Bearing Capacity

Terzaghi (1943) presented a comprehensive theory for the ultimate bearing capacity of rough shallow foundations. This theory assumes that the soil fails via General Shear Failure, extending from the base of the footing out to the surface.

1. The Main Equation (Ultimate Bearing Capacity)

The general form of the ultimate bearing capacity ($q_u$) for a Strip Foundation is expressed as the sum of resistance due to cohesion, overburden (surcharge), and the weight of the soil:

Where:

• $c'$ = Cohesion of soil
• $q$ = Effective overburden pressure ($\gamma D_f$)
• $\gamma$ = Unit weight of soil
• $B$ = Width of the foundation
• $N_c, N_q, N_\gamma$ = Bearing Capacity Factors (defined below)

2. Bearing Capacity Factors

The terms $N_c$, $N_q$, and $N_\gamma$ are nondimensional factors that are solely functions of the soil friction angle, $\phi'$. They determine the magnitude of resistance provided by the soil.

3. Shape Factors

The original equation applies to strip footings ($L \gg B$). For other foundation geometries, Terzaghi introduced specific Coefficients (Shape Factors) that modify the Cohesion term ($N_c$) and the Unit Weight term ($N_\gamma$).

• For Square Footings ($B \times B$):
  • The coefficient for the cohesion term ($N_c$) increases to 1.3.
  • The coefficient for the unit weight term ($N_\gamma$) decreases to 0.4.
• For Circular Footings (Diameter $B$):
  • The coefficient for the cohesion term ($N_c$) increases to 1.3.
  • The coefficient for the unit weight term ($N_\gamma$) decreases to 0.3.

4. Modified Ultimate Bearing Capacity ($q_u$)

Applying the shape factors defined above results in the following modified equations: