fundamentos m.suelos(1)

7/25/2019 Fundamentos M.suelos(1)

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FUNDAMENTOS MECANICA DE SUELOS

(Terzaghi) La mecnica de suelos es la aplicacin de las leyes de la Mecnica

y la Hidrulica a los problemas de ingeniera que tratan con sedimentos y otrasacumulaciones no consolidadas de partculas slidas producidas por ladesintegracin mecnica o descomposicin qumica de las rocas,independientemente de que tengan o no contenido de materia orgnica

Suelos: Constitucin Interna del Globo Terrestre

Ncleo

CortezaSuelo


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Un suelo saturado tiene un contenido de Humedad del 38% y un Peso Especfico deSlidos de 2.73. Calcule el ndice de Vacos, Porosidad y Peso Unitario Saturado.

Tenemos que: W= Ww = Yw*Vw = Vw__ = Vh* = _Ws Ys*Vs Gs*(Vh/) Vh*Gs Gs

Como el suelo esta saturado Vw = Vh y Yw = 1.0 en condiciones normales de presiny temperatura.

Despejando tenemos: = W*Gs = 0.38*2.73 = 1.04 104%

Adems sabemos que: n = ____ = ___1.04___ = 0.51 51%

1 + 1 + 1.04Para Ysat = Wt = Wt__ = Ww+Ws = W*Ws+Ws = Ws*(1+W) = Ys*(1+W) =

Vt Vh+Vs *Vs+Vs *Vs+Vs Vs*(1+) (1+)

Pero Yw = 1.0 en condiciones normales de presin y temperatura por lo que Ys Gs

As: Ysat = Gs*(1+W) = 2.73*(1+0.38) = 1.85 gr/cc.(1+) (1+1.04)


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Problema (2):

Una arena tiene una Porosidad igual a 37% y un Peso especifico de Slidos de 2.66.Se pide determinarel ndice de Vacos, Peso Unitario Seco, Humedad y Peso Unitario Saturado.Tenemos que: Yd = Ws = __Ws___ = ___Ws___ = ___Ws___ = Ys___=___Gs

Vt Vs+Vh Vs+ *Vs Vs*(1+) (1+) (1+)

Pero Yw = 1.0 en condiciones normales de presin y temperatura por lo que Ys Gs

Adems sabemos que: = __n__ =__0.37__= 0.59 59%(1- n) (1-0.37)

Reemplazando tenemos que: Yd =___Gs___=__2.66__= 1.67 gr/cc.(1+) (1+0.59)

Tenemos que: W= Ww = Yw*Vw = Vw__ = Vh* = _ = 0.59 = 0.22 22%Ws Ys*Vs Gs*(Vh/) Vh*Gs Gs 2.66

Para Ysat = Wt = Wt__ = Ww+Ws = W*Ws+Ws = Ws*(1+W) = Ys*(1+W) =Vt Vh+Vs *Vs+Vs *Vs+Vs Vs*(1+) (1+)

As: Ysat = Gs*(1+W) = 2.66*(1+0.22) = 2.04 gr/cc.(1+) (1+0.59)


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'> :?A: ;1 03: >1;?8BA@ U :> :B0:934:0 3> 4A3>1 K 48;1 A;: >8;3: 48;A14: 1

8003?A>:0 @3 >1;?8BA@ UD ';B1;: 93>1 E1@0c 34


95/169

8003?A>:0 @3 >1;?8BA@ UDC ';B1;: 93>1K E1@0c 34


96/169

'; :03;:4 280D34 4:BA0:@:4 G 3; 1B014 4A3>14 @3 ?0:;14 28;14K B:D^8b;

4:BA0:@14K @1;@3 >: K >: 93>1

D:B308:>K 48 43 03DE>:d: 3> 9:>10 @3 8E E10 4A 3JA89:>3;B3 iw034A>B:5

F[3mw*(k/)

)@2>3C3:2:3E9 ?= @6> > >=IV9 >< :6=C3:3=98= ?= 5=74=2L3@3?2?O


97/169

)$,c!)!,(&, +, #,%",'k!-!+'+ ,( "'/'/ ,/&%'&!c!)'+'/


98/169

U14 @3EF48B14 @3 4A3>14 B0:;4E10B:@14 D3;B3 3;


99/169

+69?=Ok,kkO )6=C3:3=98=> ?=5=74=2L3@3?2? ?= @6> =>87286>1H, HHO ,>5=>67=> ?= @6>=>87286>

