Soil Bearing Capacity Calculator
Compute the ultimate bearing capacity of soil beneath a square footing using Terzaghi's general bearing capacity equation. Essential for geotechnical engineers sizing shallow foundations in cohesive or frictional soils.
About this calculator
Terzaghi's bearing capacity equation for a square footing is: q_ult = 1.3·c·Nc + γ·Df·Nq + 0.4·γ·B·Nγ, where c is cohesion (kPa), γ is soil unit weight (kN/m³), Df is foundation depth (m), and B is footing width. The bearing capacity factors Nc, Nq, and Nγ are functions of the internal friction angle φ: Nq = e^(π·tan φ) · tan²(45 + φ/2) and Nc = (Nq − 1)·cot φ, Nγ ≈ (Nq − 1)·tan φ. This calculator uses the foundation depth as a proxy for B in the Nγ term. The formula assumes general shear failure, a rigid footing, and homogeneous soil. Safe bearing capacity is obtained by dividing q_ult by a factor of safety, typically 3.0.
How to use
Assume c = 20 kPa, φ = 25°, Df = 1.5 m, γ = 18 kN/m³. First compute Nq = e^(π·tan 25°) · tan²(57.5°) ≈ e^(2.188) · (1.570)² ≈ 8.93 × 2.464 ≈ 22.0. Nc = (22.0 − 1)/tan 25° ≈ 21/0.466 ≈ 45.1. Nγ ≈ (22.0 − 1)·tan 25° ≈ 21 × 0.466 ≈ 9.8. Then: q_ult = 1.3 × 20 × 45.1 + 18 × 1.5 × 22.0 + 0.4 × 18 × 1.5 × 9.8 ≈ 1,173 + 594 + 106 ≈ 1,873 kPa. Safe bearing capacity = 1,873 / 3 ≈ 624 kPa.
Frequently asked questions
What is Terzaghi's bearing capacity formula and when should I use it?
Terzaghi's formula estimates the ultimate load per unit area that soil can support before shear failure occurs beneath a shallow footing. It is most appropriate for square, circular, or strip footings at shallow depths (Df/B ≤ 1) in homogeneous soil undergoing general shear failure. For loose sands or soft clays where local or punching shear governs, modified factors or Meyerhof's extended equation are more appropriate. The formula remains widely taught and used for preliminary sizing before detailed geotechnical investigation.
How does the internal friction angle affect soil bearing capacity?
The friction angle φ controls all three bearing capacity factors (Nc, Nq, Nγ) exponentially. A dense sand with φ = 35° can have Nq ≈ 33, while a loose sand at φ = 20° yields Nq ≈ 6 — a fivefold difference. Even a 5° error in φ from lab testing can cause a 30–50% error in calculated capacity. This is why geotechnical engineers rely on multiple tests (triaxial, direct shear, SPT correlations) and apply conservative factors of safety of 2.5 to 3.0 on the ultimate value.
What factor of safety should be applied to ultimate soil bearing capacity?
A global factor of safety of 3.0 is standard for most building foundations under typical loading conditions, reducing ultimate capacity to an allowable bearing pressure. This accounts for uncertainty in soil parameters, variability across the site, and load estimation errors. A lower FOS of 2.5 may be used when extensive site investigation data exists or when loading is well-defined. Temporary structures or conditions where failure consequences are low sometimes use FOS = 2.0, but this requires careful engineering judgment and regulatory approval.