Terzaghi Bearing Capacity Equation
The Terzaghi bearing capacity equation estimates the load at which soil under a footing fails by shear, the starting point of shallow foundation design.
The equation
qult = c Nc + q Nq + 0.5 γ B Nγ
- c is cohesion, q is surcharge at founding level
- γ is soil unit weight, B is footing width
- Nc, Nq, Nγ are bearing factors that grow steeply with friction angle
Worked example
A 2 meter strip footing at 1 meter depth on sand with friction angle 30 degrees and unit weight 19: Nq is 18.4 and Nγ about 22.4, giving qult near 775 kilopascals. Divide by a safety factor of 3 for allowable pressure.
When to use it
For concentric vertical load on uniform soil. Water table at founding level roughly halves the weight term, and the factors are so sensitive to friction angle that a 2 degree error moves capacity by tens of percent.
Related Calculators and Reference
- USCS Soil Classification Tool: classify soils from lab results.
- Slope Stability Risk Calculator: run stability with uncertainty included.
- ISSMGE: the international society for soil mechanics.