Soil Bearing Capacity Calculator Formula
Understand the math behind the soil bearing capacity calculator. Each variable explained with a worked example.
Formulas Used
Ultimate Bearing Capacity
qu = cohesion * nc + unit_weight * depth * nq + 0.5 * unit_weight * width * ngammaAllowable Bearing (FoS=3)
qa = (cohesion * nc + unit_weight * depth * nq + 0.5 * unit_weight * width * ngamma) / 3Variables
| Variable | Description | Default |
|---|---|---|
cohesion | Soil Cohesion (c)(kPa) | 20 |
unit_weight | Soil Unit Weight (gamma)(kN/m^3) | 18 |
depth | Foundation Depth (Df)(m) | 1.5 |
width | Foundation Width (B)(m) | 2 |
nc | Bearing Factor Nc | 17.7 |
nq | Bearing Factor Nq | 7.4 |
ngamma | Bearing Factor Ngamma | 5 |
How It Works
Terzaghi's Bearing Capacity Theory
The bearing capacity of a shallow foundation depends on soil properties, foundation depth, and width.
Formula (strip footing)
q_u = c Nc + gamma Df Nq + 0.5 gamma B Ngamma
The three terms represent cohesion resistance, surcharge (overburden) resistance, and self-weight resistance. Nc, Nq, and Ngamma are dimensionless bearing capacity factors that depend on the soil friction angle.
Worked Example
A 2 m wide strip footing at 1.5 m depth, c=20 kPa, gamma=18 kN/m^3, phi=20 deg.
cohesion = 20unit_weight = 18depth = 1.5width = 2nc = 17.7nq = 7.4ngamma = 5
- 01Cohesion term: 20 x 17.7 = 354 kPa
- 02Surcharge term: 18 x 1.5 x 7.4 = 199.8 kPa
- 03Width term: 0.5 x 18 x 2 x 5.0 = 90 kPa
- 04q_u = 354 + 199.8 + 90 = 643.8 kPa
- 05q_a = 643.8 / 3 = 214.6 kPa (with FoS = 3)
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