Slope stability – definition of the stability number: For a cohesive soil embankment of height H with cohesion C, factor of safety F, and unit weight gamma, the stability number is defined as which of the following?

Introduction / Context:
The stability number is a convenient non-dimensional index in slope stability for purely cohesive or predominantly cohesive soils. It relates the available shear strength to destabilizing body forces and the required factor of safety F, guiding preliminary design and checks against failure.

Given Data / Assumptions:

• C = cohesion (shear strength intercept).
• gamma = unit weight of soil.
• H = slope or embankment height.
• F = factor of safety against shear failure.

Concept / Approach:
The classical definition used with charts (e.g., Taylor stability charts) is stability number Ns = C / (F * gamma * H). It captures the ratio of available average shear strength (reduced by F) to the mobilizing stress gamma * H, allowing quick parametric estimation of safe slope geometries.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: numerator has stress units; denominator gamma * H also has stress units; ratio is dimensionless.

Why Other Options Are Wrong:

• Options B and D invert the intended ratio.
• Option C places F in the numerator, which would increase Ns with higher safety factor—nonphysical for design indices.
• Option E omits the safety factor, unsuitable for design checks.

Common Pitfalls:
Confusing Ns with stability charts for frictional soils; mixing unit weight with density; forgetting that F reduces available strength.

Final Answer:
C / (F * gamma * H)