When should a raft (mat) foundation be adopted? Select the rule-of-thumb criterion based on the total area of individual footings compared with the building’s plan area.

Introduction / Context:
A raft (mat) foundation spreads building loads over a large area, reducing contact pressure and accommodating variable soil conditions. Designers often use a rule-of-thumb trigger to decide when a raft is more economical and functional than multiple isolated footings.

Given Data / Assumptions:

• Comparison between total area of all individual footings and the building’s plan area.
• Normal building loads on moderately compressible soils.

Concept / Approach:
If numerous isolated footings would occupy a large fraction of the site footprint, consolidating them into a single mat simplifies construction, improves differential settlement performance, and may reduce cost. A commonly cited benchmark is when the sum of individual footing areas is at least about half of the plan area.

Step-by-Step Solution:
Estimate total area of isolated footings required from column loads and allowable soil pressure.Compare with building plan area.If total footing area ≥ 50% of plan area, a raft is typically preferred.

Verification / Alternative check:
Beyond the 50% rule, a raft is also preferred where soil is weak/heterogeneous, basements are planned, or differential settlement control is critical. These considerations support the economic/functional crossover near the 50% threshold.

Why Other Options Are Wrong:

• 10–40%: At these levels, isolated or combined footings usually remain economical and practical; a raft is not yet justified solely by area coverage.

Common Pitfalls:
Treating the 50% threshold as absolute; ignoring groundwater, basement requirements, and settlement analysis which may argue for a raft even at lower coverage.

Final Answer:
50% or more of the plan area (i.e., when individual footings would cover ≥50% of the building plan)