The Procedure and Formulations for Terzaghi (1943) Bearing Capacity Calculations

The calculation tool given above for calculating bearing capacity of a shallow foundation follows the procedure given in "Foundation Analysis and Design, 5th Edition (Joseph E. Bowles) - Chapter 4. The details of the Terzaghi (1943) method
for calculating bearing capacity of shallow foundations is given below.

## Ultimate Bearing Capacity

The bearing capacity is calculated according to the following equations for Terzaghi (1943) method.

$$q_{ult} = c N_{c} s_{c} + \overline{q}N_{q} + 0.5 \gamma_{e} B N_{\gamma} s_{\gamma} $$

### Bearing Capacity Factors

The bearing capacity factors N_{c}, N_{q} and N_{γ}; are calculated as follows:

$$N_{q} = {{a^2} \over {acos^2(45+\phi/2)}},\qquad a=e^{(0.75 \pi - \phi/2)tan\phi}$$

$$N_{c} = (N_{q}-1)cot\phi$$

$$N_{\gamma} = {{tan\phi} \over 2} \left({{K_{py}} \over cos^2\phi}-1\right)$$

### Shape Factors

Shape factors s_{c} and s_{γ} are selected according to shape of the foundation. For strip foundations s_{c} = 1 and s_{γ} = 1, for round foundations s_{c} = 1.3 and s_{γ} =
0.6 and for square foundations s_{c} = 1.3 and s_{γ} = 0.8.

### Effect of Water table, γ_{e} Term

The average effective unit weight of the soil (γ_{e}) considering the depth to water table below base of footing (d_{w}) and the depth of wedge zone (H) is calculated as follows;

$$ \gamma_e = (2H-d_w){d_w \over H^2}\gamma_{wet} + {\gamma' \over H^2}(H-d_w)^2 $$

Where,

$$ H = 0.5 B tan(45+\phi/2)$$

## Allowable Bearing Capacity

$$ q_{all} = {q_{ult} \over FS} $$