Soil Bearing Capacity Calculator

Calculate ultimate and allowable bearing capacity using Terzaghi's equation.

Typical Soil Parameters:

  • Soft clay: c=10-25 kPa, φ=0°
  • Stiff clay: c=50-100 kPa, φ=0°
  • Loose sand: c=0, φ=28-30°
  • Dense sand: c=0, φ=35-40°

Terzaghi's Bearing Capacity Equation

The bearing capacity of a shallow foundation is the maximum pressure the underlying soil can sustain before shear failure occurs. Terzaghi (1943) derived the classical general bearing capacity equation that remains the foundation of geotechnical design:

Ultimate bearing capacity (strip footing):
q_u = c·Nc + q·Nq + 0.5·γ·B·Nγ

Net allowable bearing capacity:
q_all = (q_u - γ·Df) / FS

where c = cohesion (kPa or psi), Nc, Nq, Nγ = dimensionless bearing capacity factors, q = overburden pressure = γ·Df, γ = unit weight of soil (kN/m³ or pcf), B = footing width (m or ft), Df = depth of footing, FS = factor of safety (typically 3)

The three terms represent distinct contributions: the first term captures cohesion resistance (dominant in clays), the second captures surcharge from the soil above the footing, and the third captures frictional resistance from the soil below. In purely cohesive soils (φ = 0), Nq = 1 and Nγ = 0, simplifying the equation to q_u = 5.14c + q — the classic undrained bearing capacity for soft clays.

Typical Bearing Capacities and Failure Modes

Indicative allowable bearing capacities (net, FS = 3) for common soil types:

  • Soft clay (N = 2-4): 50-100 kPa (7-15 psi) — sensitive to disturbance, settlement governs
  • Stiff clay (N = 8-15): 100-200 kPa (15-29 psi) — stable, moderate settlement
  • Loose sand (N = 4-10): 75-150 kPa (11-22 psi) — risk of liquefaction under cyclic loads
  • Dense sand (N = 30-50): 200-500 kPa (29-73 psi) — excellent bearing, low settlement
  • Dense gravel: 300-600 kPa (44-87 psi)
  • Weathered rock: 600-1,500 kPa (87-218 psi)

Field Investigation: SPT Correlation

The Standard Penetration Test (SPT) N-value — the number of blows of a 63.5 kg hammer falling 760 mm to drive a split-spoon sampler 300 mm — is the most widely used in-situ test worldwide. N-values correlate empirically with bearing capacity and relative density:

  • N = 0-4: very loose / very soft — bearing capacity typically below 50 kPa (7 psi)
  • N = 10-30: medium dense sand / firm clay — 150-250 kPa (22-36 psi)
  • N = 30-50: dense sand / stiff clay — 250-450 kPa (36-65 psi)
  • N greater than 50: very dense — foundation design rarely controlled by bearing capacity

Factor of Safety and Settlement Governs Design

A factor of safety of 3 is the traditional geotechnical standard for bearing capacity — it implies ultimate failure load is three times the applied working load. However, in practice many foundations are designed by settlement limits rather than shear failure:

  • Rigid structures (framed buildings): Maximum total settlement 25 mm; maximum differential settlement 20 mm (angular distortion 1/500)
  • Flexible structures (tanks, embankments): Can tolerate 75–100 mm total settlement if uniform
  • Sensitive finishes (curtain walls, tile): Angular distortion limit 1/1,000

Sandy soils generally settle quickly during construction and reach near-final settlement within weeks. Clay soils undergo long-term consolidation that can continue for years or decades — particularly in soft estuarine or marine clays. The Terzaghi bearing capacity equation addresses shear failure only; separate consolidation settlement analysis is always required for clay soils.

Worked Example: Strip Footing on Cohesive Soil

Given: Strip footing, B = 1.5 m wide, D_f = 0.8 m depth, stiff clay: c = 80 kPa, φ = 0°, γ = 19 kN/m³, FS = 3

Bearing capacity factors (φ = 0°): N_c = 5.14, N_q = 1, N_γ = 0

Overburden: q = 19 × 0.8 = 15.2 kPa

Ultimate capacity: q_u = (80 × 5.14) + (15.2 × 1) + 0 = 411 + 15.2 = 426.2 kPa

Net allowable: q_a = (426.2 − 15.2) / 3 = 137 kPa

Allowable load per metre run: 137 × 1.5 = 205 kN/m

Water Table Effects

The groundwater table significantly reduces effective stress in the soil, which reduces the contribution of overburden and self-weight terms in the bearing capacity equation:

  • Water table at surface: Use submerged unit weight (γ_sat − γ_w ≈ 9–10 kN/m³) throughout. Bearing capacity can be reduced by 30–50% relative to dry conditions.
  • Water table at footing base: The N_q term uses full unit weight, but the N_γ term uses submerged weight. Intermediate reduction.
  • Water table below 1.5B from footing base: No reduction required for typical shallow foundations.
  • Artesian conditions: Upward seepage reduces effective stress further and can cause piping or heave — these require specialist analysis and are outside the scope of this calculator.

Disclaimer

This calculator is provided for educational and informational purposes only. While we strive for accuracy, users should verify all calculations independently. We are not responsible for any errors, omissions, or damages arising from the use of this calculator.

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