Slope stability terminology: For a base failure mode of a slope (failure surface passing well below the toe), what is the appropriate qualitative value of the depth factor Df?

Introduction / Context:
In slope stability (particularly circular slip analysis for earth embankments), different failure modes are identified: face (or slope) failure, toe failure, and base failure. The “depth factor” Df is a qualitative indicator describing the relative position of the critical slip circle center or the depth of the failure surface with respect to the slope dimensions. This question checks the conceptual association of Df with the base failure mechanism.

Given Data / Assumptions:

• Homogeneous slope, classical circular slip concept.
• Failure mode: base failure (deep-seated slip passing well below the toe).
• Depth factor Df indicates comparatively shallow, equal, or deeper positions of the failure with respect to slope height.

Concept / Approach:

Base failure is characterized by a deep slip surface. Unlike toe failure (shallower) or face failure (shallowest), the failure surface in base failure extends under the slope and emerges well beyond the toe. Therefore, the depth factor corresponding to base failure is taken greater than unity to reflect this deeper mechanism.

Step-by-Step Solution:

Verification / Alternative check:

Standard illustrative charts and example problems in slope stability categorize deeper, base-type slips with parameters indicating greater embedment below the toe, consistent with Df > 1 as a qualitative descriptor.

Why Other Options Are Wrong:

(a) Df = 1 and (b) Df < 1 match face or toe type shallower mechanisms; (d) and (e) are not representative of deep-seated base failure.

Common Pitfalls:

Mixing up toe failure (shallower) with base failure (deeper); treating Df as a precise numeric constant rather than a qualitative indicator.

Final Answer:

Df > 1