bab 3 irbang

Perancangan Irigasi Dan Bangunan Air

BAB III

ANALISA STABILITAS BENDUNG

Gaya–gaya yang bekerja pada tubuh bendung, akibat :

1. Tekanan air.

2. Tekanan lumpur.

3. Tekanan berat sendiri bendung.

4. Gaya gempa.

5. Gaya angkat (uplift pressure).

III.1. Tekanan Air

III.1.1.Tekanan Air Normal

Gambar 3.1 Diagram Tekanan Akibat Air Normal

= 1 ton/m3

Pa1 = = = 6,661 ton`

Pa2 = b . h . = (1,217).(3,65).(1)= 4,442 ton

Tabel. 3.1 Perhitungan Tekanan Air Normal

34


Bagian berat (ton) lengan (m) momen (t m) V H x y Mr Mo

Pa1 6.661 4.318 28.763Pa2 4.442 6.398 28.420

jumlah 4.442 6.661 28.420 28.763

III.1.2 Tekanan Air Banjir (Flood)

Gambar 3.2 Diagram Tekanan Akibat Air Banjir

Pf1 = = = 6,661 ton

Pf2 = b . h . = 1,953.(3,65).(1) = 7,128 tonPf3 = b . h . = 1,217 .(3,65).(1) = 4,442 tonPf4 = b . h . = 1,71.(1,953).(1) = 3,340 ton

Pf5 = = = 4,234ton

Pf6 = = = -4,234 ton

Tabel.3.2 Perhitungan Tekanan Air Banjir

Bagian berat (ton) Lengan (m) Momen (t m)

35


V H x y Mr MoPf1 6.661 4.318 28.763Pf2 7.128 4.746 33.832Pf3 4.442 6.391 28.389 Pf4 3.340 6.121 20.442 Pf5 4.234 0.971 4.111 Pf6 -4.234 3.471 -14.696

jumlah 12.016 9.556 38.246 62.595

III.1. 3 Tekanan Lumpur

= 0,6 ton/m3

θ = 300

Ka = tan2 (450 – θ/2)

= tan2 (450 – 30o/2)

= 0,333

Keterangan :

γlumpur = berat volume lumpur (t/m3)

θ = sudut gesek dalam

Ka = tekanan lumpur aktif

Gambar 3.3 Diagram Tekanan Akibat Lumpur

PL1 = . Ka . . h2

36


= .(0,333).(0,6).(3,65)2

= 1,331 ton

PL2 = .b.h

= 0,6.(1,217).(3,65)

= 2,665 ton

Tabel.3.3 Perhitungan Tekanan Lumpur

Bagian berat (ton) Lengan (m) Momen (t m) V H x y Mr Mo

PL1 1.331 4.318 0 5.747PL2 2.665 6.398 17.052

jumlah 2.665 1.331 17.052 5.747

III.2. Tekanan Berat Sendiri Bendung

Berat volume pasangan batu = 2,2 t/m2

Gambar 3.4 Diagram Tekanan Akibat Berat Sendiri Bendung

37


Pada badan bendung yang berbentuk parabola, luas penampang digunakan pendekatan :

A = 2/3 . L . H

W1 = b . h . = 1,217 . 1,601 . 2,2 = 4,287 ton

W2 = b . h . = 0,882. 5,181 . 2,2 = 10,053 ton

W3 = b . h . = 1,9 . 3,006 . 2,2 = 12,565 ton

W4 = b . h . = 1,50 . 2,506 . 2,2 = 8,270 ton

W5 = b . h . = 1,50 . 2,5 . 2,2 = 8,250 ton

W6 = 2/3.b. h . = 2/3.0,882.0,031. 2,2 = 0,040 ton

W7 = 2/3 . b. h . = 2/3 . 1,9 .1,174 . 2,2 = 3,272 ton

W8 = 1/2 . b. h . = 1/2 . 1,50 . 1,50 . 2,2 = 2,475 ton

W9 = 1/2 . b. h . = 2/3 . 1,50 . 1,50 . 2,2 = 2,475 ton

Tabel 3.4 Perhitungan Tekanan Berat Sendiri Bendung

segmen berat (ton) Lengan (m) Momen (t m) x y Mr Mo

W1 4.287 6.391 2.700 27.395 11.574W2 10.053 5.336 4.090 53.644 41.118W3 12.565 3.950 4.003 49.632 50.298W4 8.270 2.255 2.750 18.648 22.742

