Q2: The soil has a liquid limit of 50%. Following the A-line, in the plasticity chart as per IS: 1498 1970, the corresponding plastic limit is:
📝 Detailed Explanation
Casagrande’s A-line is the empirical boundary on the plasticity chart that separates clays (above the line) from silts (below the line), and it is one of the few plasticity-chart relationships given as a fixed, memorizable formula: Ip = 0.73(WL − 20). Because plasticity index is also defined as Ip = WL − WP, knowing the liquid limit and assuming the soil plots exactly on the A-line lets you solve directly for the plastic limit.
✅ Why “28.1%” Is Correct
Substituting WL = 50% into the A-line equation gives Ip = 0.73(50 − 20) = 0.73 × 30 = 21.9%. Since Ip = WL − WP, rearranging gives WP = WL − Ip = 50 − 21.9 = 28.1%.
Casagrande’s plasticity chart plots plasticity index (Ip) against liquid limit (WL). The A-line (Ip = 0.73(WL−20)) separates clays (C, above the line) from silts (M, below); the commonly-cited U-line marks the practical upper bound of naturally occurring soils.
🔑 Key Point
The A-line equation, Ip = 0.73(WL − 20), is worth memorizing outright — it is the single most frequently tested numeric relationship on the plasticity chart.
💡 Key Concepts for Students
- The A-line is empirical (fitted from real soil test data), not derived from first principles — treat it as a memorized formula, not something to re-derive.
- Soils plotting above the A-line are classified as clays (C); soils below it are classified as silts (M) or organic soils (O).
- The A-line equation only applies for WL ≥ 20%; below that, a horizontal Ip = 0 line is typically used as the boundary instead.
- This same technique — assume the point lies exactly on the A-line, then use Ip = WL − WP to solve for whichever limit is missing — is reused across many plasticity-chart numeric questions.