Ultimate Bearing Capacity Calculator

Compute ultimate bearing capacity of shallow foundations using Terzaghi, Meyerhof, and Hansen methods. Accurate method‑specific corrections for shape, depth, water table, eccentricity, and local shear.

Below ground surface. Use a large value if no water.
Soft clay (φ=0, c=50 kPa) Dense sand (φ=38°, c=0) Das example (φ=25°, c=20)

Understanding Ultimate Bearing Capacity

The ultimate bearing capacity (qult) is the maximum pressure that a foundation can sustain without shear failure. It is a function of soil strength (c, φ), unit weight (γ), footing geometry (width B, length L, embedment Df), and groundwater conditions.

General Equation (after Terzaghi, 1943)

qult = c Nc sc dc + γ Df Nq sq dq + 0.5 γ B Nγ sγ dγ

where Nc, Nq, Nγ are bearing capacity factors (function of φ); s and d are shape and depth factors (method‑dependent); and corrections for water table and eccentricity are applied.

Failure Modes

  • General shear failure: Occurs in dense/stiff soils; well-defined failure surface, sudden collapse. Standard formulas apply.
  • Local shear failure: Occurs in loose/soft soils; settlement becomes excessive before failure; reduced strength parameters (c', φ') are used.
  • Punching shear failure: Occurs in very loose soils; foundation punches into soil with minimal surface heave.

Bearing Capacity Factors (Vesić / Hansen)

For φ > 0, Nq = eπ tanφ tan²(45+φ/2); Nc = (Nq - 1) cotφ; Nγ is method‑specific. This calculator uses Terzaghi's Nγ (2(Nq+1)tanφ) for Terzaghi method, Meyerhof's Nγ ((Nq-1)tan(1.4φ)) for Meyerhof, and Hansen's Nγ (1.5(Nq-1)tanφ) for Hansen.

Shape and Depth Factors by Method

MethodShape factors (square/circular)Depth factors
Terzaghisc=1.3, sq=1.2, sγ=0.8 (square); sγ=0.6 (circular)dc=dq=dγ=1.0 (no depth factor)
Meyerhof / Hansensc=1+Nq/Nc, sq=1+tanφ, sγ=0.6 (square/circ.)
Rectangular: sc=1+(B/L)(Nq/Nc), sq=1+(B/L)tanφ, sγ=1-0.4(B/L)		dc=1+0.4k, dq=1+2tanφ(1-sinφ)²k, dγ=1.0 (k = Df/B if Df/B≤1 else atan(Df/B) rad)

Water Table Correction

The unit weight in the third term (γ) is replaced by an effective weight depending on water table location:

  • If Dw ≥ Df + B → no correction (use γ).
  • If Dw ≤ Df → use γ' = γsat - γw (submerged unit weight) for the third term.
  • If Df < Dw < Df + B → weighted average: γeff = (γ·(Dw-Df) + γ'·(Df+B-Dw)) / B.

Eccentricity and Inclination

Eccentricity reduces the effective width: B' = B - 2e. For Meyerhof and Hansen, the reduced B' is used. Inclined loads (not implemented here) further reduce capacity through inclination factors ic, iq, iγ.

Typical Soil Parameters

Soil typec (kPa)φ (°)γ (kN/m³)
Soft clay10-40016-18
Stiff clay50-1000-518-20
Loose sand028-3216-18
Dense sand035-4218-21

Frequently Asked Questions

Ultimate bearing capacity (qult) is the pressure at which the soil fails in shear. Allowable bearing capacity (qallow) = qult / FS, where FS is a factor of safety (typically 2.5–3) to account for uncertainties and serviceability.

Meyerhof includes shape, depth, and inclination factors, making it more suitable for rectangular footings, eccentric/inclined loads, and layered soils. Terzaghi is simpler and often conservative for strip footings under vertical load.

Rising water table reduces the effective unit weight of soil, decreasing the third term (0.5 γ B Nγ). If the water table is above the base, the surcharge term (γ Df) may also be affected. The calculator automatically applies corrections based on Dw.

Local shear failure occurs in loose/soft soils where settlement becomes excessive before a full failure mechanism develops. Use the local shear checkbox to reduce c and tanφ by 2/3, as recommended by Terzaghi for such soils.

Eccentricity reduces the effective footing width (B' = B - 2e). For Meyerhof and Hansen, the reduced width is used in the third term and for shape factors. For Terzaghi, we also apply B' (an approximate approach) to maintain consistency.

Common assumptions: homogeneous soil, rigid footing, general shear failure, base rough, no soil above base (except surcharge), and Mohr-Coulomb failure criterion. Modifications extend applicability to real conditions.