1. CONCEPT EXPLANATION (Exam-Focused)

1. Water Content ($w$)

• Ratio of weight of water to weight of solids.

• Indicates moisture condition of soil.

  $$w = \frac{W_w}{W_s}$$

2. Specific Gravity ($G$)

• Ratio of unit weight of soil solids to water.

• Typical range: 2.6 – 2.75

  $$G = \frac{\gamma_s}{\gamma_w}$$

3. Void Ratio ($e$)

• Ratio of volume of voids to volume of solids.

• Important for settlement & permeability.

  $$e = \frac{V_v}{V_s}$$

4. Porosity ($n$)

• Ratio of volume of voids to total volume.

  $$n = \frac{V_v}{V}$$

• Relation between $e$ and $n$:

  $$n = \frac{e}{1+e}$$

5. Degree of Saturation ($S$)

• Percentage of voids filled with water.

  $$S = \frac{V_w}{V_v}$$

6. Unit Weight

Type	Formula
Bulk	$$\gamma = \frac{W}{V}$$
Dry	$$\gamma_d = \frac{W_s}{V}$$
Saturated	$$\gamma_{sat} = \frac{W_{sat}}{V}$$
Submerged	$$\gamma’ = \gamma_{sat} – \gamma_w$$

7. Consistency Limits (Atterberg Limits)

• Used for fine-grained soils.

Limit	Meaning
Liquid Limit (LL)	Plastic \to Liquid state
Plastic Limit (PL)	Semi-solid \to Plastic state
Shrinkage Limit (SL)	No volume change boundary

Indexes:

• Plasticity Index:

  $$PI = LL – PL$$

• Liquidity Index:

  $$LI = \frac{w – PL}{PI}$$

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2. IMPORTANT FORMULAS (Most Repeated)

Formula	Usage
$$w = \frac{W_w}{W_s}$$	Water content
$$e = \frac{V_v}{V_s}$$	Void ratio
$$n = \frac{e}{1+e}$$	Porosity
$$\gamma_d = \frac{\gamma}{1+w}$$	Dry unit weight
$$\gamma_{sat} = \frac{(G+e)\gamma_w}{1+e}$$	Saturated unit weight
$$S = \frac{wG}{e}$$	Degree of saturation (or $Se = wG$)
$$PI = LL – PL$$	Plasticity index

⭐ Most Important in Exams:

Void ratio relation, degree of saturation formula ($Se=wG$), and dry unit weight.

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3. SHORT NOTES / ONE-LINERS

• Coarse soils $\to$ low plasticity

• Higher void ratio $\to$ lower strength

• $n$ is always $< 1$, but $e$ can be $> 1$

• For fully saturated soil $\to S = 100\%$

• Clay soils $\to$ high $LL$ & $PI$

• If $PI = 0 \to$ Non-plastic soil

• Shrinkage limit is independent of moisture

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4. SOLVED EXAMPLES

Example 1 (Numerical – SSC JE)

A soil has: $G = 2.7$, $e = 0.6$, $\gamma_w = 9.81 \text{ kN/m}^3$.

Find $\gamma_{sat}$.

Solution:

Example 2 (Conceptual)

Which soil shows maximum volume change?

Answer: Clay (due to high plasticity)

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5. MCQs (Exam Level – 50)

Q1. Void ratio is defined as:

A) $V/V_v$

B) $V_v/V_s$

C) $V_s/V$

D) $V/V_s$

✅ Ans: B – Ratio of voids to solids.

Q2. If $e = 0.8$, find $n$.

✅ Ans: 0.44

Q3. For saturated soil, degree of saturation is:

A) 0

B) 50%

C) 100%

D) 75%

✅ Ans: C

Q4. Plasticity index represents:

A) Strength

B) Compressibility

C) Plastic range

D) Permeability

✅ Ans: C

Q5. Typical $G$ value of soil?

A) 1.5

B) 2.65

C) 4.0

D) 0.9

✅ Ans: B

Q6. If the void ratio of a soil sample is 1.0, its porosity will be:

A) 0.25

B) 0.33

C) 0.50

D) 0.75

✅ Ans: C

Q7. Which of the following soil has the highest plasticity?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D – Clay has finest particles and highest plasticity.

Q8. Degree of saturation of completely dry soil is:

A) 0

B) 25%

C) 50%

D) 100%

For dry soil, $V_w = 0$.

✅ Ans: A

Q9. Void ratio of a soil is 0.6. What is its porosity?

A) 0.375

B) 0.50

C) 0.60

D) 0.80

✅ Ans: A

Q10. Which of the following is always less than 1?

A) Void ratio

B) Porosity

C) Water content

D) Degree of saturation

✅ Ans: B – Porosity is always $< 1$.

Q11. Void ratio of soil can be:

A) Less than 1 only

B) Equal to 1 only

C) Greater than 1

D) Always less than porosity

✅ Ans: C – $e$ can exceed 1 in loose soils.

Q12. For saturated soil:

A) Air content = 0

B) Water content = 0

C) Porosity = 0

D) Void ratio = 0

✅ Ans: A

Q13. Which unit weight is maximum?

