Ultimate Bearing Capacity of Square Footing: Calculation and Design

Name: Lesson 3. Ultimate Bearing Capacity of Square Footing Using Plaxis 3D
Uploaded: 2026-02-18
Duration: 13 min 42 s
Description: A practical guide to estimating the ultimate bearing capacity of square footings using soil properties, theory, and safety factors for safe foundation design.

A practical guide to estimating the ultimate bearing capacity of square footings using soil properties, theory, and safety factors for safe foundation design.

Load Capacity Team

February 18, 2026·5 min read

Load Capacity Soil Bearing Capacity Static Load Capacity Maximum Load Bearing Capacity

Bearing Capacity Guide - Load Capacity (illustration)

Quick AnswerDefinition

In geotechnical terms, the ultimate bearing capacity of square footing is the maximum load the soil can resist before failure under a square foundation. This quick guide explains how engineers estimate it using classical theories, how footing dimensions and soil properties influence results, and how safety factors convert the ultimate capacity into a safe, serviceable design.

Theoretical foundations and key terms

In geotechnical engineering, the ultimate bearing capacity of square footing is the maximum load a soil layer can resist before shear failure under a square foundation. This capacity depends on soil strength parameters (cohesion c, effective friction angle phi'), soil unit weight gamma, and the footing geometry. Terminology like overburden pressure, eccentric loading, and consolidation state influence the calculation. Engineers use this concept to determine whether a footing can safely transfer vertical loads from structures such as columns and walls into the soil without experiencing excessive settlement or shear failure. The ultimate capacity serves as a ceiling; the design must use an allowable capacity obtained by applying a factor of safety that accounts for uncertainties in soil properties, workmanship, and loading conditions. A clear understanding of this concept is essential for reliable foundation design and for communicating risk levels to project stakeholders. This article, following Load Capacity guidance, emphasizes shape factors, soil testing, and proper interpretation of lab and field data.

Classic bearing capacity equations for square footings

Terzaghi’s bearing capacity theory provides the starting point for estimating qult for a shallow, loaded foundation. For a square footing of width B resting on a homogeneous soil layer, the general expression is qult = cNc + qNq + 0.5gammaB*Ngamma, where q is the effective vertical stress at the footing base (q = sigma'v) and gamma is the soil unit weight. Nc, Nq, and Ngamma are bearing-capacity factors that depend on the material friction angle phi'. For a square footing, the factor values are derived from charts or tables that are referenced in geotechnical handbooks. In practice, engineers use charts or software to obtain Nc, Nq, and Ngamma for the given phi'. The ultimate value refers to the soil’s resistance just before failure and is not the same as the service-load capacity. To convert qult into a safe design value, apply a factor of safety FS, so qu_allowable = qult / FS. Groundwater effects, footing eccentricity, and partial embedment may modify the expression and the resulting design value. Load Capacity emphasizes that these calculations are estimates and should be validated with site data.

Factors affecting ultimate bearing capacity

Several factors govern the ultimate capacity of square footings. Soil properties such as cohesion (c), friction angle (phi'), and unit weight (gamma) directly influence Nc, Nq, and Ngamma. The depth to the foundation (Df) affects the overburden pressure q, while groundwater conditions alter effective stress and buoyancy. Footing geometry, particularly the width B for square footings, determines the gamma-term contribution. Loading type matters: vertical, eccentric, or inclined loads can reduce the ultimate capacity through soil-pile interaction or non-uniform stress distribution. Seasonal variability, soil layering, and settlement criteria also shape the usable capacity. In practice, engineers document a set of assumed conditions (e.g., homogeneous soil, shallow foundation) and verify sensitivity by performing parametric checks across likely phi' and c ranges. Load Capacity notes that conservative estimates often come from using lower-bound Nc, Nq, Ngamma values and applying a robust FS to account for uncertainty.

Step-by-step calculation workflow for designers

A structured workflow helps ensure consistency across projects. Start by collecting soil data from lab tests or in-situ testing. Then determine the footing geometry and depth. Next, compute q' (the effective overburden stress) as q' = gamma * Df. Lookup Nc, Nq, and Ngamma from phi' charts or tables. Compute the ultimate bearing capacity qult = cNc + q'Nq + 0.5gammaB*Ngamma. Apply an appropriate factor of safety FS to obtain qu_allowable = qult / FS. Finally, compare the allowable capacity to the actual vertical load; if the load exceeds qu_allowable, consider design adjustments or ground improvement. This workflow is standard practice in Load Capacity guidance and is applicable to many shallow foundation scenarios.

Practical example: illustrative calculation (illustrative/hypothetical)

To illustrate the workflow, consider a hypothetical, well-documented soil with phi' = 25°, c = 20 kPa, gamma = 18 kN/m³, footing width B = 2.0 m, and embedment depth Df = 1.2 m. From phi' charts, assume Nc ≈ 28, Nq ≈ 19, Ngamma ≈ 16. The effective stress is q' = gamma * Df = 18 * 1.2 = 21.6 kPa. The ultimate bearing capacity then equals qult = 2028 + 21.619 + 0.5182*16 ≈ 560 + 410.4 + 288 = 1258.4 kPa. If a safety factor FS = 3 is used, the allowable capacity is qu_allowable ≈ 419.5 kPa. This illustrative calculation demonstrates the method and highlights how changes in phi', c, B, Df, and FS affect the result. In real projects, use site-specific data and charts forNc, Nq, and Ngamma and document all assumptions.

