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.
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
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.
