ASTM D1196 plate load test: modulus and subgrade reaction

Updated: August 4, 2026 · ISKRIT

A plate load test loads a rigid circular plate in steps and records settlement. Two numbers come out of the same curve: an elastic modulus and a modulus of subgrade reaction, and they answer different design questions.

The formula

For a rigid circular plate on an elastic half-space:

E = (1 − ν²) · (π/4) · D · Δp / Δs

The π/4 factor, 0.7854, is the rigid-plate shape coefficient. D is the plate diameter and Δp/Δs is the slope of the linear portion of the pressure-settlement curve. ASTM D1196 applies no embedment correction, which is the practical difference from the Russian GOST 20276 procedure, where a tabulated coefficient accounts for testing at the bottom of a borehole and the shape factor is rounded to 0.79.

Modulus of subgrade reaction

The other result is simply the inverse slope:

k = Δp / Δs

It has units of stress per length and is what a Winkler foundation model consumes. It is not a soil property. It depends on plate size, on the depth of the influenced zone and therefore on the layering underneath, and a k measured on a 300 mm plate cannot be applied to a 3 m footing without a size correction.

Worked

A 300 mm plate on sand, ν = 0.30. Over the straight part of the curve a 0.2 MPa increment produces 0.12 cm of settlement, so Δs/Δp = 0.6 cm/MPa.

E = (1 − 0.09) · 0.7854 · 30 / 0.6 = 35.7 MPa
k = 1 / 0.6 = 1.67 MPa/cm = 167 MN/m³

Choosing the linear segment

Both results are slopes, so both hinge on which steps you call linear. The first step is usually excluded because it contains seating of the plate; the last steps are excluded once the curve bends into yielding. Reporting the pressure range used is therefore not optional, and a report that gives E without it cannot be audited.

Questions

Why does a bigger plate give a lower k? Because it stresses a deeper zone, and deeper material is usually less stiff than the compacted surface layer.

Is one loading cycle enough? For a modulus, yes; for compaction acceptance, no, and that is what the DIN two-cycle procedure exists for.

Enter the load steps and get E, k and the segment used in the plate load test calculator, part of the field testing tool.