Worked Example: Shallow Foundation Bearing Capacity

This worked example demonstrates how to find the ultimate bearing capacity ( $q_u$ ) and allowable bearing capacity ( $q_{all}$ ) of a continuous footing using Terzaghi's equation.

1. Problem Statement

A continuous strip footing is to be built $1.2 \text{ m}$ deep in a cohesive soil. The footing is $2.0 \text{ m}$ wide. The soil properties are: unit weight $\gamma = 18 \text{ kN/m}^3$ , cohesion $c = 30 \text{ kPa}$ , and friction angle $\phi = 20^\circ$ . For $\phi = 20^\circ$ , Terzaghi’s bearing capacity factors are approximately $N_c = 17.7$ , $N_q = 7.4$ , and $N_\gamma = 5.0$ . Calculate the ultimate bearing capacity and the allowable bearing capacity using a Factor of Safety of 3.

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2. Given Data

Soil Cohesion (c)

kPa

Soil Unit Weight (gamma)

kN/m³

Depth of Foundation (Df)

Width of Foundation (B)

Factor Nc

Factor Nq

Factor Ngamma

Factor of Safety (FS)

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3. Formula and Calculation

Calculate the surcharge pressure ( $q$ ): $q = \gamma \times D_f$ For initial values: $q = 18 \times 1.2 = 21.6 \text{ kPa}$

Apply Terzaghi's equation for ultimate bearing capacity ( $q_u$ ): $q_u = c N_c + \gamma D_f N_q + 0.5 \gamma B N_\gamma$ For initial values:

$q_u = (30 \times 17.7) + (21.6 \times 7.4) + (0.5 \times 18 \times 2.0 \times 5.0)$
$q_u = 531 + 159.84 + 90 = 780.84 \text{ kPa}$

Calculate the allowable bearing capacity ( $q_{all}$ ):

Error: Formula civil-shallow-foundation-bearing-capacity not found in the Formula Registry.

Conclusion: The footing can safely support an applied pressure of up to approximately $260 \text{ kPa}$ .

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