Bearing Capacity

Bearing Capacity

Input Data:

Cohesion, c = psf
Soil density, γ = pcf
Found. depth, D = ft
Ang. of repose, φ =
Found. width, B = ft
Factor of Safety =
Results:

Nq =
Nγ =
Nc =
Ultimate bearing cap. = psf
Allowable bearing cap. = psf

Terzaghi's Ultimate Bearing Capacity Equation

For saturated, submerged soils:

qu = qc + qq + qγ = cNc + qNq + ½γ'BNγ . . . for strip foundations

qu = qc + qq + qγ = cNc + qNq + 0.3γ'BNγ . . . for circular or square foundations

  • qc, qq, q . = load contributions from cohesion, soil weight and surcharge
  • Nc, Nq, N . = bearing capacity factors for cohesion, soil weight and surcharge
  • c = cohesion strength of soil
  • q = soil weight
  • γ' = effective bulk density of soil ( γ' = γ - γw )
  • B = width of the foundation

Soil weight is calculated as q = γ'D, where D is the depth of penetration of the foundation

NOTE: γ' is used only for the portion of the soil that is submerged, otherwise the bulk density γ is used (neither is a dry weight!)

For shallow foundations:

  • Nq = eπ tanφ tan2(45 + φ/2)
  • Nγ = (Nq - 1) tan(1.4φ)
  • Nc = (Nq - 1) cotφφ > 0
  • Nc = π + 2 = 5.14φ = 0, clay
  • for deep foundations Nc ≈ 9

Allowable bearing capacity (qa)

qa = qu / FS

For Sandy Soils

Cohesionless soil (80% or more sand), c = 0, φ from table:

Soil Type φ (degrees)
Loose sand 27-35
Medium sand 30-40
Dense sand 35-45
Gravel with some sand 34-48
Silt 26-35

For Clay Soils

Cohesive soil, assume φ = 0, c from table:

Consistency psfkN/m2
Very soft 0 - 500 0 - 48
Soft 500 - 1,000 48 - 96
Medium 1,000 - 2,000 96 - 192
Stiff 2,000 - 4,000 192 - 384
Very stiff 4,000 - 8,000 384 - 766
hard > 8,000 > 766

Blow Count (N, blows/ft or blows/30 cm)

N is the average blows per foot in the stratum, number of blows of a 140-pound hammer falling 30 inches to drive a standard sampler (1.42" I. D., 2.00" O. D.) one foot. The sampler is driven 18 inches and blows counted the last 12 inches.

Sand Clay
Density N N Undrained Compressive
strength (psf)
Very loose 0-4 <2 <500 Very soft
Loose 4-10 2-4 500-1,000 Soft
Medium 10-30 4-8 1,000-2,000 Medium
Dense 30-50 8-15 2,000-4,000 Stiff
Very dense >50 15-30 4,000-8,000 Very stiff


>30 >8,000 Hard

ESTIMATION OF SOIL PARAMETERS FROM STANDARD PENETRATION TESTS

Granular Soil (Sand)

Description Very Loose Loose Medium Dense Very Dense
Standard penetration resistance corr'd, N'*0 4 10 30 50
Approx. angle of internal friction, (φ)degrees**25 – 30 27 – 32 30 – 35 35 – 40 38 – 43
Approx. range of moist unit weight, (γ)pcf** 70 – 100 90 – 115 110 – 130 120 – 140 130 – 150

* N' is SPT value corrected for overburden pressure.
** Use larger values for granular material with 5% or less fine sand and silt.

Cohesive soils (Clay)

(Rather unreliable, use only for preliminary estimate purposes).

Consistency Very Soft Soft Medium Stiff Very Stiff Hard
qu, ksf 0 0.5 1.0 2.0 4.0 8.0
Field standard penetration Resistance, N 0 2 4 8 16 32
γ(moist) pcf 100 – 120 110 – 130 120 – 140

NOTE: The reliability of SPT values to determine shear strength of cohesive soils is poor. The SPT values in cohesive soils should not be used for determination of shear strengths for final design.