Analisa Stabilitas Bendung (BETA ver.)

BAB III ANALISA STABILITAS STABILITAS BENDUNG BE NDUNG

Gaya–gaya yang bekerja pada tubuh bendung, akibat : 1.

Tekanan air.

2.

Tekanan lu lumpur.

3.

Tekana kanan n ber berat at sendi sendiri ri bend bendun ung. g.

4.

Gaya ge gempa.

5.

Gaya angkat (uplift pressure. pressure.

3.1 Tekanan kanan Air 3.1.1 3.1.1 Tekanan kanan Air Normal Normal

Gambar 3.1 !iagram Tekanan Tekanan "kibat "ir #$rmal % air & 1 t$n'm3

a1 &

1 2

.%air .h .h 2

a2 & b . h . % air

&

1 2

.(1) .( ) )

2

& (4.*5.().(1

& 1* t$n & 2+.1 t$n

41

Tabel. 3.1 erhitungan Tekanan "ir #$rmal agian

erat (t$n /

a1 a2

29.1

umlah

29.1

-engan (m 0



$men (tm y

18

r

$

5.92 10.57

106.56 307.59

18

307.59

106.56

3.1.2 Tekanan Air Banjir (Flood ( Flood )

Gambar 3.2 !iagram Tekanan "kibat "kibat "ir anjir

 1 &

1 1 2 . %air . h 2 & .(1) .( ) ) 2 2

 2 & b . h . % air  3 & b . h . % air  4 & b . h . % air 1 . %air . h 2  5 & 2  ) &

& 2.2.().(1 & 4. 4.*5.().(1 & 5.35.(2.2.(1 &

− 1 . %air . h 2 2

& 1* t$n

1 2

.(1).( 2.*4)

& 13.2 t$n & 2+.1 t$n & 11.1 t$n

2

& 4.3 t$n &

−

1 2

.(1) .( 2.*4)

2

&

64.3 t$n

42

Tabel.3.2 erhitungan erhit ungan Tekanan "ir anjir agian 1 2 3 4 5 ) jumlah

erat (t$n

-engan (m

/

0



y

$men (t m r $

18

6.65

119.70

13.20

7.56

99.79

29.10

10.57

307.59

11.77 4.03

10.33 0.95

121.58 3.83 19.92

4.03 13.22

37.23

4.94

452.92

219.49

3.1.3 Tekanan Lumpur

7

& .) t$n'm 3 & 3

8a

& tan2 (45 – 7'2

γ lumpur

& tan2 (45 – 3$'2 & ,333 8eterangan :

%lumpur

& berat 9$lume lumpur (t'm 3

7

& sudut gesek dalam

8a

& tekanan lumpur akti

43

Gambar 3.3 !iagram Tekanan "kibat "kibat -umpur -1 & &

1 2 1 2

. 8 a . γ lumpur . h2 .(,333.(,).()2

& 3.5+) t$n -2 &

γ lumpur

.b.h

& .).(4.*5.() & 1.4) t$n

Tabel.3.3 erhitungan Tekanan -umpur agian

berat (t$n /

-1 -2 jumlah 3.2 3.2

-engan (m 0



3.596 17.46 17.46

$men (t m r $

y 5.92

10.57

21.291 184.552

3.596

184.552

21.291

Tekana kanan n Bera Beratt Sen Senir irii Ben Benun un! !

erat 9$lume pasangan batu γ pasangan &

2.2 t'm2

Gambar 3.4 !iagram Tekanan "kibat "kibat erat endiri endung

44

ada badan bendung yang berbentuk parab$la, luas penampang digunakan pendekatan : " & 2'3 . - . 0

5/8 H

H

3/8 H

3/8 L

5/8 L

L

;1

&b.h.

γ pasangan

& ) . 3.5) . 2.2

& 4.1 t$n

;2

&b.h.

γ pasangan

& 1.4+. 4.3) . 2.2

& 14.2+ t$n

;3

&b.h.

γ pasangan

& 2 . 4.+ . 2.2

& 21.5) t$n

;4

&b.h.

γ pasangan

& 2 . 5 . 2.2

& 22

;5

&b.h.

γ pasangan

& 3 . 4. 2.2

& 2).4 t$n

;)

& 1'2 .b. h .

γ pasangan

& 1'2 .1.5 . 3 . 2.2

& +.+ t$n

;

& 1'2 . b. h .

γ pasangan

& 1'2 ..+5 . 1.*+ . 2.2

& 2.)3 t$n

;*

& 2'3 . b. h .

γ pasangan

& 2'3 . 1.*3 . 1.)3 . 2.2

& 4.33 t$n

;+

& b. h .

& .5. 1.5 . 2.2

& 1.)5 t$n

;1

& 2'3 . b. h .

& 2'3 . .3 . 1.4 . 2.2

& .4) t$n

;11

& b. h .

