Calculator Inputs
Example Data Table
| Case | q (kPa) | B×L (m) | Df (m) | Layer top (m) | H (m) | e0 | σ'0 / σ'p (kPa) | Δσ method | Sp (mm) | Si (mm) | Total (mm) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Example | 150 | 2×3 | 1.0 | 1.5 | 4.0 | 0.90 | 80 / 120 | 2:1 approximation | ~58.00 | ~10.08 | ~72.00 |
Formula Used
Stress increase (2:1 approximation)
At depth z below the footing base: Δσ = q × (B×L) / [(B+z)(L+z)].
Here, z is the distance from the footing base to the layer mid-depth.
Primary consolidation settlement
For one-dimensional consolidation: S = (H/(1+e0)) × [Cr·log10(σ'p/σ'0) + Cc·log10(σ'f/σ'p)], where applicable.
The calculator automatically selects NC/OC segments using σ'0, σ'p, and σ'f=σ'0+Δσ.
Immediate (elastic) settlement
Si = q·B·(1−ν²)·Is / Es, with Es in kPa.
Use Is to represent shape and rigidity effects.
Time-rate and secondary settlement
Time factor: Tv = Cv·t / Hd². Degree of consolidation: series solution for U(Tv).
Secondary: Ss = (Cα·H/(1+e0))·log10(t2/t1).
How to Use This Calculator
- Enter net foundation pressure and footing dimensions.
- Define the compressible layer depth, thickness, and void ratio.
- Provide effective stresses at the layer mid-depth and preconsolidation pressure.
- Select a stress method or input a manual stress increase.
- Optional: enter elastic and time parameters for immediate and time-rate results.
- Click Calculate to view results above, then export CSV or PDF.
Technical Notes
Why settlement prediction matters in design
Settlement affects serviceability, alignment, and cracking risk. This calculator separates immediate, primary, and secondary components, so you can see which mechanism dominates. Use it to compare options such as changing footing size, lowering net pressure, or improving soil. Results support early feasibility and help prioritize site investigation targets.
Primary consolidation behavior for layered soils
For compressible cohesive layers, primary settlement is governed by effective stress change and compressibility parameters. The tool follows a standard one-dimensional approach using void ratio, layer thickness, and logarithmic stress ratios. If the final stress crosses preconsolidation pressure, it applies recompression first and virgin compression afterward.
Estimating stress increase beneath footings
Stress transfer is simplified using a practical 2:1 spread method or a user-defined Δσ. The 2:1 option is convenient for preliminary sizing and sensitivity checks, while manual Δσ is suited to refined analyses using influence charts, numerical methods, or detailed stress distribution outputs.
Time-rate effects and drainage conditions
Consolidation rate depends on Cv, drainage path length, and time. Select single or double drainage to set Hd, then the calculator computes Tv and an average degree of consolidation U. The “primary at time t” result estimates how much of primary settlement may occur by the chosen time, supporting construction sequencing and monitoring plans.
Interpreting outputs and applying engineering judgment
Treat outputs as screening-level estimates unless inputs come from representative laboratory and field data. Review sensitivity to σ'0, σ'p, Cc, and Δσ. Check that net pressure reflects overburden relief and that stresses are effective. For critical structures, confirm with project standards, multiple soil layers, and settlement criteria for differential movement.
Example Data
The following example values match the default form inputs and provide a realistic starting point for shallow footing assessment.
| Parameter | Value | Unit |
|---|---|---|
| Net pressure q | 150 | kPa |
| Footing size B × L | 2 × 3 | m |
| Embedment depth Df | 1.0 | m |
| Layer top depth | 1.5 | m |
| Layer thickness H | 4.0 | m |
| Void ratio e0 | 0.90 | — |
| Compression / recompression | Cc 0.28, Cr 0.05 | — |
| Effective stresses | σ'0 80, σ'p 120 | kPa |
| Cv and drainage | 2.0×10⁻⁷, double | m²/s |
| Evaluation time | 1 | year |
FAQs
1) What does the calculator consider “total settlement”?
It sums immediate settlement, primary consolidation settlement, and optional secondary settlement. If you set Cα to zero, secondary settlement is excluded from the total.
2) When should I use manual Δσ instead of the 2:1 method?
Use manual Δσ when you already have a stress increase from charts, elastic solutions, or numerical models. The 2:1 method is best for preliminary checks and fast comparisons.
3) Why do σ'0 and σ'p need to be effective stresses?
Consolidation depends on changes in effective stress within the soil skeleton. Using total stress can overestimate settlement, especially where pore pressures are significant.
4) What happens if σ'0 + Δσ is below σ'p?
The layer behaves overconsolidated for that stress range, and the calculator uses Cr rather than Cc. This typically produces smaller primary settlement for the same Δσ.
5) How is the consolidation time effect computed?
It calculates Tv from Cv, time, and drainage path Hd, then estimates average degree of consolidation U using a series approximation. Primary settlement at time t is Sp × U.
6) Can I use this for multiple soil layers?
Yes, by running separate calculations for each compressible layer and summing the settlements. Use layer-specific H, e0, indices, σ'0, σ'p, and Δσ at each layer depth.
7) What should I review before accepting the results?
Check units, net pressure assumptions, representative compressibility values, and realistic effective stresses. Compare against allowable total and differential settlement criteria for the structure.