Question

Based on the Casagrande's plasticity chart, plasticity index (in %) of inorganic clays having a liquid limit of 40 %, ranges between

• A. 18.0 and 28.8
• B. 14.6 and 28.8
• C. 14.6 and 23.4
• D. 18.0 and 43.8

Hint:

Use the A-line PI = 0.73(LL-20) for the lower bound and the U-line PI = 0.9(LL-8) for the upper bound, both at LL = 40%.

Answer 1

The Correct Option is B

Casagrande's plasticity chart uses two straight reference lines on a plot of plasticity index $PI$ against liquid limit $LL$ to classify fine grained soils, and this question asks for the band those two lines mark out at $LL=40\%$.

1. 18.0 and 28.8: the upper value 28.8 is correct, that is the U-line value, but 18.0 does not come from the A-line equation at $LL=40$, so the lower bound is wrong.
2. 14.6 and 28.8: check both. The A-line gives $PI=0.73(LL-20)=0.73(20)=14.6$, and the U-line gives $PI=0.9(LL-8)=0.9(32)=28.8$. Both numbers match exactly.
3. 14.6 and 23.4: the lower value 14.6 is right, the A-line value, but 23.4 is not the U-line value at $LL=40$, so the upper bound is wrong here.
4. 18.0 and 43.8: neither number matches the A-line or U-line computation at $LL=40$, so this pairing is wrong on both ends.

Working the two chart lines directly: the A-line, the boundary below which soils are silts or organic soils rather than clays, gives $PI=0.73(40-20)=14.6$ at this liquid limit. The U-line, the practical ceiling above which real soils essentially never plot, gives $PI=0.9(40-8)=28.8$. An inorganic clay with $LL=40\%$ plots somewhere between these two lines.

Let's summarize:

• A-line: $PI=0.73(LL-20)$, gives 14.6% at $LL=40\%$, the lower bound for clays.
• U-line: $PI=0.9(LL-8)$, gives 28.8% at $LL=40\%$, the practical upper bound.

The correct option is (B): 14.6 and 28.8.