Slope Stability for Small/Limited Slopes – Typical Shape of the Slip Surface For slopes of limited extent in common soils, what is the most frequently assumed or observed shape of the surface of slippage (failure surface) used in analysis and design?

Introduction / Context:
In practical slope stability problems—road cuts, small embankments, and excavations—the assumed geometry of the slip surface strongly influences the calculated factor of safety. For many everyday slopes, engineers idealize the failure surface as circular to enable limit equilibrium methods and straightforward construction of trial slip circles.

Given Data / Assumptions:

• Homogeneous soil or layered soils approximated locally as homogeneous.
• Slope is of limited height and extent (typical highway and earthwork cases).
• Drainage conditions considered within total or effective stress analyses.

Concept / Approach:

The circular slip surface assumption underpins several classic methods (Swedish circle/Fellenius, Bishop simplified). It is consistent with observed rotational failures in cohesive and c–φ soils of limited height. While noncircular surfaces may occur (planar in rock or highly stratified soils, composite in large earth dams), the circular arc remains the most common and tractable idealization for small to moderate slopes.

Step-by-Step Solution:

Verification / Alternative check:

Field back-analyses of numerous small slope failures show near-circular head-to-toe scars, validating this assumption for many cases.

Why Other Options Are Wrong:

Parabolic/elliptical assumptions are not standard for routine designs; planar (straight) failures are more typical in rock masses or along weak bedding planes, not the general case for small soil slopes.

Common Pitfalls:

Applying circular arcs to very tall or strongly layered slopes where noncircular or composite surfaces govern; ignoring pore-pressure effects that shift the critical circle.

Final Answer:

Circular arc