Stabilitas Lereng Menggunakan Metode Fellenius Dan SLOPE/W 2007

APLIKASI KOMPUTER TEKNIK SIPIL

Stabilitas Lereng Menggunakan Metode Fellenius Dan SLOPE/W 2007

Nama

: Yogi Oktopianto

NPM

: 16309875

Fakultas

: Teknik Sipil dan Perencanaan

Jurusan

: Teknik Sipil

Dosen

: Juniarso, ST.,MT

JURUSAN TEKNIK SIPIL UNIVERSITAS GUNADARMA 2012

1

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1. DATA TANAH

Diketahui suatu lereng dengan data sebagai berikut : 3

γ = 17,4 kN/m θ = 10,74

0

C = 13 kN/ m

Rad (θ) = 0,1874 2

tan (θ) = 0,1897

Gambar Penampang Lereng

2. PERHITUNGAN FAKTOR KEAMANAN (FS) a. Metode Fellenius Tanpa Pengaruh Air Pori

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Tabel Perhitungan Metode Fellenius Panjang Irisan (L)

Luas Irisan (m2)

Sudut tiap Irisan (α)

Radians

Sin α

a

b

c

d

1

3.24

1.70

67.00

2

2.23

4.13

3

1.83

4

Cos α

Berat Irisan (Wt) (Luas* )

Wt*sin α

Wt*cos α

e

f

g

h

I

1.17

0.92

0.39

29.58

27.23

11.56

60.00

1.05

0.87

0.50

71.86

62.23

35.93

5.87

54.00

0.94

0.81

0.59

102.14

82.63

60.04

1.60

7.25

49.00

0.86

0.75

0.66

126.15

95.21

82.76

5

1.45

8.31

44.00

0.77

0.69

0.72

144.59

100.44

104.01

6

1.35

8.46

40.00

0.70

0.64

0.77

147.20

94.62

112.76

7

1.27

8.30

36.00

0.63

0.59

0.81

144.42

84.89

116.84

8

1.21

8.02

32.00

0.56

0.53

0.85

139.55

73.95

118.34

9

1.16

7.65

29.00

0.51

0.48

0.87

133.11

64.53

116.42

10

1.12

7.19

25.00

0.44

0.42

0.91

125.11

52.87

113.38

11

1.90

6.66

22.00

0.38

0.37

0.93

115.88

43.41

107.45

12

1.06

6.05

18.00

0.31

0.31

0.95

105.27

32.53

100.12

13

1.04

5.37

15.00

0.26

0.26

0.97

93.44

24.18

90.25

14

1.03

4.64

12.00

0.21

0.21

0.98

80.74

16.79

78.97

15

1.02

3.84

8.00

0.14

0.14

0.99

66.82

9.30

66.17

16

1.01

2.98

6.00

0.10

0.10

0.99

51.85

5.42

51.57

17

1.00

2.07

2.00

0.03

0.03

1.00

36.02

1.26

36.00

18

1.00

1.10

0.02

0.00

0.00

1.00

19.14

0.01

19.14

19

0.58

0.45

0.00

0.00

0.00

1.00

7.83

0.00

7.83

Jumlah

26.10

871.50

1,429.54

No

Nilai Faktor Keamanan: F 

C . L

tan . W . cos sin W . sin

13 x 26,10

0,1897 x1426,54 871,50

0,70 ( Lereng Labil )

Bersasarkan Nilai Faktor Keamanan Lereng dan Intensitas Longsor (Bowles, 1989)

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b. Perhitungan Menggunakan SLOPE/W 2007

Selain dilakukan perhitungan manual menggunakan metode Fellenius, dilakukan juga perhitungan menggunakan SLOPE/W 2007 untuk mengevaluasi hasil perhitungan secara manual dan program Komputer. Setelah dilakukan running, maka untuk melihat bagian project yang kritis terhadap sliding adalah adalah sebagai berikut: berikut:

Titik yang ditinjau F = 0 70

Gambar Output SLOPE/W 2007

Dari hasil SLOPE/W 2007 di dapatkan nilai factor keamanan keamanan F = 0,7 (Lingkaran merah titik  yang ditinjau) yang nilainya sama dengan menggunakan metode Fellenius. Sementara nilai factor keamanan minimum diperoleh F = 0,6. Dari kedua perhitungan tersebut berdasarkan

