Pavement engineering – unit of the coefficient of subgrade modulus (k) The coefficient of subgrade modulus k (modulus of subgrade reaction) is defined as the pressure per unit surface deflection for a plate/area on subgrade. What is its correct SI unit?

Introduction:
Rigid pavement and slab-on-grade analyses often model the soil support with a Winkler spring foundation. The modulus of subgrade reaction k links applied contact pressure to deflection. Using correct units avoids errors when converting test data to design input.

Given Data / Assumptions:

• k = pressure / deflection.
• Pressure in kN/m^2, deflection in m.
• Linear spring analogy for small deflections.

Concept / Approach:

Because k equals pressure divided by deflection, its unit is (kN/m^2) per m = kN/m^3. Laboratory/field values are sometimes reported as kN/m^3 (SI) or pci (pounds per cubic inch) in US practice; do not confuse with elastic modulus or bearing capacity units.

Step-by-Step Solution:

Verification / Alternative check:

Dimensionally, k behaves like a spring constant per unit area, consistent with a foundation of independent springs model.

Why Other Options Are Wrong:

kN/m^2 is pressure, not stiffness per deflection; kN/m is a line stiffness; kN·m is a moment; kN/m^4 is not applicable here.

Common Pitfalls:

Mixing up k with elastic modulus of soil; failing to convert mm to m when computing k from plate load tests.

Final Answer:

kN/m^3