Foundation classification: A foundation is called shallow if its depth is less than or equal to its width. Which of the following depth choices therefore qualify as shallow foundations?

Introduction / Context:
Foundations are grouped into shallow and deep types based on the embedment depth relative to foundation width (or least lateral dimension). This classification guides analysis methods and construction techniques.

Given Data / Assumptions:

• Shallow foundation definition: depth D_f ≤ width B (or least lateral dimension).
• Depth options provided are fractions up to and including equality with width.

Concept / Approach:
Shallow foundations transfer loads to the near-surface soils; typical forms include isolated footings, strip footings, and raft foundations. All the listed depths are ≤ the width, so each option satisfies the criterion for being shallow.

Step-by-Step Reasoning:
Check each option against D_f ≤ B.1/4 B, 1/2 B, 3/4 B, and D_f = B all satisfy D_f ≤ B.Therefore, all listed choices are shallow.

Verification / Alternative check:
In contrast, deep foundations (e.g., piles, drilled shafts) typically have D_f >> B and transfer load by end bearing and/or skin friction at deeper strata.

Why Other Options Are Wrong:
Individual selections are not wrong, but the comprehensive correct choice is the option that includes all qualifying depths.

Common Pitfalls:

• Assuming a single fixed ratio (e.g., D_f = B/2) defines shallow; the accepted definition is D_f ≤ B.

Final Answer:
all the above