& .. 1.+3 . 2.2

& .15 t$n

γ pasangan

γ pasangan

γ pasangan

t$n

Tabel Tabel 3.4 erhitungan Tekanan Tekanan erat endiri endung egmen

erat (t$n

-engan (m

$men (t m

45

;1 ;2 ;3 ;4 ;5 ;) ; ;* ;+ ;1 ;11 ;12 umlah 3.3

< +.5 *.*2 ).5 4. 1.5 +.35 +.2* *.24 .43 ).23 4.33

1+.* 24.1 33. 22. 2).4 1.1* .21 3.* 4.)* 3.) 4.4 +.+

2.00

=

r

$

2.51

188.10

49.64

7.43 6.00 4.50

217.98 214.50 88.00

183.52 198.00 99.00

2.00 11.32 11.89

39.60 11.02 1.94

52.80 13.35 2.49

11.30 9.93

31.93 34.76

43.79 46.46

9.62 7.67

23.47 19.07

36.21 33.73

5.00

19.80 890.16

49.50 808.48

153.92

Ga"a Gempa 3.3. 3.3.1 1 Ge Gemp mpa a #ori #ori$o $ont ntal al •

Gaya 0$ri>$ntal (0 & 8 h . ?; & .1 . 153.92 & 15.392 t$n

•

$men akibat gempa h$ri>$ntal :  & 8 h . ?1 & .1 . 808.48 & 80.848 tm

8eterangan : 0

& gaya gemp empa h$ri>$ntal (t (t

8 h

& k$eisien gempa h$ri>$ntal, ($ndasi batu : 8 h & ,1

/1

& berat sendiri bendung (t

1 & m$men guling akibat berat sendiri (tm

3.3. 3.3.2 2 Ge Gemp mpa a %ertik rtikal al •

Gaya /e /ertikal (/ (/

& 8 9 . ?; & .5 . 153.92 & .)+) t$n

•

$men akibat gempa 9ertikal : r

& 8 9 . ?r1 & .5 . 890.16 & 44.5* tm

8eterangan :

4)

