Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2017 — 04-Geol-A6 Soil Mechanics. Three-hour, closed-book exam; a Casio or Sharp approved calculator, compass and ruler are permitted. Six questions constitute the complete 100-mark paper: Questions 1–5 are compulsory; Question 6 offers five 5-mark optional items of which the source asks for three.
Check: the source's own Instruction 3 is internally contradictory (it states "SIX (6) questions constitute a complete exam paper" then instructs "ANSWER QUESTIONS 1 TO 5" plus "choose three (3) more" for Question 6, i.e. 8 total). Questions 1–5 and all 5 optional items of Question 6 are answered below.
Given. Percent-passing grain-size data for Soils A and B (Table Q1, below); Soil A: $LL=30\%$, $PL=17.5\%$; Soil B: $LL=70\%$, $PL=25\%$.
Find. USCS group symbol and group name for Soil A and Soil B.
Approach. Plot both gradations on a semi-log grain-size chart, read $D_{10}$, $D_{30}$, $D_{60}$ for Soil A to get $C_u$, $C_c$, then locate both soils' plasticity relative to the A-line to decide the fines type.
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
100
100
0.375 in
9.5
100
100
No. 4
4.76
100
100
No. 8
2.38
97
100
No. 20
0.84
77
97
No. 40
0.42
20
92
No. 100
0.15
15
82
No. 200
0.075
6
75
Fig. Q1 — grain-size distribution, Soils A and B, with $D_{10}$/$D_{30}$/$D_{60}$ construction for Soil A.
Soil A — read $D_{10}$, $D_{30}$, $D_{60}$ (log-linear interpolation between bracketing sieve points).
$D_{60}$ (60% passing, between No.20/0.84 mm/77% and No.40/0.42 mm/20%): $D_{60}=\boxed{0.683\text{ mm}}$.
$D_{30}$ (30% passing, same bracket): $D_{30}=\boxed{0.474\text{ mm}}$.
$D_{10}$ (10% passing, between No.100/0.15 mm/15% and No.200/0.075 mm/6%): $D_{10}=\boxed{0.102\text{ mm}}$.
Soil A — gradation coefficients. $C_u=\dfrac{D_{60}}{D_{10}}=\dfrac{0.683}{0.102}=\boxed{6.69}$; $\quad C_c=\dfrac{D_{30}^2}{D_{60}D_{10}}=\dfrac{0.474^2}{0.683\times0.102}=\boxed{3.23}$.
Soil A — fines type from the plasticity chart. $PI=LL-PL=30-17.5=\boxed{12.5\%}$. A-line at $LL=30$: $PI_A=0.73(30-20)=7.3$. Since $PI=12.5>PI_A=7.3$ and $PI>7$, the fines plot above the A-line → clayey (C).
Soil A — group symbol. Passing No.200 $=6\%<50\%$ → coarse-grained. Passing No.4 $=100\%$ (0% gravel), so the coarse fraction is entirely sand-size → a SAND. Fines $=6\%$ falls in the 5–12% dual-symbol band (neither "clean" nor "with fines"), so both a gradation symbol and a fines symbol are reported. Gradation: $C_u=6.69\ge6$ but $C_c=3.23$ narrowly exceeds the $1
Soil B — group symbol. Passing No.200 $=75\%\ge50\%$ → fine-grained. $PI=LL-PL=70-25=\boxed{45\%}$. A-line: $PI_A=0.73(70-20)=36.5$. Since $PI=45>PI_A=36.5$ (and $PI_A
