>
.
>
.
2M
∑
=
+
lƒ
l
ElC






>
.
MX *. W$+#+6qA VA PDK+#X*/'PDBF
lƒ
lƒ
s
s
l
l
lƒ
l
ElC
FFF
ElCElCElC

M

M

M



M

>
.
>
.

>
.
>
.
+
++
+
+
+
=
+
∑
=
∑
=
+
lƒ
l
ElC





>
.
MX *. WK+#X* PDK+#X*/'PDBF
lƒ
lƒ
s

s
l
l
lƒ
l
ElC
FFF
ElCElCElC











>
.
>
.
>
.
>
.
+
++
+

+
+
=
+
∑
=
lƒ
lƒlƒ
s
ss
l
ll
lƒ
l
ElC
FFF
ElCElCElC






>
Nl
>
Nl
>
Nl
>

.
+
×
++
+
×
+
+
×
=
+
∑
=
(sƒ