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.
