Terzaghi's equation - foundation engineering — 5-topic bundle

Terzaghi's ultimate bearing capacity ($q_u$) equation for a strip footing (the basic form) is:

$q_u = c N_c + q N_q + 0.5 \gamma B N_\gamma$

Where:
* $c$ = cohesion of the soil
* $q = \gamma D_f$ = surcharge pressure at footing level ($D_f$ is depth of footing, $\gamma$ is unit weight of soil above footing)
* $\gamma$ = unit weight of soil below footing
* $B$ = width of the footing
* $N_c, N_q, N_\gamma$ = Terzaghi's bearing capacity factors (dimensionless, depend on friction angle $\phi$)

When we design a foundation, we're really trying to make sure it won't fail or settle excessively under the building's weight. The allowable bearing capacity is the maximum pressure a foundation can apply to the soil without causing shear failure or unacceptable settlement. It's essentially the "safe" load.

Terzaghi's bearing capacity equation provides a theoretical ultimate bearing capacity for shallow foundations. However, real-world applications require careful consideration of several factors not directly included in the base formula. You're not just plugging numbers; you're making informed engineering judgments.

When designing foundations, one of your primary goals is to ensure the soil beneath can safely support the building's weight without excessive settlement or outright failure. This is where bearing capacity comes in. It's the maximum average contact pressure between the foundation and the soil that doesn't produce shear failure in the soil.

Terzaghi's bearing capacity equation is a fundamental tool for shallow foundation design. It predicts the ultimate bearing capacity ($q_u$), which is the maximum pressure a foundation can exert on the soil without causing shear failure. This equation is based on a simplified model of soil failure, assuming a general shear failure mechanism.

The equation is given by:

$q_u = c N_c + q N_q + 0.5 \gamma B N_\gamma$