Modulus of Subgrade Reaction (K) — Multi-Layer Method

The modulus of subgrade reaction, commonly called the k-value, quantifies how stiff the ground is beneath a concrete slab. It is defined as the ratio of applied pressure to the resulting surface deflection:

A higher k-value means a stiffer subgrade that deflects less under load. In slab-on-ground design, the k-value directly impacts the required slab thickness needed to carry the applied loads.

Two Types of K-Value

The k-value is not a single quantity: in practice, three distinct definitions appear and must not be confused.

The static k-value is determined by the ASTM D1196 plate load test: a rigid steel plate is loaded incrementally on the prepared subgrade surface and the resulting settlements are recorded. By convention, k is taken at a deflection of 1.27 mm (0.05 in).

The dynamic k-value is obtained by back-calculation from the Falling Weight Deflectometer (FWD): a standard impulse load is dropped and k is back-calculated from the measured deflection bowl. FWD-derived dynamic k-values are consistently found to be approximately twice the static k-value on the same subgrade, because pore water pressures do not have time to dissipate under the brief dynamic load.

This calculator outputs both values. Use the appropriate k-value for the design method you are applying.

Calculation Method

The calculator implements the Palmer-Barber multi-layer method, which combines the Burmister elastic layer solution with an Ullidtz rigid-plate correction. Unlike traditional methods based solely on subgrade CBR, this method accounts for the contribution of intermediate subbase layers, producing more accurate results for multi-layer support systems.