SOIL MECHANICS – CHAPTER 8
SHEAR STRENGTH OF SOIL (MOHR–COULOMB THEORY)
(SSC JE | RRB JE | OSSC JE – VERY HIGH WEIGHTAGE & NUMERICAL-HEAVY)
👉 3–5 questions every exam
👉 Pure scoring chapter if formulas + concepts are clear
👉 Direct numericals + tricky conceptual MCQs
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🔹 1. ONE-PAGE PRECISE ONE-LINER NOTES (EXAM FOCUSED)
🔸 Shear Strength
- Maximum resistance offered by soil against shear stress
- Governs bearing capacity, slope stability, earth pressure
🔸 Mohr–Coulomb Failure Theory (MOST IMPORTANT)
Where:
- τ = shear stress at failure
- c = cohesion
- σ′ = effective normal stress
- φ = angle of internal friction
🔸 Components of Shear Strength
1️⃣ Cohesion (c) → electro-chemical bonding
2️⃣ Friction (φ) → interlocking & roughness
🔸 Effective Stress Principle
- u = pore water pressure
- Shear strength depends on effective stress
🔸 Drained vs Undrained Conditions
| Condition | Pore pressure | Parameters |
| Drained | Dissipated | c′, φ′ |
| Undrained | Not dissipated | cu (φ = 0) |
🔸 Special Soil Conditions (EXAM FAVOURITE)
| Soil | c | φ |
| Pure clay (UU test) | cu | 0 |
| Dry sand | 0 | φ |
| Saturated sand | 0 | φ |
| Cohesionless soil | 0 | φ |
🔹 2. TYPES OF SHEAR TESTS (VERY IMPORTANT)
🔸 Direct Shear Test
✔ Simple & quick
✔ Failure plane is pre-determined
❌ Non-uniform stress distribution
🔸 Triaxial Compression Test (MOST RELIABLE)
| Test | Drainage | Parameters |
| UU | No drainage | cu |
| CU | Drainage during consolidation | c′, φ′ |
| CD | Full drainage | c′, φ′ |
🔸 Unconfined Compression Test (UCT)
- Special case of triaxial test
- σ₃ = 0
🔹 3. IMPORTANT MOHR CIRCLE RESULTS (DIRECT QUESTIONS)
🔸 Principal Stresses
- Major → σ₁
- Minor → σ₃
🔸 Shear Strength at Failure
🔸 Normal Stress on Failure Plane
🔸 Angle of Failure Plane
(measured from major principal plane)
🔹 4. IMPORTANT FORMULAS (EXAM READY)
🔸 Factor of Safety (Shear)
🔸 Shear Strength in Total Stress (Undrained)
🔸 Shear Strength in Effective Stress
🔹 5. IMPORTANT NUMERICAL EXAMPLES (SSC JE LEVEL)
🔢 Example 1 (Direct Mohr–Coulomb)
Given:
c = 20 kN/m²
φ = 30°
σ′ = 100 kN/m²
🔢 Example 2 (Pure Clay – Undrained)
Given:
cu = 50 kN/m²
🔢 Example 3 (UCT)
Given:
Unconfined compressive strength
🔢 Example 4 (Mohr Circle)
σ₁ = 300 kN/m²
σ₃ = 100 kN/m²
🔢 Example 5 (Failure Plane Angle)
φ = 30°
🔹 6. 50 EXAM-LEVEL MCQs
(25 THEORY + 25 NUMERICAL)
🟢 THEORY MCQs (1–25)
Q1. Shear strength of soil depends on:
- Total stress
B. Pore pressure
C. Effective stress ✅
D. Void ratio only
Q2. For pure clay under undrained condition:
- c = 0, φ ≠ 0
B. c ≠ 0, φ = 0 ✅
C. c = 0, φ = 0
D. c ≠ 0, φ ≠ 0
Q3. Mohr–Coulomb failure envelope is:
- Curved
B. Parabolic
C. Straight line ✅
D. Circular
Q4. Which test is most reliable for shear strength?
