SOIL MECHANICS – CHAPTER 4
PERMEABILITY OF SOIL (DARCY’S LAW)
(SSC JE | RRB JE | OSSC JE – NUMERICAL HEAVY CHAPTER)
⚠️ Most scoring chapter in Soil Mechanics
👉 3–5 questions almost every exam
👉 Direct numericals + tricky concept MCQs
🔹 1. ONE-PAGE PRECISE ONE-LINER NOTES (EXAM FOCUSED)
🔸 Permeability (k)
- Ability of soil to allow water to flow through its voids
- Depends on:
- Grain size
- Void ratio
- Soil structure
- Viscosity of water
- Degree of saturation
🔸 Coefficient of Permeability (k)
- Velocity of flow under unit hydraulic gradient
- Units:
- m/s (SI)
- cm/s (CGS)
🔸 Darcy’s Law (MOST IMPORTANT)
Where:
- = discharge (m³/s)
- = coefficient of permeability (m/s)
- = hydraulic gradient
- = cross-sectional area (m²)
🔸 Hydraulic Gradient (i)
- = head loss (m)
- = length of soil sample (m)
🔸 Velocity of Seepage
🔸 Seepage Velocity (IMPORTANT TRAP)
- = porosity
- Always greater than discharge velocity
🔸 Validity of Darcy’s Law
✔ Laminar flow
✔ Fully saturated soil
✔ Mostly valid for sands
❌ Not valid for clays at high gradients
🔸 Typical Permeability Values
| Soil | k (m/s) |
| Gravel | 10⁻¹ to 10⁻³ |
| Sand | 10⁻³ to 10⁻⁵ |
| Silt | 10⁻⁵ to 10⁻⁷ |
| Clay | < 10⁻⁷ |
🔹 2. FACTORS AFFECTING PERMEABILITY (DIRECT MCQs)
| Factor | Effect |
| Grain size ↑ | k ↑ |
| Void ratio ↑ | k ↑ |
| Temperature ↑ | k ↑ |
| Viscosity ↑ | k ↓ |
| Degree of saturation ↓ | k ↓ |
🔹 3. LAB TESTS FOR PERMEABILITY
🔸 Constant Head Test (Coarse Soils)
🔸 Falling Head Test (Fine Soils)
Where:
- = area of standpipe
- = area of soil sample
🔹 4. IMPORTANT FORMULAS (EXAM READY)
🔸 Relation with Temperature
🔸 Relation with Void Ratio
🔸 Discharge Velocity
🔹 5. IMPORTANT NUMERICAL EXAMPLES (SSC JE LEVEL)
🔢 Example 1 (Easy – Direct Darcy)
Given:
k = 2 × 10⁻⁴ m/s
i = 0.5
A = 0.02 m²
🔢 Example 2 (Moderate – Hydraulic Gradient)
Given:
Head loss = 3 m
Length = 1.5 m
🔢 Example 3 (Constant Head Test)
Q = 0.001 m³
L = 0.5 m
A = 0.01 m²
h = 1 m
t = 100 s
🔢 Example 4 (Falling Head Test)
a = 1 cm²
A = 50 cm²
L = 20 cm
t = 60 s
h₁ = 50 cm
h₂ = 25 cm
🔢 Example 5 (Seepage Velocity)
v = 2 × 10⁻⁴ m/s
n = 0.4
🔢 Example 6 (Temperature Correction)
k₁ = 5 × 10⁻⁵ m/s at 20°C
μ₂ > μ₁ ⇒ k decreases
🔹 6. 50 EXAM-LEVEL MCQs
(25 THEORY + 25 NUMERICAL)
🟢 THEORY MCQs (1–25)
Q1. Darcy’s law is valid for:
A. Turbulent flow
B. Unsaturated soil
C. Laminar flow in saturated soil ✅
D. Clay soil only
Q2. Permeability depends on:
A. Grain size
B. Void ratio
C. Temperature
D. All of these ✅
Q3. Unit of permeability in SI system is:
A. m/s ✅
B. m²/s
C. m³/s
D. N/m²
Q4. Which soil has highest permeability?
A. Clay
B. Silt
C. Sand
D. Gravel ✅
Q5. Falling head test is used for:
A. Gravel
B. Sand
C. Clay ✅
D. Rock
🟡 NUMERICAL MCQs (26–50)
Q26. k = 10⁻³ m/s, i = 1, A = 0.01 m². Q = ?
A. 10⁻³
B. 10⁻⁵
C. 10⁻⁶
D. 10⁻⁵ m³/s ✅
Q27. Head loss = 4 m, length = 2 m. i = ?
A. 1
B. 2 ✅
C. 3
D. 4
Q28. v = 3 × 10⁻⁴ m/s, n = 0.3. Seepage velocity = ?
A. 10⁻⁴
B. 10⁻³
C. 10⁻⁴
D. 10⁻³ m/s ✅
Q29. Which parameter increases permeability most?
A. Increase in viscosity
B. Decrease in temperature
C. Increase in void ratio ✅
D. Increase in clay content
Q30. Darcy’s law fails in:
A. Sand
B. Gravel
C. Saturated soil
D. Turbulent flow ✅
🔥 EXAM TRICKS & SHORTCUTS
✔ Q = k i A → most repeated formula
✔ Seepage velocity ≠ discharge velocity
✔ Falling head → clay, constant head → sand
✔ k ↓ when viscosity ↑
✔ Remember typical k values order