Example 1
SW-SM dual symbol: sand, 8% fines, Cu=8, Cc=1.5, ML fines
Given
- gravel percent
- 10
- sand percent
- 82
- fines percent
- 8
- cu
- 8
- cc
- 1.5
- liquid limit
- 30
- plastic limit
- 26
Assumptions
- Classification follows the ASTM D2487 (USCS) flowchart for inorganic soils; organic soils (OL/OH/PT) are not evaluated.
- Result: SW-SM (well-graded sand with silt)
Solution steps
Gradation summary
Fines (passing the No. 200 sieve) decide the top-level split: 50% or more fines is fine-grained, less is coarse-grained.
fines = 8 %; sand = 82 %; gravel = 10 %
Coarse-grained soil: gravel or sand?
With less than 50% fines the soil is coarse-grained; the larger coarse fraction names it.
fines = 8 % < 50 %; gravel = 10 % ≤ sand = 82 % → sand
Borderline fines: dual symbol
Fines between 5% and 12% take a dual symbol: gradation (W/P) first, fines type (M/C) second.
5 % ≤ fines = 8 % ≤ 12 %
Gradation shape: well or poorly graded?
Well-graded sand requires Cu ≥ 6 with Cc between 1 and 3.
Cu = D60/D10 and Cc = D30² / (D10·D60)
Cu = 8 and Cc = 1.5; limits: Cu ≥ 6 and 1 ≤ Cc ≤ 3 → well graded
Plasticity chart (A-line) check
The A-line PI = 0.73(LL − 20) separates clays (on or above) from silts (below); the hatched CL-ML zone is PI between 4 and 7 on or above the A-line.
PI_A-line = 0.73·(LL − 20)
A-line at LL = 30: PI_A = 0.73 × 10 = 7.3; soil PI = 4 (below the A-line)
Classification: SW-SM
Group symbol SW-SM — well-graded sand with silt (ASTM D2487 group name).
Results
Fines content (passing No. 200)
8
Gravel fraction
10
Sand fraction
82
Coefficient of uniformity Cu = D60/D10
8
Coefficient of curvature Cc = D30²/(D10·D60)
1.5
Plasticity index PI = LL − PL
4
Where this answer was checked
- source
- ASTM D2487 flowchart criteria (as tabulated in the NCEES FE Reference Handbook) — 5–12% fines → dual symbol; Cu ≥ 6 and 1 ≤ Cc ≤ 3 → SW; PI below A-line → M
- verified by
- hand-recomputed
- derivation
- Fines 8% < 50 → coarse; sand 82 > gravel 10 → S. 5 ≤ 8 ≤ 12 → dual. Gradation: Cu = 8 ≥ 6 and Cc = 1.5 in [1,3] → W. Fines: PI = 30 − 26 = 4; A-line = 0.73(30−20) = 7.3; 4 < 7.3 → below A-line → ML → M. Symbol SW-SM, name 'well-graded sand with silt' (gravel 10% < 15% adds no modifier).