### How to calculate modulus of subgrade reaction?

The modulus of subgrade reaction ks is a function of the contact pressure and allowable settlement on an unit area of soil. it's also referred to as Pressure per unit settlement.

On the opposite hand, the safe bearing capacity is that the maximum pressure which the soil can carry safely without risk of shear failure. The unit for bearing capacity is KN/m2, whereas the unit for Subgrade modulus is kN/m3. As per Joseph Bowles the modulus of subgrade reaction may be a conceptual relationship between soil pressure and deflection.

Though, modulus of subgrade reaction and bearing pressure is said to be related to each other, there's no reliable correlation between modulus of subgrade reaction and soil bearing capacity because they're measurements of entirely different characteristics of a soil. the rationale , soil and its properties vary from place to put , there's significant effect on the sort of soil in layers below etc.

However, J E Bowles has attempted to offer a relationship which is:

k = 40 x SF x qa,

where SF is factor of safety considered in bearing pressure calculation and qa is allowable soil bearing capacity. Permissible settlement of 25mm is taken into account in deriving this equation. If permissible settlement is 50mm, 20 to be taken rather than 40.

So, you can employ the above equation in determining the Soil Subgrade Modulus.