Question 3 of 6: Grain-size analysis of four soils

Question 3: Grain-size analysis of four soils (10 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.

Given. Four grain-size distribution curves (Figure 2): D is the finest (about 30 % finer than 0.002 mm, 100 % passing at about 63 μm — clay and silt only); C is a very widely graded soil running from clay size (under 10 % finer than 0.002 mm) through silt and sand into coarse gravel; B is a near-vertical curve confined to medium sand (roughly 0.25–0.6 mm, D₁₀ ≈ 0.3 mm); and A is a coarse, well-spread sand–gravel curve from about 0.1 mm to 62 mm (D₁₀ ≈ 0.8 mm).

Find. (i) the uniform soil and its C_u/alias; (ii) the soil of highest saturated shear strength; (iii) the soils ranked by increasing permeability.

(i) The uniform soil is Soil B. Its distribution curve is the steepest — almost vertical — and is confined to a narrow band of medium sand (about 0.25–0.6 mm). A near-vertical curve means nearly all particles are the same size, which is the defining feature of a uniformly graded soil: a poor spread of sizes, few or no intermediate particles, and therefore a loose, easily disturbed packing (small particles cannot fill the voids between large ones). The coefficient of uniformity C_u = D₆₀/D₁₀ measures this spread. For a truly uniform soil C_u approaches unity, and per ASTM D2487 (Unified Soil Classification) a sand is only “well graded” if C_u ≥ 6 (gravel ≥ 4) together with 1 ≤ C_c ≤ 3; a uniform/single-size soil falls well below these limits, with C_u typically about 1–3. In the literature a uniform soil is also called a poorly graded soil (USCS group symbols SP or GP).

(ii) Soil A has the highest shear strength under saturated conditions. Soil A is a coarse, well-graded gravel-to-sand: a wide range of sizes lets small grains wedge into the voids between larger grains, producing a dense, highly interlocked, frictional skeleton with a high angle of internal friction (φ' commonly 38–45°). Being coarse-grained and highly permeable, it also drains almost instantly, so under saturated loading it develops negligible excess pore pressure and mobilises its full drained strength τ = σ' tanφ' with essentially no undrained penalty. The finer soils (especially D) are more compressible, less frictional, and prone to positive excess pore pressure that reduces effective stress and hence strength when sheared saturated. Soil A is therefore the strongest.

(iii) Ascending order of permeability: D < C < B < A. Permeability is governed principally by the effective grain size and the fines content, with Hazen's rule k ∝ D₁₀² capturing the dominant trend. Ranking by increasing D₁₀ (coarseness):

• D (lowest k): the finest soil, rich in clay/silt-sized particles with the smallest D₁₀; its sub-micron, tortuous pore throats and adsorbed water give the least permeability.
• C: a very widely graded clay-to-gravel mixture; its D₁₀ (≈ 0.003 mm) is larger than D's but still clay-sized, because roughly a quarter of the soil is finer than 0.01 mm and those fines fill the voids between the coarse grains, so k stays low.
• B: a clean, uniform medium sand (D₁₀ ≈ 0.3 mm) with essentially no fines; open, well-connected pores raise k above C.
• A (highest k): the coarsest, gravelly soil with the largest D₁₀ (≈ 0.8 mm) and almost no fines; its large interconnected voids give the greatest permeability.

The order therefore follows grain size from finest to coarsest: D < C < B < A.