3.&

/

& gaya gempa 9ertikal (t

8 9

& k$eisien gempa 9ertikal, ($ndasi batu : 8 9 & ,5

r1

& m$men tahanan akibat berat sendiri (tm

Ga"a An!kat (Uplift Pressure) Pressure) 3.&. 3.&.1 1 Air Air Nor Normal mal

?-

&

-h @ -9

&

32.*5 @ 1+.2

&

52.5 m

A0 & B &

422. 422.45 45 m – 415. 415.) ) m & ).*5 ).*5m m 0 –

B & 0 –

-

Σ-

. A0 A0

- .().*5 52.5

B & 0 – .131) -  8eterangan : 0

& tinggi muka air dari titik yang diCari (m

-

& panjang rayapan (m

?-

& t$ t$tal ray rayap apaan (m (m

A0

& ting tinggi gi muka muka air air n$r n$rma mall (m (m

B

& uplift pressure di pressure di titik  (t'm 2

Gambar 3.5 Dayapan Gaya "ngkat

4

Tabel Tabel 3.5 erhitungan Gaya "ngkat "kibat "ir #$rmal agian

Gambar

Gaya angkat per 1 m panjang (t

0& y&

4 .(1,4+ @ 5,33 & 13,54 t 2

 h  2a + b    3  a + b  4  2.1,4+ + 5,33 & 1,53+)  3  1,4+ @ 5,33

&   a6b m

y t$tal & 4 – 1,53+) & 2,4)4 m /&

c b6C

1.8 m

b

y&

3 .( ),253 @ 5,33 & 1,+*55 t 2

 h  2a + b    3  a + b  3  2.),253 @ 5,33 & 1,4*5 1,4*5  3  ),253 @ 5,33

&   m

y t$tal & 3 – 1,4*5 & 1,5215 m 4.89 m

4.616 m

0& y& C6d

2 2

.(4,5+)* @ ),253 & 1,*4+* t

 h  2a + b    3  a + b  2  2.4,5+)* @ ),253 & ,+4+1 ,+4+1  3  4,5+)* @ ),253

&   m

y t$tal & 4 – ,+4+1 & 3,5+ m d6e

/& &

2 2

.(5,1125 .(5,1125 @ 4,5+)* & 14,5)4 t

 h  2a + b    3  a + b  2  2.5,1125 @ 4,5+)*  & 1,434 1,434   3  5,1125 @ 4,5+)*

&  m

4*

 t$tal & ) – 1,434 & 4,52)) m 0& y&

1 2

.(3,45)3 @ 5.1125 & *,5)** t

 h  2a + b    3  a + b

 1  2.3,45)3 @ 5.1125 &   & ,+35) ,+35)   3  3,45)3 @ 5.1125

e6 m

y t$tal & 2 – ,+35) & 1,)44 m

/& & 6g

3 2

.(3,*1 @ 3,45)3 & ,25)4 t

h 2a + b      3  a + b

 3  2.2,552 + 2,5

&   & ,+*42 m   3  2,552 + 2,5  t$tal & * – ,+*42 & ,15* m

0& g6h

y&

2 2

.(3,*1 @ ,315* & 1),)3+ t

 h  2a + b    3  a + b  2  2.2,5 + 3,+24  & 1,341+ m   3  2,5 + 3,+24

& 

y t$tal & 3 – 1,341+ & 1,)5*1 m /& & h6i

3 .(,*315 @ ,315* & 22,21 t 2

 h  2b + a    3  a + b  3  2.3,+24 + 4,221

&   & 1,4*3 m   3  3,+24 + 4,221  t$tal &11 – 1,4*3 & +,51 m

4+

3

0& y& i6j

2

.(3,1++ @ 4,221 & 1+,)*1 t

 h  2a + b    3  a + b  3  2.3,1++ + 4,221  & 1,45 m   2  3,1++ + 4,221

& 

y t$tal & 3 – 1,45 & 1,5+43 m

Tabel 3.) Gaya "ngkat "kibat "ir #$rmal

Titik a 4 b 3 c 2 d 2 E 1 F 3 G 2 h 3 i 3 j

0 (m 8.0500

B (t'm2

- (m 52.0500

Bplit E$rCe (t /

0

-engan (m 

48.0500 45.0500 43.0500 41.0500 40.0500

2.517

37.0500

6.525

77.844

4.174

35.0500

1.929

20.470

6.437

32.0500

9.515

189.388

6.832

29.0500

2.618

43.430

4.227

B-"0

•

10.606

3.779

16.589 8.0500

36.217

4.648

19.904 11.0500

11.085

4.010

-10.612 11.0500

26.954

4.385

11.930 9.0500

21.672

1.055

4.214 9.0500

1.564

6.121

9.032 10.0500

$

1.517 10.506

10.0500

r

5.727 17.772

12.0500

y

1.200 -13.854

12.0500

$men (t m

58.639

6.843

42.142

Gaya "ngkat :

0

&  u . ?0

& ,5 ,5 . ().* ().*4 43

& 3.42 .421) t

/

&  u . ?/

& ,5 . (5*.)3+

& 2+.31+ t

 &  u . ? & ,5 . (395.525  & 1+.)2) tm r &  u . ?r & ,5 . (42.142  !imana : 3.4.2

& 21.1 tm

u & k$eisien reduksi untuk untuk jenis tanah keras (5 F

"ir anjir

5

395.525

B

& 0 6

L x

Σ L

. A0

A0 & 0 b & 424.435 – 415.) & *.*35m

- . *.*35 52.5

B

& 0 6

B

& 0 6 .15 - 

8eterangan : 0

& tin tingg ggii muk mukaa air air banji anjirr dari ari titi titik k yang ang diCar iCarii (m (m

