If the modulus of subgrade reaction of a soil is 20 kg/cu.cm when tested with a 30 cm diameter plate, the corrected modulus of subgrade reaction for the standard diameter plate will be -

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This question was previously asked in

RSMSSB JE Civil (Degree) May 2022 Official Paper

Answer 1

Concepts:

Modulus of Subgrade Reaction:

It is defined as the pressure per unit deformation of the subgrade at specific pressure or deformation. It is expressed as:

k = p/Δ

Here,

'k' is the modulus or coefficient of subgrade reaction,

'p' is the pressure, and 'Δ ' is the deformation of soil settlement.

The relation between modulus of sub-grade reaction (k)and plate diameter (d) is given as:

k × d = constant

The standard size plate has dia = 75 cm

Calculation:

Given data;

k1 = 20 kg/cu.cm , d1= 30 cm, and d2 = 75 cm

k₂ = the corrected modulus of subgrade reaction for the standard diameter plate

The relation between modulus of sub-grade reaction (k)and plate diameter (d) is given as:

k × d = constant

So

k1 × d1= k2 × d2

20 × 30 = K2 × 75

∴ k2 = 8 kg/cu.cm

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