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W5 8.250 0.753 3.756 6.212 30.987W6 0.040 5.231 6.692 0.210 0.268W7 3.272 4.188 5.953 13.701 19.476W8 2.475 2.506 4.506 6.202 11.152W9 2.475 1.000 7.500 2.475 18.563

jumlah 51.686 178.120 206.177

III.3. Gaya Gempa

III.3.1. Gempa Horizontal

Gaya Horizontal (H) = Kh . ΣW

= 0,1 . 51,685 = 5,169 ton

Momen akibat gempa horizontal :

M0 = Kh . ΣM01

= 0,1 . 206,177 = 20,618 tm

Keterangan :

H = gaya gempa horizontal (t)

Kh = koefisien gempa horizontal, (Pondasi batu : Kh = 0,10)

V1 = berat sendiri bendung (t)

M01 = momen guling akibat berat sendiri (tm)

III.3.2. Gempa Vertikal

Gaya Vertikal (V) = Kv . ΣW

= 0,05 . 51,685

= 2,584 ton

39


Momen akibat gempa vertikal :

Mr = Kv . ΣMr1

= 0,05. (178,120)

= 8,906 tm

Keterangan :

V = gaya gempa vertikal (t)

Kv = koefisien gempa vertikal, (Pondasi batu : Kv = 0,05)

Mr1 = momen tahanan akibat berat sendiri (tm)

III.4. Gaya Angkat (Uplift Pressure)

III.4.1. Air Normal

ΣL = Lh + Lv

= 16,5 + 13,6

= 30,1 m

ΔH = 103,65 – 100 = 3,65 m

Ux = Hx – . ΔH

Ux = Hx – .(3,65)

Ux = Hx – 0,121 Lx

Keterangan :

Hx = tinggi muka air dari titik yang dicari (m)

Lx = panjang rayapan (m)

ΣL = total rayapan (m)

ΔH = tinggi muka air normal (m)

40


Ux = uplift pressure di titik x (t/m2)

Gambar 3.5 Rayapan Gaya Angkat

Tabel 3.5 Perhitungan Gaya Angkat Akibat Air Normal

Bagian Gambar Gaya angkat per 1 m panjang (t)

a-b

H = .(0,609 + 3,411) = 5,025 t

y =

= = 0,96 m

y total = 2,5 – 0,96 = 1,54 m

41


b-c

V = .(3,411 + 3,593) = 5,253 t

x =

= = 0,744 m

x total = 1,50 - 0,744 = 0,756 m

c-d

H = .(2,274 + 3,593) = 4,400 t

y =

= = 0,694 m

y total = 1,5 – 0,694 = 0,806 m

d-e

V = .(2,274 + 2,456) = 3,548 t

x =

= = 0,74 m

x total = 1,50 – 0,74 = 0,76 m

42


e-f

H = .(1,577 + 2,456) = 2,017 t

y =

= = 0,464 m

y total = 1,00 – 0,464 = 0,536 m

f-g

V = .(1,577 + 1,807) = 3,215 t

x =

= = 0,928 m

x total = 1,90 – 0,928 = 0,972 m

g-h

H = .(1,807 + 2,928) = 2,368 t

y =

= = 0,461 m

y total = 1,0 – 0,461 = 0,539 m

43


h-i

V = .(2,928 + 3,182) = 6,416 t

x =

= = 1,035 m

x total =2,1 – 1,035 = 1,065 m

i-j

H = .(2,127 + 3,182) = 3,185 t

y =

= = 0,56 m

y total = 1,2 – 0,56 = 0,64 m

Tabel 3.6 Gaya angkat akibat air normal

Titik Hx (m) Lx (m) Ux (t/m2) Uplift Force (t) Lengan (m) Momen (t m)

