This document discusses methods for analyzing slope stability using the method of slices. It describes Taylor diagrams, the basic theory of slicing slopes, and calculating the safety factor. The ordinary and Bishop methods of slices are explained. The Bishop method is recommended as it includes interslice normal forces and satisfies moment equilibrium, though it neglects interslice shear forces. A safety factor between 1.3 to 1.5 is recommended for critical slopes, and 1.5 for cut slopes in fine-grained soils.

1. METHOD OF SLICES
БИЕ ДААЛТ

2. LEARNING OUTCOMES
• SLOPE STABILITY BASED ON TAYLOR DIAGRAM
• BASIC THEORY OF SLICE OF SLOPES
• CALCULATION OF SAFETY FACTOR

3. TAYLOR DIAGRAM FOR COHESION 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 = stability number
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 FOR COHESIVE SOIL AND >53O
𝐷 =
𝐷𝑒𝑝𝑡ℎ 𝑜𝑓 ℎ𝑎𝑟𝑑 𝑙𝑎𝑦𝑒𝑟
ℎ𝑖𝑔ℎ 𝑜𝑓 𝑠𝑙𝑜𝑝𝑒𝑠
Hard layer
Z=depth of hard
layer
High
of
slopes

6. SLOPES STABILITY FOR COHESION LESS
SOIL;  >0 (TAYLOR, 1948)

7. THE SLICED METHOD
YULVI ZAIKA

8. 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

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) METHOD OF SLICES

12. • 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
• 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 =
𝑠𝑢𝑚 𝑜𝑓 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 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

18. BISHOP METHOD
- Also known as Simplified Bishop method
- Includes interslice normal forces
- Neglects interslice shear forces
- Satisfies only moment equilibrium

21. 3. Simplified Bishop Method

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 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

25. 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

26. 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