Shallow Foundation Bearing Capacity Calculator
What this shallow foundation bearing capacity calculator does
This tool estimates the ultimate and allowable bearing capacity of shallow foundations using the classic Terzaghi general shear failure equation. It is intended for geotechnical and structural engineers, students, and other practitioners performing preliminary design checks on spread, strip, or mat foundations.
Given the soil cohesion c, friction angle φ, unit weight γ, footing width B, foundation depth Df, and a chosen factor of safety, the calculator returns:
- Ultimate bearing capacity, qult
- Allowable bearing capacity, qall = qult / FS
The default setup assumes SI units: kPa for stresses, kN/m³ for unit weight, and meters for dimensions. Do not mix unit systems in one calculation.
Terzaghi bearing capacity equation (general shear)
For a strip footing of width B at depth Df in homogeneous soil, Terzaghi’s general shear bearing capacity equation is often written as:
where:
- qult = ultimate bearing pressure
- c = soil cohesion
- γ = total unit weight of soil
- Df = depth of foundation
- B = footing width
- Nc, Nq, Nγ = bearing capacity factors depending only on φ
The bearing capacity factors for Terzaghi’s strip footing solution can be expressed as:
In the equation for qult, the three terms correspond physically to:
- cNc: shear resistance from soil cohesion
- γDfNq: surcharge (overburden) above footing level
- 0.5γBNγ: effect of the soil’s own weight beneath and around the footing
Ultimate vs allowable bearing capacity
The Terzaghi equation provides an estimate of the ultimate pressure at which a general shear failure mechanism would form. For design, this is reduced by a factor of safety (FS) to obtain an allowable bearing pressure:
qall = qult / FS
Common choices of FS are in the range of 2 to 3 for building foundations, depending on the level of uncertainty in soil parameters, variability across the site, and the consequences of failure. The calculator applies this simple division to compute qall once you supply the factor of safety.
Typical parameter values and interpretation
The table below gives indicative ranges for soil parameters often used with Terzaghi-type calculations. Actual design should always be based on site-specific investigation and testing.
| Soil type (approximate) | c (kPa) | φ (degrees) | γ (kN/m³) | Comments |
|---|---|---|---|---|
| Soft clay | 10 – 25 | 0 – 15 | 16 – 18 | Low strength; capacity dominated by cohesion; settlement often critical. |
| Stiff clay | 50 – 150 | 15 – 25 | 18 – 20 | Higher undrained strength; still sensitive to consolidation and creep. |
| Loose sand | < 5 | 25 – 30 | 16 – 18 | Low φ; settlement and liquefaction (if saturated) can govern design. |
| Dense sand | < 5 | 32 – 40 | 18 – 21 | High friction angle; bearing capacity often high, settlement relatively small. |
| Silty sand / sandy silt | 0 – 20 | 25 – 35 | 17 – 20 | Intermediate behavior; properties sensitive to moisture content. |
| Gravelly soil | 0 – 10 | 30 – 40 | 19 – 22 | High stiffness and strength; careful characterization can be difficult. |
Use these ranges only for educational or very rough preliminary estimates. For any real project, parameters should come from laboratory tests (e.g., triaxial, direct shear, consolidated undrained tests) or in-situ tests (e.g., SPT, CPT, vane shear) interpreted by a qualified geotechnical engineer.
Worked example (SI units)
Consider a strip footing on medium-dense sand with:
- c = 25 kPa
- φ = 30°
- γ = 18 kN/m³
- B = 2.0 m
- Df = 1.5 m
- FS = 3.0
1. Compute bearing capacity factors for φ = 30° (typical textbook values):
- Nq ≈ 18.4
- Nc ≈ 30.1
- Nγ ≈ 22.4
2. Evaluate each term in Terzaghi’s equation:
- cNc = 25 × 30.1 ≈ 753 kPa
- γDfNq = 18 × 1.5 × 18.4 ≈ 497 kPa
- 0.5γBNγ = 0.5 × 18 × 2.0 × 22.4 ≈ 403 kPa
3. Sum to obtain the ultimate bearing capacity:
qult ≈ 753 + 497 + 403 ≈ 1,653 kPa
4. Apply the factor of safety:
qall = 1,653 / 3.0 ≈ 551 kPa
The calculator follows these same steps numerically, using your chosen input parameters and the appropriate bearing capacity factors based on φ.
Comparison: ultimate vs allowable capacity and design usage
| Aspect | Ultimate capacity (qult) | Allowable capacity (qall) |
|---|---|---|
| Definition | Calculated pressure at onset of a shear failure mechanism under the footing. | Service-level pressure allowed after dividing qult by a factor of safety. |
| How it is used | Intermediate theoretical result; not used directly for service load design. | Compared to applied contact stress from structural loads to size the footing. |
| Influence of FS | Independent of FS; based solely on soil parameters and footing geometry. | Decreases as FS increases; higher FS yields more conservative design. |
| Safety margin | No explicit margin; represents an approximate failure threshold. | Includes margin for parameter uncertainty, site variability, and modeling simplifications. |
| Typical magnitude | Largest of the two; often several times service stress levels. | Roughly 1/2 to 1/3 of qult, depending on chosen FS. |
Assumptions and limitations of this calculator
The Terzaghi-based approach implemented here is intentionally simplified. Key assumptions and limitations include:
- Homogeneous, isotropic soil: The soil beneath the footing is assumed uniform with constant c, φ, and γ.
- Strip footing idealization: The equation is derived for a long strip footing; use on isolated or circular footings requires correction factors not included here.
- General shear failure mode: The method targets general shear failure; it may not be accurate for local or punch shear conditions, particularly in very loose sands or very soft clays.
- No groundwater corrections: Effects of water table position, buoyant unit weight, and pore water pressure are not explicitly modeled.
- Vertical, concentric loading only: Eccentric loads, inclined loads, moment effects, and dynamic or seismic actions are ignored.
- No settlement check: The calculator estimates bearing capacity only. It does not evaluate immediate or consolidation settlement, total or differential movements, or overall stability.
- No code-specific factors: National and local design codes (e.g., Eurocode 7, AASHTO, local building codes) may require additional partial factors, load combinations, or correction factors that are not included.
Because of these simplifications, the output should be treated as a preliminary and educational estimate, not as a final design value. Final foundation design must be performed and/or checked by a qualified geotechnical engineer familiar with the site conditions and applicable standards.
Further reading
For deeper background on Terzaghi bearing capacity theory and shallow foundation design, see for example:
- Terzaghi, K., Peck, R. B., and Mesri, G. Soil Mechanics in Engineering Practice.
- Bowles, J. E. Foundation Analysis and Design.
- Das, B. M. and Sobhan, K. Principles of Foundation Engineering.
These references discuss parameter selection from laboratory and field tests, the influence of groundwater, footing shape and depth factors, and settlement analyses that should accompany any bearing capacity check.