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Terzaghi’s Bearing Capacity Calculation For Foundations

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How to Calculate Bearing Capacity of a Foundation

The bearing capacity of a foundation is the ability of the soil to support the loads applied by a structure without excessive settlement or failure. It is crucial in foundation design to ensure stability and safety.

1. Types of Bearing Capacity

  1. Ultimate Bearing Capacity (qᵤ) – Maximum pressure the soil can withstand before failure.
  2. Safe Bearing Capacity (qₛ) – Maximum pressure the soil can safely carry with a factor of safety (FOS).
  3. Net Bearing Capacity (qₙ) – The ultimate bearing capacity minus the overburden pressure.

2. Terzaghi’s Bearing Capacity Equation (For Shallow Foundations)

Terzaghi’s equation is used for calculating ultimate bearing capacity (qᵤ) for strip footings:

qu = cNc + γDfNq + 0.5γBNγ

Where:

  • qᵤ = Ultimate bearing capacity (kN/m²)
  • c = Cohesion of soil (kN/m²)
  • γ = Unit weight of soil (kN/m³)
  • D_f = Depth of foundation (m)
  • B = Width of foundation (m)
  • N_c, N_q, N_γ = Bearing capacity factors (depending on soil type and friction angle (φ))

For square and circular footings, correction factors apply.

3. Calculation Steps

Step 1: Determine Soil Properties

  • Obtain cohesion (c), angle of internal friction (φ), and unit weight (γ) from soil testing (Standard Penetration Test – SPT or Plate Load Test).
  • Determine depth of foundation (D_f) and width of footing (B).

Step 2: Get Bearing Capacity Factors

  • Using φ (angle of friction), obtain N_c, N_q, N_γ from Terzaghi’s tables.

Step 3: Calculate Ultimate Bearing Capacity (qᵤ)

Use the Terzaghi equation to compute qᵤ.

Step 4: Apply Factor of Safety

The safe bearing capacity (qₛ) is obtained by dividing qᵤ by the factor of safety (FOS) (typically FOS = 2.5 to 3).

qs=quFOSqₛ = \frac{qᵤ}{FOS}qs​=FOSqu​​

Step 5: Check Against Allowable Settlement

Ensure that the settlement is within permissible limits (25mm for shallow foundations, 40mm for deep foundations as per IS 6403).

4. Example Calculation

Given Data:

  • Soil Type: Dense Sand
  • Unit Weight (γ): 18 kN/m³
  • Cohesion (c): 0 (for sand, c = 0)
  • Friction Angle (φ): 35°
  • Foundation Depth (D_f): 1.5m
  • Foundation Width (B): 2.0m
  • Factor of Safety (FOS): 3.0

Step 1: Get Bearing Capacity Factors

For φ = 35°, from Terzaghi’s table:

  • N_c = 57.8, N_q = 41.4, N_γ = 42.4

Step 2: Calculate Ultimate Bearing Capacity

qu =(0×57.8)+(18×1.5×41.4)+(0.5×18×2.0×42.4)

qu​= 0+1117.8+763.2 = 1881 kN/m²

Step 3: Calculate Safe Bearing Capacity

qs=18813=627 kN/m²

So, the Safe Bearing Capacity (qₛ) = 627 kN/m².

5. Bearing Capacity for Different Soil Types (Typical Values)

Soil TypeSafe Bearing Capacity (kN/m²)
Soft Clay50 – 100
Medium Clay100 – 150
Dense Sand250 – 450
Gravel300 – 600
Hard Rock (Granite)1000 – 5000

6. Alternative Methods for Bearing Capacity Calculation

  1. Meyerhof’s Method – Includes shape and depth factors.
  2. Hansen & Vesic Methods – Consider footing inclination and eccentricity.
  3. Plate Load Test (IS 1888:1982) – Direct field test for safe bearing capacity.
  4. SPT (Standard Penetration Test – IS 2131:1981) – Indirect field method using N-values.

7. Conclusion

  • Terzaghi’s formula is widely used for shallow foundations.
  • Plate Load Test is recommended for practical verification.
  • Different methods are used based on soil type, structure load, and field conditions.
CLICK HERE TO DOWNLOAD THE EXCEL CALCULATION OF TERZAGHIS BEARING CAPACITY CALCULATION
TERZAGHI BEARING CAPACITY CALCULATION FOR FOUNDATIONDownload
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