BEARING CAPACITY EQUATIONS
Terzaghi (1943) derived bearing capacity equations based on Prandtl (1920) failure mechanism and the limit equilibrium method for a footing at a depth Df below the ground level of a homogeneous soil. For most shallow footings, the depth Df, called the embedment depth, accounts for frost action, freezing, thawing, and other environmental effects. Building codes provide guidance as to the minimum depth of embedment for footings. Terzaghi assumed the following:
1. The soil is a semi-infi nite, homogeneous, isotropic, weightless, rigid–plastic material.
2. The embedment depth is not greater than the width of the footing (f , B).
3. General shear failure occurs.
4. The angle u in the wedge (Figure is f'. Later, it was found (Vesic, 1973) that u 5 458 1 f'/2.
5. The shear strength of the soil above the footing base is negligible. Later, Meyerhof (1951) considered the shear resistance above the footing base.
6. The soil above the footing base can be replaced by a surcharge stress (gDf).
7. The base of the footing is rough.
A plethora of bearing capacity equations, based on limiting equilibrium (e.g., Terzaghi, 1943; Meyerhof, 1963; Hansen, 1970; and Vesic, 1973) has been proposed. We will consider only a set of equations.
Conventional failure surface
for general soil failure that has found general use in geotechnical practice. General shear failure is likely to occur in dense, coarse-grained soils with relative density greater than 70% and in stiff, fi ne-grained soils. Terzaghi suggested that for local shear failure, f9p and su be reduced to 2/3 their values. We will consider two limiting conditions. One is short-term condition that requires a total stress analysis (TSA). TSA is applicable to fi ne-grained soils, and the shear strength parameter is the undrained shear strength, su. The other is long-term condition that requires an effective stress analysis (ESA). ESA is applicable to all soils, and the shear strength parameter is the peak friction angle, f'p, from plane strain tests.
The ultimate net bearing capacity equations for general failure are
According to Equation, the bearing capacity of fi ne-grained soils is not dependent on the size of the footing.
The gross bearing capacity is
Allowable Bearing Capacity
The allowable bearing capacity is
where FS is a factor of safety ranging from 2 to 3; FS 5 3 is most often used. In practice, some geotechnical engineers use Nq rather than (Nq 2 1) in Equation and neglect the term gDf in Equation for conservative design.