Para un solo estrato el caudal q es:


100/169

q

q = k*i*A = K*(h/L)*H*1m

-A:;@1 34Bc 3; 0b?8D3; 3> B1B:> u 34 >: 4AD: @3 >14 34 @3:d:;@15

/10 >1 B:;B15


101/169

Para la determinacin de k : Coeciente de permeabilidad promedio para la ltracin@3 :?A: 3; 43;B8@1 E30E3;@8:0 : >14 E>:;14 @3 34B0:B828


102/169

/10 >1 B:;B15

L310@3;:;@1 G 033DE>:d:;@15

';B1;


103/169

r:G 9:0814 DbB1@14 E:0: @3B30D8;:0 >: E30D3:^8>8@:@ @3 >14 4A3>145

+37=:86>O*3 ^:4:; 3; E0A3^:4 34 >:

D3@8 : 1DbB081 : E:0B80 @3 >: E0A3^: @3 8@:1 : E0A3^: =108d1;B:> @3 :08@:@C

"J86?6 2 527837 ?= @2 : > B P @ B 8 > ^8>8@ @


104/169

34B:^>31D3B0P: @3 A; D:B308:> G 4A E30D3:^8>8@:@

3H84B3; 0:d1;34 E:0: 3 :14

:03;1414 ?0A3414K >14 E1014 3;B03 >:4 E:0BP:4 D8;30:>34 41; 03>:B89:D3;B3

?0:;@34 G E10 3>>1 >: E30D3:^8>8@:@ 034A>B: B: K 3; 14 @3 D3;10 B:D:V1K >14 E1014 G P14 3;B03 >14 ?0:;14 41; Dc4

E3JA3V14K E10 >1 34B14 D:B308:>34 41; @3 D3;10 E30D3:^8>8@:@C

$34?0:: E0c =310 @3>


105/169

E

@8cD3B014 323A?:0K :A;

E:0: 3414 4A3>14 K >: 9:08:: B: 3H:

2F0DA>: 43: 3C

#,%",'",&%$ +, )'%H' )$(/&'(&,)203 DbB1@1 Dc4 48DE>3 E:0: @3B30D8;:0 3>

28 8 B @ ^8>8@ @ @ > "


106/169

1C ";:

DA34B0: @3 4A3>1 @3 c03: B0:;49304:> % G >1;?8BA@

UK : D3; 8;14 E134K 3> B83DE1 @3 E0A3^: 43

=::0?1 JA3 @3I: @3 430 E0c


107/169

&:


108/169

:B0:9834: A;: DA34B0: @3 4A3>1C %> 3I3: E0A3^: 43 >>3;: @3

:?A: 3> BA^1 930B8K 1^4309c;@143 4A @34

:?A: :B0:9834: >: DA34B0:C

)69>3?=729?6 : : >3G @3 $:0 D84D1 B83DE1K 3; 3> BA^1 930B8 K 3> :?A: =:^0c B3;8@1 A;@34 91>AD3; @3 :?A: JA3 :B0:934F >: DA34B0: 3; 3>

B83DE1 @B E1@0c 3HE034:0435

?\[ g 2?P

U:4 31 D84D1C


109/169

jm'mXP]-Zm?8[ g2?P @ E30D3cD3B01 @3 3 EA3@3 A4:043 41>1 3; 4A3>14 03>:B89:D3;B3

E30D3:^>3 ?3;30:>D3;B3 :03;: G >8D14 1 D3d:4 @3 3414 D:B308:>34K ;1

E>c4B8: E30D3:^8>8@:@ @3 :0>:4 43 @3B30D8;: 3; >:^10:B1081 :E0A3^: @3 8@:: ^:I: E30D3:^8>8@:@ @3 >:4 :0>:4

@:0P: >A?:0 : B83DE14 B:; >:0?14 JA3 >: 39:E10:14


110/169

U: E30D3:^8>8@:@ 43 93 :231


111/169

JA3 EA3@3; 8;A80 :>?1 @3 ?0:9:4 EA3@3; 430 >8


112/169

,@ =C=:86 ?= @2> 27=92> 46F=?3K2>K 43 210D:; 1 43 E01@A1JA3 @3 :03;: ;1 EA3@3 34


113/169

-A:;@1 3> :?A: JA3 34Bc :B0:E:@: 3; 3> ^>1JA3 @3 :03;: ;1 EA3@3 348 4A3>1 G E830@3 >:


