Soil Mechanics: Atterberg Limits, Soil Classification & In-situ Density

Liquid Limit Apparatus & Grooving Tools

• Casagrande cup device with crank, cam-follower, brass cup, hard-rubber base.
• Key dimensions (approx.): cup Ø $ext{ ≈ }50\,\text{mm}$, drop height $ext{ ≈ }10\,\text{mm}$, hard-rubber base thickness $\sim12\,\text{mm}$.
• Grooving tools supplied:
 ◦ Standard (ASTM / BS) tool for ordinary soils.
 ◦ Special narrow tool for silts or very soft clays.
• Handle, adjusting screw and brass cup identified in Fig. 2.7.

Liquid-Limit (LL) Test Procedure (Casagrande method)

• Sample preparation:
 ◦ Oven-dry soil, sieve on BS No. 36 (0.425 mm); discard coarser fraction.
 ◦ Mix $\approx100\,\text{g}$ soil with distilled water to putty-like consistency.
• Place soil in cup (depth $\approx10\,\text{mm}$); strike off surface level.
• Cut groove through centre line of cam-follower with grooving tool.
• Crank at 2 rev s⁻¹; record blows (N) to close groove $12\,\text{mm}$ (½ in.) along bottom.
• Collect $\approx15\,\text{g}$ of tested soil → weigh wet, oven-dry at 105!\unicode{x2013}110^\circ\text{C}, determine moisture content $w\,(\%).$
• Repeat at least 5 times: 3 results with $15\le N\le25$ and 2–3 with 25<N\le40.
• Plot $w$ (natural scale) vs. $N$ (log scale); read $w$ at $N=25$ ⇒ Liquid Limit.

Plastic Limit (PL) & Plasticity Index (PI)

• Plastic Limit: water content at which soil begins to crumble when rolled into $3\,\text{mm}$ (⅛ in.) threads.
• Plasticity Index: $PI = LL - PL$.
• Moisture content determination identical to LL test.

Plasticity Concepts & Indices

• Index limits:
 ◦ Low plasticity (USCS): $LL<50$, symbol $L$.  ◦ High plasticity (USCS): $LL>50$, symbol $H$.
 ◦ BS 5930 subclasses: $LL<35$ (L), $35\le LL<50$ (I), $50\le LL<70$ (H), $75\le LL<90$ (V), $LL>90$ (E).
• Consistency Index: $CI = \dfrac{LL-w}{PI}$ (state of natural soil).
• A-line equation (Casagrande chart): $PI = 0.73\,(LL-20)$ separates silts (below) from clays (above).

Unified Soil Classification System (USCS)

• Primary symbols:
 ◦ $G$ = Gravel, $S$ = Sand, $M$ = Silt, $C$ = Clay, $O$ = Organic, $Pt$ = Peat.
• Secondary symbols:
 ◦ $W$ Well-graded, $P$ Poorly-graded, $M$ w/ non-plastic fines, $C$ w/ plastic fines.
• Plasticity modifiers for fine soils: $L$ (low plasticity), $H$ (high plasticity).
• Coarse-grained criteria (>$50\%$ retained on No. 200, 0.063 mm):
 ◦ Well-graded gravels $GW$: Cu>4 and $1<Cc<3$.  ◦ Poorly-graded gravels $GP$: fail above criteria.  ◦ Silty gravels $GM$ & Clayey gravels $GC$: fines $>12\%$, location vs. A-line defines $M$ or $C$.
 ◦ Dual symbols (e.g. GW!\unicode{x2013}GM) if fines 5!\unicode{x2013}12\%.
• Fine-grained (>$50\%$ passing No. 200):
 ◦ $ML$, $CL$, $OL$ (LL

British Soil Classification System (BS 5930)

• Two-stage coding: main term + qualifiers.
• Main groups:
 ◦ Coarse soils – Gravels (G), Sands (S).
 ◦ Fine soils – Silts (M), Clays (C).
 ◦ Organic (O), Peat (Pt).
• Fines content:
 ◦ Slightly silty/clayey (0–5 %), Silty/Clayey (5–15 %), Very silty/clayey (15–35 %).
• Plasticity qualifiers for fine soils: L, I, H, V, E (see ranges above).
• Grading qualifiers for coarse soils:
 ◦ $W$ Well-graded, $P$ Poorly-graded, $Pu$ Uniform, $Pg$ Gap-graded.
• Example code: $G\,F\,CH$ ⇒ gravelly very clayey soil, high plasticity clay fraction.
• Plasticity chart for BS (Fig. 1.6) mirrors Casagrande but with BS ranges.

Particle-Size Distribution (PSD)

• Size scale (BS):
 ◦ Clay <0.002\,\text{mm}, Silt 0.002\unicode{x2013}0.06\,\text{mm}, Sand 0.06\unicode{x2013}2\,\text{mm}, Gravel 2\unicode{x2013}60\,\text{mm}, Cobbles 60\unicode{x2013}200\,\text{mm}.
• Plot: % passing vs. particle size (logarithmic abscissa) – reference curve provided (Page 7).

