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Method of-slices
- 1. METHOD OF SLICES БИЕДААЛТ
- 2. LEARNING OUTCOMES • SLOPESTABILITY BASED ON TAYLOR DIAGRAM • BASIC THEORY OF SLICE OF SLOPES • CALCULATION OF SAFETY FACTOR
- 3. TAYLOR DIAGRAM FORCOHESION SOIL( = 0) 𝑊1 = 𝑎𝑟𝑒𝑎 𝐸𝐹𝐶𝐵 . 𝛾. 1 𝑊2 = 𝑎𝑟𝑒𝑎 𝐴𝐸𝐹𝐷 . 𝛾. 1 𝑀 𝑑 = 𝑊1 𝑦1 − 𝑊2 𝑦2 𝑀𝑟 = 𝑐 𝑑 𝐿 𝐴𝐸𝐵 𝑅 = 𝑐 𝑑 𝑅2 𝛼 𝑀𝑟 = 𝑀 𝑑 𝑐 𝑑 𝑅2 𝛼 = 𝑊1 𝑦1-𝑊2 𝑦2 𝑐 𝑑 = 𝑊1 𝑦1−𝑊2 𝑦2 𝑅2 𝛼
- 4. Nd = stabilitynumber 𝑐 𝑑 = 𝑐 𝑢 𝑆𝐹 𝑆𝐹 = 𝑐 𝑢 𝑅2 𝛼 𝑊1 𝑦1 − 𝑊2 𝑦2 𝑁 𝑑 = 𝑐 𝑑 𝛾𝐻 Because 𝑆𝐹 = 𝑐 𝑢 𝑐 𝑑 than 𝑁𝑑 = 𝑐 𝑢 𝑆𝐹 𝛾𝐻 𝐻𝑐 = 𝑐 𝑢 𝛾𝑁 𝑑
- 5. STABILITY DIAGRAM FORCOHESIVE SOIL AND >53O 𝐷 = 𝐷𝑒𝑝𝑡ℎ 𝑜𝑓 ℎ𝑎𝑟𝑑 𝑙𝑎𝑦𝑒𝑟 ℎ𝑖𝑔ℎ 𝑜𝑓 𝑠𝑙𝑜𝑝𝑒𝑠 Hard layer Z=depth of hard layer High of slopes
- 6. SLOPES STABILITY FORCOHESION LESS SOIL; >0 (TAYLOR, 1948)
- 7.
- 8. SLICED METHOD • THISMETHOD CAN BE USED FOR SOIL IN DIFFERENT SHEARING RESISTANCE ALONG THE FAILURE PLANE • PROPOSED BY FELLENIUS ,BISHOP, JANBU, ETC • ASSUMED CIRCULAR FAILURE PLANE
- 9. REGULATION OF SLICES 1.SLICED PERFORMED VERTICAL DIRECTION 2. THE WIDTH OF THE SLICE DOES NOT HAVE THE SAME MEASUREMENT 3. ONE SLICE MUST HAVE ONE TYPE OF SOIL IN THE FAILURE SURFACE 4. THE WIDTH OF THE SLICE MUST BE SUCH THAT THE CURVE (FAILURE PLANE) CAN BE CONSIDERED A STRAIGHT LINE 5. THE TOTAL WEIGHT OF SOIL IN A SLICE IS THE SOIL WEDGE ITSELF, INCLUDING WATER AND EXTERNAL LOAD
- 10. FELLENIUS (ORDINARY) METHODOF SLICES
- 12. • FIRSTLY ITIS ASSUMED THAT THE SIDE FORCES T AND E MAY BE NEGLECTED AND SECONDLY, THAT THE NORMAL FORCE N, MAY BE DETERMINED SIMPLY BY RESOLVING THE WEIGHT W OF THE SLICE IN A DIRECTION NORMAL TO THE ARC, AT THE MID POINT OF THE SLICE • 𝑁 = 𝑊 𝑐𝑜𝑠𝛼 • WHERE IS THE ANGLE OF INCLINATION OF THE POTENTIAL FAILURE ARC TO THE HORIZONTAL AT THE MID POINT OF THE SLICE • THE DRIVING FORCE IS 𝑊 𝑠𝑖𝑛𝛼
- 13. FORMULATION • 𝐹𝑆 = 𝑠𝑢𝑚𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒𝑠 𝑠𝑢𝑚 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑚𝑜𝑣𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 = 𝑅.𝜏 𝑚𝑎𝑥 𝑅 𝑊 𝑠𝑖𝑛𝛼 • 𝐹𝑆 = 𝑐′ 𝑏 𝑠𝑒𝑐𝛼+𝑊 𝑐𝑜𝑠𝛼 𝑡𝑎𝑛𝜑 𝑊𝑠𝑖𝑛𝛼 • IF SUBMERGED. 𝑁 = 𝑊 𝑐𝑜𝑠𝛼 − 𝑢𝑙 • WHERE: 𝑙 = 𝑏 𝑠𝑒𝑐𝛼 • 𝐹𝑆 = 𝑐′ 𝑏 𝑠𝑒𝑐𝛼+(𝑊 𝑐𝑜𝑠𝛼 −𝑢 𝑏 𝑠𝑒𝑐𝛼) 𝑡𝑎𝑛𝜑 𝑊𝑠𝑖𝑛𝛼
