In the case of Atterberg limits of a soil, the shrinkage index of the soil will be equal to:
- Athe difference between the plastic limit and shrinkage limitCorrect
- Bthe sum of shrinkage ratio and flow index
- Cthe difference between the liquid limit and plastic limit
- Dthe difference between the liquid limit and shrinkage limit
Solution
Concept
Shrinkage index is the range of water content between the plastic limit and the shrinkage limit.
Formula
Is = wP - wS
Step-by-step solution
1. Atterberg limits: Liquid limit (wL), Plastic limit (wP), Shrinkage limit (wS). 2. Plasticity index IP = wL - wP. 3. Shrinkage index Is = wP - wS. 4. So shrinkage index = plastic limit minus shrinkage limit. Answer is A.
Explanation
Shrinkage index tells the range of water content in which soil is in the semi-solid state. This range is between the plastic limit and the shrinkage limit. So Is = wP - wS.
Why the other options are wrong
B: Shrinkage ratio and flow index are different properties. Their sum has no meaning. C: wL - wP is the plasticity index, not the shrinkage index. D: wL - wS is the range from liquid to solid state, not the shrinkage index.
Shortcut
Order is LL > PL > SL. PI = LL - PL (upper range). SI = PL - SL (lower range).
Common mistake
Mixing up plasticity index (LL - PL) and shrinkage index (PL - SL).
Correct answer: A) the difference between the plastic limit and shrinkage limit