METHOD OF SLICES
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METHOD OF SLICES YULVI ZAIKA LEARNING OUTCOMES • SLOPE STABILITY BASED ON TAYLOR DIAGRAM • BASIC THEORY OF SLICE OF SLOPES • CALCULATION OF SAFETY FACTOR TAYLOR DIAGRAM FOR COHESION SOIL(ο¦ = 0) π1 = ππππ πΈπΉπΆπ΅ . πΎ. 1 π2 = ππππ π΄πΈπΉπ· . πΎ. 1 ππ = π1 π¦1 − π2 π¦2 ππ = ππ πΏπ΄πΈπ΅ π = ππ π 2 πΌ ππ = ππ ππ π 2 πΌ = π1 π¦1 -π2 π¦2 π1 π¦1 −π2 π¦2 ππ = π 2 πΌ ππ’ ππΉ ππ’ π 2 πΌ ππΉ = π1 π¦1 − π2 π¦2 ππ = ππ πΎπ» π Because ππΉ = ππ’ than ππ = π ππ’ ππ = ππΉ πΎπ» π»π = ππ’ πΎππ Nd = stability number STABILITY DIAGRAM FOR COHESIVE SOIL AND ο’>53O π·= High of slopes π·πππ‘β ππ βπππ πππ¦ππ βππβ ππ π πππππ Z=depth of hard layer Hard layer SLOPES STABILITY FOR COHESION LESS SOIL; ο¦ >0 (TAYLOR, 1948) THE SLICED METHOD YULVI ZAIKA SLICED METHOD • THIS METHOD CAN BE USED FOR SOIL IN DIFFERENT SHEARING RESISTANCE ALONG THE FAILURE PLANE • PROPOSED BY FELLENIUS ,BISHOP, JANBU, ETC • ASSUMED CIRCULAR FAILURE PLANE 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 FELLENIUS (ORDINARY) METHOD OF SLICES • FIRSTLY IT IS 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 • π = π πππ πΌ • WHERE ο‘ IS THE ANGLE OF INCLINATION OF THE POTENTIAL FAILURE ARC TO THE HORIZONTAL AT THE MID POINT OF THE SLICE • THE DRIVING FORCE IS π π πππΌ FORMULATION • πΉπ = • πΉπ = π π’π ππ ππππππ‘ πππ₯πππ’π πππ ππ π‘πππ ππππππ π π’π ππ ππππππ‘ ππ πππ£πππ πππππ π ′ π π πππΌ+π πππ πΌ π‘πππ ππ πππΌ • IF SUBMERGED. π = π πππ πΌ − π’π • WHERE: π = π π πππΌ • πΉπ = π ′ π π πππΌ+(π πππ πΌ −π’ π π πππΌ) π‘πππ ππ πππΌ = π .ππππ₯ π π π πππΌ STEP BY STEP PROCEDURE 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 BISHOP METHOD - Also known as Simplified Bishop method - Includes interslice normal forces - Neglects interslice shear forces - Satisfies only moment equilibrium 3. Simplified Bishop Method 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 OTHERS • SIMPLIFIED JANBU METHOD - 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 RECOMMENDED STABILITY METHODS OMS IS 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 REMARKS ON SAFETY FACTOR 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