V H x y Mr Moa 4.251 30.100 0.609 5.025 1.540 7.739b 6.751 27.600 3.411 5.253 0.756 3.971 c 6.751 26.100 3.593 4.400 0.806 3.546d 5.251 24.600 2.274 3.548 0.760 2.696 e 5.251 23.100 2.456 2.017 0.536 1.081f 4.251 22.100 1.577

44


3.215 0.972 3.125 g 4.251 20.200 1.807 2.368 0.539 1.276h 5.251 19.200 2.928 6.416 1.065 6.833 i 5.251 17.100 3.182 3.185 0.640 2.038j 4.051 15.900 2.127

JUMLAH 18.432 16.995 16.626 15.681

Gaya Angkat :

H = fu . ΣH = 0,50 . (16,995) = 8,498 t

V = fu . ΣV = 0,50 . (18,432) = 9,216 t

M0 = fu . ΣM0 = 0,50 . (15,681) = 7,841 tm

Mr = fu . ΣMr = 0,50 . (16,626) = 8,313 tm

Dimana : fu = koefisien reduksi untuk jenis tanah keras (50 %)

III.4.2. Air Banjir

Ux = Hx - . ΔH

ΔH = Hb = 105,603 -100 = 5,603 m

Ux = Hx - . 5,603

Ux = Hx - 0,186 Lx

Keterangan :

Hx = tinggi muka air banjir dari titik yang dicari (m)

Lx = panjang rayapan (m)

ΣL = total rayapan (m)

ΔH = beda tinggi M.A.B dengan muka air di hilir (m)

Ux = uplift pressure di titik x (t/m2)

Tabel 3.7 Perhitungan gaya angkat akibat air banjir

Bagian Gambar Gaya angkat per 1 m panjang (t)

45


a-b

H = .(0,605 + 3,570) = 5,219 t

y =

= = 0,954 m

y total = 2,5 – 0,954 = 1,546 m

b-c

E

V = .(3,570 + 3,849) = 5,564 t

x =

= = 0,741 m

x total = 1,50 - 0,741 = 0,759 m

c-d

H = .(2.628 + 3,849) = 4,858 t

y =

= = 0,703 m

y total = 1,50 – 0,703 = 0,797 m

46


d-e

V = .(2,628 + 2,907) = 4,151 t

x =

= = 0,737 m

x total = 1,50 – 0,737 = 0,763 m

e-f

H = .(2,093 + 2,907) = 2,905 t

y =

= = 0,473 m

y total = 1,00 – 0,473 = 0,527 m

f-g

V = .(2,093 + 2,447) = 4,313 t

x =

= = 1,151 m

x total = 1,90 – 1,151 = 0,749 m

47


g-h

H = .(2,447 + 3,633) = 3,04 t

y =

= = 0,467 m

y total = 1,0 – 0,467 = 0,533 m

h-i

V = .(3,633 + 4,023) = 8,039 t

x =

= = 1,032 m

x total =2,1 – 1,032 = 1,068 m

i-j

H = .(3,047 + 4,023) = 4,242 t

y =

= = 0,572 m

y total = 1,2 – 0,572 = 0,628 m

Tabel 3.8 Gaya angkat akibat air banjir

Titik Hx (m) Lx (m) Ux (t/m2) Uplift Force (t) Lengan (m) Momen (t m)

V H x y Mr Moa 6.204 30.100 0.605 5.219 1.546 8.069b 8.704 27.600 3.570 5.664 0.759 4.299

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c 8.704 26.100 3.849 4.858 0.797 3.872d 7.204 24.600 2.628 4.151 0.763 3.167 e 7.204 23.100 2.907 2.905 0.527 1.531f 6.204 22.100 2.093 4.313 0.749 3.230 g 6.204 20.200 2.447 3.04 0.533 1.620h 7.204 19.200 3.633 8.039 1.068 8.586 i 7.204 17.100 4.023 4.242 0.628 2.664j 6.004 15.900 3.047

JUMLAH 22.167 20.264 19.282 17.756

Gaya angkat :

