SOIL MECHANICS – CHAPTER 9
EARTH PRESSURE THEORIES (RANKINE + COULOMB)
(SSC JE | RRB JE | OSSC JE – VERY HIGH WEIGHTAGE & NUMERICAL-HEAVY)
👉 3–5 questions every exam
👉 Direct Ka/Kp numericals + condition-based traps
👉 Extremely scoring if formulas & assumptions are clear
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🔹 1. ONE-PAGE PRECISE ONE-LINER NOTES (EXAM FOCUSED)
🔸 Earth Pressure
- Lateral pressure exerted by soil on retaining structures
- Depends on soil properties + wall movement
🔸 Types of Earth Pressure
| Type | Condition of Wall |
| At-rest (K₀) | Wall does not move |
| Active (Kₐ) | Wall moves away from soil |
| Passive (Kₚ) | Wall moves towards soil |
🔸 Order of Earth Pressure
🔹 2. RANKINE’S EARTH PRESSURE THEORY (MOST IMPORTANT)
🔸 Assumptions
✔ Backfill is dry, cohesionless, homogeneous
✔ Ground surface is horizontal
✔ Wall is smooth & vertical
✔ No wall friction (δ = 0)
🔸 Rankine Earth Pressure Coefficients
🔸 Important Relations (VERY FAVOURITE)
🔸 Active Earth Pressure (Dry Soil)
- Acts at H/3 from base
🔸 Passive Earth Pressure
🔹 3. EFFECT OF COHESION (IMPORTANT TRAPS)
🔸 Active Earth Pressure (c ≠ 0)
🔸 Depth of Tension Crack
⚠️ No tensile stress in soil
🔹 4. COULOMB’S EARTH PRESSURE THEORY
🔸 Assumptions
✔ Considers wall friction (δ)
✔ Backfill may be inclined
✔ Failure surface is plane
🔸 Coulomb Active Earth Pressure Coefficient
⚠️ Formula usually not solved in exams
👉 Used conceptually only
🔸 Comparison (EXAM FAVOURITE)
| Rankine | Coulomb |
| Wall friction ignored | Wall friction considered |
| Simpler | More general |
| Failure surface curved | Failure surface plane |
🔹 5. IMPORTANT SPECIAL CASES
🔸 At-Rest Earth Pressure
(For normally consolidated soil)
🔸 Effect of Water Table
- Use submerged unit weight below W.T.
- Add hydrostatic pressure separately
🔹 6. IMPORTANT NUMERICAL EXAMPLES (SSC JE LEVEL)
🔢 Example 1 (Direct Ka, Kp)
Given: φ = 30°
🔢 Example 2 (Active Earth Pressure)
H = 6 m
γ = 18 kN/m³
φ = 30° → Ka = 0.333
🔢 Example 3 (Point of Application)
Resultant earth pressure acts at:
🔢 Example 4 (At-Rest Pressure)
φ = 30°
🔢 Example 5 (Conceptual)
Which earth pressure is maximum?
👉 Passive earth pressure
🔹 7. 50 EXAM-LEVEL MCQs
(25 THEORY + 25 NUMERICAL)
🟢 THEORY MCQs (1–25)
Q1. Active earth pressure develops when wall:
- Moves towards soil
B. Does not move
C. Moves away from soil ✅
D. Rotates about top
Q2. Rankine theory assumes wall is:
- Rough
B. Inclined
C. Smooth ✅
D. Stepped
Q3. For cohesionless soil, Rankine’s Ka depends on:
- c
B. γ
C. φ ✅
D. H
Q4. Point of application of active earth pressure is:
- H/2
B. H/3 from base ✅
C. H/3 from top
D. H/4
Q5. Which pressure is greatest?
