Civil Engineering PE Geotechnical Engineering and Slope Stability 1 — Questions and Answers
Question 1: The factor of safety for slope stability is defined as the ratio of:
- Driving forces to resisting forces
- Resisting forces to driving forces (Correct answer)
- Cohesion to friction angle
- Normal stress to shear stress
Correct answer: Resisting forces to driving forces
Factor of safety equals resisting moment (or force) divided by driving moment (or force), with FS > 1 indicating a stable slope.
Question 2: For a soil with friction angle φ = 30°, Rankine's active earth pressure coefficient Ka equals:
- 0.50
- 0.33 (Correct answer)
- 0.25
- 3.00
Correct answer: 0.33
Ka = tan²(45° − φ/2) = tan²(30°) ≈ 0.33 for φ = 30°.
Question 3: Bishop's simplified method of slices assumes that:
- All interslice forces are zero
- Interslice shear forces are zero (Correct answer)
- The failure surface is planar
- Pore water pressure is negligible
Correct answer: Interslice shear forces are zero
Bishop's simplified method neglects interslice shear forces while retaining normal interslice forces, improving accuracy over the ordinary method.
Question 4: Jaky's formula for the coefficient of earth pressure at rest (K₀) for a normally consolidated soil is:
- K₀ = 1 + sin φ
- K₀ = 1 − sin φ (Correct answer)
- K₀ = tan²(45° − φ/2)
- K₀ = tan²(45° + φ/2)
Correct answer: K₀ = 1 − sin φ
Jaky's empirical formula K₀ = 1 − sin φ gives a reliable approximation for normally consolidated cohesionless soils.
Question 5: For a cohesionless infinite slope under drained conditions, the factor of safety simplifies to:
- FS = c′/(γz sin β cos β)
- FS = tan φ′/tan β (Correct answer)
- FS = γz cos²β tan φ′/c′
- FS = sin β/(cos β tan φ′)
Correct answer: FS = tan φ′/tan β
When c′ = 0, Terzaghi's infinite slope equation reduces to FS = tan φ′/tan β, independent of slice weight.
Question 6: Tension cracks at the crest of a cohesive slope reduce stability primarily because they:
- Increase cohesion along the failure surface
- Can fill with water, adding a hydrostatic driving force (Correct answer)
- Reduce the weight of the sliding mass
- Increase the effective normal stress on the failure plane
Correct answer: Can fill with water, adding a hydrostatic driving force
Water-filled tension cracks add a lateral hydrostatic force that increases the driving moment and reduces the factor of safety.
Civil Engineering PE Geotechnical Engineering and Slope Stability 1
The factor of safety for slope stability is defined as the ratio of: