In geotechnical and structural engineering, the modulus of subgrade reaction (k-value) is a critical parameter used to evaluate the stiffness and load-bearing capacity of soil. It provides the relationship between the applied pressure and the resulting soil settlement. The Subgrade Modulus Calculator simplifies this calculation, enabling engineers to quickly determine the soil's support capacity for foundations, pavements, and other structures.

Formula for Modulus of Subgrade Reaction

The modulus of subgrade reaction (kk

k) is calculated using the following formula:

$k = \frac{P}{\Delta}$

Where:

• P = Applied pressure (e.g., psi or kN/m²)
• F = Total applied load (e.g., pounds or kilonewtons)
• A = Area over which the load is applied (e.g., ft² or m²)

Example Calculation

If a load of 120 kN causes a deflection of 15 mm (0.015 m), the subgrade modulus would be calculated as:

$k = \frac{\text{120kN}}{\text{0.015 m}} = 8000 \, \text{kN/m³.}$

Final Answer:

The modulus of subgrade reaction (k) is 8000 kN/m³

Common FAQs

What is the modulus of subgrade reaction?

The modulus of subgrade reaction (denoted as k) is a measure of the stiffness or support capacity of a soil subgrade when subjected to an applied load. It describes how much the soil deflects (or compresses) under a given pressure.

In simple terms, it indicates how well the soil can resist deformation under load, making it a key parameter in geotechnical engineering, especially for designing foundations, pavements, and slabs.

What is the modulus of subgrade reaction used for?

The modulus of subgrade reaction (k-value) is used to evaluate the stiffness or load-bearing capacity of soil in structural and geotechnical engineering. It helps engineers design foundations, slabs, and pavements by estimating how much the soil will settle or deform under an applied load.

What are the units of the modulus of subgrade reaction?

The units of the modulus of subgrade reaction depend on the measurement system:

• SI Units: Kilonewtons per cubic meter $\text{kN/m}^3$
• Imperial Units: Pounds per square inch per inch ($\text{psi/in}$ )

These units describe the relationship between soil pressure and the corresponding settlement or deflection.