Shallow Foundation Elastic (Immediate) Settlement
The serviceability check soil-bearing-capacity calls separate: a footing can be far below its bearing strength yet settle too much. The theory-of-elasticity immediate settlement Se = q B (1 - nu^2) Is / Es (Is ~0.82 rigid square) gives a 6 ft footing at 3 ksf on medium sand 0.64 in - under the customary 1 in limit - but halve the modulus and the same footing fails at 1.29 in. Sizes the footing against movement, not strength; consolidation and embedment are separate. A design aid, not the geotechnical engineer's report.
Formula and source
Se_ft = q B (1 - nu^2) Is / Es; Se_in = 12 Se_ft.
The theory-of-elasticity immediate (elastic) settlement of a shallow foundation, Se = q B (1 - nu^2) Is / Es, with the shape-and-rigidity influence factor Is (~0.82 rigid square, ~0.95 flexible-square average, larger for strips), as compiled in Bowles (Foundation Analysis and Design) and the customary geotechnical texts, by name.
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