H = fu . ΣH = 0,50 . (20,264) = 10,132 t

V = fu . ΣV = 0,50. (22,167) = 11,084 t

M0 = fu . ΣM0 = 0,50 . (17,756) = 8,878 tm

Mr = fu . ΣMr = 0,50 . (19,282) = 9,641 tm

Tabel 3.9 Akumulasi Beban-Beban pada Bendung

No Keterangan Gaya (t) Momen ( t m) Vertikal Horisontal Mr Mo1 2 3 4 5 6

Tekanan Air

a Air Normal 4.442 6.661 28.420 28.763b Air Banjir 12.016 9.556 48.862 63.918c Tekanan Lumpur 2.665 1.331 17.052 5.747d Berat Sendiri Bendung 51.686 - 178.120 206.177 Gaya Gempa e Gempa Horisontal - 5.169 20.618 20.618f Gempa Vertikal 2.584 - 8.906 8.906 Gaya Angkat g Air Normal 9.216 8.498 8.313 7.840h Air Banjir 11.084 10.132 9.641 8.878

III.5. Kontrol Stabilitas Bendung

Kombinasi gaya-gaya yang bekerja pada bendung :

49


III.5.1. Tanpa Gempa

Tegangan ijin tanah σ’= 16,5 t/m2

1. Keadaan Air Normal dengan Uplift Pressure

ΣH = a(4) + c(4) + g(4)

= 6,661 + 1,331 + 8,498 = 16.49 t

ΣV = a(3) + c(3) + d(3) + g(3)

= 4,442 + 2,665 + 51,686 + 9.216 = 68,009 t

ΣMr = a(5) + c(5) + d(5) + g(5)

= 28,420 + 17,052 + 178,120 + 8,313 = 231,905 tm

ΣM0 = a(6) + c(6) + g(6)

= 28,763 + 5,747 + 7,840 = 42,35 tm

Kontrol :

a) Terhadap guling (over turning)

SF = = .............. ≥ 1,50 (OK!)

b) Terhadap geser (sliding)

SF = = .......≥ 1,20 (OK!)

keterangan : f = koefisien geser``

c) Terhadap daya dukung tanah (over stressing)

Resultante beban vertikal bekerja sejarak a dari titik O.

a = =

Resultante beban vertikal bekerja sejarak e dari pusat berat bendung.

e = =

Jarak e masih terletak di dalam ‘ Bidang Kern’

e = 0,713 m <

e < 1,167 m

Tegangan yang terjadi pada tanah akibat beban – beban pada bendung :

50


σ =

=

=

=

Tegangan izin tanah dasar (σ’) =1,65 kg/cm2 = 16,5 t/m2

Tegangan tanah dikontrol per 1 meter panjang bendung :

σmin = = 3,778 t/m2 > 0 (OK!)

σmax = = 15,653 t/m2 < σ’= 16,5 t/m2 (OK!)

Gambar 3.6 Tegangan Izin Bendung

51


2. Keadaan Banjir dengan Uplift Pressure

ΣH = b(4) + c(4) + h(4)

= 9,556 + 1,331 + 10,132 = 21,019 t

ΣV = b(3) + c(3) + d(3) + h(3)

= 12,016 + 2,665 + 51,686 + 11,084 = 77,451 t

ΣMr = b(5) + c(5) + d(5) + h(5)

= 48,862+ 17,052 + 178,120 + 9,641 = 253,675 tm

ΣM0 = b(6) + c(6) + h(6)

= 63,918 + 5,747 + 8,878 = 78,543 tm

Kontrol :

a) Terhadap guling (over turning)

SF = = ≥ 1,50 (OK !)

b) Terhadap geser (sliding)

SF = = ≥ 1,20 (OK !)

keterangan : f = koefisien geser

c) Terhadap daya dukung tanah (over stressing)


a = =


e = = < = 1,167 m

Tegangan pada tanah dasar

σ =

σmin = = 9,746 t/m2 > 0 (OK !)

52


σmax = = 12,383 t/m2 < σ’= 16,5 t/m2 (OK !)

