SOIL PRESSURES — ISOLATED FOOTING

What this page computes

The calculator determines the ground pressures under a rigid isolated footing, rectangular, loaded by an axial force and by moments about two directions. The model: a rigid plate resting on a bed of Winkler springs that carry no tension — the soil can push, but not pull.

The no-tension Winkler model

A rigid plate settles as a plane: \(w(x,y) = a + b\,x + c\,y\). Since pressure is proportional to settlement, it too varies linearly over the contact area:

\(p(x,y) = t \,(n_x x + n_y y - d) \quad \text{in the contact zone}, \qquad p = 0 \text{ elsewhere}\)

The essential part is the no-tension condition: where the linear distribution would give negative pressure, the soil lifts off (\(p = 0\)) and the footing bears only on the remaining area. The position of the zero-pressure line is found by enforcing equilibrium of the three actions (\(N\), \(M_x\), \(M_y\)) through Newton iteration over the actual contact area.

Why lift-off matters

As long as the eccentricity stays within the middle third (the section kern), the whole footing is compressed and the distribution is simply bilinear. When the eccentricity leaves the kern, a corner or edge lifts off, and the pressure concentrates on the remaining area — \(p_{max}\) rises sharply. A calculation that ignores lift-off (the bilinear formula applied blindly) gives negative corner pressures, physically impossible, and underestimates the real \(p_{max}\).

The formulation here has no discrete cases: the zero-pressure line rotates and shifts continuously with the load, so the result is smooth at any eccentricity, biaxial included.

Input data

• Footing dimensions \(L \times B\).
• \(N\) — the axial force (compression).
• \(M_x\), \(M_y\) — the moments about the two directions, or equivalently the eccentricities \(e_x = M_y/N\), \(e_y = M_x/N\).

What to do with the result

The maximum pressure \(p_{max}\) is compared with the allowable pressure / bearing capacity of the soil (a separate geotechnical check). The pressure distribution is then the loading for the structural design of the footing — see the full isolated footing.

Assumptions and limitations

• Perfectly rigid footing: the pressure varies linearly. A flexible footing (thin raft) gives a nonlinear distribution, which requires a plate-on-elastic-foundation analysis.
• Winkler model (independent springs): it does not account for coupling between points through the soil mass. The real stress bulb diffuses stress laterally — see the stress bulb.
• It gives the contact pressures, not absolute settlements (those require the soil reaction modulus and the layer depth).
• It does not check bearing capacity or overturning — these are separate geotechnical checks.

Related calculations

• Isolated footing (full design) — the same pressures + reinforcement + punching + brief + DXF drawing
• Stress bulb — the diffusion of stress with depth under the footing
• Earth pressure — for retaining-wall foundations