# Modulus of Subgrade Reaction

The modulus of subgrade reaction (k) is used as a primary input for rigid pavement design. It estimates the support of the layers below a rigid pavement surface course (the PCC slab).

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- Last updated: 2026-11-01
- Review: reviewed by licensed professional engineers on the previous Pavement Interactive site, where reviewers were not recorded by name

The modulus of subgrade reaction (k) is used as a primary input for [rigid pavement](https://pavementinteractive.org/glossary/rigid-pavement/) design. It estimates the support of the layers below a rigid pavement [surface course](https://pavementinteractive.org/glossary/surface-course/) (the PCC slab). The k-value can be determined by field tests or by correlation with other tests. There is no direct laboratory procedure for determining k-value.

The modulus of subgrade reaction came about because work done by Westergaard during the 1920s developed the k-value as a spring constant to model the support beneath the slab (Figure 1).

![Modulus of subgrade reaction (k).](https://pavementinteractive.org/wp-content/uploads/2007/08/ModulusK1.jpg)

*Figure 1.* Modulus of subgrade reaction (k).

The reactive pressure to resist a load is thus proportional to the spring deflection (which is a representation of slab deflection) and k (Figure 2):

$$P = k\Delta$$

where:

- $$P$$ = reactive pressure to support deflected slab
- $$k$$ = spring constant = modulus of subgrade reaction
- $$\Delta$$ = slab deflection

![Relation of load, deflection and modulus of subgrade reaction (k).](https://pavementinteractive.org/wp-content/uploads/2007/08/ModulusK2.jpg)

*Figure 2.* Relation of load, deflection and modulus of subgrade reaction (k).

The value of k is in terms of MPa/m (pounds per square inch per inch of deflection, or pounds per cubic inch - pci) and ranges from about 13.5 MPa/m (50 pci) for weak support, to over 270 MPa/m (1000 pci) for strong support. Typically, the modulus of subgrade reaction is estimated from other strength/stiffness tests, however, in situ values can be measured using the plate bearing test.

## Related Tests

[Plate Load Test](https://pavementinteractive.org/reference-desk/design/design-parameters/plate-load-test/)