-

& panjang rayapan (m

?-

& t$tal rayapan (m

A0

& beda tinggi .". dengan muka air di hilir (m

B

& uplift pressure di titik  (t'm2

Tabel Tabel 3. erhitungan gaya angkat akibat a kibat air banjir agian

Gambar

Gaya angkat per 1 m panjang (t

0& y& a6b

4 .(1,4+ @ 5,33 & 13,54 t 2

 h  2a + b    3  a + b  4  2.1,4+ + 5,33 & 1,53+)  3  1,4+ @ 5,33

&   m

y t$tal & 4 – 1,53+) & 2,4)4 m

51

/& y& b6C

3 .( ),253 @ 5,33 & 1,+*55 t 2

 h  2a + b    3  a + b  3  2.),253 @ 5,33 & 1,4*5 1,4*5  3  ),253 @ 5,33

&   m

y t$tal & 3 – 1,4*5 & 1,5215 m

0& y& C6d

2 2

.(4,5+)* @ ),253 & 1,*4+* t

 h  2a + b    3  a + b  2  2.4,5+)* @ ),253 & ,+4+1 ,+4+1  3  4,5+)* @ ),253

&   m

y t$tal & 4 – ,+4+1 & 3,5+ m /& & d6e

2 2

.(5,1125 .(5,1125 @ 4,5+)* & 14,5)4 t

 h  2a + b    3  a + b  2  2.5,1125 @ 4,5+)*  & 1,434 1,434   3  5,1125 @ 4,5+)*

&  m

 t$tal & ) – 1,434 & 4,52)) m 0& y&

1 2

.(3,45)3 @ 5.1125 & *,5)** t

 h  2a + b    3  a + b

 1  2.3,45)3 @ 5.1125 &   & ,+35) ,+35)   3  3,45)3 @ 5.1125

e6 m

y t$tal & 2 – ,+35) & 1,)44 m

52

/& & 6g

3 2

.(3,*1 @ 3,45)3 & ,25)4 t

 h  2a + b    3  a + b  3  2.2,552 + 2,5

&   & ,+*42 m   3  2,552 + 2,5  t$tal & * – ,+*42 & ,15* m

0& y&

g6h

2 2

.(3,*1 @ ,315* & 1),)3+ t

 h  2a + b    3  a + b  2  2.2,5 + 3,+24  & 1,341+ m   3  2,5 + 3,+24

& 

y t$tal & 3 – 1,341+ & 1,)5*1 m /& & h6i

3 .(,*315 @ ,315* & 22,21 t 2

 h  2b + a    3  a + b  3  2.3,+24 + 4,221

&   & 1,4*3 m   3  3,+24 + 4,221  t$tal &11 – 1,4*3 & +,51 m 3

0& y& i6j

2

.(3,1++ @ 4,221 & 1+,)*1 t

 h  2a + b    3  a + b  3  2.3,1++ + 4,221  & 1,45 m   2  3,1++ + 4,221

& 

y t$tal & 3 – 1,45 & 1,5+43 m

Tabel Tabel 3.* Gaya "ngkat "kibat "ir anjir

53

Titik a 4 b 3 c 2 d 3 e 2 f 2 g 3 h 3 i 3 j

0 (m 10.0735

- (m

2

B (t'm 

52.0500

Bplit E$rCe (t

-engan (m

/



0

48.0500 45.0500 43.0500 41.0500

4.012

40.0500

2.515

37.0500

6.528

35.0500

1.934

22.928

7.098

32.0500

9.517

209.969

7.610

29.0500

2.598

49.611

5.121

B-"0

•

88.163

4.757

19.096 10.0735

11.720

4.246

22.062 13.0735

39.352

5.075

-11.855 13.0735

11.681

4.734

13.504 11.0735

28.003 1.050

4.661 11.0735

22.085

6.393

9.810 12.0735

1.559

$

1.521 11.128

12.0735

r

5.882 18.413

14.0735

y

1.200 -14.164

14.0735

$men (t m

63.789

8.865

45.013

438.499

Gaya angkat :

0

&  u . ?0 & ,5 . (8.865

& 4.4325 t

/

&  u . ?/ & ,5. (63.789 

& 31.*+43 t

 &  u . ? & ,5 . (438.499  & 21+.24+ tm r &  u . ?r & ,5 . ( 80.7419  & 22.5) tm Tabel Tabel 3.+ "kumulasi eban6eban pada endung #$

8eterangan

1

2

"   ! H E G 0

Tekanan "ir "ir #$rmal "ir anjir Tekanan -umpur erat endiri endung Gaya Gempa Gempa 0$ris$ntal Gempa /ertikal Gaya "ngkat "ir #$rmal "ir anjir

Gaya (t /ertikal 0$ris$ntal 3 4

$men ( t m r $ 5 )

9.3160 13.2232 5.5896 153.9225

23.4613 37.2298 4.6876 -

95.9548 141.0171 57.5729 890.1630

175.9594 321.3782 35.1567 808.4758

7.6960

15.3920 -

80.8480 44.5080

80.8480 44.5080

29.3197 31.8943

3.4216 4.4325

21.0710 22.5067

197.7626 219.2497

54

3.' 3.'

ont ontro roll Sta Stail ilit ita* a* Be Ben nun un! !

8$mbinasi gaya6gaya yang bekerja pada bendung :

3.'. 3.'.1 1 Tanp npa a Ge Gemp mpa a

Tegangan Tegangan ijin tanah IJ& 35 t'm2 1. 8eadaan 8eadaan "ir "ir #$rmal #$rmal dengan dengan Bplit Bplit ressure ressure ?0 & a(4 a(4 @ C(4 C(4 @ g(4 g(4 & 23.4613 @ 4.6876 – 3.42 3.421) 1) & 31.5 31.54 4 t ?/ & a(3 a(3 @ C(3 C(3 @ d(3 d(3 @ g(3 g(3 & +.31) @ 5.5*+) @ 153.+225 @ 2+.31+ & 1+*.14* 1+*.14* t ?r & a(5 @ C(5 @ d(5 @ g(5 & +5.+54* @ 5.52+ @ *+.1)3 @ 2.+52) & 14).)434 tm ? & a() @ C() @ g() & 15.+5+4 @ 35.15) @ 1+.)2) & 4*.** tm

8$ntr$l : a Terhad erhadap ap guli guling ng (over (over turning  E &

∑  r 14).)434 = 2.)41 .............. K 1,5 & 4*.** ∑ 

(L8M

b Terhadap Terhadap geser ( sliding sliding  E &

 ∑ /

∑0

&

. . 1+*.14* 31.54

= 4.3+35 .......K 1,2

(L8M

keterangan :  & k$eisien geserNN C Terhadap Terhadap daya dukun dukung g tanah tanah (over (over stressing  •

Desultante beban 9ertikal bekerja sejarak a dari titik L. a &

•

∑  r − ∑   14).)434 4*.*5*5 & 1+*.145* ∑/ −

=

3.311 m

Desultante beban 9ertikal bekerja sejarak e dari pusat berat bendung. e &

 2

− a & 11 − 3.311 = 2.1*++ m 2

55

•

arak e masih terletak di dalam O idang 8ernJ e & 2.1 2.1*+ *++ + mP

B

)

=

11 )

e Q 1,*33 m •

Tegang gangan an yang ang terj terjad adii pada pada tana tanah h akib akibat at beba beban n – beba beban n pada pada bendung :

∑/

 . 

