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

Step 1: Recall the Casagrande plasticity chart lines.
Casagrande's plasticity chart plots plasticity index \(PI\) against liquid limit \(LL\) and uses two reference lines to classify fine-grained soils: the A-line, \[ PI=0.73(LL-20) \] which separates clays (above the line) from silts and organic soils (below), and the U-line, \[ PI=0.9(LL-8) \] which forms the practical upper boundary above which almost no natural soil plots.

Step 2: Compute the A-line value at \(LL=40\%\). \[ PI_A=0.73(40-20)=0.73\times20=14.6\% \] This is the minimum plasticity index a soil at this liquid limit needs to be classed as an inorganic clay; below this line it would classify as silt or organic clay/silt instead.

Step 3: Compute the U-line value at \(LL=40\%\). \[ PI_U=0.9(40-8)=0.9\times32=28.8\% \] This is the practical upper limit; inorganic clays at this liquid limit essentially never plot with a plasticity index above this value.

Step 4: State the range and match to the options.
Inorganic clays with \(LL=40\%\) plot with plasticity index between the A-line and U-line values, between 14.6% and 28.8%, matching option B exactly. Option A uses the wrong lower bound, option C uses too low an upper bound, and option D uses the wrong pair of lines entirely.

Final Answer:
The plasticity index of inorganic clays with \(LL=40\%\) ranges between 14.6% and 28.8%. \[ \boxed{14.6\%\ \text{to}\ 28.8\%} \]