Soil Mechanics Quick Reference - IS 2720 & IS 1498

1. Soil Classification — IS 1498:1970 (Based on Unified Soil Classification)

Symbol	Full Name	Key Property	Cu / Cc Criteria
GW	Well-graded Gravel	Coarse, <5% fines, D50>4.75mm	Cu≥4, 1≤Cc≤3
GP	Poorly-graded Gravel	Uniform or gap-graded gravel	Fails GW criteria
GM	Silty Gravel	Gravel with silt fines, PI<4	Atterberg limits below A-line
GC	Clayey Gravel	Gravel with clay fines, PI>7	Atterberg limits above A-line
SW	Well-graded Sand	Sand, <5% fines, D50 0.075–4.75mm	Cu≥6, 1≤Cc≤3
SP	Poorly-graded Sand	Uniform sand	Fails SW criteria
SM	Silty Sand	Sand with silt fines, PI<4	—
SC	Clayey Sand	Sand with clay fines, PI>7	—
ML	Inorganic Silt (Low plasticity)	Fine, LL<50, below A-line	—
CL	Inorganic Clay (Low-Med plasticity)	Fine, LL<50, above A-line, PI>7	—
OL	Organic Silt/Clay (Low plasticity)	LL<50, organic odor	—
MH	Inorganic Silt (High plasticity)	Fine, LL>50, below A-line	—
CH	Inorganic Clay (High plasticity)	Fine, LL>50, above A-line	Black cotton soil typical
OH	Organic Clay (High plasticity)	LL>50, organic	—
Pt	Peat / Highly Organic soil	Dark colour, fibrous, organic >75%	Not suitable for construction

Plasticity Chart (Casagrande): A-line: PI = 0.73(LL - 20)
U-line (upper boundary): PI = 0.9(LL - 8)
Cu = D60/D10 Cc = D30² / (D10 × D60)

2. Atterberg Limits — Definitions

Limit	Definition	Test Method	Significance
Liquid Limit (LL)	Water content at which soil transitions from plastic to liquid state	Casagrande cup (IS 2720 Pt.5) or Fall cone	Upper bound of plasticity
Plastic Limit (PL)	Minimum water content at which soil can be rolled into 3mm thread	Thread rolling (IS 2720 Pt.5)	Lower bound of plasticity
Plasticity Index (PI)	PI = LL – PL	Calculated	Range of plastic behaviour
Shrinkage Limit (SL)	Water content below which no volume change occurs on drying	IS 2720 Pt.6	Volume stability
Liquidity Index (LI)	LI = (w – PL) / PI	Calculated	LI>1: liquid; LI<0: semi-solid
Activity (A)	A = PI / % clay fraction (<2μm)	Calculated	A<0.75 inactive; 0.75–1.25 normal; >1.25 active (swelling)

3. Compaction Tests — IS 2720

Parameter	Standard Proctor (IS 2720 Pt.7)	Modified Proctor (IS 2720 Pt.8)
Mould volume	944 cm³ (1000 mL)	944 cm³ (1000 mL)
Rammer mass	2.6 kg	4.9 kg
Drop height	310 mm	450 mm
No. of layers	3	5
Blows per layer	25	25
Compaction energy	592 kJ/m³	2700 kJ/m³
Equivalent field test	Light compaction (AASHTO T99)	Heavy compaction (AASHTO T180)

Maximum Dry Density: γd = G × γw / (1 + e)
Zero Air Void line: γd = G × γw / (1 + wG/Sr) [Sr=1 for ZAV]
Field compaction requirement: typically 95–98% of MDD

4. Bearing Capacity — Terzaghi's Equations

Footing Type	General Bearing Capacity Formula
Strip Footing	qu = c·Nc + q·Nq + 0.5·γ·B·Nγ
Square Footing	qu = 1.3c·Nc + q·Nq + 0.4·γ·B·Nγ
Circular Footing	qu = 1.3c·Nc + q·Nq + 0.3·γ·B·Nγ
Net Ultimate BC	qnet,ult = qu – q = qu – γ·Df
Safe Bearing Capacity	qsafe = qnet,ult / FOS + γ·Df (FOS = 3 typically)
For φ=0 (pure clay)	qu = 5.14·Cu + γ·Df (Nc=5.14, Nq=1, Nγ=0)

