Bearing Capacity Equation for Square, Rectangular, and Circular Foundations
Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - General Shear Failure
Terzaghi (1943) developed a rational bearing capacity equation for strip footing, by assuming the bearing capacity failure of the foundation in general shear mode. Terzaghi's bearing equation is given by:
qu = CNc + γ1DfNq + 0.5Bγ2Nγ
qu= Ultimate Bearing Capacity of the soil
C= Cohesion
γ1,γ2= Unit weight of the soil above and below the footing level
Nc,Nq,Nγ= Bearing capacity factors that are a function of friction angle
Df= Depth of the foundation below the ground level
B = Width or diameter of the footing
L= length of the footing
Fig:- Square, Rectangular, and Circular Strip Footings
Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - General Shear Failure
Terzaghi modified the above bearing capacity equation by introducing shape factors for different shapes of the foundation. Then for
1. Square Foundations
qu = 1.3CNc + γDfNq + 0.4BγNγ
2.Circular Foundations
qu = 1.3CNc + γDfNq + 0.3BγNγ
3. Rectangular Foundations
Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - Local Shear Failure
The above equations were derived from the assumptions of general shear failure. When local shear failure comes into play, the shear parameters in the equations i.e. the c and ф are reduced to a lower limit. Hen e, here instead of c we use Ĉ = 0.67c; and instead of Ф, we use ቔ = 0.67tanФ;
The values of Nc, Nq, and Nγ, also change to reduced values that are obtained from Terzaghi's bearing capacity factors for the general shear failure graph, where the bearing capacity factors corresponding to reduced Ф i.e, 0.67tanФ, must be determined.
Then the bearing capacity for:
Ultimate Bearing Capacity for Cohesionless and Cohesive Soils
When the soil is cohesionless, the cohesion factor c = 0; If c =0; the bearing capacity factor Nc = 0; Then the equations for qu can be modified accordingly
Fig
If the soil is cohesive, then the angle of frictional resistance, Ф = 0; then the bearing capacity factors from the graph above, Nγ = 0; Nq= 1; and Nc = 5.7; Based on which the qu equation is determined.