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3. PERHITUNGAN FAKTOR KEAMANAN ( DENGAN TERASERING) a. Metode Fellenius Tanpa Pengaruh Air Pori

Gambar Dimensi Terasering

Gambar Lereng Dengan Teterasering

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Tabel Perhitungan Metode Fellenius Berat

Sudut

Panjang

Luas

Irisan

Irisan

(L)

(m )

a

b

c

d

1

3.24

1.61

67.00

1.17

2

2.23

3.21

60.00

3

1.83

3.90

4

1.60

5

Sin

Cos

Irisan

Wt*sin

Wt*cos

α

α

(Wt)

α

α

g

h

i

0.92 0.39

28.01

25.79

10.95

1.05

0.87 0.50

55.85

48.37

27.93

54.00

0.94

0.81 0.59

67.86

54.90

39.89

4.33

49.00

0.86

0.75 0.66

75.34

56.86

49.43

1.45

4.57

44.00

0.77

0.69 0.72

79.52

55.24

57.20

6

1.35

5.38

40.00

0.70

0.64 0.77

93.61

60.17

71.71

7

1.27

6.22

36.00

0.63

0.59 0.81

108.23

63.61

87.56

8

1.21

6.95

32.00

0.56

0.53 0.85

120.93

64.08

102.55

9

1.16

7.49

29.00

0.51

0.48 0.87

130.33

63.18

113.99

10

1.12

7.20

25.00

0.44

0.42 0.91

125.28

52.95

113.54

11

1.90

6.66

22.00

0.38

0.37 0.93

115.88

43.41

107.45

12

1.06

6.06

18.00

0.31

0.31 0.95

105.44

32.58

100.28

13

1.04

5.38

15.00

0.26

0.26 0.97

93.61

24.23

90.42

14

1.03

4.64

12.00

0.21

0.21 0.98

80.74

16.79

78.97

15

1.02

3.85

8.00

0.14

0.14 0.14 0.99

66.99

9.32

66.34

16

1.01

2.99

6.00

0.10

0.10 0.10 0.99

52.03

5.44

51.74

17

1.00

2.08

2.00

0.03

0.03 0.03 1.00

36.19

1.26

36.17

18

1.00

1.11

0.02

0.00

0.00 0.00 1.00

19.31

0.01

19.31

19

0.58

0.18

0.00

0.00

0.00 1.00

3.13

0.00

3.13

Jumlah

26.10

678.20

1,228.56

No

2

tiap Irisan

C . L

tan . W . cos

W  si

(Luas* )

(α)

Nilai Faktor Keamanan: F 

Radians

e

f

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b. Perhitungan Menggunakan SLOPE/W 2007

Titik yang ditinjau F= 0.80

Gambar Output SLOPE/W 2007

Dari hasil SLOPE/W 2007 di di dapatkan nilai factor keamanan keamanan F = 0,8 (Lingkaran merah titik 

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4. PERHITUNGAN FAKTOR FAKTOR KEAMANAN ( DENGAN TERASERING TIPE 2) a. Metode Fellenius Tanpa Pengaruh Air Pori

Gambar Dimensi Terasering Tipe 2

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Tabel Perhitungan Metode Fellenius Lereng Tipe 2 Berat

Sudut

Panjang

Luas

Irisan

Irisan

(L)

(m )

a

b

c

d

e

f

1

3.24

1.61

67.00

1.17

0.92

2

2.23

3.21

60.00

1.05

3

1.83

3.95

54.00

4

1.60

4.33

5

1.45

6

Sin

Cos

Irisan

Wt*sin

Wt*cos

α

α

(Wt)

