Question 3 of 6: Grain-Size Distribution — Uniformity/Gradation and USCS Classification
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper format. 04-Agric-A2 Soil Physics & Mechanics,
National Exams May 2017 — a three-hour open-book examination;
any non-communicating calculator is permitted. The cover page states that five (5)
questions constitute a complete exam paper and that only the first five as they
appear in the answer book are marked, that each question is of equal value, and that
some questions require a written answer whose clarity and organization matter for
marks. All six printed questions are worked here, because the set is a study resource
rather than a timed attempt; on exam day a candidate submits only the first five, in
order.
Reference texts. B.M. Das, Principles of Geotechnical
Engineering, 9th ed. (weight-volume relationships, permeability, grain-size
analysis, USCS classification, compaction, slope stability, well hydraulics); R.F.
Craig, Craig's Soil Mechanics, 9th ed. (effective stress, seepage and flow
nets, shear strength); USDA NRCS National Engineering Handbook (compaction
and earthwork field practice).
Question 3: Grain-Size Distribution — Uniformity/Gradation and USCS Classification (20 marks)
Given. Grain-size distribution curves for soils A, B, C
(inorganic) and D (organic) — Figure 2 below. Soil D: liquid limit LL = 52%,
plastic limit PL = 22%.
Find. The inorganic soil (A, B or C) with the highest
Cu and the one with the lowest Cc (a); the USCS group symbol and
group name for soil D (b).
[Figure not reproduced: Figure 2 (redrawn to scale from the exam figure): particle-size distributions of soils A, B, C and D. See the official exam paper.]
Approach. Read D10, D30 and D60
off each curve (a smooth curve fitted in log-size through the three plotted points on
each curve, avoiding a false kink at the middle point), then compute
Cu = D60/D10 and
Cc = D30²/(D10D60) for the three
inorganic soils. For soil D, first use its curve to check the percent passing the
No. 200 (0.075 mm) sieve to confirm it is fine-grained, then classify from LL and PI
on the USCS plasticity chart.
Chart-read grain sizes and gradation parameters.
$$C_u=\frac{D_{60}}{D_{10}}, \qquad C_c=\frac{D_{30}^2}{D_{10}D_{60}}$$
Soil
D10 (mm)
D30 (mm)
D60 (mm)
Cu
Cc
A (gravel)
1.44
3.91
15.6
10.9
0.68
B (medium sand)
0.129
0.203
0.356
2.8
0.90
C (silt-to-gravel)
0.0043
0.073
2.26
≈520
0.54
a) Highest Cu, lowest Cc. Soil C's curve
spans from clay/silt sizes all the way to gravel (D10≈0.004 mm to
D60≈2.3 mm), so
$$C_{u,C}=\frac{2.26}{0.0043}\approx\boxed{520}$$
far above A (10.9) and B (2.8) — soil C has, by a wide margin, the
highest uniformity coefficient. Its curve's shape, however, rises
comparatively quickly through the fine end and then flattens through the coarse end,
which pulls D30 down close to D10 on the log scale and gives
$$C_{c,C}=\frac{(0.073)^2}{(0.0043)(2.26)}\approx\boxed{0.54}$$
the lowest coefficient of gradation of the three (below A's 0.68 and
B's 0.90). Soil C therefore takes both answers.
b) Fines content and Atterberg limits for soil D. Reading soil
D's curve at 0.075 mm gives about 99% passing, so more than half the sample is finer
than the No. 200 sieve and soil D falls in the fine-grained branch of
the USCS chart. With LL = 52% and PL = 22%,
$$PI=LL-PL=52-22=\boxed{30\%}$$
Since LL = 52% ≥ 50%, soil D is in the "H" (high plasticity) group. Comparing PI
to the A-line,
$$PI_{A\text{-line}}=0.73(LL-20)=0.73(32)=23.4\%$$
PI = 30% is above the A-line value of 23.4%, which places soil D on the "clay" side
of the chart. Combined with the stated organic nature of soil D, this gives:
