Understanding Bearing Capacity

The bearing capacity of soil is a fundamental concept in geotechnical engineering. It describes the ability of soil to support the loads applied to the ground by a foundation. If the load exceeds the soil's capacity, the foundation may experience excessive settlement or even failure, endangering the entire structure. Designers therefore assess bearing capacity early in a project to choose an appropriate footing size and depth.

This calculator implements Terzaghi's classic bearing capacity equations, which remain a cornerstone of shallow foundation design. The approach considers three components contributing to the ultimate load a strip footing can support: cohesion, surcharge from the soil above the footing base, and unit weight acting over the footing width. By applying a factor of safety, we obtain an allowable load that provides a margin against uncertainty in soil properties and construction quality.

Terzaghi's Formula in Detail

Terzaghi derived bearing capacity factors , $\mathrm{N\_q}$, and $\mathrm{N\_\backslash gamma}$ that depend solely on the soil's friction angle $\phi$. They are calculated as follows:

The ultimate bearing capacity for a strip footing of width $B$ embedded at depth $D$ is then:

Where $c$ is the soil cohesion, $\gamma$ the unit weight, and $D$ the depth of the footing base below the ground surface. Dividing the ultimate capacity by a factor of safety yields the allowable bearing capacity. Engineers subtract the overburden pressure $\gamma D$ to obtain the net allowable value often quoted in building codes.

Using the Calculator

Enter your footing width and embedment depth in meters, along with the soil unit weight in kilonewtons per cubic meter. Provide the soil's cohesion and friction angle in degrees. Cohesion represents how the soil sticks together when sheared, while the friction angle describes the internal friction between particles. Typical sands have very low cohesion and friction angles between 30 ° and 40 °, whereas clays exhibit higher cohesion but smaller friction angles.

The factor of safety accounts for uncertainty in soil properties, loading conditions, and construction practices. Building codes often recommend values between 2.5 and 3.5. The default here is 3. Adjust the value to match your local guidelines or engineering judgment.

Interpreting Results

The calculator outputs two key numbers: the ultimate bearing capacity and the net allowable bearing capacity. Ultimate capacity is the theoretical load per square meter that would cause failure if applied all at once. In practice, we limit foundation loads to a fraction of that value to prevent excessive settlement. The net allowable capacity subtracts the weight of soil above the footing, providing a direct comparison to the structural loads you plan to apply.

If your calculated allowable capacity is less than the expected building load divided by the footing area, you may need a larger foundation or ground improvement. Increasing the embedment depth can sometimes help because the soil above the footing contributes confinement pressure, raising $\mathrm{N\_q}$. On the other hand, soils with low cohesion or loose structure might require deep foundations such as piles, which bear on stronger strata below.

Example Calculation

Consider a 1 m wide strip footing resting 1.5 m below ground in sand with a unit weight of 18 kN/m³, zero cohesion, and a friction angle of 35 °. Using the equations above, the factors are $\mathrm{N\_q}$ ≈ 33, $\mathrm{N\_c}$ ≈ 42, and $\mathrm{N\_\backslash gamma}$ ≈ 42. The ultimate capacity works out to around 642 kPa. With a factor of safety of 3, the allowable capacity is roughly 214 kPa, and the net allowable after subtracting surcharge is about 188 kPa. This number indicates the maximum pressure the foundation should transmit to the soil.

Limitations and Assumptions

Terzaghi's theory assumes a continuous strip footing on homogeneous soil. It does not capture footing shape factors, load inclination, or groundwater effects. For square footings or circular foundations, modified formulas introduce correction factors. High groundwater tables effectively reduce the unit weight, while sloping ground alters the surcharge term. In many real projects, engineers perform site-specific investigations and may run laboratory triaxial tests or in-situ vane shear tests to refine these estimates.

This calculator therefore provides a starting point rather than a final design. Use it to explore how changes in footing width or soil strength affect capacity. When planning a major structure, consult geotechnical engineers for detailed recommendations tailored to the local geology and expected loads.

Safety Considerations

Building on weak soil without adequate support can lead to settlement, cracks, and potentially catastrophic failure. Always cross-check field measurements, use conservative assumptions, and verify your numbers with qualified professionals. Even small residential projects can benefit from a quick bearing capacity estimate to ensure footings are wide enough to distribute loads safely.

Conclusion

By applying Terzaghi's bearing capacity theory, this calculator gives you a convenient way to gauge how much load the soil beneath a shallow foundation can sustain. Use it during preliminary design or educational studies to appreciate the interplay between soil strength, footing dimensions, and safety factors. Because all calculations run locally in your browser, no data leaves your device, making it easy to experiment with various what-if scenarios until you feel confident in your design approach.