- 14. STEP BY STEPPROCEDURE 1. DRAW CROSS-SECTION TO NATURAL SCALE 2. SELECT FAILURE SURFACE 3. DIVIDE THE FAILURE MASS INTO SOME SLICES 4. COMPUTE TOTAL WEIGHT ( WT ) OF EACH SLICE 5. COMPUTE FRICTIONAL RESISTING FORCE FOR EACH SLICE N TANΦ – UL 6. COMPUTE COHESIVE RESISTING FORCE FOR EACH SLICE CL 7. COMPUTE TANGENTIAL DRIVING FORCE (T) FOR EACH SLICE 8. SUM RESISTING AND DRIVING FORCES FOR ALL SLICES AND COMPUTE FS
- 18. BISHOP METHOD - Alsoknown as Simplified Bishop method - Includes interslice normal forces - Neglects interslice shear forces - Satisfies only moment equilibrium
- 21. 3. Simplified BishopMethod
- 23. RECOMMENDED STABILITY METHODS •ORDINARY METHOD OF SLICES (OMS) IGNORES BOTH SHEAR AND NORMAL INTERSLICE FORCES AND ONLY MOMENT EQUILIBRIUM • BISHOP METHOD - ALSO KNOWN AS SIMPLIFIED BISHOP METHOD - INCLUDES INTERSLICE NORMAL FORCES - NEGLECTS INTERSLICE SHEAR FORCES - SATISFIES ONLY MOMENT EQUILIBRIUM
- 24. OTHERS • SIMPLIFIED JANBUMETHOD - INCLUDES INTERSLICE NORMAL FORCES - NEGLECTS INTERSLICE SHEAR FORCES - SATISFIES ONLY HORIZONTAL FORCE EQUILIBRIUM • SPENCER METHOD - INCLUDES BOTH NORMAL AND SHEAR INTERSLICE FORCES - CONSIDERS MOMENT EQUILIBRIUM - MORE ACCURATE THAN OTHER METHODS
- 25. RECOMMENDED STABILITY METHODS OMSIS CONSERVATIVE AND GIVES UNREALISTICALLY LOWER FS THAN BISHOP OR OTHER REFINED METHODS FOR PURELY COHESIVE SOILS, OMS AND BISHOP METHOD GIVE IDENTICAL RESULTS FOR FRICTIONAL SOILS, BISHOP METHOD SHOULD BE USED AS A MINIMUM RECOMMENDATION: USE BISHOP, SIMPLIFIED JANBU OR SPENCER
- 26. REMARKS ON SAFETYFACTOR USE FS = 1.3 TO 1.5 FOR CRITICAL SLOPES SUCH AS END SLOPES UNDER ABUTMENTS, SLOPES • CONTAINING FOOTINGS, MAJOR RETAINING STRUCTURES USE FS = 1.5 FOR CUT SLOPES IN FINE-GRAINED SOILS WHICH CAN LOSE STRENGTH WITH TIME