114/169


115/169


116/169

c')&$%,/ +,&,%"!('(&,/ ,( -' -!)0,c'))!`(


117/169

+3>873L8@:@ @3 >88DE8:4NC U:4 :03;:4 >8D14:4 G

?0:9:4 B:D^8b; 41; 4A434 : >88@:@34 @3 >8>: >834C

#=>6 ?=@ 7=:


118/169

>:4 E:0BP:4 :AD3;B:; : D3@8@: JA3 43 8;: E0348F; @3>

03: B3;48F; 3;B03 >:4 E:0BP:4K

D3;10 430c >: E01^:^8>8@:@ @3 JA3 1: >8


119/169

: :


120/169

U: @328;8:4 48?A83;B34 1^4309:


121/169

U: B3;48F; @3E3;@3 @3> EA;B1 G @3 >: 1083;B:: 43: 1083;B:


122/169

U: A;8@:@ @3 B3;48F; 3; 3> *. 34 3> /: ME:4N JA3 43 @328;3 JA3 EA3@3; A4:043 De>B8E>14 tE:QSRRR/:[ 3> =/:Q SRR /:[ 1

3> &E:=10 Pa

'?2582:3E9 ?= @2 ?=C393:3E9 :@A>3:2 2 @2 4=:A93:2 ?= >O -1D1 43:;A; 4A3>1 34 A; D3@81 DA>B82c48 34BA@81

3; @3B:>>3 @3 >:4 B3;481;34 : >:4 JA3 43 93 41D3B8@1 :4 2:434

@3> 4A3>1K 3; 34E3 >: 2:43 4F>8@: : B0:9b4 @3> 34JA3>3B1 D8;30:> @3> 4A3>1K

;1 : 34: @3 B0:^:I1 3; >: JA3 43 @34:001>>:; >14 B0:^:I14

8;?3;8308>34C

%4P : 34: ?31BbB:;B34 @3 0323080 B1@14 >14 342A30d14 E0193;83;B34 @3 >:

34B0A


123/169

Q #l*

%4P 43 8;B01@A:4 E08D30:4 48DE>828


124/169

E J E E J

;A>:4C /10 B:;B1K >:4 B0:


125/169

U: @3210D:3D3;B1 @82303; @3 91>AD3; M@3 B:D:V15 @HK @GK @dN

EA3@3 @34


126/169

D198D83;B14 @3 4F>8@1 0P?8@1N G @3210D: E:0:>3>3EPE3@1 3>3D3;B:> @3 >: 28?A0: D1@8281;?8BA@348;834 @HK @GK @d @3 D:;30: JA3 E01G314 B034 3I34 108?8;:>34

E:4:; : 9:>30 MSgN@HK MSgGN@GK MSgdN@dK 034E31034 @3 G Gd


127/169

dC

$84B10481;34 1 @3210D::034 : >14 9:>1034 HGK GdK dHC

$3 >: D84D: 210D: JA3 >:4 B3;481;34 43 : 2A30d: ;10D:> 03E:0B8@: E10 A;8@:@ @3 c03: JA3 43B0:;4D8B3 @3 E:0BP: : E:0BP:K 3; A; :?03?:@1 @3 E:0BP:4 1 018D3;B3 3; D:B308:>34 ?31>F?8 ?0:;A>:0C

U: B3;48F; 3233 E10 3I3DE>1 @3 JA3 3> :?A: 34:

:03;: D1I:@: :> E03481;:0>:K >: B3;48F; 32314 ?0:;14 @3 :03;:

:AD3;B: 3HEA>4:;@1 3> :?A: 3; 4A 8;B30810C '> 34BA@81 @3 >: B3;48F; 3238@:@ @3 B:>A@34K 3> :483;B1 @3 A;:

34B0A: >8


128/169

(30d:?=8 2A3 3> E08D301 3; E01E1;30 A;: 210DA>: E:0: >: B3;48F; 323 3> Bb0D8;1 323: B3;48F; :@: JA3 30:

32314 JA3 43 D198:; 1 JA3 :d:D83;B14C '4B:

B3;48F; 03E0343;B:^: >: D3@8: @3 >: B3;48F; 41E10B:@: E10 3> 34JA3>3B1

@3> 4A3>1C

U: B3;48F; 323 M N G B3;48F; 8;B304B8 1 E0348F; @3 >14 E1014

@3 :?A: MA NK 3;B1;D3;B3 E:0: 3I3DE>14 48DE>34C

Q r4A3>1n 4A3>1" Q rp n p

'> E08;