I& " ± R y

∑/ & b  . b y

±

∑ / . e . ,5 . b  1 12

&

&

∑/ b  . b y

±

3

. b  . b y

).∑/.e 2

b  . b y

∑ V  1 ± ) . e   b   b . b y   x

Tegangan Tegangan i>in tanah dasar (IJ & 3,5 kg'Cm 2 & 35 t'm2 •

Tegangan Tegangan tanah dik$ntr$l per 1 meter panjang bendung : Imin

&

1+*.14*  1 − ) . (2.1*++)   2   & 63.53 t'm Q  11 11  

(Tidak

L8M Ima &

1+*.14*  1 + ) . (2.1*++)   2 2   & 3+.53) t'm P IJ& 35 t'm 11 11  

(Tidak L8M

2. 8eadaan 8eadaan anjir anjir dengan dengan Bplit Bplit ressure ressure ?0 & b(4 b(4 @ C(4 C(4 @ h(4 h(4 & 3.22+* @ 4.)*) – 4.4325

& 4).34+* t

?/ & b(3 b(3 @ C(3 C(3 @ d(3 d(3 @ h(3 h(3 & 13.2 13.223 232 2 @ 5.5* 5.5*+) +) @ 153 153.+ .+22 225 5 @ 31.* 31.*+4 +43 3

& 24. 24.)2 )2+5 +5 t

?r & b(5 @ C(5 @ d(5 @ h(5 & 142.11 @ 5.52+ 5.52+ @ *+.1)3 *+.1)3 @ 22.5) & 1111 1111.25+* .25+* tm ? & b() @ C() @ h()

5)

& 321.3*2 @ 35.15) @ 21+.24+

& 55.*4) tm

8$ntr$l : a Terhad erhadap ap guli guling ng (over (over turning  E &

∑  r 1111 .25+* = 1.+3 & ∑   55.*4)

K 1,5

(L8 M b Terhadap Terhadap geser ( sliding sliding  E &

 ∑ /

∑0

&

, . (24.)2+5 4).34+*

= 3.+4

K 1,2

(L8 M keterangan :  & k$eisien geser C Terhadap Terhadap daya dukun dukung g tanah tanah (over (over stressing  •


•


•

∑  r − ∑   1111.25+* − 55.*4) = 2.)1)* m & 24.)2+5 ∑/  2

− a & 11 − 2.)1)* = 2.**32 m 2

Tegangan Tegangan pada tanah dasar I

&

Imin &

 ∑ /  1 ± ) . e  b  . b y  b    24.)2+5  1− ) . (2.**32 )   & 61.)52+ t'm 2 Q    11. (1 )  11 

(Tidak

L8 M Ima &

24.)2+5  1 + ) . (2.**32)   & 4.*5*3 t'm 2 P IJ& 35 t' t'm m2   11. (1 )  11 

(Tidak L8 M

3.'. 3.'.2 2 Den! Den!an an Gemp Gempa a #ori$ #ori$on onta tall

Tegangan Tegangan ijin tanah (dengan gempa IJ& 35 t'm 2  1,3 & 45.5 t'm 2 1. 8eadaan 8eadaan "ir "ir #$rmal #$rmal dengan dengan Bplit Bplit ressure ressure

5

?0 & a(4 a(4 @ C(4 C(4 @ e(4 e(4 @ g(4 g(4 & 23.4)13 @ 4.)*) @ 1),)31+ – 4,4)+4

& 44,+)4 t

?/ & a(3 a(3 @ C(3 C(3 @ d(3 d(3 @ g(3 g(3 & 6.85 @ 4,44 @ 1)),31* 6 1,2)34

& 14),*+5 t

?r & a(5 @ C(5 @ d(5 @g(5 & , @ 4),)2 @ ++4,443 @ 3),*)**

& 1155,)33 tm

? & a() @ C() @ e() @ g() & +5,55)2 +5,55)2 @ 1*,+21 1*,+21 @ +,25 +,251 1 @ 21,1 21,1+31 +31 & 415,242 415,242 tm 8$ntr$l : a. Terhadap Terhadap guling (over turning  E &

∑  r 1155,)33 = 2,*3 & ∑   415,242

K 1,5

(L8 M b. Terhadap Terhadap geser ( sliding sliding  E &

 ∑ /

∑0

&

, . (14),*+5) 44,+)4

= 2,2*)+ K 1,2

(L8 M

keterangan :  & k$eisien geser C. Terhadap Terhadap daya dukung tanah (over (over stressing  •


