Foundation detailing: In cantilever retaining wall foundations, the toe projection of the base slab (distance from stem face to front edge) is commonly taken as which proportion of the total base width for preliminary sizing?

Introduction / Context:
Preliminary proportioning of cantilever retaining walls includes selecting a sensible toe projection to satisfy stability (overturning, sliding, and bearing) and facilitate economical reinforcement layouts. A practical starting fraction of the base width helps streamline early design before detailed checks.

Given Data / Assumptions:

• Conventional cantilever retaining wall with base slab divided into toe and heel.
• Preliminary sizing stage (detailed stability checks to follow).
• Typical soil parameters and surcharge; no extreme conditions assumed.

Concept / Approach:
A common rule of thumb is to start with a toe projection about one third of the total base width, with the remaining two thirds toward the heel under the backfill. This initial proportion generally leads to acceptable bearing pressure distribution and adequate lever arm for resisting overturning, subject to refinement by calculations.

Step-by-Step Solution:
Adopt a preliminary base width B from empirical relations (often 0.5H–0.7H).Propose toe ≈ B/3 and heel ≈ 2B/3 for initial layout.Perform stability checks and adjust toe/heel as needed to satisfy safety factors and serviceability.

Verification / Alternative check:
Trial sections with toe near B/3 frequently yield bearing pressure diagrams with the resultant kept within the middle third, facilitating economical reinforcement.

Why Other Options Are Wrong:

• One sixth of overall height: Not a standard proportioning rule for toe projection.
• Equal to heel slab: The heel is commonly larger than the toe.
• Below ground surface / variable regardless of stability: Not meaningful sizing guidance.

Common Pitfalls:
Fixing toe width without running stability checks; final dimensions must be validated for overturning, sliding, and bearing stress limits.

Final Answer:
as one third of the base