Bearing Capacity Equations for Square, Rectangular and Circular Strip Footings

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:

q_u = CN_c + γ₁D_fN_q + 0.5Bγ₂N_γ

 

• q_u= Ultimate Bearing Capacity of the soil
• C= Cohesion
• γ₁,γ₂= Unit weight of the soil above and below the footing level 
• N_c,N_q,N_γ= 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

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

q_u = 1.3CN_c + γD_fN_q + 0.4BγN_γ

2. Circular Foundations

q_u = 1.3CN_c + γD_fN_q + 0.3BγN_γ

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 N_c, N_q, and N_γ, 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:

1. Strip Foundation 

2. Square Foundation

3. Circular Foundation

4. Rectangular Foundation

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.

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.

Also Read: Vibroflotation - Ground Improvement Technique