Question

For a given soil sample,

C_c = coefficient of gradation

C_u = coefficient of uniformity

D₁₀ = effective size

D₃₀ = diameter through which 30% of the total soil mass is passing

If C_c = 1.0 and C_u = 4.0, then what would be the value of D₃₀/D₁₀ ?

1. 2.00
2. 1.25
3. 1.50
4. 1.75

Answer 1

Correct Answer - Option 1 : 2.00

Given,

C_c = 1.0

C_u = 4.0

Coefficient of curvature (C_c):

\(C_c = \frac {D^2_{30}}{D_{60} × D_{10}}\)

Coefficient of uniformity (C_u):

\(C_u = \frac {D_{60}}{D_{10}}\)

D₁₀ → effective size

D₅₀ → average size

So,

\(C_c = \frac {D^2_{30}}{D_{60} × D_{10}}\)

C_c = 1

\(1 = \frac {D^2_{30}}{D_{60} × D_{10}}\)

D²₃₀ = D₆₀ × D₁₀     ...1)

and also given,

C_u = 4.0

\(\frac {D_{60}}{D_{10}} = 4\)

D₆₀ = 4D₁₀

Putting the value of D₆₀ in equation 1)

D²₃₀ = 4D₁₀ × D₁₀

\(\left(\frac {D_{30}}{D_{10}}\right)^2 = 4\)

\(\frac {D_{30}}{D_{10}} = 2\)