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
2. Bearing Capacity Factors
The terms $N_c$, $N_q$, and $N_\gamma$ are nondimensional factors solely dependent on the soil friction angle, $\phi'$. They dictate the magnitude of failure resistance.
$$ N_c = (N_q - 1)\cot\phi' $$
$$ N_\gamma = \frac{1}{2}\left(\frac{K_{p\gamma}}{\cos^2\phi'} - 1\right)\tan\phi' $$
3. Modified Equations for Shape
The original equation applies strictly to continuous strip footings ($L \gg B$). For other geometric shapes, Terzaghi introduced specific multipliers (Shape Factors) that adjust the influence of cohesion ($N_c$) and soil weight ($N_\gamma$).
- Strip Footing (General Form) $ \displaystyle q_u = c' N_c + q N_q + 0.5 \gamma B N_\gamma $
- Square Footing ($B \times B$) $ \displaystyle q_u = 1.3 c' N_c + q N_q + 0.4 \gamma B N_\gamma $
- Circular Footing (Diameter $B$) $ \displaystyle q_u = 1.3 c' N_c + q N_q + 0.3 \gamma B N_\gamma $