In-Situ Dry Density by Sand-Replacement (BS 1377 §14A/14B)

Scope & Applicability

• Soils with $\ge90\%$ passing 25 mm sieve; compacted layers $\le200\,\text{mm}$ thick.
• Combines BS 14A (small-hole) & 14B (medium-hole); adapted for student lab.

Apparatus

• Pouring cylinder with shutter & conical base.
• Calibration can: Ø $150\,\text{mm}$, height $200\,\text{mm}$ (medium kit).
• Glass plate (≈50 × 50 cm), metal tray with central 150 mm hole, excavation tools.
• Oven 105!\unicode{x2013}110^\circ\text{C}, metal tins with lids, 1 g-readable balance.
• Standard dry sand: passes 0.6 mm, retained on 0.3 mm sieve; uniform & air-dry.

Calibration

1. Constant initial mass in cylinder: $W$.
2. Determine mean sand mass in cone: $W_c$.
3. Find volume of calibration can $V_c$ (weigh water).
4. Dispense sand into can, weigh dispensed mass $W_s$.
5. Bulk density of sand: $\gamma<em>s = \dfrac{W</em>s}{V_c}\,(\text{g cm}^{-3})$.

Field Test Steps

1. Prepare flat test area ≈45 cm square.
2. Place tray, cut cylindrical hole Ø ≈150 mm, depth ≤200 mm; collect all excavated soil.
3. Remove tray; position filled cylinder centrally, open shutter, allow sand to flow (no vibration).
4. Close shutter, weigh cylinder ⇒ final weight $W_f$.
5. Mass of sand in hole: $W<em>h = (W - W</em>f) - W_c$.
6. Volume of hole: $V<em>h = \dfrac{W</em>h}{\gamma_s}$.
7. Weigh wet excavated soil $W_{wet}$; determine moisture content $M$ by oven-drying (or Speedy moisture meter).
8. Dry density: $\rho<em>d = \dfrac{W</em>{dry}}{V<em>h} = \dfrac{W</em>{wet}}{V_h\,(1+M)}\,(\text{g cm}^{-3})$.

Data-Sheet Headings (Page 8)

• Calibration: $W,\;W<em>f,\;W</em>c,\;W<em>s,\;V</em>c,\;\gamma<em>s$. • Field: $W</em>{cy\,0},\;W<em>{cy\,1},\;W</em>h,\;W<em>{wet},\;V</em>h,\;\rho<em>b,\;M,\;\rho</em>d$.

Laboratory Recording – Liquid-Limit Sheet (Pages 10, 13)

• Columns: sample #, blows $N$, tin mass, wet mass $W<em>2$, dry mass $W</em>3$, water mass $(W<em>2-W</em>3)$, dry-soil mass $(W<em>3-W</em>1)$, moisture content $w$, $\log N$.
• Plot $w$ vs. $\log N$; $w$ at $N=25$ ⇒ $LL$.
• Calculate $PI,\,CI$ as defined above.

Key Formulas (LaTeX form)

• Plasticity Index: $PI = LL - PL$.
• Consistency Index: $CI = \dfrac{LL - w}{PI}$.
• Coefficient of Uniformity: $C<em>u = \dfrac{D</em>{60}}{D<em>{10}}$. • Coefficient of Curvature: $C</em>c = \dfrac{D<em>{30}^2}{D</em>{10}\,D<em>{60}}$. • Moisture content (mass basis): $M = \dfrac{W</em>{water}}{W<em>{dry}}$. • Bulk density of sand: $\gamma</em>s = \dfrac{W<em>s}{V</em>c}$.
• Hole volume: $V<em>h = \dfrac{(W - W</em>f) - W<em>c}{\gamma</em>s}$.
• Dry density of soil: $\rho<em>d = \dfrac{W</em>{dry}}{V<em>h}$,  Bulk density: $\rho</em>b = \dfrac{W<em>{wet}}{V</em>h}$.

Practical & Interpretive Notes

• Avoid vibration during sand pouring – compaction alters $\gamma_s$.
• Clean & dry device after each LL trial to prevent adhesion effects.
• For LL graph, use linear scale for moisture, log for blows – yields near-straight line.
• Dual USCS symbols flag borderline gradations (e.g. SM!\unicode{x2013}SC, GW!\unicode{x2013}GM).
• Organic soils given suffix $O$ (USCS) or ‘‘O’’ descriptor (BS). Peat always $Pt$.
• High LL (>90 %) in BS system classified ‘‘E’’ – extremely high plasticity.
• Sand replacement not suitable for gap-graded gravelly fills; use core cutter or nuclear gauge instead.
• Calibration must be repeated if sand batch, moisture, or apparatus changes.