Civil Engineering PE Geotechnical Engineering and Slope Stability

Question 1

The factor of safety for slope stability is defined as the ratio of:

Accepted Answer

Resisting forces to driving forces

Answer

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:

Accepted Answer

0.33

Answer

Ka = tan²(45° − φ/2) = tan²(30°) ≈ 0.33 for φ = 30°.

Question 3

Bishop's simplified method of slices assumes that:

Accepted Answer

Interslice shear forces are zero

Answer

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:

Accepted Answer

K₀ = 1 − sin φ

Answer

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:

Accepted Answer

FS = tan φ′/tan β

Answer

When c′ = 0, Terzaghi's infinite slope equation reduces to FS = tan φ′/tan β, independent of slice weight.

Civil Engineering PE Practice Test