Atterberg Limits Plasticity Index Calculator

Atterberg limits are water contents, expressed as a percentage of dry mass, that mark where a remoulded fine-grained soil changes consistency state. The liquid limit is the water content at the plastic to liquid boundary and the plastic limit marks the semi-solid to plastic boundary, so the plasticity index PI = LL - PL measures the width of the plastic range. Under ASTM D4318 the liquid limit is the water content at which a 13 mm groove closes after 25 blows of the Casagrande cup, and the plastic limit is the water content at which a thread crumbles when rolled to 3.2 mm diameter. Both tests are run only on the fraction passing the 425 micrometre sieve, so the result describes the fines, not the whole soil. The Casagrande chart plots PI against LL and separates clays from silts with the A-line, PI = 0.73(LL - 20), while a vertical boundary at LL = 50 divides low from high plasticity, giving the CL, CH, ML and MH groups of the Unified Soil Classification System. The U-line, PI = 0.9(LL - 8), is an empirical upper bound; points plotting above it usually indicate a testing error. Practitioners read PI below 7 as slightly plastic, 7 to 17 as medium, and above 17 as highly plastic with growing shrink-swell risk. Activity, defined as PI divided by the percentage finer than 2 micrometres, points at mineralogy: roughly 0.4 for kaolinite, near 0.9 for illite, and well above 1.25 for smectite and montmorillonite. Derived correlations such as the Terzaghi and Peck compression index Cc = 0.009(LL - 10) and the normally consolidated strength ratio near 0.11 + 0.0037 PI are useful for preliminary work but carry substantial scatter and should not replace consolidation or triaxial testing on critical projects. Results are also sensitive to operator technique and to whether the sample was air dried before testing.

Albert Atterberg was a Swedish agricultural chemist working at Kalmar who studied the consistency of clays for ceramics and soil tillage. In 1911 he published a set of consistency limits describing how a clay-water mixture passes through solid, semi-solid, plastic and liquid states, and it is the liquid and plastic limits from that scheme that survive in engineering practice. Atterberg original procedures were manual and depended heavily on the judgement of the person performing them, which limited reproducibility between laboratories. Arthur Casagrande, working at Harvard under Karl Terzaghi influence, converted the tests into repeatable standards. Around 1932 he introduced the mechanical liquid limit device, a brass cup dropped a fixed 10 mm onto a hard base with a standard grooving tool, which removed most of the operator dependence. His 1948 paper on the classification and identification of soils presented the plasticity chart and the A-line, which became the backbone of the Airfield Classification System he developed for the US Army Corps of Engineers during the Second World War. That system was broadened into the Unified Soil Classification System in the early 1950s and is now codified as ASTM D2487, with the limits themselves standardized in ASTM D4318. Alec Skempton introduced the activity ratio in 1953 to link plasticity to clay mineralogy. British and European practice took a different route for the liquid limit, adopting the fall cone method with an 80 g, 30 degree cone penetrating 20 mm, which is generally regarded as less operator sensitive than the Casagrande cup.