K = Pressure / Deflection

p ∞ Δ

p = KΔ

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