Metode bishop
- 2. Bishop’s Method Circular Slip Surface Free-Body Diagram Slice
- 3. Gaya Vertikal Nj cos θj + Tj sin θj – Wj – Xj + Xj+1 = 0 Nj’ cos θj = Wj + Xj - Xj+1 - Tj sin θj – ujlj cos θj Rasio Tekanan Air Pori (ru) ru = ujbj Wj = γw Zw j γZ j Kesetimbangan Momen 𝑇𝑗 = Wjxj R = Wj sin θj
- 4. Factor Safety FS = τf τm = τf j τj Effective Stress Analysis (ESA) FS = Nj tan ∅′ j Tj mj = 1 cos 𝜃 𝑗+ tan ∅′ j sin θj FS FS = Wj(1 − ru) tan ∅′ j mj Wj sin θj FS = 𝑊 𝑗mj tan ∅′ j Wj sin θj
- 5. Apabila air tanah berada di bawah permukaan tergelincir, ru = 0 FS = Wj tan ∅′ j mj Wj sin θj Total Stress Analysis (TSA) FS = su jlj Wj sin θj bj = lj cos θj, FS = su j bj cos θj Wj sin θj
- 6. Estimate the factors of safety consider case tension crack and filled with water. su = 30 kPa Φ’ = 33o γw = 9.8 kN/m3 γsat = 18 kN/m3 R = 14.3 m TCM/R = 23.7 kN FS = 0.95 (asumsi) Kedalaman tension crack(Zcr ) = 2 𝑠 𝑢 𝛾 = 2 x 30 18 = 3.33 m Contoh Soal
- 7. Penyelesaian
- 8. Slice b (m) z (m) W (kN) Zw (m) ru θ mj W sin θ ESA TSA 1 4.9 1 88.2 1 0.544 -23 1.53 -34.462 39.923 159.695 2 2.5 3.6 162 3.6 0.544 -10 1.15 -28.131 55.115 76.157 3 2 4.6 165.6 4.6 0.544 0 1 0.000 48.991 60.000 4 2 5.6 201.6 5 0.486 9 0.91 31.537 61.224 60.748 5 2 6.5 234 5.5 0.461 17 0.86 68.415 70.482 62.742 6 2 6.9 248.4 5.3 0.418 29 0.83 120.427 77.897 68.601 7 2 6.8 244.8 4.5 0.360 39.5 0.83 155.712 84.409 77.758 8 2.5 5.3 238.5 2.9 0.298 49.5 0.86 181.357 93.519 115.483 9 1.6 1.6 46.08 0.1 0.034 65 0.96 41.763 27.750 113.578 Jumlah 536.617 559.310 794.761 FS 1.042 1.481