Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Stability of slopes
Question Statement:
Which of the following statements regarding slope stability analysis methods in geotechnical engineering are correct?
Options:
(A) Taylor's stability number is defined as $S_n = \frac{c_m}{\gamma H} = \frac{c}{F_c \gamma H}$
(B) The Swedish Slip Circle method (Ordinary Method of Slices) assumes circular failure surfaces and neglects inter-slice forces
(C) Bishop's simplified method satisfies overall moment equilibrium and vertical force equilibrium for each slice, yielding higher factors of safety than the Ordinary Method
(D) In a purely cohesionless dry sand slope ($c = 0$), the factor of safety is completely independent of slope height and equals $\frac{\tan\phi'}{\tan\beta}$
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements are foundational principles in geotechnical slope engineering:
- Statement A: Taylor's dimensionless stability number $S_n = \frac{c}{\gamma H_c}$.
- Statement B: Ordinary Method of Slices neglects interslice tangential and normal forces.
- Statement C: Bishop's simplified method accounts for vertical equilibrium and produces accurate FOS within $2-5\%$ of rigorous solutions.
- Statement D: For an infinite cohesionless slope, $FOS = \frac{\tau_f}{\tau} = \frac{\sigma' \tan\phi'}{\sigma' \tan\beta} = \frac{\tan\phi'}{\tan\beta}$, which is entirely independent of slope height $H$.