•

∑ M − ∑ M  ∑ V r

&

1155,)33 − 415,242 14),*+5

= 5,43 m


 2

− a &

11 2

− 5,43 = ,45+ m


&

∑ V  1 ± ) . e   b . b y  b    x

Imin &

14),*+5  ) . ( ,45+ )  1 −  & 1,53 t'm 2 11 . (1)  11 

Ima &

14),*+5  ) . ( ,45+ )  1 +  & 1),2+ t'm 2 P IJ& 22,5 t'm 2 11 . (1)  11 

Q

(L8 M

(L8 M

5*

2. 8eadaan 8eadaan "ir "ir #$rmal #$rmal tanpa Bplit Bplit ressure ressure ?0 & a(4 a(4 @ C(4 C(4 @ e(4 e(4 & 2,3* @ 5,4212 @ 1),)31+

& 4+,433 t

?/ & a(3 a(3 @ C(3 C(3 @ d(3 d(3 & ).*5 @ 4,44 @ 1)),31*

& 1*,15+ t

?r & a(5 @ C(5 @ d(5 & , @ 4),)2 @ ++4,443

& 111*,)4 tm

? & a() @ C() @ e() & +5,55)2 @ 1*,+21 @ +,251

& 24,51 tm

8$ntr$l : a. Terhadap Terhadap guling (over turning  E &

∑  r 111* ,)4 = 5,4 & 24,51 ∑ 

K 1,5

(L8 M b. Terhadap Terhadap geser ( sliding sliding  E &

 ∑ /

∑0

&

, . (1*,15+ ) 4+,433

= 2,522*

K 1,2

(L8 M keterangan :  & k$eisi en geser C. Terhadap Terhadap daya dukung tanah (over (over stressing  •


•

∑  r − ∑   111* ,)4 − 24,51 = 5,131 m & 1*,15+ ∑/


 2

−a&

11 2

− 5,131 = ,3)*3 m P

 )

& 1,*333 m


&

 ∑ /  1 ± ) . e  b  . b y  b   

5+

Ima &

1*,15+  ) . ( ,3)*3 )  1 +  & 11. (1)  11 

1+,44++ t'm2PIJ&22,5 t'm2

(L8 M Imin &

1*,15+  ) . ( ,3)*3)  1 −  & 12,+425 t'm 2 Q  11. (1)  11 

(L8 M

3. 8eadaan 8eadaan "ir "ir anjir anjir dengan dengan Bplit Bplit ressure ressure ?0 & b(4 b(4 @ C(4 C(4 @ e(4 e(4 @ h(4 h(4 & 3+,)4 ,)4)* @ 5,42 5,4212 12 @ 1),)3 ,)31+ – 5,)) 5,))2 2

& 5), ),4 t

?/ & b(3 b(3 @ C(3 C(3 @ d(3 d(3 6 h(3 h(3 & 12,)4)) @ 4,44 @ 1)),31* 6 34,44*

& 14*,+5 t

?r & b(5 @ C(5 @ d(5 @ h(5 & 11 11,1 ,1*2 *2 @ 4),) 4),)2 2 @ ++4,4 ++4,443 43 @ 4,3 4,31 1

& 11+ 11+1,5 1,543 43 tm

? & b() @ C() @ () @ h() & 1)),1 @ 1*,+21 @ 4+,222 @ 235,1+31 & 51,3+ tm


∑  r 11+1,543 = 2,334+ & ∑   51,3+

K 1,5

(L8 M

K 1,2

(L8 M

b. Terhadap Terhadap geser ( sliding sliding  E &

 ∑ /

∑0

&

, . (14*,+5 ) 35),4

= 1,*))



•

∑  r − ∑   11+1,543 − 51,3+ = 4,534 m & 14*,+5 ∑/


 2

− a &

11 2

− 4,534 = ,+2)) m P

 )

& 1,*33 m

)


&

Ima &

 ∑ /  1 ± ) . e  b  . b y  b    14*,+5  ) . ( ,+2)) )  1 +  & 2,3*5) t'm 2 P IJ& 22,5 t'm 2 11. (1)  11 

(L8 M Imin &

14*,+5  ) . ( ,+2)) )  1 −  & ),)+) t'm2 11. (1)  11 

Q

(L8 M

4. 8eadaan 8eadaan "ir "ir anjir anjir tanpa Bplit Bplit ressure ressure ?0 & b(4 b(4 @ C(4 C(4 @ e(4 e(4 & 3+,)4)* @ 5,4212 @ 1),)31+

& )1, t

?/ & b(3 b(3 @ C(3 C(3 @ d(3 d(3 & 12,)4)) @ 4,44 @ 1)),31*

& 1*3,45 t

?r & b(5 @ C(5 @ d(5 @ e(5 & 11 11,1 ,1* *2 2 @ 4),) 4),)2 2 @ ++4, ++4,44 443 3 @ +, +,2 251 51

& 1241 1241,1 ,1+ + tm tm

? & b() @ C() @ e() & 1)),1 @ 1*,+21 @ +,251

& 25,11) tm


∑  r 1241,1+ = 2,334+ & ∑   25,1))

