CivilSolve

Geotechnical

Terzaghi Bearing Capacity

Terzaghi ultimate bearing capacity of a shallow strip, square, or circular footing: q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ, with the shape factors applied automatically and the N-factors taken from the problem (every textbook tabulates slightly different Terzaghi/Meyerhof values, so give the ones your problem provides). Divides by the factor of safety for the gross allowable capacity. Use for: 'compute the ultimate/allowable bearing capacity', footing capacity checks. Not for: settlement, eccentric/inclined loads, or water-table corrections (state the effective unit weight yourself if the water table is high).

Direct solving is free and needs no account. Have a word problem instead? Submit it as text.

Inputs

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Worked examples

These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.

Example 1

square footing in dense sand (the motivating exam problem)

Given

footing shape
square
width
2 m
depth
1.5 m
unit weight
18 kN/m^3
nc
57.8
nq
41.4
ngamma
42.4
factor of safety
3

Assumptions

  • Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.

Solution steps

  1. Assemble the three capacity terms

    Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.

    q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ

    cohesion term = 0 kPa; surcharge term = 1118 kPa; width term = 610.6 kPa

  2. Ultimate capacity

    Sum the three contributions.

    q_ult = sum of the terms

    q_ult = 1728.4 kPa

    = 1728.4 kPa

  3. Gross allowable capacity

    Divide the ultimate capacity by the factor of safety. (Some texts subtract the surcharge first for a NET allowable — check which your course uses.)

    q_allow = q_ult / FS

    q_allow = 1728.4 kPa / 3 = 576.12 kPa

    = 576.12 kPa

Results

Ultimate bearing capacity q_ult

1728.4kPa

Gross allowable bearing capacity

576.12kPa

Where this answer was checked
source
Terzaghi q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ — 2×2 m, Df = 1.5 m, γ = 18, φ = 35° factors given, FS = 3
verified by
hand-recomputed
derivation
c = 0. Surcharge: 18·1.5·41.4 = 1117.8. Width: 0.8·0.5·18·2·42.4 = 610.56. q_ult = 1728.4 kPa; q_allow = 576.1 kPa.

Example 2

strip footing in c-φ soil

Given

footing shape
strip
width
1.5 m
depth
1 m
unit weight
17 kN/m^3
cohesion
25 kPa
nc
17.7
nq
7.4
ngamma
5

Assumptions

  • Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.

Solution steps

  1. Assemble the three capacity terms

    Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.

    q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ

    cohesion term = 442.5 kPa; surcharge term = 125.8 kPa; width term = 63.75 kPa

  2. Ultimate capacity

    Sum the three contributions.

    q_ult = sum of the terms

    q_ult = 632.05 kPa

    = 632.05 kPa

Results

Ultimate bearing capacity q_ult

632.05kPa

Where this answer was checked
source
Terzaghi with cohesion, strip shape factors 1.0 — B = 1.5, Df = 1, γ = 17, c = 25; Nc = 17.7, Nq = 7.4, Nγ = 5.0
verified by
hand-recomputed
derivation
1·25·17.7 = 442.5; 17·1·7.4 = 125.8; 1·0.5·17·1.5·5 = 63.75. q_ult = 632.05 kPa.

Example 3

circular footing shape factors (1.3 / 0.6)

Given

footing shape
circular
width
2 m
depth
1 m
unit weight
18.5 kN/m^3
cohesion
10 kPa
nc
37.2
nq
22.5
ngamma
19.7

Assumptions

  • Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.

Solution steps

  1. Assemble the three capacity terms

    Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.

    q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ

    cohesion term = 483.6 kPa; surcharge term = 416.3 kPa; width term = 218.7 kPa

  2. Ultimate capacity

    Sum the three contributions.

    q_ult = sum of the terms

    q_ult = 1118.5 kPa

    = 1118.5 kPa

Results

Ultimate bearing capacity q_ult

1118.5kPa

Where this answer was checked
source
Terzaghi circular sc = 1.3, sγ = 0.6 — D = 2 m, Df = 1, γ = 18.5, c = 10; Nc = 37.2, Nq = 22.5, Nγ = 19.7
verified by
hand-recomputed
derivation
1.3·10·37.2 = 483.6; 18.5·1·22.5 = 416.25; 0.6·0.5·18.5·2·19.7 = 218.67. q_ult = 1118.5 kPa.