III.5.2. Dengan Gempa Horizontal

Tegangan ijin tanah (dengan gempa) σ’= 16,5 t/m2 x 1,3 = 21,45 t/m2


ΣH = a(4) + c(4) + e(4) + g(4)

= 6,661 + 1,331 + 5,169 + 8,498 = 21,659 t

ΣV = a(3) + c(3) + d(3) + g(3)

= 4,442 + 2,665 + 51,686 + 9,216 = 68,009 t

ΣMr = a(5) + c(5) + d(5) +g(5)

= 28,420 + 17,052 + 178,120 + 8,313 = 231,905 tm

ΣM0 = a(6) + c(6) + e(6) + g(6)

= 28,763 + 5,747 + 20,618 + 7,840 = 62,968 tm

Kontrol :

a). Terhadap guling (over turning)

SF = = ≥ 1,50 (OK !)

b).Terhadap geser (sliding)

SF = = ≥ 1,20 (OK !)


c). Terhadap daya dukung tanah (over stressing)


a = =


e = = < = 1,167 m


53


σ =

σmin = = 1,255 t/m2 > 0 (OK !)

σmax = = 18,176 t/m2 < σ’= 21,45 t/m2 (OK !)

2. Keadaan Air Normal tanpa Uplift Pressure

ΣH = a(4) + c(4) + e(4)

= 6,661 + 1,331 + 5,169 = 13,161 t

ΣV = a(3) + c(3) + d(3)

= 4,442 + 2,665 + 51,686 = 58,793 t

ΣMr = a(5) + c(5) + d(5)

= 28,420 + 17,052 + 178,120 = 223,592 tm

ΣM0 = a(6) + c(6) + e(6)

= 28,763 + 5,747 + 20,618 = 55,128 tm

Kontrol :


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)




a = =


54


e = = < = 1,167 m


σ =

σmax = = 12,97 t/m2 < σ’= 21,45 t/m2 (OK !)

σmin = = 3,828 t/m2 > 0 (OK !)

3. Keadaan Air Banjir dengan Uplift Pressure

ΣH = b(4) + c(4) + e(4) + h(4)

= 9,556 + 1,331 + 5,169 + 10,132 = 26,188 t

ΣV = b(3) + c(3) + d(3) + h(3)

= 12,016 + 2,665 + 51,686 + 11,084 = 77,451 t

ΣMr = b(5) + c(5) + d(5) + h(5)

= 48,862 + 17,052 + 178,120 + 9,641 = 253,675 tm

ΣM0 = b(6) + c(6) + e(6) + h(6)

= 63,918 + 5,747 + 20,618 + 8,878 = 99,161 tm

Kontrol :


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)




55


a = =


e = = < = 1,167 m


σ =

σmax = = 15,853 t/m2 < σ’= 21,45 t/m2 (OK !)

σmin = = 6,275 t/m2 > 0 (OK !)

4. Keadaan Air Banjir tanpa Uplift Pressure

ΣH = b(4) + c(4) + e(4)

= 9,556 + 1,331 + 5,169 = 16,056 t

ΣV = b(3) + c(3) + d(3)

= 12,016 + 2,665 + 51,686 = 66,367 t

ΣMr = b(5) + c(5) + d(5) + e(5)

= 48,862 + 17,052 + 178,120 + 20,618 = 264,652 tm

ΣM0 = b(6) + c(6) + e(6)

= 63,918 + 5,747 + 20,618 = 90,283 tm

Kontrol :


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)


56




a = =


e = = < = 1,167 m


σ =

σmax = = 16,575 t/m2 < σ’= 21,45 t/m2 (OK !)

σmin = = 2,387 t/m2 > 0 (OK !)

III.5.3. Dengan Gempa Vertikal

Tegangan ijin tanah (dengan gempa) σ’= 16,5 t/m2 x 1,3 = 21,45 t/m2


ΣH = a(4) + c(4) + g(4)

= 6,661 + 1,331 + 8,498 = 16,49 t

ΣV = a(3) + c(3) + d(3) + f(3) - g(3)

= 4,442 + 2,665 + 51,686 + 2,584 - 9,216 = 52,161 t

ΣMr = a(5) + c(5) + d(5) + f(5) + g(5)

= 28,420 + 17,052 + 178,120 + 8,313 = 231,905 tm

ΣM0 = a(6) +c(6) + f(6) + g(6)

= 63,918 + 5,747 + 8,906 + 7,840 = 86,411 tm

Kontrol :


SF = = ≥ 1,50 (OK !)