5. Bearing Capacity Factors (Terzaghi)

φ (°)	Nc	Nq	Nγ
0	5.14	1.00	0.00
5	6.49	1.57	0.45
10	8.35	2.47	1.22
15	10.98	3.94	2.50
20	14.83	6.40	5.39
25	20.72	10.66	10.88
30	30.14	18.40	22.40
35	46.12	33.30	48.03
40	75.31	64.20	109.41

6. SPT Correlation Table (IS 2131)

N-value (blows/300mm)	Relative Density (Sand)	Friction Angle φ (approx.)	Consistency (Clay)	Undrained Shear Strength Cu (kPa)
0 – 4	Very Loose (<15%)	<28°	Very Soft	<25
4 – 10	Loose (15–35%)	28° – 30°	Soft	25 – 50
10 – 30	Medium Dense (35–65%)	30° – 36°	Medium Stiff	50 – 100
30 – 50	Dense (65–85%)	36° – 41°	Stiff	100 – 200
>50	Very Dense (>85%)	>41°	Very Stiff / Hard	>200

7. Typical Shear Strength Parameters

Soil Type	Cohesion c (kPa)	Friction Angle φ	Remarks
Clean Gravel (GW/GP)	0	32° – 40°	—
Clean Sand (SW)	0	30° – 37°	—
Silty Sand (SM)	0 – 5	28° – 34°	—
Inorganic Silt (ML)	5 – 15	26° – 32°	—
Low plasticity clay (CL)	10 – 40	20° – 28°	Drained parameters
High plasticity clay (CH)	20 – 80	10° – 20°	Black cotton: c=0, φ=0 (undrained)
Stiff fissured clay	0 – 10	8° – 15°	Residual strength

8. Permeability (k) — Typical Values

Soil Type	k (m/s)	Drainage Condition
Clean gravel	10⁻² – 1	Very freely draining
Coarse sand	10⁻⁴ – 10⁻²	Freely draining
Fine/medium sand	10⁻⁶ – 10⁻⁴	Draining
Silty sand	10⁻⁷ – 10⁻⁶	Poor drainage
Silt (ML)	10⁻⁹ – 10⁻⁷	Very poor drainage
Clay	< 10⁻⁹	Practically impermeable

Darcy's Law: v = k × i Q = k × i × A
Hazen's formula: k (m/s) = 1.0 × 10⁻² × D10² (mm) [for loose clean sands only]

9. Consolidation Parameters — Typical Values

Parameter	Symbol	Typical Range	Remarks
Compression index	Cc	0.1 – 1.5	Cc ≈ 0.009(LL–10) for NC clays
Swelling/recompression index	Cs	Cc/5 to Cc/10	For OC clays
Coefficient of consolidation	Cv	10⁻⁸ – 10⁻⁶ m²/s	Higher for sandy soils
Coefficient of volume compressibility	mv	10⁻⁴ – 10⁻² m²/kN	—

Primary consolidation settlement: S = Cc × H / (1+e0) × log10[(p0 + Δp)/p0]
Time factor: Tv = Cv × t / Hdr²
For 90% consolidation: Tv = 0.848

10. IS 2720 Test Methods Summary

IS 2720 Part	Test Name	Purpose
Part 2	Determination of moisture content	Oven-drying at 105–110°C
Part 3	Specific gravity (Pycnometer)	Particle density
Part 4	Grain size analysis (Sieve + Hydrometer)	PSD curve, Cu, Cc
Part 5	Atterberg limits (LL, PL)	Plasticity classification
Part 6	Shrinkage factors	Shrinkage limit
Part 7	Standard Proctor compaction	MDD, OMC (light)
Part 8	Modified Proctor compaction	MDD, OMC (heavy)
Part 10	Unconfined compressive strength	Cu of cohesive soils
Part 11	CBR (California Bearing Ratio)	Pavement subgrade strength
Part 12	Consolidation test (Oedometer)	Cc, Cv, mv
Part 13	Direct shear test	c, φ (drained)
Part 14	Triaxial test (UU, CU, CD)	c, φ at different drainage conditions
Part 15	Permeability (constant/falling head)	k of soil
Part 16	Swell index	Expansive soil potential