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Geotechnical Engineering-II [Lec #26: Slope Stability]

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 #26: Slope Stability]

  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 # 26 13-Dec-2017
  2. 2. 2 STABILITY OF SLOPES Slope An exposed ground surface that stands at an angle with the horizontal is called an unrestrained slope.
  3. 3. 3 TYPES OF SLOPES A) w.r.t. Method of Construction 1. Natural Slopes 2. Man-made / Engineered Slopes Embankments, earthen dams, river dikes, excavation trenches, etc. Engineered SlopeNatural Slope
  4. 4. 4 TYPES OF SLOPES B) w.r.t. Extents 1. Infinite Slopes Having constant slope of infinite extent, e.g. long slope of a mountain face. 2. Finite Slopes Slopes of limited heights and extents, e.g. typical man-made slopes Finite SlopeInfinite Slope
  5. 5. 5 TYPES OF SLOPES C) w.r.t. Slope Material 1. Cohesionless 2. Cohesive Cohesionless Cohesive
  6. 6. 6 STABILITY OF SLOPES A slope is said to be stable if it meets a prescribed need for a fixed period of time with a suitable safety factor (FOS). Nova Frebergo, Brazil January 13, 2011 California, USA January, 1997
  7. 7. 7 CAUSES OF SLOPE FAILURE
  8. 8. 8 CAUSES OF SLOPE FAILURE
  9. 9. 9 CAUSES OF SLOPE FAILURE
  10. 10. 11 TYPES/MODES OF SLOPE FAILURE Toe Failure  Failure surface passing through toe of slope  Material of slope is homogeneous  Relatively steep slope angles
  11. 11. 12 TYPES/MODES OF SLOPE FAILURE Base Failure  Failure surface passing through foundation  Foundation soil somehow weaker than slope material  Relatively gentle slopes
  12. 12. 13 SLOPE STABILIZING MEASURES
  13. 13. 14 SLOPE STABILIZING MEASURES
  14. 14. 15 SLOPE STABILIZING MEASURES
  15. 15. 16 LIMIT EQUILIBRIUM ANALYSIS  Most common quantitative measure of slope stability  Stability of slope expressed in terms of factor of safety just before failure 𝐹𝑂𝑆 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒 𝐷𝑖𝑠𝑡𝑢𝑟𝑏𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒 𝐹𝑂𝑆 = 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑆𝑜𝑖𝑙 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 Failure Surface FOS < 1 FOS = 1 FOS > 1 Typical design criterion for stable slope; FOS > 1.5 → Failure → Verge of failure/Just stable → Stable
  16. 16. 17 SLOPE STABILITY ANALYSIS Infinite Slope Assumptions: 1. Slope face is planar and of infinite extent 2. Failure surface is║to slope face 3. Water surface is║to slope face 𝐹𝑂𝑆 = 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑆𝑜𝑖𝑙 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 L H h a a b c d
  17. 17. 18 SLOPE STABILITY ANALYSIS Infinite Slope Case-A: c-f Soil (c>0; f>0) L H h a W a b c d T N a Available Shear Strength of Soil (tr) tr 𝜏 𝑟 = 𝑐′ + 𝜎 𝑛′ ∙ tan 𝜑′ Normal stress on the failure plane 𝜎 𝑛 = 𝑁 ( 𝐿 cos 𝛼)(1) = 𝛾𝐻𝐿 cos 𝛼 ( 𝐿 cos 𝛼)(1) = 𝛾𝐻𝑐𝑜𝑠2 𝛼 𝑊 = 𝛾𝐻𝐿 𝑁 = 𝑊 cos 𝛼 = 𝛾𝐻𝐿 cos 𝛼 𝑇 = 𝑊 sin 𝛼 = 𝛾𝐻𝐿 sin 𝛼 𝑭𝑶𝑺 = 𝑨𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑺𝒐𝒊𝒍 𝑨𝒑𝒑𝒍𝒊𝒆𝒅 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒔𝒔
  18. 18. 19 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
  19. 19. 20 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
  20. 20. 21 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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