Question 6 of 7: Grain-Size Distribution, Gradation Coefficients, and USCS Classification

Question 6: Grain-Size Distribution, Gradation Coefficients, and USCS Classification (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Plot percent finer against grain size on a semi-log axis, read D₁₀, D₃₀, D₆₀ by log-linear interpolation between the bracketing sieve points, and compute $C_u = D_{60}/D_{10}$, $C_c = D_{30}^2/(D_{10}D_{60})$. Classify each soil's coarse-fraction gradation against the USCS well-graded criteria and its fines against the plasticity chart (A-line), then compare fines content and classification to judge permeability for the leaching-bed recommendation.

1. a/b) Sample 1 — interpolate D₁₀, D₃₀, D₆₀ and compute C_u, C_c. Log-linear interpolation between the bracketing sieve points (e.g. for D₁₀, between 9% at 0.075 mm and 11% at 0.15 mm) gives $$D_{10} = 0.106\ \text{mm}, \qquad D_{30} = 0.601\ \text{mm}, \qquad D_{60} = 2.144\ \text{mm}$$ $$C_u = \frac{D_{60}}{D_{10}} = \frac{2.144}{0.106} = \boxed{20.2}, \qquad C_c = \frac{D_{30}^2}{D_{10}D_{60}} = \frac{0.601^2}{(0.106)(2.144)} = \boxed{1.59}$$ Both the breadth test ($C_u \ge 6$) and the shape test ($1 \le C_c \le 3$) for a well-graded sand are satisfied.
2. b) Sample 2 — C_u, C_c not obtainable from sieve data alone. The finest sieve tested (#200, 0.075 mm) still shows 35% finer for Sample 2, so the curve never reaches the 30% or 10% lines within the tested range — D₃₀ and D₁₀ would require a hydrometer test on the material passing #200. Only D₆₀ falls within range: $D_{60,2} \approx 0.78\ \text{mm}$. C_u and C_c for Sample 2 are therefore reported as not determinable from the given sieve data.

c) Which soil is more poorly graded? Sample 1 clearly meets both numeric USCS well-graded criteria ($C_u = 20.2 \ge 6$, $1 \le C_c = 1.59 \le 3$) and is therefore well graded. Sample 2's gradation coefficients cannot be computed from the sieve data (its D₁₀ lies below the finest sieve tested), but its coarse fraction is comparatively narrow — from the #4 to #40 sieve, percent finer only falls from 100% to 53%, a much smaller spread than Sample 1 shows over the same range (92% to 24%) — and, with 35% fines, its overall behaviour is fines-dominated rather than gradation-dominated. On the available evidence, Sample 2 is the more poorly graded (or at least, not demonstrably well-graded) of the two.

d) Which soil for the leaching bed? A leaching bed needs the fill with the higher permeability. Fines content is the dominant control on K for a granular soil: Sample 1 has only 9% passing #200 and is non-plastic, while Sample 2 carries 35% fines that are moderately plastic (see part e), which packs and clogs the pore network and sharply reduces permeability relative to a clean, well-graded sand. Sample 1 is recommended.

e) USCS classification of the recommended soil (Sample 1). With 9% passing #200, more than 50% of the sample is retained on #200 (coarse-grained), and of that coarse fraction almost all passes #4 (92% of the whole sample, i.e. >90% of the coarse fraction) so it is sand-dominated. Fines between 5% and 12% require a dual symbol; because C_u and C_c meet the well-graded criteria and the fines are non-plastic (silty, not clayey), Sample 1 classifies as SW-SM (well-graded sand with silt).