Calculate ultimate and allowable bearing capacity in real time using Terzaghi and Meyerhof formulas. Shape, depth, eccentricity corrections and elastic settlement included.
What exactly is "bearing capacity"? Is it just how much weight the ground can hold?
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Basically, yes! It's the maximum average pressure a soil can withstand before it fails and the structure sinks. In practice, we never push it to the absolute limit. That's where the "Safety Factor" slider in the simulator comes in—it divides the ultimate capacity to give us a safe design pressure.
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Wait, really? So the formula has three parts. What's the "q" term for?
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Good observation! The $q$ term represents the strength from the soil around the foundation. It's the overburden pressure, calculated as $q = \gamma \times D_f$, where $D_f$ is the embedment depth. Try increasing the "Embedment Depth Df" in the simulator—you'll see the capacity jump because deeper foundations have more confining soil around them, making them much stronger.
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That makes sense. But why are there two methods, Terzaghi and Meyerhof? Which one should I trust?
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Terzaghi's is the classic, simpler theory. Meyerhof's is more advanced and generally more accurate for real-world shapes and depths because it includes better "shape and depth factors". For instance, for a long strip footing (like a wall), set "Foundation Type" to "Strip" and compare results. Meyerhof's factors will adjust more precisely for that geometry.
Physical Model & Key Equations
The core equation calculates the Ultimate Bearing Capacity (q_ult), the pressure causing soil shear failure. It sums three contributions: cohesion, surcharge from depth, and soil weight.
Variables: $c$ = cohesion (kPa), $q = \gamma D_f$ = overburden pressure, $\gamma$ = soil unit weight (kN/m³), $B'$ = effective width (accounts for eccentricity). $N_c, N_q, N_\gamma$ are bearing capacity factors depending only on the friction angle $\phi$. $s$ and $d$ are shape and depth correction factors.
A key innovation in Meyerhof's method is the treatment of eccentric loads. If a column isn't perfectly centered, the effective area reduces, drastically cutting capacity.
$$B' = B - 2e_B, \quad L' = L - 2e_L$$
Physical Meaning: Here, $e$ is the load eccentricity. The simulator's "Eccentricity e" parameter lets you model this. The foundation behaves as if it's smaller, using $B'$ and $L'$ in the calculation. This is critical for designing foundations for retaining walls or industrial equipment with large sideways forces.
Frequently Asked Questions
B is the actual width of the foundation. B' is the effective width considering eccentric loading, calculated as B' = B - 2e (where e is the eccentricity). When eccentricity exists, the bearing capacity decreases, so calculations are performed using B'.
Yes, it is possible. When φ = 0, the bearing capacity factors become constants, such as Nc = 5.14 (Terzaghi's formula), and the ultimate bearing capacity is calculated solely based on the cohesion c.
The calculation of elastic settlement requires the foundation width B, applied load, elastic modulus E of the ground, and Poisson's ratio ν. Assuming a uniform ground, the immediate settlement is estimated based on elastic theory.
Based on the Terzaghi-Meyerhof formula, factors corresponding to the foundation shape (square, rectangular, circular) and embedment depth are automatically calculated. The user only needs to input the foundation shape and dimensions, and these factors are applied accordingly.
Real-World Applications
Shallow Foundation Design for Buildings: This is the most direct use. Engineers use tools like this for initial sizing of footings for houses, commercial buildings, and towers. Before running complex 3D FEM analysis in software like PLAXIS, they verify approximate sizes and soil parameters here.
Industrial Equipment & Silo Foundations: Heavy machinery, turbines, or grain silos create massive concentrated loads, often with moment forces that cause eccentricity. Calculating the reduced bearing capacity with eccentricity is essential to prevent tilting or catastrophic settlement.
Geotechnical CAE Model Validation: In advanced Finite Element Method (FEM) simulations of soil-structure interaction, the results from a detailed model are often checked against classical bearing capacity formulas. A large discrepancy can indicate a problem with the mesh or constitutive model in the CAE software.
Assessment of Existing Foundations & Retrofits: When adding a new floor to an old building, engineers must check if the existing footings can take the extra load. This calculator provides a quick, conservative estimate of the original design capacity based on soil reports.
Common Misconceptions and Points to Note
When you start using this calculation formula, there are a few pitfalls you're likely to encounter. First is the "relationship between cohesion c and internal friction angle φ". The handling of these two parameters is fundamentally different for clay and sand. For example, with saturated clay (φ≈0), short-term bearing capacity is calculated using only cohesion c, but in the long term, as water drains out, the strength changes (consolidation settlement). Conversely, for sand (c≈0), the internal friction angle φ is everything; if the groundwater level rises and you don't consider the submerged unit weight, you'll overestimate the capacity. In the tool, if you change "γ (soil unit weight)" from 18 kN/m³ to 10 kN/m³ (submerged unit weight), you can see the bearing capacity drop significantly.
Next is the "magic number-ization of the Factor of Safety FS". While FS=3 is often used for residential foundations, it's not a universal solution. For instance, when you have abundant site investigation data with low variability, or for temporary structures with less strict allowable settlement, FS=2.5 might be considered. On the other hand, for foundations supporting precision machinery sensitive to differential settlement, you must always use settlement calculations alongside bearing capacity. I strongly recommend using this tool's "Settlement" tab in conjunction with the bearing capacity calculation.
Finally, don't overlook the "applicability limits of the formula". This Terzaghi-Meyerhof formula assumes a relatively homogeneous soil stratum. In real-world sites, it's common to have a stiff layer under a soft layer (two-layer soil) or sloping ground. In such cases, different theories or corrections are needed. When you tweak parameters in the tool and think, "Huh, the bearing capacity is this high?", the trick to avoiding mistakes in practice is to pause and ask yourself, "Are these conditions realistic?"