K 1,5

(L8 M

K 1,2

(L8 M


 ∑ /

∑0

&

, . (1*3,45) )1,

= 2,*



∑  r − ∑   1241,1+ − 25,11) = 5,2)* m & 1*3,* ∑/ )1

•


 2

− a &

11 2

− 5,2)* = ,2232 m P

 )

& 1,*33 m


&

 ∑ /  1 ± ) . e  b  . b y  b   

Ima &

1*3,45  ) . ( ,2232)  1 +  & 11. (1)  11 

1*,31 t'm 2 P IJ& 22,5 t'm2

(L8 M Imin &

1*3,45  ) . ( ,2232 )  1 −  & 14,)441 t'm2 11. (1)  11 

Q

(L8 M

3.'.3 3.'.3 Den!a Den!an n Gempa Gempa %ertikal rtikal

Tegangan Tegangan ijin tanah (dengan gempa IJ& 1),2 t'm 2  1,3 & 21,) t'm 2

1. 8eadaan 8eadaan "ir "ir #$rmal #$rmal dengan dengan Bplit Bplit ressure ressure ?0 & a(4 a(4 @ C(4 C(4 @ g(4 g(4 & 2,3* @ 5,4212 – 4,4)+4

& 2*,332 t

?/ & a(3 a(3 @ C(3 C(3 @ d(3 d(3 @ (3 (3 6 g(3 g(3 & ).*5 @ 4,44 @ 1)),31* @ *,315+ 6 31,2)34

&

155,211 t ?r & a(5 @ C(5 @ d(5 @ (5 @ g(5 & , @ 4),)2 @ ++4,443 @ 4+,222 @ 3),*)**

& 125,355 tm

? & a() @ C() @ ()@ g() & +5,55)2 @ 1*,+21 @ 4+,222 @ 21,44

& 34,+3+ tm


∑  r 125,355 = 3,214* & ∑   3,4+3+

K 1,5

(L8 M

)2

b. Terhadap Terhadap geser ( sliding sliding 

 ∑ /

E &

∑0

&

, . (155,211) 2*,332

= 3,*34*

K 1,2

(L8 M keterangan :  & k$eisien geser C. Terhadap Terhadap daya dukung tanah (over (over stressing  •


•

∑ M − ∑ M  ∑ V r

&

125,355 − 34,+3+ 155,211

= 5,353 m


 2

−a&

11 2

− 2,23)* = ,14+ m


∑ /  ) . e  1 ±  b  . b y  b    155,211  ) . ( ,14+ )  1 −  & 12,+5* t'm 2 Q  & 11. (1)  11  &

Imin

Ima

(L8 M 155,211  ) . ( ,14+ )  1 +  & 15,2)2 & 15,2)2  t'm2 P IJ& 22,5 t'm2 11. (1)  11  (L8 M

2. 8eadaan 8eadaan "ir "ir #$rmal #$rmal tanpa Bplit Bplit ressure ressure ?0 & a(4 a(4 @ C(4 & 2,3* @ 5,4212

& 32,*1 t

?/ & a(3 a(3 @ C(3 C(3 @ d(3 d(3 @ (3 (3 & ).*5 @ 4,44 @ 1)),31* @ *,315+

& 1*),45 t

?r & a(5 @ C(5 @ d(5 @ (5 & , @ 4),)2 @ ++4,443 @ 4+,222

& 11)*,4) 11)*,4) tm

? & a() @ C() @ () & +5,55)2 @ 1*,+21 @ 4+,222

& 1)4,1++ tm

8$ntr$l : a. Terhadap Terhadap guling (over turning 

)3

E &

∑  r 11)*,4*) = ,11)3 & 1)4 , 1++ ∑ 

K 1,5

(L8 M

K 1,2

(L8 M


 ∑ /

∑0

&

, . (1*),45) 32,*1

= 3,++5



•

∑  r − ∑   11)*,4*) − 1)4,11+ = 5,3*) m & 1*),45 ∑/


 2

− a &

11 2

− 5,3*) = ,113+ m

P

 )

& 1,*33 m


&

Ima &

∑ /  ) . e  1 ±  b  . b y  b    1*), 45  ) . ( ,113+ )  1 +  & 1*,5 1*,55 5 t'm2 P IJ& IJ& 22, 22,5 5 t'm t'm2 11 . (1)  11 

(L8 M Imin &

1*),45  ) . ( ,113+ )  1 −  & 15,*++5 t'm 2 11 . (1)  11 

Q

(L8 M

3. 8eadaan 8eadaan "ir "ir anjir anjir dengan dengan Bplit Bplit ressure ressure ?0 & b(4 b(4 @ C(4 C(4 @ h(4 h(4 & 3+,)4)* @ 5,4212 – 5,))2

