Shallow Foundation Bearing Capacity

Concept

Every structure must transfer its loads to the underlying soil safely. A shallow foundation (such as a spread footing) distributes these loads over a sufficiently large area near the ground surface. The "ultimate bearing capacity" of the soil is the maximum pressure the foundation can exert before the soil beneath it fails in shear, plunging the foundation downward and heaving the adjacent soil upward. The design must ensure that the actual applied pressure is significantly lower than this ultimate capacity by applying a global Factor of Safety (FS).

Formula & Method

The foundational framework for calculating bearing capacity was developed by Karl Terzaghi. For a continuous (strip) footing, the ultimate bearing capacity ($q_u$) is determined by three components: the cohesion of the soil, the weight of the soil overburden (depth of the footing), and the internal friction/weight of the soil under the footing.

$q_u = c N_c + q N_q + \frac{1}{2} \gamma B N_\gamma$

Where:

• $c$ = Soil cohesion.
• $q = \gamma D_f$ = Surcharge pressure from the soil at the depth of the foundation ($D_f$).
• $\gamma$ = Unit weight of the soil.
• $B$ = Width of the footing.
• $N_c, N_q, N_\gamma$ = Terzaghi's dimensionless bearing capacity factors, which depend purely on the soil's angle of internal friction ($\phi$).

The allowable bearing capacity ($q_{all}$) is then found by dividing by a Factor of Safety (typically 3):

$q_{all} = \frac{q_u}{FS}$

Variables & Units

• $q_u$ = Ultimate bearing capacity, in kPa or psf.
• $q_{all}$ = Allowable bearing capacity, in kPa or psf.
• $c$ = Cohesion of the soil, in kPa or psf.
• $\gamma$ = Unit weight of the soil, in kN/m$^3$ or pcf.
• $D_f$ = Depth of the foundation below ground surface, in meters (m) or feet (ft).
• $B$ = Width of the footing, in meters (m) or feet (ft).
• $\phi$ = Angle of internal friction of the soil, in degrees.
• $N_c, N_q, N_\gamma$ = Bearing capacity factors.

Worked Example

A detailed interactive calculation example for shallow foundation bearing capacity can be found at Worked Example: Shallow Foundation Bearing Capacity.

Engineering Meaning

The three terms in Terzaghi's equation physically represent different resisting mechanisms. The $c N_c$ term represents the soil's inherent "stickiness" or cohesion resisting the shear failure. The $q N_q$ term represents the weight of the dirt above the foundation base acting to hold down the soil that is trying to heave upward. The $\frac{1}{2} \gamma B N_\gamma$ term represents the resistance provided by the friction and weight of the soil wedge directly below the footing. In purely cohesive soils (like clay, $\phi=0$), the $N_\gamma$ term vanishes. In purely granular soils (like clean sand, $c=0$), the cohesion term vanishes.

Engineering Check

Bearing capacity calculations are highly sensitive to the location of the groundwater table. If the water table rises to the level of the footing, the effective unit weight of the soil drops by roughly half due to buoyancy. This drastically reduces the $N_q$ and $N_\gamma$ contributions, potentially causing the foundation to fail. Always design for the highest anticipated seasonal groundwater level.

Explicit Exclusions

This foundational article excludes corrections for rectangular or circular footing shapes, load eccentricity, inclined loading, and the separate (but equally critical) limit state of foundation settlement analysis. It also excludes deep foundations like piles or drilled shafts.