Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2014 — 04-Geol-06, Soil Mechanics. Three-hour, closed-book exam; one of two approved calculators permitted. Six questions of equal value (20 marks each, Q6 split 5 marks per sub-part); the paper instructs candidates to answer only the first five questions appearing in the answer book — all six are answered here as a complete study resource.
Reference texts: Das, Principles of Geotechnical Engineering — USCS classification (Q1), phase relations (Q2, Q6d), consolidation theory (Q4), flow nets and seepage (Q5), permeability testing (Q6a/c); Craig, Craig's Soil Mechanics — lateral earth pressure coefficients and limit-equilibrium slope stability (Q3), effective stress and consistency limits (Q6b); EGBC Geoscience Professional Practice Guidelines for assumption-disclosure conventions.
Given. Sieve analysis (percent finer) for Soil A and Soil B (Table Q1); Soil A: $w_L=9\%$, $w_P=7\%$; Soil B: $w_L=70\%$, $w_P=25\%$.
Table Q1 — Percent Finer
Metric Sieve
US Sieve
Soil A (%)
Soil B (%)
75 mm
3 in
100
100
50 mm
2 in
100
100
25 mm
1 in
90
100
19 mm
0.75 in
86
100
9.5 mm
0.375 in
80
100
4.76 mm
No. 4
65
100
2.38 mm
No. 8
50
100
0.84 mm
No. 20
30
100
420 μm
No. 40
15
95
250 μm
No. 60
10
82
150 μm
No. 100
9
80
75 μm
No. 200
6
75
Find. The USCS group symbol for Soil A and for Soil B, with the gradation and plasticity data supporting each.
Approach. Plot both curves on the semi-log grain-size chart, read $D_{10}$, $D_{30}$, $D_{60}$ where needed, split each soil into gravel/sand/fines by the No. 4 and No. 200 sieves, then apply the USCS coarse- or fine-grained branch (gradation coefficients or the plasticity chart / A-line) as appropriate.
Figure Q1 — grain-size distribution curves for Soil A and Soil B, with the No. 200 and No. 4 sieve lines marking the silt–sand and sand–gravel boundaries.
Soil A — split into gravel, sand and fines. Percent finer than the No. 4 sieve (4.76 mm) is 65%, so percent retained on No. 4 (gravel) is $100-65=35\%$. Percent finer than the No. 200 sieve (75 μm) is 6% (fines). Sand is the remainder between the two sieves.
$$\text{Gravel}=100-65=\boxed{35\%},\qquad \text{Sand}=65-6=\boxed{59\%},\qquad \text{Fines}=\boxed{6\%}$$
Sand (59%) exceeds gravel (35%), so more than half of the coarse fraction is smaller than 4.76 mm → Soil A is a sand (S). Fines = 6% falls in the 5–12% borderline band, which the USCS chart requires a dual symbol for.
Soil A — gradation coefficients. Reading $D_{10}$, $D_{30}$, $D_{60}$ from the curve (log-linear interpolation between bracketing sieve points): $D_{30}=0.84\text{ mm}$ lands exactly at the No. 20 sieve point (30% finer); $D_{10}=0.25\text{ mm}$ lands exactly at the No. 60 sieve point (10% finer); $D_{60}$ interpolates between the No. 8 (2.38 mm, 50%) and No. 4 (4.76 mm, 65%) points.
$$C_u=\frac{D_{60}}{D_{10}}=\frac{3.78}{0.25}=\boxed{15.1},\qquad C_c=\frac{D_{30}^2}{D_{10}D_{60}}=\frac{0.84^2}{0.25\times3.78}=\boxed{0.75}$$
The sand well-graded criteria are $C_u>6$ and $1SP (poorly graded).
Soil A — fines qualifier and final symbol. $I_P=w_L-w_P=9-7=\boxed{2\%}$. With $I_P<4$, the fines plot below the A-line (non-plastic, silt-like) → qualifier M. Combining the borderline fines content (5–12%) with the poorly-graded sand and non-plastic fines gives the dual symbol
$$\boxed{\text{Soil A} = SP\text{-}SM}$$
(poorly graded sand with silt).
Soil B — coarse/fine split and plasticity. Percent finer than the No. 200 sieve is 75%, so more than half the sample is finer than 75 μm → Soil B is fine-grained (silt or clay), classified from the Atterberg limits rather than the gradation curve. $I_P=w_L-w_P=70-25=\boxed{45\%}$. The A-line value at $w_L=70\%$ is
$$I_{P,\text{A-line}}=0.73(w_L-20)=0.73(70-20)=\boxed{36.5\%}$$
Since $I_P=45\%>36.5\%$, Soil B plots above the A-line, and $w_L=70\%>50\%$ places it in the high-plasticity band.
Soil B — final symbol. Above the A-line with $w_L>50\%$ → inorganic clay of high plasticity.
$$\boxed{\text{Soil B} = CH}$$
(fat clay).