& 3+,4* t

?/ & b(3 b(3 @ C(3 C(3 @ d(3 d(3 @ (3 (3 6 h(3 h(3 & 12,) 12,)4) 4)) ) @ 4,4 4,44 4 @ 1)) 1)),3 ,31* 1*  @ *,3 *,315 15+ + – 34, 34,44 44* *

& 15, 15,2 23 3t

?r & b(5 @ C(5 @ d(5 @ h(5 & 11,1*2 @ 4),)2 @ ++4,443 @ 4,31

& 11+1,543 tm

? & b() @ C() @ () @ h() )4

& 1) 1)),1 @ 1* 1*,+21 @ 4+ 4+,222 @ 23 235,1+31

& 4 4,) tm

8$ntr$l : d.Terhadap guling (over ( over turning  E &

∑  r 11+1,543 = 2,5352 & 4 , ) ∑ 

K 1,5

(L8 M

K 1,2

(L8 M

e. Terhadap Terhadap geser geser ( sliding  E &

 ∑ /

∑0

&

, . (15,23) 3+,4*

= 2,+3)

keterangan :  & k$eisien geser . Terhadap Terhadap daya daya dukung tanah (over (over stressing  •


•

∑  r − ∑   11+1,543 − 4,) = 4,5** m & 15,23 ∑/


 2

− a &

11 2

− 4,5** = ,+122 m P

 )

& 1,*33 m


&

Ima &

 ∑ /  1 ± ) . e  b  . b y  b    15,23  ) . ( ,+122)  1 +  & 21,4114 t'm 2 P IJ& 22,5 t'm 2 11 . (1)  11 

(L8 M Imin &

15,23  ) . ( ,+122 )  1 −  & *,51*5 t'm2 11 . (1)  11 

Q

(L8 M

)5

4. 8eadaan 8eadaan "ir "ir anjir anjir tanpa Bplit Bplit ressure ressure ?0 & b(4 @ C(4 & 3+,)4)* @5,4212

& 45,)* t

?/ & b(3 b(3 @ C(3 C(3 @ d(3 d(3 @ (3 (3 & 12 12,)4)) @ 4,44 @ 1)),31* @ *,315+

& 1+ 1+1,21 t

?r & b(5 @ C(5 @ d(5 @ (5 & 11 11,1 ,1* *2 2 @ 4),) 4),)2 2 @ ++4, ++4,44 443 3 @ 4+, 4+,2 222 22

& 12 12,* ,*+4 +4 tm tm

? & b() @ C() @ () & 1)),1 @ 1*,+21 @4+,222

& 234,*13 tm


∑  r 12,*+4 = 5,1143 & 234,*13 ∑ 

K 1,5

(L8 M

K 1,2

(L8 M


 ∑ /

∑0

&

, . (1+1,21) 45,)*

= 2,+*



•

∑  r − ∑   12,*+4 − 234,*13 = 5,3*+ m & 1+1,21 ∑/


 2

− a &

11 2

− 5,3*+ = ,4)1 m P

 )

& 1,*33 m


&

∑ /  ) . e  1 ±  b  . b y  b   

))

Ima &

1+1,21  ) . ( ,4)1 )  1 +  & 21,514 t'm 2 P IJ& 22,5 t'm 2 11 . (1)  11 

(L8 MM Imin &

1+1,21  ) . ( ,4)1)  1 −  & 13,+34 t'm 2 11 . (1)  11 

Q

(L8MM

Tabel Tabel 3.1 "kumulasi "kumulasi 8$mbinasi Gaya6Gaya yang ekerja pada Tubuh Tubuh endung Te!an!an Tana, Tanpa Gempa Den!an Gempa

Somina*i !a"a !a"a + !a"a !a"a paa tuu, enun!

1.

2.

3.

Tanpa gempa a. "ir n$rmal @ gaya angkat b. "ir banjir @ gaya angkat !engan gempa h$ri>$ntal a. "ir n$rmal @ gaya angkat b. "ir n$rmal C. "ir banjir @ gaya angkat d. "ir banjir !engan gempa 9ertikal a. "ir n$rmal @ gaya angkat b. "ir n$rmal C. "ir banjir @ gaya angkat d. "ir banjir

Gulin!

Ge*er

/a0  1'

/in

/a0

/in

 22'

≥ 1'

≥ 12

3,5534 2,*351

3,)2+4 2,)45+

12.23** 15,+21*

14,4)+ 11,1)1

6 6

6 6

2,*3 5,4) 2,334+ 2,334+

2.2*)+ 2,522* 1,*)) 2,**

6 6 6 6

6 6 6 6

1),2+ 1+,44++ 2,3*5) 1*,31

1,5 12,+425 ),)+) 14,)441

3,214* ,11)3 2,5352 5,1143

3,*34* 3,++5 2,+3) 2,+*

6 6 6 6

6 6 6 6

15,2)2 1*,55 21,4114 21,514

12,+5* 15,*++5 *,51*5 13,+34

tm2

45

45

tm2

)

Analisa Stabilitas Bendung (BETA ver.)

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