α

α

g

h

i

0.39

28.01

25.79

10.95

0.87

0.50

55.85

48.37

27.93

0.94

0.81

0.59

68.73

55.60

40.40

49.00

0.86

0.75

0.66

75.34

56.86

49.43

4.48

44.00

0.77

0.69

0.72

77.95

54.15

56.07

1.35

4.46

40.00

0.70

0.64

0.77

77.60

49.88

59.45

7

1.27

4.30

36.00

0.63

0.59

0.81

74.82

43.98

60.53

8

1.21

4.11

32.00

0.56

0.53

0.85

71.51

37.90

60.65

9

1.16

4.57

29.00

0.51

0.48

0.87

79.52

38.55

69.55

10

1.12

5.11

25.00

0.44

0.42

0.91

88.91

37.58

80.58

11

1.90

5.58

22.00

0.38

0.37

0.93

97.09

36.37

90.02

12

1.06

5.88

18.00

0.31

0.31

0.95

102.31

31.62

97.30

13

1.04

5.75

15.00

0.26

0.26

0.97

100.05

25.89

96.64

14

1.03

4.64

12.00

0.21

0.21

0.98

80.74

16.79

78.97

15

1.02

3.84

8.00

0.14

0.14

0.99

66.82

9.30

66.17

16

1.01

2.98

6.00

0.10

0.10

0.99

51.85

5.42

51.57

17

1.00

2.07

2.00

0.03

0.03

1.00

36.02

1.26

36.00

18

1.00

1.08

0.02

0.00

0.00

1.00

18.79

0.01

18.79

No

2

tiap Irisan

Radians

(Luas* )

(α)

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b. Perhitungan Menggunakan SLOPE/W 2007

Titik yang ditinjau F = 0,9

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5. PERHITUNGAN FAKTOR FAKTOR KEAMANAN ( DENGAN TERASERING TIPE 3) a. Metode Fellenius Tanpa Pengaruh Air Pori

Gambar Dimensi Terasering Tipe 3

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Tabel Perhitungan Metode Fellenius Lereng Tipe 2

No

Panjang

Luas

Irisan

Irisan 2

Berat

Sudut tiap Irisan

Radians

Sin α

Cos α

Irisan

Wt*sin

Wt*cos

(Wt)

α

α

(L)

(m )

a

b

c

d

e

f

g

h

I

1

2.03

0.92

60.00

1.05

0.87

0.50

16.01

13.86

8.00

2

1.72

2.49

54.00

0.94

0.81

0.59

43.33

35.05

25.47

3

1.41

3.76

49.00

0.86

0.75

0.66

65.42

49.38

42.92

4

1.31

4.48

44.00

0.77

0.69

0.72

77.95

54.15

56.07

5

1.24

4.40

40.00

0.70

0.64

0.77

76.56

49.21

58.65

6

1.18

4.19

36.00

0.63

0.59

0.81

72.91

42.85

58.98

7

1.14

3.38

32.00

0.56

0.53

0.85

58.81

31.17

49.88

8

1.10

3.47

29.00

0.51

0.48

0.87

60.38

29.27

52.81

9

1.08

3.33

25.00

0.44

0.42

0.91

57.94

24.49

52.51

10

1.05

3.75

22.00

0.38

0.37

0.93

65.25

24.44

60.50

11

1.04

4.11

18.00

0.31

0.31

0.95

71.51

22.10

68.01

12

1.02

4.41

15.00

0.26

0.26

0.97

76.73

19.86

74.12

(Luas* )

(α)

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b. Perhitungan Menggunakan SLOPE/W 2007

Titik yang ditinjau F=1

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6. KESIMPULAN

Tabel Rekapitulasi Faktor Keamanan Penampang Lereng

FS SLOPE/W 2007

FS Metode Fellenius

Keterangan

0,7

0,7

Lereng Labil

0,8

0,8

Lereng Labil

1. Kondisi Lereng Asli

2. Terasering Tipe 1

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Dari pembahasan pembahasan dan analisis yang dilakukan didapat nilai factor keamanan keamanan pada tabel diatas yang diterapkan kedalam 4 bentuk terasering dan nilai F yang dihasilkan dari ke 4 pemodelan baik menggunakan metode Fellenius maupun SLOPE/W 2007 kondisi lereng tetap labil dimana nilai F kurang dari 1,07 (Nilai Faktor Keamanan Lereng dan Intensitas Longsor (Bowles, 1989) ) sehingga perlu tinjauan dan perhitungan kembali terhadap factor keamanan keamanan kesetabilan lereng. lereng. Maka dari itu diperlukan adanya adanya perbaikan terhadap lereng yaitu dapat dengan cara membuat dinding penahan tanah. Dinding penahan tanah merupakan bangunan penambat tanah dari pasangat batu, atau beton bertulang. Dinding penahan tanah ini digunakan untuk menahan gerakan tanah sehingga longsor dapat diatasi.