Input foundation width, embedment depth, applied load, N-value, and soil type to compute Terzaghi bearing capacity, safety factor, and consolidation settlement. Visualize the soil profile with stress bulb.
Parameters
Foundation width B (m)
m
Embedment depth Df (m)
m
Applied load q (kPa)
kPa
SPT N-value
Unit weight γ (kN/m³)
kN/m³
Soil type
Results
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Ultimate q_u [kPa]
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Safety factor F_s
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Immediate S_i [mm]
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Consolidation S_c [mm]
Soil profile & stress bulb
Consolidation settlement vs time
Theory & Key Formulas
$$S_{total} = S_i + S_c + S_s$$
全沈下量（m）：即時沈下 $S_i$（弾性）＋一次圧密沈下 $S_c$＋二次圧縮沈下 $S_s$。
$$S_i = \frac{qB(1-\nu^2)}{E} I_s$$
即時弾性沈下（m）：$q$ は基礎接地圧（kPa）、$B$ は幅（m）、$I_s$ は形状係数。
$$T_v = \frac{c_v t}{H_{dr}^2}$$
時間係数（無次元）：$c_v$ は圧密係数（m²/s）、$H_{dr}$ は排水距離（m）。
What is Foundation Settlement?
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What exactly is "foundation settlement," and why is it such a big deal in construction?
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Basically, it's the downward movement of a building's foundation into the soil. It's a big deal because if it's uneven or excessive, you get cracks, tilted walls, and structural failure. In practice, we need to predict it before we build. Try moving the "Applied Load (q)" slider in the simulator above—you'll see how increasing the load directly increases the calculated settlement.
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Wait, really? So the soil type must be super important. What does the "SPT N-value" control in the simulator actually mean?
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Great question. The Standard Penetration Test (SPT) N-value is a measure of soil density and strength from a field test. A low N-value, like 5, means loose, weak sand. A high value, like 40, means very dense sand. In the simulator, when you change the soil type, the N-value and other properties update, which directly changes the bearing capacity. For instance, selecting "Soft Clay" gives you a low N-value and high compressibility, leading to more settlement under the same load.
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So the "Safety Factor" is like a margin of safety? How do engineers use the results from a calculation like this?
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Exactly. The Safety Factor (FS) is the ratio of the soil's ultimate strength to the actual load. A common target is FS = 3. If your simulator shows FS less than 2, it's a red flag—the foundation is at risk of bearing failure. Engineers use these calculations to decide footing size. For example, if FS is too low, they might increase the "Foundation Width (B)" you see in the controls, which spreads the load over more soil.
Physical Model & Key Equations
The core of the analysis is Terzaghi's Bearing Capacity Formula, which calculates the ultimate pressure the soil can withstand before shear failure.
$$q_u = cN_c + qN_q + 0.5 \gamma B N_{\gamma}$$
Where: $q_u$ = Ultimate bearing capacity (kPa) $c$ = Soil cohesion (kPa) $q$ = Effective overburden pressure at foundation base = $\gamma D_f$ (kPa) $\gamma$ = Soil unit weight (kN/m³) $B$ = Foundation width (m) $N_c, N_q, N_{\gamma}$ = Bearing capacity factors, dependent on soil friction angle $\phi$
The settlement is calculated using the consolidation theory for clays or elastic methods for sands. A common form for primary consolidation settlement is:
Where: $S_c$ = Consolidation settlement (m) $C_c$ = Compression index (from soil tests) $e_0$ = Initial void ratio of the soil $H$ = Thickness of the compressible soil layer (m) $\sigma'_0$ = Initial effective stress in the soil layer (kPa) $\Delta \sigma$ = Stress increase due to the foundation load (kPa)
Frequently Asked Questions
Sandy soil has high permeability, so settlement is almost completed immediately upon loading, causing the curve to rise steeply. In contrast, clayey soil has low permeability, and it takes time for pore water to drain, resulting in a consolidation curve where settlement progresses gradually over time.
The input values for internal friction angle or cohesion may be unrealistic. In particular, for clay with an internal friction angle close to 0 degrees, setting the cohesion extremely low will reduce the bearing capacity, while inputting a very large angle will cause the bearing capacity factor to increase sharply. Please refer to standard numerical ranges based on soil type (e.g., φ=25–40° for sandy soil).
