Bearing capacity

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which will not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; while allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure.

General shear failure

A general shear failure is one where the pressure exerted by the foundation causes shearing along a curved surface beginning below the footing and extending away from it, so that soil below the footing is displaced downwards, and soil adjacent to the footing is lifted.

The general shear failure case is the one normally analyzed. Prevention against other failure modes is normally accounted for implicitly in settlement calculations. There are many different methods for computing when this failure will occur.

Terzaghi Method

Karl Terzaghi developed a method for determining bearing capacity for the general shear failure case for shallow foundations in 1943. Others (Hansen, Meyerhof, and Vesic) have made adjustments to Terzaghi's equations based on experimental and empirical data. Other research has found that the Terzaghi equations do not produce reliable results for deep foundations.

Terzaghi's equations are given below.

For square foundations:

$q_{ult}=1.3c'N_{c}+\sigma '_{zD}N_{q}+0.4\gamma 'BN_{\gamma }\$

For continuous strip foundations:

$q_{ult}=c'N_{c}+\sigma '_{zD}N_{q}+0.5\gamma 'BN_{\gamma }\$

For circular foundations:

$q_{ult}=1.3c'N_{c}+\sigma '_{zD}N_{q}+0.3\gamma 'BN_{\gamma }\$

where

$N_{q}={\frac {e^{2\pi \left(0.75-\phi '/360\right)\tan \phi '}}{2\cos ^{2}\left(45+\phi '/2\right)}}$

$N_{c}=5.7\$ for φ' = 0

$N_{c}={\frac {N_{q}-1}{\tan \phi '}}$ for φ' > 0

$N_{\gamma }={\frac {\tan \phi '}{2}}\left({\frac {K_{p\gamma }}{\cos ^{2}\phi '}}-1\right)$

c' is the effective cohesion.

σ_zD' is the vertical effective stress at the depth the foundation is lain.

γ' is the effective unit weight when saturated or the total unit weight when not fully saturated.

B is the width or the diameter of the foundation.

φ' is the effective internal angle of friction.

K_pγ is obtained graphically. Simplifications have been made to eliminate the need for K_pγ. One such was done by Coduto, given below, and it is accurate to within 10%.

$N_{\gamma }={\frac {2\left(N_{q}+1\right)\tan \phi '}{1+0.4\sin 4\phi '}}$

Punching shear failure

Punching shear failure occurs in loose soils when the block of soil immediately below the footing compresses significantly (or punches into a very soft layer below, as in the case of fills on Bay Mud or similar soils), with the shear failure occurring at the footing perimeter.

Various empirical equations have been proposed to analyse punching shear failure, though often the possibility of punching shear is eliminated by densifying the soil or using deep foundations instead of shallow foundations.

See also

• Geotechnical engineering
• Foundation
• Soil mechanics