Derive a relation between D60D10 Cu and fD 314DmDmsin314DDmD

Derive a relation between

D60/D10= Cu

and

f(D)= 3.14/(Dm-Dm)sin(3.14(D-Dm)/(DM-Dm))

where DM and Dm are the largest and smallest particle sizes present

Solution

Some commonly used measures are the uniformity coefficient. The uniformity coefficient Cu is defined as the ratio of D60 by D10. So when Cu is greater than 4 to 6, it is understood as a well graded soil and when the Cu is less than 4, they are considered to be poorly graded or uniformly graded. Uniformly graded in the sense, the soils have got identical size of the particles. For example for desert sands Cu will be approximately is equal to 1. Another coefficient to measure gradation is: Cc is equal to (D30 square) by (D60 into D10) where coefficient of gradation or coefficient of curvature is (D30 square) by (D60 into D10). For the soil to be well graded the value of coefficient of uniformity Cu has to be greater than 4 and Cc should be in the range of 1 to 3. So higher the value of Cu the larger the range of the particle sizes in the soil. So if the Cu value is high it indicates that the soil mass consists of different ranges of particle sizes