- Active
B. At-rest
C. Passive ✅
D. Hydrostatic
(Q6–Q25 include: Rankine vs Coulomb, K₀ concept, cohesion effect, water table, assumptions)
🟡 NUMERICAL MCQs (26–50)
Q26. φ = 0°, Rankine active earth pressure coefficient is:
- 0
B. 0.5
C. 1.0 ✅
D. ∞
Q27. If Ka = 0.25, Kp equals:
- 2
B. 3
C. 4 ✅
D. 5
Q28. Height of retaining wall = 5 m, γ = 20 kN/m³, Ka = 0.3
Active pressure =
A. 50
B. 75
C. 100
D. 75 kN/m ✅
Q29. At-rest earth pressure coefficient for φ = 36° is nearly:
- 0.2
B. 0.4 ✅
C. 0.6
D. 0.8
Q30. Coulomb theory differs from Rankine because it considers:
- Homogeneity
B. Cohesion
C. Wall friction ✅
D. Unit weight
🔥 EXAM TRICKS & SHORTCUTS (VERY IMPORTANT)
✔ Ka = tan²(45 − φ/2)
✔ Kp = 1/Ka
✔ Pa = ½ Ka γ H²
✔ Line of action = H/3 from base
✔ Passive pressure always maximum
✔ Rankine → smooth wall, Coulomb → rough wall
(Q31–Q50 include: cohesion numericals, tension crack depth, water-table cases, Ka/Kp traps, Rankine–Coulomb comparisons)
EARTH PRESSURE THEORIES – RANKINE & COULOMB
(SSC JE | RRB JE | OSSC JE)
Focused exactly on cohesion numericals, tension crack depth, water-table cases, Ka/Kp traps, and Rankine–Coulomb comparisons.
🟡 NUMERICAL & CONCEPTUAL MCQs (31–50)
Q31. For a cohesive soil backfill, Rankine active earth pressure at the ground surface is:
- Zero
B. Maximum
C. Tensile
D. Compressive
✅ Answer: C
✔ Soil cannot take tension → tension crack forms
Q32. Depth of tension crack in cohesive soil is given by:
-
B. ✅
C.
D.
Q33. Given:
c = 20 kN/m²,
γ = 18 kN/m³,
φ = 30° →
Depth of tension crack is:
A. 2.1 m
B. 2.7 m
C. 3.8 m ✅
D. 4.5 m
Solution:
Q34. For cohesive soil, Rankine active earth pressure below tension crack depth is:
- Zero
B. Constant
C. Linear & compressive ✅
D. Parabolic
Q35. If cohesion increases, depth of tension crack will:
- Decrease
B. Remain same
C. Increase ✅
D. Become zero
Q36. For soil with φ = 30°, the relation between coefficients is:
-
B. ✅
C.
D.
Q37. If , the value of is:
- 1.5
B. 2.0
C. 2.5 ✅
D. 4.0
Solution:
Q38. Presence of water table in backfill causes active earth pressure to:
- Decrease
B. Remain same
C. Increase ✅
D. Become zero
✔ Due to hydrostatic pressure + reduced effective stress
Q39. Below water table, earth pressure is calculated using:
- Total unit weight
B. Dry unit weight
C. Submerged unit weight + water pressure ✅
D. Saturated unit weight only
Q40. At-rest earth pressure coefficient for normally consolidated soil is:
-
B.
C. ✅
D.
Q41. Rankine theory is applicable only when wall is:
- Rough & inclined
B. Smooth & vertical ✅
C. Rough & vertical
D. Stepped
Q42. Coulomb theory is preferred over Rankine because it:
- Is simpler
B. Ignores wall friction
C. Considers wall friction & backfill slope ✅
D. Assumes curved failure surface
Q43. Failure surface assumed in Rankine theory is:
- Plane
B. Circular
C. Logarithmic spiral
D. Not defined explicitly ✅
Q44. Failure surface in Coulomb theory is assumed to be:
- Curved
B. Circular
C. Plane ✅
D. Parabolic
Q45. Which theory gives more realistic earth pressure?
- Rankine
B. Coulomb ✅
C. At-rest
D. Hydrostatic
Q46. For φ = 0°, Rankine earth pressure coefficient is:
- 0
B. 0.5
C. 1.0 ✅
D. ∞
Q47. Passive earth pressure is mobilized when wall:
- Moves away from soil
B. Remains stationary
C. Moves towards soil ✅
D. Rotates about base
Q48. Which earth pressure requires maximum wall movement to develop?
- At-rest
B. Active
C. Passive ✅
D. Hydrostatic
Q49. In Rankine theory, wall friction angle (δ) is assumed as:
- Equal to φ
B. φ/2
C. Zero ✅
D. 45°
Q50. Which statement is TRUE?
- Active pressure > Passive pressure
B. Coulomb theory ignores wall friction
C. Passive earth pressure is always maximum ✅
D. Ka depends on unit weight
🔥 FINAL EXAM RECAP (DON’T MISS)
✔ Ka = tan²(45 − φ/2)
✔ Kp = 1/Ka
✔ Pa = ½ Ka γ H²
✔ Line of action = H/3 from base
✔ Tension crack depth = 2c / (γ√Ka)
✔ Water table → add hydrostatic pressure separately
✔ Rankine = simple, Coulomb = general