Atterberg Limits Plasticity Index Calculator
Compute atterberg limits plasticity index using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
PI = LL - PL | LI = (w - PL) / PI | A-line: PI = 0.73(LL - 20)
Plasticity Index PI is the difference between liquid limit and plastic limit. Liquidity Index LI shows where natural moisture falls within the plastic range. The Casagrande A-line separates clays from silts on the plasticity chart.
Worked Examples
Example 1: Clay Soil Classification
Problem: Classify a soil with LL = 55%, PL = 22%, natural moisture = 35%.
Solution: PI = 55 - 22 = 33%\nA-line at LL=55: 0.73*(55-20) = 25.55\nPI (33) > A-line (25.55) and LL > 50\nClassification: CH (High plasticity clay)\nLI = (35-22)/33 = 0.394 (plastic state)\nCI = (55-35)/33 = 0.606 (firm consistency)
Result: PI = 33%, CH soil, LI = 0.39 (plastic, firm)
Example 2: Silt Identification
Problem: Classify soil with LL = 40%, PL = 32%, 45% clay fraction.
Solution: PI = 40 - 32 = 8%\nA-line at LL=40: 0.73*(40-20) = 14.6\nPI (8) < A-line (14.6) and LL < 50\nClassification: ML (Low plasticity silt)\nActivity = 8/45 = 0.178 (inactive)
Result: PI = 8%, ML soil, Activity = 0.18 (inactive)
Frequently Asked Questions
What are the Atterberg limits?
Atterberg limits are water content boundaries that define the transitions between different consistency states of fine-grained soils. The liquid limit (LL) is the water content at which soil transitions from a plastic to a liquid state. The plastic limit (PL) is the water content at which soil transitions from a semi-solid to a plastic state. The shrinkage limit (SL) marks the transition from semi-solid to solid. These limits, developed by Swedish scientist Albert Atterberg in 1911, are fundamental soil properties used in classification, engineering design, and construction.
What is the Plasticity Index and why does it matter?
The Plasticity Index (PI) is the numerical difference between the liquid limit and plastic limit: PI = LL - PL. It represents the range of water content over which the soil behaves plastically. Higher PI values indicate more clay content and greater plasticity. Soils with PI less than 7 are considered slightly plastic, 7-17 are medium plasticity, and above 17 are highly plastic. PI directly affects soil engineering properties including compressibility, strength, permeability, and swelling potential, making it essential for foundation design and earthwork construction.
What is the Casagrande plasticity chart?
The Casagrande plasticity chart is a graphical classification system that plots Plasticity Index versus Liquid Limit. It contains the A-line (PI = 0.73*(LL-20)) which separates clays (above) from silts (below), and a vertical line at LL = 50 separating low plasticity (left) from high plasticity (right). This creates four main zones: CL (low plasticity clay), CH (high plasticity clay), ML (low plasticity silt), and MH (high plasticity silt). The chart is a cornerstone of the Unified Soil Classification System (USCS) used worldwide in geotechnical engineering.
What do Liquidity Index and Consistency Index tell us?
Liquidity Index (LI = (w-PL)/PI) indicates where the natural water content falls relative to the Atterberg limits. LI less than 0 means the soil is in a semi-solid or solid state. LI between 0 and 1 means the soil is plastic, and LI greater than 1 means the soil is at or near liquid state. Consistency Index (CI = (LL-w)/PI) is the complement of LI (CI = 1 - LI). CI greater than 1 indicates stiff to hard soil, while CI near 0 indicates very soft soil. These indices help predict soil behavior during construction and assess slope stability.
How is the heat index calculated?
The heat index combines air temperature and relative humidity to determine perceived temperature. The NWS uses a regression equation with nine terms. At 90F with 60% humidity, the heat index is about 100F. Heat index values above 105F indicate danger. Direct sunlight can add up to 15F to the heat index value.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.