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Geotechnical Engineering-II [Lec #27: Infinite Slope Stability Analysis]

Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
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Geotechnical Engineering-II [Lec #27: Infinite Slope Stability Analysis]

  1. 1. 1 Geotechnical Engineering–II [CE-321] BSc Civil Engineering – 5th Semester by Dr. Muhammad Irfan Assistant Professor Civil Engg. Dept. – UET Lahore Email: mirfan1@msn.com Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session Lecture # 27 15-Dec-2017
  2. 2. 2 SLOPE STABILITY ANALYSIS Infinite Slope Applied Shear Stress (t) 𝜏 = 𝑇 ( 𝐿 cos 𝛼)(1) 𝜏 = 𝛾𝐻𝐿 sin 𝛼 ( 𝐿 cos 𝛼)(1) 𝜏 = 𝛾𝐻 sin 𝛼 cos 𝛼 𝐹𝑂𝑆 = 𝑐′ + 𝛾𝐻𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼 Factor of Safety (FOS) Case-A: c-f Soil (c>0; f>0) L H h a W a b c d T N a tr 𝑭𝑶𝑺 = 𝑨𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑺𝒐𝒊𝒍 𝑨𝒑𝒑𝒍𝒊𝒆𝒅 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒔𝒔 Available Shear Strength of Soil (tr) 𝜏 𝑟 = 𝑐′ + 𝛾𝐻𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′ Without considering the effect of WT
  3. 3. 3 SLOPE STABILITY ANALYSIS Infinite Slope 𝐹𝑂𝑆 = 𝑐′ + 𝜎 𝑛′ ∙ tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼 Case-A: c-f Soil (c>0; f>0)  c’ & f’; effective strength parameters  Obtained through drained triaxial test 𝜎 𝑛 = 𝜎 𝑛 ′ = 𝐴𝐵 = ℎ 𝐴𝐶 = L H h a W a b c d T N a tr A C B D a 𝐴𝐷 = ℎ 𝑤 = 𝑢 = ℎ 𝑤 = 𝑢 = 𝛾 𝑤ℎ 𝑐𝑜𝑠2 𝛼 𝐹𝑂𝑆 = 𝑐′ + (𝛾𝐻 − 𝛾 𝑤ℎ) ∙ 𝑐𝑜𝑠2 𝛼 tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼 𝛾𝐻𝑐𝑜𝑠2 𝛼 𝜎 𝑛 − 𝑢 ℎ cos 𝛼 𝐴𝐶 cos 𝛼 = ℎ 𝑐𝑜𝑠2 𝛼 𝛾 𝑤ℎ 𝑤 𝐴𝐷 = ℎ 𝑐𝑜𝑠2 𝛼 Pore water pressure, u Considering presence of WT
  4. 4. 4 SLOPE STABILITY ANALYSIS Infinite Slope Case-B: Cohesive soil (f=0) L H h a W a b c d T N a tr 𝐹𝑂𝑆 = 𝑐′ 𝛾𝐻 sin 𝛼 cos 𝛼 Case-C: Granular soil (c=0) 𝐹𝑂𝑆 = (𝛾𝐻 − 𝛾 𝑤ℎ) ∙ 𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼 𝐹𝑂𝑆 = 1 − 𝛾 𝑤ℎ 𝛾𝐻 tan 𝜙′ tan 𝛼 𝐹𝑂𝑆 = 𝑐′ + (𝛾𝐻 − 𝛾 𝑤ℎ) ∙ 𝑐𝑜𝑠2 𝛼 tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼 (For c-f soil) 𝐹𝑂𝑆 = 𝛾𝐻 1 − 𝛾 𝑤ℎ 𝛾𝐻 𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′ 𝛾𝐻 sin 𝛼 cos 𝛼
  5. 5. 5 SLOPE STABILITY ANALYSIS Infinite Slope Case-C: Granular soil (c=0) For critical case; FOS = 1 𝐹𝑂𝑆 = tan 𝜙 tan 𝛼 tan 𝛼 = tan 𝜙′ i.e. the slope is only stable up to the angle of friction of soil. 𝐹𝑂𝑆 = 1 − 𝛾 𝑤ℎ 𝛾𝐻 tan 𝜙′ tan 𝛼 For dry slope, h=0 𝛼 = 𝜙′ L H h a W a b c d T N a tr
  6. 6. 6 SLOPE STABILITY ANALYSIS Infinite Slope Case-C: Granular soil (c=0) For fully saturated slope, h=H 𝐹𝑂𝑆 = 1 − 𝛾 𝑤ℎ 𝛾𝐻 tan 𝜙′ tan 𝛼 𝐹𝑂𝑆 = 𝛾 − 𝛾 𝑤 𝛾 tan 𝜙′ tan 𝛼 𝐹𝑂𝑆 = 0.5 tan 𝜙′ tan 𝛼 For critical case; FOS = 1 1 = 0.5 tan 𝜙′ tan 𝛼 tan 𝛼 = 0.5 ∙ tan 𝜙′ i.e. a fully saturated slope will be stable only up to half of its friction angle 𝛼 = 0.5 ∙ 𝜙’ L H h a W a b c d T N a tr
  7. 7. 7 Practice Problem #1 Calculate the maximum permissible slope angle for a sandy soil having gsat = 20 kN/m3, f’ =30°, to give a FOS of 1.5 when; a. the slope is dry b. the slope is fully saturated with water table at the ground surface
  8. 8. 8 Practice Problem #2 An infinite slope is shown in the figure. The position of water table is 2m below the ground surface. Determine the change in FOS of the slope if WT is brought to a depth of 4m below the surface. gsat = 18 kN/m3 c’= 10 kPa f’ = 20° H = 6m a = 15°
  9. 9. 9 CONCLUDED REFERENCE MATERIAL Principles of Geotechnical Engineering – (7th Edition) Braja M. Das Chapter #13 Essentials of Soil Mechanics and Foundations (7th Edition) David F. McCarthy Chapter #17 Geotechnical Engineering – Principles and Practices – (2nd Edition) Coduto, Yueng, and Kitch Chapter #17

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