129/169

,>82?6 ?= 8=9>369=> D ?=C6742:369=> X)37: ?= "6P7Z1&=9>67 ?= 8=9>369=>O '; 3> 34B:@1 B3;481;:>

3B1 @3 A; EA;B1 >: 8;210D:34B:@1 B3;481;:> 41; >:4 :4 B3;481;34 43?e; B034

E>:;14 EA;B1C

$3 >:4 ;A393


130/169

E30D8B3 :0 >: B3;48F; 41^03 JA830 E>:;1 JA3 E:43 E10 @8 34B:@1 B3;481;:> @3> EA;B1C

,>;


131/169

,/Q0,"' +,- &,&%',+%$ +!c,%,()!'- +, )'0)US

.DE1;83;@1 3JA8>8^081 @3 2A30d:4 3; @803


132/169

$3 8?A:> 210D: 8DE1;83;@1 3JA8>8^081 @3 2A30d:4 3; @803


133/169

$1;@3 B G ; 41; >14 93K 034E3B3;410 @3 B3;481;34 JA3 34 8?A:> :5

'> B3;410 @3 B3;481;34 34 48DbB08 E08;@:@345


134/169

,>82?6 L3?34=9>3692@=> ?= 8=9>369=>O 'H84B3; @3 A; EA;B1 43 EA3@3 48DE>828: E01E8: ?31D3B0P: G


135/169

'4B:4 :4 1B0:4 @14K G >:4 :


136/169

EA3@3 :E>8>14 E01^>3D:4 @1;@3 >: ?31D3B0P: 43


137/169

'; ,31B3930 ^:I1 34B:4

=8EFB3484 :4 E034:4 @3 B8300:4 1 >:4 34

:;14 10B1?1;:>34

-1D1 3; 3> 3> 34B:@1 B3;481;:> 41^03 A; 3>3D3;B1

@82303; JA830: @3^3 34B:0 3; 3JA8>8^081K G 48 43 8DE1;3 343

8>8^ 8 8^> @ B 8 > B 8 > B 8 > ^


138/169

3JA8>8^081K 34 E148^>3 @3B30D8;:0 >:4 B3;481;34 ;10D:> G B:;?3; 41^03

JA830 E>:;1 @3 8;8;::;14 930B8 G =108d1;B:>C

'JA8>8^081 @3 2A30d:4 =108d1;B:>34C

'JA8>8^081 @3 2A30d:4 930B834C

U:4 48?A83;B34 03>:34 E:0: @34E3I:0 >:

B3;48F; ;10D:> G >: B3;48F; B:;?3; 41^03 3> E>:;1 @3 8;8;:


139/169

/:0: @34E3I:0 >: B3;48F; B:;?3; ^:4B: =::4 2F0DA>:4 :;B3081034C


140/169

M\N

O E:0: @34E3I:0 >: B3;48F; ;10D:>K ^:4B: =:


141/169

M_N

'; >:4 3HE03481;34 M\N G M_N 43 1^4309: JA3 >:4 B3;481;34 ;10D:> G B:;?3;

:@:4K @3E3;@3; @35


142/169

U>3?:@14 : 34B3 EA;B1 EA3@3 430 @3 ?0:; AB8>8@:@ 03>: 34B:@1 B3;481;:>

1^I3B1 @3 34BA@81 3 03E0343;B::;14K 3>


143/169

,>82?6 8=9>3692@ =9 ?6> 5@296> 6786I692@=> D =982:3E9 =9 =@ :37:


144/169

O B30;:B89: >:4 3HE03481;34 1^B3;8@:4

AB8>8d:0 3> 48?A83;B3 34C

$3> JA3 43 EA3@3 @3089:0C


145/169

-1; 34B:4 @328;8:D3;B35


146/169

U: 3


147/169

%4P 3> 34B:@1 B3;481;:> @3 A; EA;B1K B0:^:I:;@1 3; 34B:@1 @3 B3;481;34

^8@8D3;481;:>34K JA3@: 03E0343;B:@1 E10 A;: : JA3


148/169

'> 8d:@14 3; D334 E148B89:4K48 41; @3 :;1K 1 ?801 =10:081 034E3 D3@81C

%;?A>14 E148B8914 :;B8=10:081C

+3>:3E9 >6L7= =@ >3I96 ?= @6> =>C D 8=67G2 ?=@ 56@6O '; D33 34B:^>3: 34 @3 14 E148B8914 G[ :A;JA3 E10 >1 ?3;30:> 3; >: E0c8=9:32 2@ =>C


