Elastic Settlement of a Footing on Sand (Simplified)
Elastic Settlement of a Footing on Sand (Simplified)
Sands drain quickly, so unlike clay they do not undergo slow time-dependent consolidation — instead, most of their settlement under a footing happens essentially immediately as an elastic response of the soil skeleton. Estimating this immediate settlement is a standard serviceability check alongside the bearing capacity check, since a footing can satisfy strength requirements yet still settle more than a structure can tolerate. The influence factor If in this simplified form lumps together footing shape, rigidity, and depth of the influenced soil zone below the footing, and the soil modulus Es is notoriously variable — often estimated from correlations to SPT blow counts — so settlement predictions by this method are considered order-of-magnitude estimates rather than precise values.
Simplified elastic settlement is S = q*B*If/Es. where q_set is the applied bearing pressure, B_set is the footing width, I_f is a dimensionless influence factor, and E_s is the soil's elastic modulus.
Inputs
q_set := 150 kPa=150000 Pa
B_set := 2 m=2 m
I_f := 0.8=0.8
E_s := 20000 kPa=20 MPa
Settlement grows with applied pressure and footing width (more load, larger stressed zone) but is inversely resisted by the stiffness of the soil, exactly analogous to how a stiffer spring deflects less under the same load.
S_settle := q_set·B_set·I_f/E_s=12 mm
Results
A settlement on the order of a centimetre or so is a typical, generally acceptable result for a footing at this pressure and width on medium-dense sand; most structures can tolerate up to roughly 25 mm of total settlement, with differential settlement between footings being the more critical limit. Because settlement scales directly with footing width B, widening a footing to reduce bearing pressure (a common bearing-capacity fix) can partially offset its own benefit by increasing settlement — the two checks should always be run together.
Assumptions & limitations
- Homogeneous, isotropic sand with a single representative elastic modulus Es.
- Simplified elastic (Schmertmann-style) method, not a rigorous layered analysis.
- Immediate settlement only — sand does not exhibit long-term consolidation.
- Rigid footing behavior and a uniform bearing pressure assumed.