- Direct shear
B. Vane shear
C. Triaxial compression ✅
D. UCT
Q5. In unconfined compression test:
- σ₁ = 0
B. σ₃ = 0 ✅
C. σ₂ = 0
D. τ = 0
🟡 NUMERICAL MCQs (26–50)
Q26. c = 25 kN/m², φ = 0°, σ = 80 kN/m²
Shear strength =
A. 25
B. 80
C. 105
D. 25 kN/m² ✅
Q27. φ = 30°. Angle between failure plane and major principal plane is:
- 30°
B. 45°
C. 60° ✅
D. 75°
Q28. σ₁ = 200 kN/m², σ₃ = 80 kN/m²
Maximum shear stress =
A. 60
B. 80
C. 120
D. 60 kN/m² ✅
Q29. If pore water pressure increases, shear strength will:
- Increase
B. Decrease ✅
C. Remain same
D. Double
Q30. In UU test, shear strength parameter obtained is:
- c′
B. φ′
C. cu ✅
D. φ
🔥 EXAM TRICKS & SHORTCUTS
✔ τ = c + σ′tanφ → most repeated formula
✔ Pure clay (UU) → φ = 0
✔ Dry/saturated sand → c = 0
✔ UCT → cu = qu/2
✔ Failure plane angle = 45 + φ/2
✔ Shear strength ↓ when pore pressure ↑
(Q31–Q50 include: failure plane angle traps, UCT numericals, drained vs undrained MCQs, Mohr circle substitutions)
SHEAR STRENGTH OF SOIL – MOHR–COULOMB THEORY
(SSC JE | RRB JE | OSSC JE)
Focused exactly on failure-plane angle traps, UCT numericals, drained vs undrained concepts, and Mohr-circle substitutions.
🟡 NUMERICAL & CONCEPTUAL MCQs (31–50)
Q31. Angle of internal friction of soil is 40°.
Angle between failure plane and major principal plane is:
A. 45°
B. 55°
C. 60°
D. 65° ✅
Solution:
Q32. Angle between failure plane and minor principal plane is:
-
B.
C. ✅
D. φ
Q33. In an unconfined compression test, if
,
the undrained cohesion is:
A. 45 kN/m²
B. 60 kN/m²
C. 90 kN/m² ✅
D. 180 kN/m²
Solution:
Q34. In UCT, the angle of internal friction (φ) for saturated clay is assumed as:
- 0° ✅
B. 15°
C. 30°
D. 45°
Q35. Major principal stress in UCT is equal to:
- qu
B. qu / 2
C. qu + σ₃
D. qu (since σ₃ = 0) ✅
Q36. A triaxial test in which pore pressure is not measured and no drainage is allowed is:
- CD test
B. CU test
C. UU test ✅
D. Direct shear test
Q37. Parameters obtained from CD triaxial test are:
- cu
B. c, φ (total stress)
C. c′, φ′ (effective stress) ✅
D. φ = 0
Q38. In drained condition, shear strength depends on:
- Total stress
B. Effective stress ✅
C. Pore pressure
D. Water content only
Q39. Increase in pore water pressure causes shear strength to:
- Increase
B. Remain same
C. Decrease ✅
D. Double
Q40. For a cohesionless soil, Mohr–Coulomb equation reduces to:
- τ = c
B. τ = σ
C. τ = σ tanφ ✅
D. τ = c + σ
Q41. Given:
σ₁ = 400 kN/m², σ₃ = 200 kN/m²
Maximum shear stress is:
A. 100
B. 150
C. 200
D. 100 kN/m² ✅
Solution:
Q42. Normal stress on the plane of maximum shear is:
- σ₁
B. σ₃
C. (σ₁ − σ₃)/2
D. (σ₁ + σ₃)/2 ✅
Q43. In Mohr circle, the radius represents:
- Normal stress
B. Shear stress
C. Maximum shear stress ✅
D. Cohesion
Q44. Failure envelope for Mohr–Coulomb criterion is:
- Circle
B. Parabola
C. Straight line touching Mohr circles ✅
D. Ellipse
Q45. If φ = 0°, soil behaves as:
- Sand
B. Gravel
C. Pure clay under undrained condition ✅
D. Over-consolidated clay
Q46. Which soil shows only frictional resistance?
- Saturated clay
B. Organic clay
C. Dry sand ✅
D. Soft clay
Q47. Shear strength mobilized at failure plane is maximum when:
- σ is maximum
B. τ is maximum
C. Mohr circle touches failure envelope ✅
D. σ₃ = 0
Q48. Increase in normal stress on a soil sample causes shear strength to:
- Decrease
B. Remain constant
C. Increase for φ ≠ 0 ✅
D. Become zero
Q49. In UU test on saturated clay, increase in confining pressure will:
- Increase cu
B. Decrease cu
C. Not change cu significantly ✅
D. Make φ non-zero
Q50. Which statement is TRUE?
- Drained test gives cu
B. Undrained test gives c′ and φ′
C. UCT is a special case of triaxial test with σ₃ = 0 ✅
D. Failure plane angle is independent of φ
🔥 FINAL EXAM RECAP (MUST REMEMBER)
✔ τ = c + σ′tanφ → core formula
✔ Failure plane angle = 45° + φ/2
✔ UCT → cu = qu / 2, φ = 0
✔ UU → total stress, CD/CU → effective stress
✔ Mohr circle touches envelope at failure