What is the critical height of the slope in GATE Civil 2026 Set-1 Q56?

The critical height is 5.21 m. Using Taylor's stability chart for slope angle β=22° and φ′=15°, the stability number Ns ≈ 6.83. Critical height Hc = Ns × c′/γ = 6.83 × 12/15.72 = 5.21 m. This is the maximum height at which the slope can stand with a factor of safety of 1.

What is Taylor's stability chart and how is it used in GATE Civil 2026 Set-1 Q56?

Taylor's stability chart provides the stability number Ns = γHc/c′ as a function of slope angle β and friction angle φ. For given β and φ, Ns is read from the chart. The critical height is then Hc = Ns × c/γ. For β=22° and φ′=15°, Ns ≈ 6.83, giving Hc = 6.83 × 12/15.72 = 5.21 m.

What does critical height of a slope mean in geotechnical engineering?

Critical height is the maximum height at which a slope can stand without failing, corresponding to a factor of safety of exactly 1. For slopes higher than the critical height, the driving forces exceed the resisting forces and the slope becomes unstable. It depends on soil cohesion, friction angle, unit weight, and slope angle.

Critical Height Infinite Slope Cohesive Soil Taylor Stability | GATE Civil 2026 Set-1 Q56

Civil Engineering > GATE 2026 SET-1 > Slope Stability

An infinite slope with slope angle β = 22° consists of soil with the following properties:

Unit weight γ = 15.72 kN/m³
Cohesion c′ = 12 kPa
Angle of internal friction φ′ = 15°

The critical height of the slope (in m) is ______ (rounded off to two decimal places).

Correct : 5.21

The critical height of a slope is the maximum height at which the slope remains stable (Factor of Safety = 1). For a cohesive frictional soil, this is determined using Taylor''s stability chart.
The stability number N_s is obtained from Taylor''s chart for slope angle β = 22° and angle of friction φ′ = 15°. For these values, N_s ≈ 6.83.
The critical height is then:
H_c = N_s × c′/γ
H_c = 6.83 × 12/15.72
H_c = 81.96/15.72
H_c = 5.21 m
Taylor''s stability chart is the standard method for determining critical heights of slopes in cohesive frictional soils, where both cohesion and friction contribute to stability. The critical height decreases as the slope angle increases or as soil strength decreases.
Correct answer: 5.21 m ✓

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