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BEARING CAPACITY OF SOIL (TERZAGHI THEORY) #SOIL MECHANICS

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SOIL MECHANICS – CHAPTER 10

BEARING CAPACITY OF SOIL (TERZAGHI THEORY)

(SSC JE | RRB JE | OSSC JE – EXTREMELY HIGH WEIGHTAGE & NUMERICAL-HEAVY)

👉 3–5 sure questions every exam
👉 Direct qult / qsafe numericals + failure-mode traps
👉 One of the MOST scoring chapters

 

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🔹 1. ONE-PAGE PRECISE ONE-LINER NOTES (EXAM FOCUSED)

🔸 Bearing Capacity

🔸 Terzaghi’s Bearing Capacity Theory

✔ Shallow foundation
✔ Soil is homogeneous, isotropic
✔ Failure is by shear
✔ Base of footing is rough & horizontal
✔ Load is vertical & central

🔸 Types of Shear Failure (VERY IMPORTANT)

Failure Soil Type Settlement
General shear Dense sand / stiff clay Sudden, small
Local shear Medium dense sand Gradual
Punching shear Loose sand / soft clay Large

🔸 Bearing Capacity Terms

Term Meaning
Ultimate (qult) Pressure at failure
Net ultimate (qnu) qult − γDf
Safe (qsafe) qult / FOS
Net safe (qns) qnu / FOS

🔹 2. TERZAGHI BEARING CAPACITY EQUATIONS (MOST IMPORTANT)

🔸 For Strip Footing

Where:

🔸 Shape Factor Modifications (IMPORTANT)

Footing Equation
Strip
Square
Circular

🔹 3. BEARING CAPACITY FACTORS (MUST MEMORIZE)

🔸 As per Terzaghi

φ Nc Nq Nγ
0° 5.7 1.0 0
30° 30 18.4 22
35° 46 33 48

🔸 Special Relations

 

🔹 4. SPECIAL CASES (EXAM FAVORITES)

🔸 Pure Clay (φ = 0°)

🔸 Water Table Effect

🔸 Factor of Safety

🔹 5. IMPORTANT NUMERICAL EXAMPLES (SSC JE LEVEL)

🔢 Example 1 (Pure Clay)

Given: c = 25 kN/m², φ = 0°

🔢 Example 2 (Strip Footing – c–φ Soil)

Given:
c = 20 kN/m², φ = 30°
γ = 18 kN/m³, Df = 1 m, B = 2 m
Nc = 30, Nq = 18.4, Nγ = 22

 

🔢 Example 3 (Safe Bearing Capacity)

If FOS = 3,

🔢 Example 4 (Failure Mode – Conceptual)

Dense sand → General shear failure

🔢 Example 5 (Shape Effect)

Square footing gives higher bearing capacity than strip footing (same B)

🔹 6. 50 EXAM-LEVEL MCQs

(25 THEORY + 25 NUMERICAL)

🟢 THEORY MCQs (1–25)

Q1. Terzaghi’s bearing capacity theory is applicable to:

  1. Deep foundations
    B. Shallow foundations only ✅
    C. Pile foundations
    D. Rafts only

Q2. Bearing capacity failure in dense sand is:

  1. Punching shear
    B. Local shear
    C. General shear ✅
    D. No failure

Q3. For φ = 0°, bearing capacity depends on:

  1. γ only
    B. B only
    C. c only ✅
    D. Df only

Q4. Which footing gives maximum bearing capacity?

  1. Strip
    B. Rectangular
    C. Square
    D. Circular

✅ Answer: C (highest shape factor)

Q5. Safe bearing capacity is obtained by:

  1. qult − γDf
    B. qult / FOS ✅
    C. qnu × FOS
    D. γB

🟡 NUMERICAL MCQs (26–50)

Q26. c = 30 kN/m², φ = 0°. qult =

  1. 150
    B. 171
    C. 180
    D. 171 kN/m² ✅

Q27. Which term vanishes when φ = 0°?

  1. cNc
    B. γDfNq
    C. 0.5γBNγ ✅
    D. All terms

Q28. Increase in depth of foundation causes bearing capacity to:

  1. Decrease
    B. Remain same
    C. Increase ✅
    D. Become zero

Q29. Bearing capacity factor Nγ depends on:

  1. c
    B. γ
    C. φ ✅
    D. Df

Q30. For loose sand, the expected failure is:

  1. General shear
    B. Local shear
    C. Punching shear ✅
    D. No failure

🔥 EXAM TRICKS & SHORTCUTS (MUST REMEMBER)

✔ φ = 0° → qult = 5.7c
✔ Strip footing formula is base formula
✔ Square footing → 1.3cNc & 0.4γBNγ
✔ General > Local > Punching (bearing capacity)
✔ Safe = Ultimate / FOS
✔ Water table → use γ′

(Q31–Q50 include: water-table numericals, net vs gross traps, square/circular footing numericals, FOS conversions, Nc–Nq–Nγ substitutions)

BEARING CAPACITY OF SOIL – TERZAGHI THEORY

(SSC JE | RRB JE | OSSC JE)

Focused exactly on water-table numericals, net vs gross traps, square/circular footing numericals, FOS conversions, and Nc–Nq–Nγ substitutions.

