Quick answer The ultimate bearing capacity of soil is given by Terzaghi's equation qu=c·Nc·Fcs+q·Nq·Fqs+½·γ·B·Nγ·Fγs. Bearing-capacity factors such as Nq=e^(π·tanφ)·tan²(45+φ/2) increase sharply with the internal friction angle φ, and the allowable bearing capacity=qu/safety factor.
Compute ultimate and allowable soil bearing capacity using a Terzaghi-type equation with Meyerhof/Vesic-style shape factors. Adjust cohesion, friction angle, foundation geometry, and shape factor to instantly see how Nc, Nq, and Nγ influence your design.
Soil & Foundation Parameters
Cohesion c
kPa
Friction angle φ
°
Unit weight γ
kN/m³
Foundation width B
m
Embedment depth Df
m
Footing Shape
Safety factor FS
While paused, move the sliders to update the result instantly.
As the load grows, the central wedge and log-spiral slip surfaces develop; when the contact pressure reaches the ultimate bearing capacity qu the soil shears and the sides heave. Change φ, c, B, Df to update qu and the factors live.
Results
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Nc
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Nq
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Nγ
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Ultimate qu (kPa)
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Allowable qa (kPa)
qu, qa vs Internal Friction Angle φ
qu and qa vs friction angle φ (0–45°) using current c, γ, B, Df
qu, qa vs Foundation Width B
qu and qa vs foundation width B (0.5–5 m) using current c, φ, γ, Df
What exactly is "soil bearing capacity"? Is it just how much weight the ground can hold?
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Basically, yes! It's the maximum average pressure the soil can withstand before it fails and the foundation sinks. In practice, we calculate an "ultimate" capacity ($q_u$), then divide by a safety factor to get the "allowable" pressure ($q_a$) we can safely design for. Try moving the "Cohesion" slider in the simulator above to see how a sticky clay soil can dramatically increase the calculated capacity.
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Wait, really? So the formula has three parts. What's the "surcharge" term ($qN_q$) for?
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Good observation! That term accounts for the soil beside the foundation. The "q" is the pressure from the soil column of depth $D_f$ around the footing. A common case is a basement wall footing—the deeper it's buried, the more the surrounding soil helps hold it up. In the simulator, increase the "Embedment Depth" ($D_f$) and watch the allowable capacity ($q_a$) rise, even if you don't change the soil's strength.
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So the "Friction Angle" must be super important too. What happens if I set it to zero, like for very soft clay?
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Exactly! For $\phi = 0$, the bearing capacity factors $N_q$ and $N_\gamma$ collapse to specific values. The capacity then depends almost entirely on cohesion ($c$). This models "undrained" clay conditions. Try it: set Friction Angle to 0 and Cohesion to, say, 50 kPa. Then, change the Foundation Width ($B$). You'll see the capacity barely changes, which is a key characteristic of clay versus sandy soil.
Physical Model & Key Equations
The ultimate bearing capacity $q_u$ is calculated using Terzaghi's general formula, which sums contributions from soil cohesion, surcharge from surrounding soil, and the soil's self-weight and friction.
These equations show the exponential relationship with $\phi$. A small increase in friction angle causes a large increase in $N_q$, which is why sandy soils ($\phi \gt 30°$) can have very high bearing capacity even with zero cohesion.
Real-World Applications
Residential Footing Design: Engineers use this calculation daily to size concrete footings for houses. For instance, on sandy soil, they might determine a 0.5m wide strip footing is sufficient, while on soft clay, they might need to recommend deep piles instead.
Industrial Slab Design: The heavy loads from factory machinery or warehouse storage racks must be supported by the ground floor slab. Calculating the bearing capacity ensures the slab won't crack or settle unevenly under point loads.
Bridge Abutment Design: The massive concrete supports at the ends of a bridge exert tremendous pressure on the ground. Geotechnical engineers perform this analysis, often with high safety factors, to ensure long-term stability.
Retaining Wall Stability Check: A key mode of failure for a retaining wall is it sliding forward or tilting due to the pressure of the soil behind it. The bearing capacity of the soil under the wall's base is a critical part of this check.
Common Misunderstandings and Points to Note
When using this tool for calculations, there are several pitfalls that beginners in particular often fall into. The first is the "selection of representative values for input parameters". For example, even if you input "internal friction angle φ=30°", sandy soil on-site is not uniform. In design, careful judgment is required, such as adopting the lower limit or average value from multiple test results. When experimenting with the tool, try comparing how the results change between "φ=25° and 35°" to get a feel for parameter sensitivity.
The second point is "converting calculation results to allowable bearing capacity". The "ultimate bearing capacity" output by this tool is the value at which the ground is on the verge of failure. In actual design, a safety factor FS (typically 3) is applied for safety, dividing the ultimate value to obtain the "allowable bearing capacity". If the ultimate bearing capacity is 300 kN/m², the actual allowable capacity is around 100 kN/m². It is extremely dangerous to forget this safety factor and use the ultimate value directly.
The third point is the "applicability limits of Terzaghi's formula". This formula assumes relatively shallow foundations (where the embedment depth Df is less than the foundation width B). Different theories are needed for deep foundations (like piles), sloping ground, or dynamic loads during earthquakes. Also, for clay with φ=0, Nγ=0, but this is for long-term stability calculations. A different approach is needed for short-term conditions (immediately after construction). Please understand that this tool is merely a "first step".