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Bryan Stanley
Design Engineering
Asked a question 2 years ago

Coefficient of Subgrade Reaction?

What is the Coefficient of Subgrade Reaction?

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Coefficient of Subgrade Reaction?

K = Pressure / Deflection

p ∞ Δ

p = KΔ

Where, p = reaction pressure, Δ = deflection, K = mod. of subgrade reaction


In simple, it is a measure of grounds ability to resist immediate elastic deform under load. It is defined as the pressure needed to deform the subgrade by a given unit dist. SI expression is Mpa/m, & that is the unit used. Americans used pci.

The modulus of subgrade reaction describes the soil’s short-term, elastic response to loading. That is the subgrade property we need to know to determine slab thkness in most design methods.

100pci = 27.2Mpa/m

To calculate the Mod of Subgrade Reaction, Plate bearing test is conducted. A graph is plotted with the mean settlement (mm) on x axis & load (kg/cm2)on y-axis. The pressure p corresponding to settlement of 1.25mm is obtained from the graph. The mod. of subgrade reaction K is calculated from the relation given below.

K = P/0.125 Mpa/cm 

Relation betn k value & CBR

An existing correlation betn k-value (k in pci) & CBR, used in FAA airfield pavement thkness design (Advisory circular 150/5320-6E, FAA 2009) is k = (1500 CBR/26)0.7788 Where k is in pci or lb/in3

Soaked CBR (%)2345710152050100
k-value (MPa/m)2128354248556269140220

Note: 100pci = 2.77 kg/cm3 = 27.2 MPa/m

On the other hand, a commonly used conversation formula developed by Packard (Barker & Alexander, 2012) for the Portland Cement Association (PCA): k = 53.438 CBR0.5719

Design of Rigid Pavement

Based on K- value

Axle load (Single & Tandem)

Max temp differential in °C variation during day & night time.

Flexural strength

Slab thkness is decided with the help of chart given by IRC 58-2015 P 36-72

The coefficient of subgrade reaction is referred as the ratio between the pressure against the footing or mat and the settlement at a given point expressed as the coefficient of subgrade reaction which is defined as the ratio between the pressure against the footing or mat and the settlement at a given point which is expressed as ;
ks = q/S

ks = coefficient of subgrade reaction
q = pressure on the footing or mat at a given point
S = settlement of the same point of the footing or mat in the corresponding unit of length

i. The value of k is independent of the magnitude of pressure.
ii. The value of s has the same value for every point on the surface of the footing.

Raul Jimenez
Senior Project Manager

Hi, In simple words coefficient of subgrade reaction is the function of stiffness and compressibility of soil.

It is also known as Modulus of subgrade reaction. It is pressure sustain by a sample of soil under a rigid plate of std diameter/unit settlement measured at a specified pressure.

According to IRC, Value of  K should be measured at the 1.25 mm settlement.

Its value is in the range of 0.05 to 0.15.