149/169

41; >14 E148B8914 G[ :A;JA3 E10 >1 ?3;30:> 3; >: E0c>:@1 41^03 3> 48?;1 @3 >14 342A30d14 :4 G :4 28?A0:4 M:N G M^N 48?A83;B34C

A%

s

B

@H

@G

@4

!8?A0: M^N!8?A0: M:N

'; 3> 43 DA34B0: A; 34E31 4AI3B1 : A; 342A30d1 930B8 K JA343 4AE1;3 3> E08; D:G10 G : A; 342A30d1 >:B30:> c;?A>1 34 3> JA3 210D: A; E>:;1JA830: BB E>:;1 =108d1;B:> AA 3; 3> : 342A30d1


150/169

JA830: BB , E>:;1 =108d1;B:> AA , 3; 3> : 342A30d1E08; D:G10C '; >: 28?A0: M^N :@G:3 @3> 34E31 JA3 3>3D3;B1 B08:;?A>:0 0:G:@1 @3 >: 28?A0: M:NC '>c;?A>1 43 D8@3 3; 43;B8@1 @3 >:4 D:;3>:4 @3> 03>1IC"; :;c>8484 @3> 3JA8>8^081 @3 343 E084D: B08:;?A>:0 : @3498: 342A30d1 ;10D:> G 3> 034A>B:;B3 3; 3>3>3D3;B1 B08:;?A>:0K 43 ?3;30:K :4PK 3; 3> 43;B8@1 @3 >:4 D:;3>:4 @3> 03>1IK

43;B8@1 JA3 43

342A30d1


151/169

L

)

$

s- MgN

g X

%

MYN

X

'> :4 31034 E148B8914 @3> c;?A>1


152/169

)^4b09343 JA3 3; 343 14 9:>1034 E148B8914 @3> c;?A>1 :E:03:4C U:4 EA;B1 $ @:; >14342A30d14 ;10D:> G B:;?3; JA3 : E>:;1 8;8;:@1

D14B0:@1 3; >: 28?A0: M^NC

'; A; K 48 >14 342A30d14 E08;34 ;1 41; =108d1;B:> G

930B8K 034E3


153/169

) % s-

$ /

X

M:N

M^N

En ese punto, ligados a una direccin AA, que forma un ngulo : @80339:;@1 3> c;?A>1 X3; 43;B8@1 @3 >:4 D:;3>:4 @3> 03>1IK


154/169

? IK

: E:0B80 @3> 3I3 =108d1;B:>[ 48; 3D^:0?1K >: E148P;3: paralela a la direccin d, E>:;1 3; JA3 : 342A30d1 E08; D:G10 [ 34B: >P;3: EA;B1 /K >>:D:@1 E1>1[ E10 / EA3@3 B0:d:043 :=10: 1B0: >P;3:

paralela a la direccin AA; esta lnea forma con PB un ngulo K E10 :4 : @82303;B34 @8038@:@ @3 D:4:4

@3 B8300:K 34B:^>3: 03>:14 342A30d14 E08;34 :: D:4:K 4AEA34B: 3; 34B:@1 @3 2:>>: 8;:4 B3108:4 @3 2:>>: Dc4 8DE10B:;B34 3; 3> 34B:@1 : @3 >:

D3: 3> D:B308:> 2:>>:

342A30d1


155/169

@3> 342A30d1 ;10D:> : >A?:0

?31DbB0814 342A30d14 >:K 34C

*8 3; A; EA;B1 @:@1K 3> 14 342A30d14

::4 @84B8;B:4 @803>:K 3; 343

EA;B1 ;1 3H84B80c ;8;?A;: 43: 8;>:@1C *8 3> :4 >P;3:4 @3 2:>>:K @3 >: 28?A0:

:@IA;B:K =:^0c A; EA;B1 @3> EA;B1 $N JA3 03E0343;B: A;14

342A30d14 B:>34 JA3 4:B842:: :C


156/169

)

$

$

% s

-

L

L

XQ WRa g

-39=2> ?= c2@@2 =9 =@ :G7:


157/169

Q _] g lX

#1 EA3@3; 430 03:>34 >14 P;3:4 @3 2:>>:K EA34 3;