57



SF = = ≥ 1,20 (OK !)




a = =


e = = < = 1,167 m


σ =

σmin = = 2,910 t/m2 > 0 (OK !)

σmax = = 11,993 t/m2 < σ’= 21,45 t/m2 (OK !)

2. Keadaan Air Normal tanpa Uplift Pressure

ΣH = a(4) + c(4)

= 6,661 + 1,331 = 7,992 t

ΣV = a(3) + c(3) + d(3) + f(3)

= 4,442 + 2,665 + 51,686 + 2,584 = 61,377 t

ΣMr = a(5) + c(5) + d(5) + f(5)

= 28,420 + 17,052 + 178,120 + 8,906 = 232,498 tm

ΣM0 = a(6) + c(6)

= 28,763 + 5,747 = 34,51 tm

Kontrol :


58


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)




a = =


e = = < = 1,167 m


σ =

σmax = = 10,587 t/m2 < σ’= 21,45 t/m2 (OK !)

σmin = = 6,95 t/m2 > 0 (OK !)

3. Keadaan Air Banjir dengan Uplift Pressure

ΣH = b(4) + c(4) + h(4)

= 9,556 + 1,331 + 10,132 = 21,019 t

ΣV = b(3) + c(3) + d(3) + f(3) – h(3)

= 12,016 + 2,665 + 51,686 + 2,584 – 11,084 = 57,867 t

ΣMr = b(5) + c(5) + d(5) + h(5)

= 48,862 + 17,052 + 178,120 + 9,641 = 253,675 tm

ΣM0 = b(6) + c(6) + f(6) + h(6)

= 63,918 + 5,747 + 8,906 + 8,878 = 87,449 tm

59


Kontrol :


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)




a = =


e = = < = 1,167 m


σ =

σmax = = 12,709 t/m2 < σ’= 21,45 t/m2 (OK !)

σmin = = 3,824 t/m2 > 0 (OK !)

4. Keadaan Air Banjir tanpa Uplift Pressure

ΣH = b(4) + c(4)

= 9,556 + 1,331 = 10,887 t

ΣV = b(3) + c(3) + d(3) + f(3)

= 12,016 + 2,665 + 51,686 + 2,584 = 68,951 t

ΣMr = b(5) + c(5) + d(5) + f(5)

60


= 48,862 + 17,052 + 178,120 + 8,906 = 252,94 tm

ΣM0 = b(6) + c(6)

= 63,918 + 5,747 = 69,665 tm

Kontrol :


SF = = ≥ 1,50 (OK !)


SF = = ≥ 1,20 (OK !)




a = =


e = = < = 1,167 m


σ =

σmax = = 16,959 t/m2 < σ’= 21,45 t/m2 (OK !!)

σmin = = 2,741 t/m2 > 0 (OK !!)

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Tabel 3.10 Akumulasi Kombinasi Gaya-Gaya yang Bekerja pada Tubuh Bendung

Kombinasi gaya – gaya pada tubuh

bendung

SFTegangan Tanah

Tanpa Gempa Dengan Gempa

Guling

1,5

Geser

1,2

Max

< 16,5

t/m2

Min

> 0

Max

< 21,45

t/m2

Min

> 0

1.

Tanpa gempa

a. Air normal + gaya angkat 5,476 2,887 15,653 3,778 - -

b. Air banjir + gaya angkat 3,23 2,579 12,383 9,746 - -

2.

Dengan gempa horizontal

a. Air normal + gaya angkat 3,683 2,198 - - 18,176 1,255

b. Air normal 4,056 3,127 - - 12,97 3,828

c. Air banjir + gaya angkat 2,558 2,07 - - 15,853 6,275

d. Air banjir 2,931 2,893 - - 16,575 2,387

3. Dengan gempa vertikal

a. Air normal + gaya angkat 2,684 2,214 - - 11,993 2,916

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b. Air normal 6,795 5,376 - - 10,587 6,95

c. Air banjir + gaya angkat 2,901 1,927 - - 12,709 3,824

d. Air banjir 3,631 4,433 - - 16,959 2,741

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bab 3 irbang

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