A) Dry

B) Submerged

C) Bulk

D) Saturated

✅ Ans: D

Q14. Submerged unit weight is given by:

A) $\gamma_{sat} + \gamma_w$

B) $\gamma – \gamma_w$

C) $\gamma_{sat} – \gamma_w$

D) $\gamma_d – \gamma_w$

✅ Ans: C

Q15. If PI = 0, soil is:

A) Clay

B) Silt

C) Non-plastic

D) Organic

✅ Ans: C

Q16. Plasticity index represents:

A) Moisture content

B) Strength

C) Plastic range

D) Permeability

✅ Ans: C

Q17. Which limit is determined using Casagrande apparatus?

A) PL

B) LL

C) SL

D) PI

✅ Ans: B

Q18. Shrinkage limit is the water content at which:

A) Soil becomes plastic

B) Volume change stops

C) Soil becomes liquid

D) Air voids disappear

✅ Ans: B

Q19. For fine-grained soils, consistency limits are used to:

A) Find permeability

B) Classify soil

C) Determine strength

D) Find compaction

✅ Ans: B

Q20. Which soil has maximum compressibility?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D

Q21. If water content increases, shear strength:

A) Increases

B) Decreases

C) Constant

D) Zero

✅ Ans: B

Q22. High liquid limit indicates:

A) Low compressibility

B) High compressibility

C) Low permeability

D) High density

✅ Ans: B

Q23. Which soil shows maximum permeability?

A) Clay

B) Silt

C) Sand

D) Peat

✅ Ans: C

Q24. Porosity of soil depends on:

A) Particle size only

B) Shape only

C) Packing only

D) All of the above

✅ Ans: D

Q25. For fully saturated soil, air content is:

A) 100%

B) 50%

C) 0%

D) 25%

✅ Ans: C

Q26. Which relation is correct?

A) $n = e(1+e)$

B) $e = \frac{n}{1+n}$

C) $n = \frac{e}{1+e}$

D) $e = n(1+e)$

✅ Ans: C

Q27. Dry unit weight is always:

A) Greater than bulk

B) Less than bulk

C) Equal to bulk

D) Independent

✅ Ans: B

Q28. Which test is used for plastic limit?

A) Cone penetration

B) Hydrometer

C) Rolling thread

D) Sieve analysis

✅ Ans: C

Q29. Water content is expressed in:

A) Ratio

B) Percentage

C) Decimal

D) Volume

✅ Ans: B

Q30. Which soil is most suitable for embankments?

A) Clay

B) Silt

C) Sand

D) Peat

✅ Ans: C

Q31. Degree of saturation can be:

A) More than 100%

B) Equal to 100%

C) Less than 0

D) Always 50%

✅ Ans: B

Q32. Void ratio is independent of:

A) Volume of voids

B) Volume of solids

C) Total volume

D) Particle shape

✅ Ans: C

Q33. Which soil has highest shrinkage?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D

Q34. Plasticity index is used for:

A) Soil classification

B) Compaction

C) Permeability

D) Consolidation

✅ Ans: A

Q35. Higher void ratio means:

A) Higher density

B) Lower permeability

C) Lower strength

D) Higher strength

✅ Ans: C

Q36. Which is correct order?

A) $LL < PL < SL$

B) $PL < SL < LL$

C) $SL < PL < LL$

D) $PL < LL < SL$

✅ Ans: C

Q37. In organic soils, liquid limit is:

A) Low

B) Medium

C) High

D) Zero

✅ Ans: C

Q38. If soil is fully saturated:

A) $e = 0$

B) $n = 0$

C) $S = 100\%$

D) $w = 0$

✅ Ans: C

Q39. Which soil is least permeable?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D

Q40. Bulk unit weight includes:

A) Only solids

B) Solids + water

C) Solids + air

D) Only voids

✅ Ans: B

Q41. Which parameter is dimensionless?

A) Unit weight

B) Void ratio

C) Volume

D) Weight

✅ Ans: B

Q42. Plastic limit is found by:

A) Cone test

B) Casagrande cup

C) Rolling thread method

D) Pycnometer

✅ Ans: C

Q43. Which soil has highest specific surface area?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D

Q44. Increase in porosity leads to:

A) Increase in strength

B) Decrease in permeability

C) Decrease in density

D) No change

✅ Ans: C

Q45. Shrinkage limit depends on:

A) Moisture content

B) Grain size

C) Mineralogy

D) Both B & C

✅ Ans: D

Q46. Which of the following is NOT a consistency limit?

A) Liquid limit

B) Plastic limit

C) Shrinkage limit

D) Flow limit

✅ Ans: D

Q47. Which index indicates relative consistency?

A) PI

B) LI

C) SI

D) CI

✅ Ans: B

Q48. For cohesionless soil, PI is:

A) High

B) Medium

C) Zero

D) Negative

✅ Ans: C

Q49. Which soil shows maximum capillarity?

A) Gravel

B) Sand

C) Silt

D) Clay

✅ Ans: D

Q50. Which parameter is used to indicate volume change?

A) Water content

B) Void ratio

C) Degree of saturation

D) Unit weight

✅ Ans: B