Settlement of Foundations Notes

Settlement of Foundations

Components of settlement (immediate, primary consolidation, secondary), elastic settlement with influence factors, settlement of footings on sand from SPT and plate load tests, consolidation settlement of clay layers and Skempton–Bjerrum correction, differential settlement and angular distortion, permissible settlements (IS 1904), causes and remedial measures — with solved numericals.

Last reviewed 16 Sept 2026 · 6 min read

Settlement and why it matters

Settlement is the vertical downward movement of a foundation. Every foundation settles; the design objective is to keep the total and especially the differential settlement within limits that the structure can tolerate without damage to structure, finishes or services.

Components

S = S_{i} + S_{c} + S_{s}

Component	Cause	Dominant in	Time
Immediate (elastic) $S_{i}$	Elastic distortion of soil (clays at constant volume; sands with volume change)	Sands; also clays under undrained loading	Instantaneous (during construction)
Primary consolidation $S_{c}$	Expulsion of pore water	Saturated clays	Months to years
Secondary compression $S_{s}$	Creep of the soil skeleton	Organic soils, highly plastic clays	Long-term

Immediate (elastic) settlement

Based on the theory of elasticity for a flexible or rigid footing on a semi-infinite elastic medium:

FormulaElastic settlement

S_{i} = q B \frac{1 - μ ^{2}}{E _{s}} I_{f}

$q$ = net foundation pressure; $B$ = width (or diameter); $E_{s}$ = modulus of elasticity of soil; $μ$ = Poisson's ratio (≈ 0.5 for saturated clays under undrained loading, 0.25–0.35 for sands); $I_{f}$ = influence factor depending on shape, rigidity and the point considered.

Typical influence factors (surface footing, semi-infinite medium):

Shape	Flexible — centre	Flexible — corner/edge	Flexible — average	Rigid
Circle	1.00	0.64 (edge)	0.85	0.79
Square	1.12	0.56 (corner)	0.95	0.82

A rigid footing settles uniformly, at roughly the average settlement of a flexible one (about 0.8 of the flexible centre value).

Settlement of footings on sand

Undisturbed sampling of sand is difficult, so settlement is estimated from field tests:

Plate load test — relates settlement of a test plate to that of the footing (Terzaghi–Peck for sand):

S_{f} = S_{p} [\frac{B _{f} ( B _{p} + 0.3 )}{B _{p} ( B _{f} + 0.3 )}]^{2} (B in m)

For clay (settlement proportional to width): $S_{f} = S_{p} \frac{B _{f}}{B _{p}}$ .

Standard penetration test (SPT) — IS 8009 and IS 6403 provide charts relating corrected $N$ , footing width and settlement (e.g. pressure causing 25 mm settlement).
Static cone penetration test — De Beer / Schmertmann methods using cone resistance.

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