Uniformity and Coefficient of Curvature

C_{u} = \frac{D _{60}}{D _{10}} C_{c} = \frac{D _{30}^{2}}{D _{10} D _{60}}

D10, D30, D60 are particle sizes with 10, 30, 60% passing. Cu is the uniformity coefficient; Cc is the coefficient of curvature (gradation). USCS well-graded sand (SW): Cu ≥ 6 and 1 ≤ Cc ≤ 3. Well-graded gravel (GW): Cu ≥ 4 and 1 ≤ Cc ≤ 3. Otherwise the soil is poorly graded (SP/GP) or gap-graded if Cc is outside 1–3.

$D_{10}$ (mm): Effective size (10% passing)
$D_{30}$ (mm): 30% passing size
$D_{60}$ (mm): 60% passing size
$C_{u}$: Uniformity coefficient
$C_{c}$: Coefficient of curvature

Step-by-step solved example

D10 = 0.10 mm, D30 = 0.30 mm, D60 = 0.60 mm. Compute Cu and Cc and classify a sand.

Grain-size curve: Cu = D60/D10, Cc = D30²/(D10 D60).

1. Cu
Cu = D60/D10 = 0.60/0.10 = 6.0.
$C_{u} = 6$
2. Cc
Cc = (0.30)²/(0.10×0.60) = 0.090/0.060 = 1.50.
$C_{c} = 1.50$
3. USCS sand
Cu ≥ 6 and 1 ≤ Cc ≤ 3 → well-graded sand (SW) if fines < 5%.

Answer: Cu = 6, Cc = 1.5 (well-graded sand)

10 practice questions

0/10 correct

1.Cu is defined as

2.D10 = 0.10, D60 = 0.60 mm. Cu =

3.D10 = 0.10, D30 = 0.30, D60 = 0.60 mm. Cc =

4.USCS well-graded sand requires

5.Cu = 1 means the soil is

6.D10 is the size with

7.Well-graded gravel (GW) uses the Cu threshold

8.If Cu = 8 but Cc = 0.4, the sand is

9.D10 = 0.20 mm, D60 = 2.0 mm. Cu =

10.Hazen’s permeability estimate uses