🟡 NUMERICAL & CONCEPTUAL MCQs (31–50)

Q31. Gross ultimate bearing capacity of soil is:

  1. Net ultimate capacity
    B. Net ultimate + surcharge pressure ✅
    C. Safe bearing capacity
    D. Net safe capacity

Explanation:

Q32. Net ultimate bearing capacity is defined as:

  1. B. ✅
    C.
    D.

Q33. If gross ultimate bearing capacity is 600 kN/m² and overburden pressure is 100 kN/m², net ultimate bearing capacity is:

  1. 500 kN/m² ✅
    B. 600 kN/m²
    C. 700 kN/m²
    D. 300 kN/m²

Q34. If net ultimate bearing capacity is 450 kN/m² and FOS = 3, net safe bearing capacity is:

  1. 150 kN/m² ✅
    B. 300 kN/m²
    C. 450 kN/m²
    D. 1350 kN/m²

Q35. Which bearing capacity is used directly for foundation design?

  1. Ultimate
    B. Net ultimate
    C. Gross ultimate
    D. Safe bearing capacity ✅

Q36. A square footing has width B. Compared to strip footing of same width, the bearing capacity is:

  1. Same
    B. Less
    C. More ✅
    D. Zero

Reason: Shape factor > 1 for square footing.

Q37. For a circular footing, the coefficient of term is:

  1. 0.5
    B. 0.4
    C. 0.3 ✅
    D. 1.0

Q38. Which footing gives maximum bearing capacity for same soil and width?

  1. Strip
    B. Rectangular
    C. Square
    D. Circular

✅ Answer: C

Q39. When water table is at the foundation base level, the unit weight used in term is:

  1. Dry unit weight
    B. Saturated unit weight
    C. Submerged unit weight
    D. Average unit weight

✅ Answer: B
(Surcharge acts above base)

Q40. When water table is at the base of footing, unit weight used in term is:

  1. Dry γ
    B. Saturated γ
    C. Submerged γ′ ✅
    D. γw

Q41. If water table is well below foundation base, bearing capacity:

  1. Increases
    B. Decreases
    C. Remains unchanged ✅
    D. Becomes zero

Q42. For φ = 0°, the bearing capacity factors are:

  1. Nc = 5.7, Nq = 1, Nγ = 0 ✅
    B. Nc = 0, Nq = 1, Nγ = 5.7
    C. Nc = 1, Nq = 5.7, Nγ = 0
    D. Nc = 0, Nq = 0, Nγ = 0

Q43. Which bearing capacity factor increases most rapidly with φ?

  1. Nc
    B. Nq
    C. Nγ ✅
    D. All equally

Q44. If φ increases, ultimate bearing capacity will:

  1. Decrease
    B. Remain constant
    C. Increase significantly ✅
    D. Become independent of γ

Q45. For pure clay, bearing capacity is independent of:

  1. c
    B. B
    C. γ
    D. φ

✅ Answer: C
(since φ = 0°, γ terms vanish)

Q46. Given:

c = 20 kN/m², φ = 30°
Nc = 30, Nq = 18.4
Which term contributes maximum to bearing capacity?
A. cNc
B. γDfNq
C. 0.5γBNγ
D. Depends on dimensions

✅ Answer: A (cohesion term dominant)

Q47. Factor of safety against bearing capacity failure is generally taken as:

  1. 1.5
    B. 2.0
    C. 2.5 to 3.0 ✅
    D. 5.0

Q48. If FOS is increased, safe bearing capacity will:

  1. Increase
    B. Decrease ✅
    C. Remain same
    D. Become zero

Q49. Terzaghi’s bearing capacity theory does NOT consider:

  1. Shape of footing
    B. Depth of footing
    C. Inclined load & base ❌
    D. Soil cohesion

✅ Correct answer: C

Q50. Which statement is TRUE?

  1. Net bearing capacity > Gross bearing capacity
    B. Square footing has lower bearing capacity than strip
    C. Bearing capacity is independent of foundation depth
    D. Water table near footing reduces bearing capacity ✅

🔥 FINAL EXAM SUMMARY (VERY IMPORTANT)

✔ qult = cNc + γDfNq + 0.5γBNγ
✔ φ = 0° → qult = 5.7c
✔ Net = Gross − γDf
✔ Safe = Ultimate / FOS
✔ Square footing > Circular > Strip
✔ Water table ↑ → Bearing capacity ↓
✔ Nγ most sensitive to φ

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