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.

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

MODULUS 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 (%)

2

3

4

5

7

10

15

20

50

100

k-value (MPa/m)

21

28

35

42

48

55

62

69

140

220

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

where, 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.