Design considerations, safety factors, and code references

Selecting an appropriate factor of safety depends on the risk profile, loading type, and reliability requirements of the project. Static loads often use FS values in the range of 2.0–3.0, while seismic or highly variable loads may require higher factors. Groundwater conditions, ramped loading around construction, and potential scour or erosion near foundations must be anticipated and mitigated. When qu_allowable falls below the anticipated vertical load, engineers may explore ground improvement (soil stabilization, compaction, drainage), deeper foundations, or different footing geometries. Design references and codes provide minimum FS guidance and method limitations; practitioners should document all choices and verify results with peer review. Load Capacity’s approach emphasizes conservative, well-documented estimates, and continuous validation with field data where feasible.

Common pitfalls and field considerations

Common mistakes include neglecting subsoil variability, failing to account for groundwater effects, ignoring settlement criteria, and using overly optimistic phi' estimates. Field conditions such as perched water tables, loose surface layers, or nearby excavation activities can reduce capacity and alter effective stress. Engineers should perform sensitivity checks across plausible phi' and c ranges and validate critical assumptions with additional tests or monitoring during construction. Taking a staged approach—design, verify, and adjust—helps ensure that the final foundation behaves as intended under real-world conditions.

Tools & Materials

Soil testing report (c, phi', gamma, Df if relevant)(Lab test data or calibrated site investigations; document measurement methods.)
Geotechnical design calculator or software(Allows quick evaluation of qult, qu_allowable, and sensitivity analyses.)
Scientific calculator or spreadsheet(For manual checks and quick derivations; include units in every step.)
Pen, ruler, and graph paper(Useful for sketching footing geometry and stress distributions.)

Steps

Estimated time: 15-30 minutes per calculation (excluding data collection and chart lookups)

1
Gather soil and design inputs
Collect soil properties (c, phi', gamma) and footing geometry (B, Df). Confirm whether groundwater affects effective stress and if eccentric or inclined loading is present. These inputs set the baseline for qult calculation.
Tip: Document assumptions and sources for each input; changes to phi' or c can significantly alter results.
2
Compute the overburden stress at the footing base
Calculate q' = gamma * Df, using chosen unit weight gamma and embedment depth Df. This term captures the vertical stress contributing to shear resistance.
Tip: Use consistent units (kN/m³ for gamma and meters for Df).
3
Obtain bearing-capacity factors Nc, Nq, Ngamma
From phi' charts or tables, retrieve Nc, Nq, Ngamma corresponding to the soil friction angle. These factors translate soil strength into the ultimate capacity.
Tip: If phi' is uncertain, perform a sensitivity check across a plausible range.
4
Compute ultimate bearing capacity qult
Use qult = c*Nc + q'*Nq + 0.5*gamma*B*Ngamma to sum the three contributing terms. Maintain consistent units (kPa for qult).
Tip: Check each term individually to catch arithmetic mistakes.
5
Apply the safety factor to obtain allowable capacity
Calculate qu_allowable = qult / FS. This provides the design-capacity metric used to compare with vertical loads.
Tip: FS selection should reflect project risk, occupancy, and consequences of failure.
6
Compare loads and assess design options
If the actual load exceeds qu_allowable, consider footing resizing, deeper foundations, or ground improvement to boost capacity.
Tip: Document decisions and provide a traceable design rationale.
7
Document results and plan field checks
Record input data, formula choices, and results. Plan any field tests or settlements monitoring to verify performance after construction.
Tip: Include notes on uncertainties and future re-evaluation if soil conditions change.

Pro Tip: Always start with high-quality soil data; the accuracy of qult hinges on phi' and c values.

Warning: Do not neglect groundwater effects; they can dramatically reduce effective stress and capacity.

Note: Keep FS conservative for critical structures and document all assumptions for peer review.

Quick Answers

What is the ultimate bearing capacity of square footing?

It is the soil’s maximum load before failure under a square footing, determined using c, phi' and gamma along with footing width. This value is then reduced by a factor of safety to yield a safe design capacity.

How do you obtain Nc, Nq, and Ngamma values?

Nc, Nq, and Ngamma are obtained from phi' charts or tables in geotechnical handbooks or software. They depend on the soil's friction angle and are used in the Terzaghi bearing capacity equation.

Why does groundwater matter for bearing capacity?

Groundwater reduces effective stress and can cause uplift or piping, lowering the footing's ultimate capacity. It must be accounted for in q' and sometimes alters the bearing capacity factors.

Can footing width affect the ultimate capacity?

Yes. The width B appears in the gamma-term of qult, so larger footings increase the contribution from the gamma term but can also alter stress distribution and settlement behavior.

How is allowable bearing capacity different from ultimate capacity?

Ultimate capacity is the soil’s theoretical maximum; allowable capacity is obtained by dividing qult by a factor of safety to ensure safe performance under uncertainty.