Base pressure under retaining wall — to keep pressure wholly compressive under a base of width b, the resultant eccentricity e must not exceed:

Introduction / Context:
For footings and retaining wall bases, keeping soil contact in compression (no tension) improves stability and avoids uplift/separation. The “middle-third rule” provides an eccentricity limit to ensure a linear base pressure diagram remains non-negative over the full base width.

Given Data / Assumptions:

• Rigid base of width b, bearing on soil with linear elastic distribution assumption.
• Resultant of vertical load and overturning moments acts at eccentricity e from the centroidal axis.
• Goal: zero tension anywhere under the base.

Concept / Approach:

Under linear bearing stress, the pressure distribution is p(x) = P/A ± 6M/(b^2). To avoid tension, the resultant must lie within the middle third of the base (the kern). For a strip base of width b, the kern limit is e ≤ b/6. If e exceeds b/6, part of the base would theoretically go into tension, which soils cannot resist, invalidating the assumption of full contact.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Compute extreme pressure p_min = P/A − 6M/(b^2). Set p_min ≥ 0 → M ≤ P b / 6 → e = M/P ≤ b/6.

Why Other Options Are Wrong:

b/3 and b/4 are too large and would permit tension; b/8 and b/10 are conservative but not the code/standard kern limit.

Common Pitfalls (misconceptions, mistakes):

Confusing kern limits for different shapes; forgetting that soil cannot take tension.

Final Answer:

b / 6