The relationship between Modulus of subgrade reaction (K), pressure sustained (p) and displacement (∆) is expressed as ________
- AK = p × ∆ p
- BK =p / ∆Correct
- CK = p + ∆
- DK =p – ∆
Solution
Concept
Modulus of subgrade reaction definition and formula
Formula
K = p / Δ
Step-by-step solution
1. Modulus of subgrade reaction (K) is the ratio of applied contact pressure (p) to the resulting settlement or displacement (∆). 2. Mathematically, K = p / ∆. 3. Therefore, option B correctly expresses this relationship. Answer: B
Explanation
The modulus of subgrade reaction (K) represents the soil stiffness under a rigid plate and is defined as the pressure sustained per unit deformation/displacement: K = p / ∆. It is typically determined using a 75 cm diameter plate at 1.25 mm deflection.
Why the other options are wrong
A) Incorrect because K is not the product of pressure and displacement. C) Incorrect because stiffness is a ratio, not a sum. D) Incorrect because stiffness is a ratio, not a difference.
Shortcut
K = Pressure / Deflection = p / ∆ (units: kg/cm3 or N/mm3).
Common mistake
Inverting the ratio or multiplying pressure by displacement.
Correct answer: B) K =p / ∆