According to Terzaghi's formula, the ultimate bearing capacity increases with a larger foundation width B, but the consolidation settlement tends to increase as the foundation width increases. This is because the load is transmitted to a deeper and wider area of the ground. By changing B in this tool and comparing the curves, you can visually confirm this trade-off.
It depends on the thickness and permeability coefficient of the clay layer, but generally it takes several months to several years. By switching the time axis to a logarithmic scale in this tool, it becomes easier to observe the initial rapid settlement and the long-term convergence trend. In design, the time to reach 90% consolidation is often used as a guideline.
Real-World Applications
Residential Building Design: Before constructing a house, engineers use this exact calculation to size the concrete footings. For instance, on soft clay, they might recommend wider footings or a deep foundation system to limit settlement and prevent cracked drywall and jammed doors.
Industrial Storage Tanks: Large tanks for oil or water exert massive loads on the ground. Settlement analysis ensures the tank settles uniformly. Differential settlement could cause a rupture, so engineers often use a ring beam foundation designed based on these principles.
Bridge Abutment Design: The supports (abutments) at the ends of a bridge transfer huge loads from the structure into the soil. Calculating bearing capacity and settlement is critical to prevent the bridge approach from sinking relative to the deck, creating a dangerous "bump."
Wind Turbine Foundations: A modern wind turbine mast presents a massive, tall structure with high overturning moments. The foundation must have ample bearing capacity and minimal tilt. These calculations are the first step in designing the large reinforced concrete mats or piles used.
Common Misunderstandings and Points to Note
When you start using this tool, there are a few points you should be careful about. First, there's the common misunderstanding that "a larger factor of safety is always better." While it certainly increases safety, it's a trade-off with economy. For instance, setting the factor of safety to 5.0 or 10.0 leads to designing an unnecessarily large foundation, causing costs to skyrocket. In practice, considering the accuracy of soil investigations and the importance of the structure, you should aim for an "appropriate" range, typically between 2.5 and 3.0.
Next, pay close attention to the "units" for parameter input. This is crucial! The tool uses [kN/m²] and [kN/m³], but field data often comes in [tf] or [g/cm³]. For example, if you mistakenly input the unit weight γ as 1.8 [tf/m³] (the correct value is 18 [kN/m³]), your calculation result will be off by a factor of 1/10, leading to a major error. Always double-check unit conversions before inputting values.
Finally, remember that this calculation assumes a "homogeneous soil" and "central loading." Real-world sites are more complex. When the soil is layered or the foundation is subjected to eccentric loading (e.g., placing machinery at the edge of a building), the formulas become much more complicated. Treat this tool's results as a "first approximation," and keep in mind that for complex conditions, specialized software or detailed analysis is necessary.
Enter soil friction angle (φ) in degrees and cohesion (c) in kPa for your soil layer
Input foundation width (B) in meters and depth (Df) in meters below ground surface
Set applied bearing pressure (q) in kPa and unit weight (γ) in kN/m³
Click calculate to obtain ultimate bearing capacity (q_u), safety factor, immediate settlement (S_i), and consolidation settlement (S_c)
Review Terzaghi bearing capacity factors automatically computed for your soil parameters
Worked Example
For a shallow square foundation on clay: B=1.5m, Df=1.0m, φ=28°, c=35kPa, γ=18kN/m³, applied q=150kPa. Terzaghi analysis yields N_c=30.14, N_q=17.69, N_γ=15.70, giving q_u=892kPa and safety factor F_s=5.95. Immediate settlement S_i=4.2mm from elastic theory (E=15MPa, μ=0.35). Primary consolidation S_c=18.7mm over 2-year period (C_c=0.28, e₀=0.82, Δσ'=145kPa). Total settlement approximately 23mm.
Practical Notes
Clay soils require undrained parameters (φ_u≈0°, c_u measured from triaxial CU tests) for short-term analysis; use drained angles for long-term consolidation estimates
Sandy foundations show minimal consolidation settlement; focus on immediate elastic displacement and bearing capacity verification
Square footings (B=L) use corrected shape factors; rectangular footings (L/B>1) increase bearing capacity by 10-25% depending on geometry
Subtract pore pressure (u) from applied stress when calculating effective stress for consolidation; account for water table elevation above foundation level