Engineering & Fluid Mechanics
Casagrande Plasticity Chart (USCS) Formula: Atterberg Plasticity Index & A-Line Soil Symbol
Classify fine-grained soils into USCS Clay vs. Silt (CL, CH, ML, MH) using Arthur Casagrande’s Plasticity Index PI = LL - PL, A-line PI_A = 0.73 * (LL - 20), and LL = 50% compressibility boundary.
How Arthur Casagrande’s 1948 A-Line separates inorganic clays (CL/CH) from silts & organic soils (ML/MH)!
In geotechnical foundation and earthwork engineering (ASTM D2487 Unified Soil Classification System, USCS), fine-grained soils (> 50% passing No. 200 sieve) are classified from two Atterberg water-content limits: Liquid Limit LL (%) and Plastic Limit PL (%), giving Plasticity Index PI = LL - PL!
Arthur Casagrande (1948, Transactions of ASCE) established two fundamental boundaries on the LL–PI Plasticity Chart: (1) Liquid Limit LL = 50 separates Low-plasticity ("L", LL < 50) from High-plasticity/fat ("H", LL >= 50) fines; and (2) the empirical A-Line PI_A = 0.73 * (LL - 20) separates Inorganic Clays ABOVE/ON the A-line (PI >= PI_A and PI > 7 -> CL or CH, plus dual CL-ML when 4 <= PI <= 7 above the A-line) from Silts below the A-line (ML or MH)! For LL = 54% and PL = 24%, PI = 30% >= PI_A = 24.82% with LL >= 50 -> Fat Clay "CH"!
| Atterberg Limits (LL %, PL %) | Soil PI = LL - PL | Casagrande A-Line 0.73*(LL - 20) | ASTM D2487 USCS Fine Soil Group |
|---|---|---|---|
| LL = 54%, PL = 24% | PI = 30% | 24.82% (PI >= A-Line) | CH — High-Plasticity (Fat) Clay |
| LL = 38%, PL = 18% | PI = 20% | 13.14% (PI >= A-Line) | CL — Low-Plasticity (Lean) Clay |
| LL = 54%, PL = 36% | PI = 18% | 24.82% (PI < A-Line) | MH — High-Plasticity Elastic Silt |
ASTM D2487 / Casagrande USCS Fine-Grained Soil Group Classifier (CH, CL, CL-ML, MH, ML)
Classifies Liquid Limit LL (B2) and Plastic Limit PL (B3) against PI = LL - PL, Casagrande’s A-line 0.73*(LL - 20), and LL = 50.
=IF(OR(B2 <= 0, B3 <= 0, B3 > B2), "Invalid Atterberg Limits (Requires LL >= PL > 0)", IF(B2 >= 50, IF(B2 - B3 >= 0.73 * (B2 - 20), "CH (High-Plasticity Fat Clay)", "MH (High-Plasticity Elastic Silt)"), IF(AND(B2 - B3 >= 4, B2 - B3 <= 7, B2 - B3 >= 0.73 * (B2 - 20)), "CL-ML (Silty Clay Dual Zone)", IF(AND(B2 - B3 > 7, B2 - B3 >= 0.73 * (B2 - 20)), "CL (Low-Plasticity Lean Clay)", "ML (Low-Plasticity Silt)"))))Casagrande A-Line Reference Plasticity Index PI_A = MAX(0, 0.73 * (LL - 20))
Computes the A-line threshold ordinate at Liquid Limit B2.
=IF(OR(B2 <= 0, B3 <= 0, B3 > B2), "Invalid Atterberg Limits (Requires LL >= PL > 0)", ROUND(MAX(0, 0.73 * (B2 - 20)), 2))Try the example
Use the original values or change them to test your understanding.