Terzaghi Bearing Capacity
Bearing capacity factors
- \(N_c = \cot(\phi) \cdot (N_q - 1)\)
- $N_q = \dfrac{e^{(\frac{3\pi}{2} - \phi)\tan\phi}} {2\cos^2(45 + \frac{\phi}{2})} $
- \(N_{\gamma} = (N_q - 1) \cdot \tan(1.4\phi) \rightarrow \text{Meyerhof (1963)}\)
There are other equations for \(N_{\gamma}\) by different authors which can be found below:
- \(N_{\gamma} = 1.5(N_q - 1) \cdot \tan(\phi) \rightarrow \text{Hansen (1970)}\)
- \(N_{\gamma} = 2(N_q + 1) \cdot \tan(\phi) \rightarrow \text{Vesic (1973)}\)
Terzaghi Bearing Capacity for Strip footing
\[q_u = cN_c + qN_q + 0.5 \gamma BN_{\gamma}\]
Terzaghi Bearing Capacity for Circular footing
\[q_u = 1.3cN_c + qN_q + 0.3 \gamma BN_{\gamma}\]
Terzaghi Bearing Capacity for Square footing
\[q_u = 1.3cN_c + qN_q + 0.4 \gamma BN_{\gamma}\]
Terzaghi Bearing Capacity for Rectangular footing
\[
q_u = \left(1 + 0.3 \cdot \dfrac{B}{L} \right) c N_c + qN_q +
\left(1 - 0.2 \cdot \dfrac{B}{L} \right) 0.5 B \gamma N_{\gamma}
\]