3>>14K 43?e; >: =8EFB3484 @3 2:>>: MQ 4 Q B:;NK ;1 3H84B3 3JA8>8^081 3;B1@14 >14 EA;B14 JA3 JA3@3; 2A30: @3 >: d1;: :4

>P;3:4 @3 2:>>:C

$3 >: 28?A0: B:D^8b; EA3@3 1^B3;3043 A;: 03>: E:0:

:E>81 K 3;323: 3HE0348F;C

M/N Q M)sl)%N Q fM)-g-sNlM)-Y-%Nh

$34B:5

MlN Q


158/169

@3 A; 484B3D: K 48;1 JA3 3I3 930B8 210D:;@1 A;: 108?3;K


159/169

'; 323: @3 >14 4A3>14 E10 20:AI1 E>c4B8


160/169

: B0:9b4 @3 >: B310P: @3 &1=0Y-1A>1D^ JA3 342A30d1 JA3K : 4A 93dK 34 2A; 342A30d1 ;10D:>

: E>:;1 3; JA3 1: 2:>>:C

'4B: =8EFB3484 @3 2:>>: =: @:@1K 3; ?3;30:>K ^A3;14 034A>B:@14 E0c14K 483DE03 G 14 342A30d14 JA3 43 14 32334 ;1 3H84B3 :e;

A;: @328;8 @3> :[ EA3@3 48?;828 E08;

c4B8 D:B308:>K 1 3> D1D3;B1 @3 >: 0AEBA0: @3>

D84D1K E10 41>1 34Bb3HE034:@: 3; Bb0D8;14 @3> 342A30d1 3 D1D3;B1 3; JA3 1: 2:>>:

U14 >:K E1@0P:; :4828


161/169

@3 2:>>: : 342A30d14 :: 2:>>: 34Bc @3B30D8;:@: E10 >: DcH8D:

@3210D:c4B8 4AI3B1 : 342A30d14C

XC (310P: @3> DcH8D1 342A30d1 ;10D:> ML:;m8;3N5 *AE1;3 JA3 >:

0AEBA0: 1 3> 2>AI1 E>c4B8 D:B308:>K 34Bc @3B30D8;:@1 E10 3>

D:G10 342A30d1 E08; G ;1 @3E3;@3 @3 >14 1B014 342A30d14

E08;34C

\C &=67G2> ?= 4AR346 =>C : 2:>>: :> 342A30d1:4 JA3 3HE308D3;B:>D3;B3 =:; 03;@8@1 >14 D3I1034

034A>B:@14


162/169

034A>B:@14C

h12Z &=67G2 ?= H8O *3?e; 34B: B310P:K >: 2:>>: 34Bc @3B30D8;:@: E10 3> DcH8D1342A30d1 3K >: 2:>>: E10 @34>8d:D83;B111 >:0?1 @3 >: 4AE3028: 03>: 342A30d1 B:;?3; :>

;10D:> M1^>83

>>:D:043 3> 1D^K P;3:4 @3 2:>>:


163/169

@3 >14 4A3>14[ =1GK :e; 64=876

c

Q /l%&:0

&:0


164/169

DA34B0:4 4:BA0:@:4K 3D3;B3 E10 E>: 34 E148^>3 :E>8>: @3> 34Eb1 >:0?1 @3 A; E>:;1 JA3 E10 >: : 8:;1 @3 2:>>:K K ?0:@A:^>3 :91>A;B:@C U: @3210D:: DA34B0: 34 D3@8@:


165/169

H7AC3:2> ?= @6> 7=> ?= 8=9:32 2@ =>C


166/169

'; >: 28?A0: @3> >: 14 342A30d14 G @803>: E:4: E10 3> 108?3; @3


167/169

-1;114 342A30d14 G 4 D:H MEA;B1 $NK 43 B0:d: 3> >: 3; $ >: 3; A;: E0A3^: @3 34B3 B8E1[ 4A 14 @14 :0JA3B8E14 JA3

:E:03: 28?A0: 48?A83;B3C

U: >3;: @3 M:N 34 03E0343;B:B89: @3 D:B308:>34 >>:D:@14 @3 2:>>: 20c?8>

G 43 3?:0 3> 342A30d1 : A; DcH8D1 ^83;

@328;8@1 M03484B3;: @3210D:: E>c4B814 JA3 >: 2:>>: 43E01@A: @3210D:


168/169


169/169

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