Terzaghi Bearing Capacity

\[q_u=cN_c+\gamma D_fN_q+\frac{1}{2}\gamma BN_\gamma\]

Variables

quultimate bearing capacity (Pa)

csoil cohesion (Pa)

gamma[γ]soil unit weight (N/m³)

Dffoundation depth (m)

Bfoundation width (m)

Ncbearing capacity factor Nc

Nqbearing capacity factor Nq

Ng[Nγ]bearing capacity factor Nγ

Description

What is this formula?

The Terzaghi Bearing Capacity equation estimates the ultimate bearing capacity of a shallow foundation resting on soil.

It is one of the most important equations in foundation engineering and forms the basis of many modern bearing capacity methods.

The formula combines the effects of soil cohesion, surcharge pressure, and soil self-weight.

When to use it

Use this formula when analyzing:

- Spread footings

- Strip footings

- Foundation design

- Bearing capacity studies

- Preliminary geotechnical design

Example

A strip footing has:

c = 25 kPa

γ = 18,000 N/m³

Df = 1.5 m

B = 2.0 m

Nc = 30.14

Nq = 18.40

Nγ = 22.40

Formula:

qu = cNc + γDfNq + 0.5γBNγ

Substitution:

qu = (25,000×30.14)+(18,000×1.5×18.40)+(0.5×18,000×2.0×22.40)

qu = 1,654,100 Pa

Result:

qu ≈ 1.65 MPa

Applications

- Foundation design

- Bearing capacity calculations

- Building foundations

- Industrial foundations

- Geotechnical investigations

Note

Terzaghi's equation is a semi-empirical model developed for shallow strip foundations under idealized conditions. Modern design methods often incorporate shape factors, depth factors, inclination factors, groundwater corrections, and code-specific safety factors. The bearing capacity factors Nc, Nq, and Nγ depend on the soil friction angle.