Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2018 — 18-Geol-A6 Soil Mechanics. Three-hour, closed-book exam; a Casio or Sharp approved calculator, a compass and a ruler are permitted. Six questions constitute the complete 100-mark paper: Questions 1–5 (10+15+20+20+20 marks) are compulsory; Question 6 offers eight 5-mark optional items of which the source asks for three.
Each reading is cross-checked below by an independent physical-consistency test (Q2: the 12%-point saturation comes out to $\approx100\%$, matching its plotted position essentially on the $S=100\%$ curve; Q4: the two digitized curves in Figure Q4-2 are treated as the overconsolidated-clay sample (upper, steep-kneed curve, per the question's own description) and an unused second dataset (lower curve, not needed for a single-sample problem); Q5: the resulting pore pressures give positive effective stress at every point and a linear uplift diagram, the expected signature of a consistent equipotential count). Assumed $G_s=2.70$ (not given) for Q2(c)'s phase relations — typical for a silty/clayey compacted fill and independently supported by the $S\approx100\%$ check above.
Given. Percent-passing grain-size data for Soils A and B (Table Q1-1, below); Soil A: $LL=30\%$, $PL=27\%$; Soil B: $LL=40\%$, $PL=30\%$.
Find. USCS group symbol and group name for Soil A and Soil B.
Approach. Plot both gradations on a semi-log grain-size chart; for Soil A (coarse-grained) read $D_{10}$, $D_{30}$, $D_{60}$ to get $C_u$, $C_c$; for Soil B (fine-grained, $>50\%$ passing No. 200) locate $LL$/$PI$ relative to the A-line.
Sieve
Size (mm)
Soil A, % passing
Soil B, % passing
3 in
75
100
100
2 in
50
100
100
1 in
25
100
100
0.75 in
19
95
100
0.375 in
9.5
80
100
No. 4
4.76
72
91
No. 8
2.38
50
80
No. 20
0.84
40
72
No. 40
0.42
35
70
No. 100
0.15
12
59
No. 200
0.075
8
55
Fig. Q1 — Grain-size distribution, Soils A and B (semi-log), with $D_{10}$/$D_{30}$/$D_{60}$ for Soil A.
Split each soil's coarse/fine fractions. Soil A: gravel $=100-72=28\%$, sand $=72-8=64\%$, fines $=8\%$ — fines $<50\%$, so Soil A is coarse-grained; sand $>$ gravel, so it is a SAND. Soil B: gravel $=100-91=9\%$, sand $=91-55=36\%$, fines $=55\%$ — fines $\ge50\%$, so Soil B is fine-grained (silt/clay).
Soil A gradation ($D_{10}$, $D_{30}$, $D_{60}$ by log-linear interpolation). Reading the plotted curve: $D_{10}=0.106$ mm, $D_{30}=0.336$ mm, $D_{60}=3.26$ mm.
$$C_u=\dfrac{D_{60}}{D_{10}}=\dfrac{3.26}{0.106}=30.7 \qquad C_c=\dfrac{D_{30}^2}{D_{10}D_{60}}=\dfrac{0.336^2}{0.106\times3.26}=0.33$$
Fines $<5\%$ → clean sand (no dual symbol needed). $C_c=0.33<1$ fails the well-graded test ($C_u>6$ AND $1\le C_c\le3$), so $\boxed{\text{Soil A} = \text{SP, poorly graded sand}}$.
Soil B plasticity. $PI=LL-PL=40-30=10\%$. A-line at $LL=40\%$: $PI_A=0.73(LL-20)=0.73(20)=14.6\%$. Since $10<14.6$, Soil B plots below the A-line, and $LL=40\%<50\%$ places it in the low-plasticity ("L") group → silt (M), not clay. With $PI=10\%>7\%$ it is clear of the ML–CL hatched borderline band.
$$\boxed{\text{Soil B} = \text{ML}}\text{, sandy silt (sand fraction }36\%\ge30\%\text{ of the total, so the "sandy" descriptor applies)}$$
