SME
Soil Mechanics · Problem type
Well or poorly graded: Cᵤ and Cc
Use this for “A sand has D₁₀ = 0.15 mm, D₃₀ = 0.45 mm and D₆₀ = 1.2 mm. Find Cᵤ and Cc. Is it well graded?”
Chart
Percent passing against grain size, on a log axis
Cᵤ
=
D₆₀
D₁₀
=
8
Cc
=
D₃₀
2
D₁₀ × D₆₀
=
1.13
This is an example. Type your own values to start a new problem.
Cᵤ
=
D₆₀ (mm)
÷
D₁₀ (mm)
Cc
=
(
D₃₀ (mm)
)
2
÷
(
D₁₀ (mm)
×
D₆₀ (mm)
)
T
Soil
example
G
Group
worked out (not typed)
Formulas
Cᵤ
=
D₆₀
D₁₀
8
=
1.2
0.15
Cc
=
D₃₀
2
D₁₀
×
D₆₀
1.125
=
0.45
2
0.15 × 1.2
G
for
T
:
well
graded
if
Cᵤ
≥
6
(sand)
or
4
(gravel)
and
1
≤
Cc
≤
3,
else
poorly
graded
8 ≥ 6 and 1 ≤ 1.125 ≤ 3, so SW, well-graded sand
Assumptions
•
D₁₀ is the grain size that 10% of the soil (by weight) is finer than; likewise D₃₀ and D₆₀.
•
Well graded: Cᵤ ≥ 6 for a sand (Cᵤ ≥ 4 for a gravel), and 1 ≤ Cc ≤ 3.
•
The three sizes are read off the sieve analysis’s curve; the curve between them is drawn smooth.
Step-by-step
WE KNOW
T: sand, D₁₀ = 0.15 mm, D₃₀ = 0.45 mm, D₆₀ = 1.2 mm
FIND
uniformity coefficient (Cᵤ), coefficient of curvature (Cc), group (G)
Step 1 · Find uniformity coefficient (Cᵤ)
Use Cᵤ = D₆₀ ÷ D₁₀
How many times bigger the 60% size is than the 10% size: the spread of sizes.
Cᵤ
=
1.2
0.15
Cᵤ = 8
Step 2 · Find coefficient of curvature (Cc)
Use Cc = D₃₀² ÷ (D₁₀ × D₆₀)
The middle size against the two ends: from 1 to 3, no band of sizes is missing.
Cc
=
0.45
2
0.15 × 1.2
Cc
=
0.45
2
0.18
Cc
=
0.2025
0.18
Cc = 1.125
Step 3 · Find group (G)
Use G for T: well graded if Cᵤ ≥ 6 (sand) or 4 (gravel) and 1 ≤ Cc ≤ 3, else poorly graded
A wide spread of sizes with none missing: the small grains fill the gaps between the big ones.
8 ≥ 6 and 1 ≤ 1.125 ≤ 3: well-graded sand
G
=
well
graded
if
Cᵤ
≥
6
and
1
≤
Cc
≤
3
G
=
well
graded
if
8
≥
6
and
1
≤
1.125
≤
3
G
=
SW,
well-graded
sand
Check
Put the numbers back in. Both sides should match.
8
=
1.2
0.15
✓
1.125
=
0.45
2
0.15 × 1.2
✓
8 ≥ 6 and 1 ≤ 1.125 ≤ 3, so SW, well-graded sand ✓
Topic check
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