Grain Size Uniformity Calculator (Cu)

The grain size distribution curve of a coarse-grained soil is summarized by a few percentile diameters read off the plot of percent finer against log particle size. D10, the effective size, is the diameter at which 10 percent of the sample by mass is finer; D30, D50, and D60 follow the same convention. The coefficient of uniformity Cu = D60 / D10 measures how wide the size range is, with values near 1 describing a single-size soil and values above 15 describing a broadly graded one. The coefficient of curvature Cc = D30 squared divided by D10 times D60 tests whether the curve is smooth between those limits or has a gap in the intermediate sizes. A soil is well graded under ASTM D2487 only when both criteria hold: Cu at least 4 for gravels or at least 6 for sands, together with Cc between 1 and 3. The percent passing the No. 200 sieve, an opening of 0.075 mm, sets the second half of the classification, with 5 percent or less giving clean symbols such as SW and SP, more than 12 percent giving SC or SM, and the 5 to 12 percent band requiring dual symbols such as SP-SM. Gradation drives practical behavior. Well graded fills compact to higher dry densities and higher friction angles because fine particles occupy the voids between coarse ones, whereas uniform sands are prone to piping and internal erosion. The effective size feeds Hazen's empirical estimate of hydraulic conductivity, k in centimeters per second roughly equal to 1.0 times D10 in millimeters squared, equivalently k = 100 times d10 in centimeters squared, an approximation intended for loose clean sands with Cu below about 5 and D10 between 0.1 and 3 mm, and it should not be applied to silty or well graded material. The sorting coefficient reported here is the square root of D60 over D10; note that Trask's original sedimentological sorting coefficient uses the quartile ratio D75 over D25 instead, so values are not interchangeable between the two conventions. Filter and drain design uses the same percentiles through Terzaghi's rules, which keep the filter D15 below about four to five times the base soil D85 to prevent particle migration.

The effective size and the uniformity coefficient were introduced by Allen Hazen, an American sanitary engineer working for the Massachusetts State Board of Health at the Lawrence Experiment Station. In reports published around 1892 and 1911 on the design of slow sand filters for municipal water supply, Hazen found that filter performance and permeability correlated with the tenth-percentile grain diameter and that the ratio D60 to D10 captured the spread of sizes. Both definitions passed directly from water treatment practice into soil mechanics. On the geological side, Johan August Udden proposed a doubling grain size scale in 1898 and Chester Wentworth revised it in 1922 into the sand, silt, and clay boundaries still cited by sedimentologists, with William Krumbein recasting it as the logarithmic phi scale in 1934. The gradation criteria used for classification came out of wartime airfield construction. Arthur Casagrande developed the Airfield Classification System in 1942 for the US Army Corps of Engineers, using the Cu and Cc pair together with the fines content and Atterberg limits to sort soils into groups with predictable engineering behavior. The Corps of Engineers and the Bureau of Reclamation revised it jointly in 1952 into the Unified Soil Classification System, which ASTM adopted as D2487 and which supplies the group symbols reported by this calculator. The laboratory procedures were standardized in parallel: sieve analysis under ASTM D6913 for particles coarser than 0.075 mm and hydrometer sedimentation, based on Stokes law settling and refined by Casagrande in the 1930s, for the finer fraction, now covered by ASTM D7928.