Example data table
| Case | H (m) | e0 | Cc | Cr | σ′0 (kPa) | Δσ (kPa) | σ′p (kPa) | Drainage | Cv (m²/day) | t (days) | Sc (m) | U (%) | Sc(t) (m) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Typical clay layer | 6.0 | 0.85 | 0.30 | 0.05 | 120 | 80 | 180 | Double | 0.0025 | 180 | 0.177 | 82 | 0.145 |
| Stiffer deposit | 4.0 | 0.65 | 0.22 | 0.04 | 160 | 60 | 220 | Single | 0.0012 | 365 | 0.075 | 70 | 0.053 |
Formula used
Final effective stress: σ′f = σ′0 + Δσ
Normally consolidated settlement:
Sc = (Cc / (1 + e0)) × H × log10(σ′f / σ′0)
Overconsolidated settlement:
If σ′f ≤ σ′p: Sc = (Cr / (1 + e0)) × H × log10(σ′f / σ′0)
If σ′f > σ′p: Sc = (Cr / (1 + e0)) × H × log10(σ′p / σ′0) + (Cc / (1 + e0)) × H × log10(σ′f / σ′p)
Drainage path: Hd = H (single drainage) or H/2 (double drainage)
Time factor: Tv = Cv × t / Hd²
Average degree of consolidation: U is estimated from Tv using the classic series solution; settlement at time t is Sc(t) = U × Sc.
How to use this calculator
- Enter the compressible layer thickness H and initial void ratio e0.
- Provide Cc and Cr from consolidation testing or correlations.
- Set σ′0 at the layer midpoint and the expected Δσ from loading.
- Enter σ′p if the soil is overconsolidated, or keep Auto mode.
- Select drainage condition to set the drainage path Hd.
- Input Cv and time t to estimate U and settlement at time t.
- Set a target U to estimate time needed to reach it.
- Press Calculate; results appear above the form, then download CSV or PDF.
Technical article
1. Why consolidation matters on sites
Primary consolidation drives long-term settlement in saturated fine-grained soils when loads increase. Predicting magnitude and rate supports foundation selection, pavement performance, and serviceability limits. The calculator combines settlement relationships with time-factor methods so designers can test scenarios quickly, compare drainage options, and communicate expected movements to stakeholders. It also aids early feasibility decisions during concept design.
2. Inputs that control compressibility
Layer thickness H and initial void ratio e0 set the compressible volume. Compression index Cc and recompression index Cr describe how void ratio changes with effective stress on the e–log σ′ curve. Use oedometer results when available; otherwise apply correlations carefully and document assumptions for independent review.
3. Effective stress and loading profile
Settlement depends on the change from initial effective stress σ′0 to final σ′f = σ′0 + Δσ. Estimate σ′0 at the layer midpoint using unit weights and groundwater position. Determine Δσ from footing pressure, embankment height, or staged loading, accounting for stress distribution and construction sequencing.
4. Normally consolidated versus overconsolidated
When σ′0 is below the preconsolidation stress σ′p, soil responds stiffer until σ′p is exceeded. If σ′f stays below σ′p, recompression with Cr dominates. If σ′f exceeds σ′p, recompression applies up to σ′p and virgin compression with Cc governs beyond, increasing ultimate settlement.
5. Rate of consolidation and time factor
The coefficient of consolidation Cv captures drainage and soil structure effects. With drainage path Hd, the time factor Tv = Cv·t/Hd² links time to average degree of consolidation U. The calculator estimates U using the classic one-dimensional solution and reports settlement at time t as Sc(t) = U·Sc. For schedule planning, compare multiple t values to map progress.
6. Drainage conditions and improvement
Double drainage halves Hd and accelerates consolidation, while single drainage slows it. Ground improvement such as vertical drains, sand blankets, or surcharge preloading effectively reduces drainage path or increases hydraulic gradients, shortening time to reach target U. Always verify improvement layouts with site-specific design methods.
7. Monitoring and construction control
Field instrumentation validates predictions and manages risk. Settlement plates, piezometers, and inclinometer data show whether excess pore pressures dissipate as expected. Compare measured settlement curves to predicted Sc(t) to adjust staging, surcharge duration, or traffic opening dates. Record all readings with timestamps for auditability.
8. Practical limits and engineering judgement
One-dimensional theory assumes vertical drainage, uniform soil properties, and small strains. Layered deposits, secondary compression, lateral strain, and stress-dependent Cv can shift outcomes. Use sensitivity checks for σ′p, Cv, and Δσ, apply conservative factors for critical structures, and align results with local codes and experience. Peer review strengthens confidence in final values.
FAQs
What is the difference between primary consolidation and secondary compression?
Primary consolidation is settlement from dissipation of excess pore water pressure. Secondary compression is long-term creep after primary consolidation, common in organic or sensitive clays, and is not included in this calculator’s main settlement estimate.
How do I estimate σ′0 and Δσ for a footing?
Compute σ′0 at the compressible layer midpoint using effective unit weights and groundwater level. Estimate Δσ using appropriate stress distribution methods for footing geometry and embedment, then apply the expected net load at construction stage.
When should I use overconsolidated mode?
Use it when preconsolidation stress σ′p exceeds the current σ′0, such as previously unloaded or aged clays. If σ′f crosses σ′p, the calculator applies recompression up to σ′p and virgin compression beyond it.
What does Cv represent and how is it obtained?
Cv reflects how quickly pore pressures dissipate, combining soil permeability and compressibility. It is usually derived from oedometer time-settlement curves using standard methods, or back-calculated from field monitoring when lab data is limited.
How does drainage condition affect time predictions?
Drainage controls the drainage path Hd. Double drainage uses Hd = H/2, increasing Tv and accelerating consolidation for the same time. Single drainage uses Hd = H, so the same Cv requires more time to reach the same U.
Why is the degree of consolidation U an average value?
The classic one-dimensional solution reports average consolidation over the layer thickness. Local consolidation varies with depth and boundary conditions, so U summarizes overall settlement progress, which is often sufficient for schedule and serviceability checks.
Can I use this tool for layered soils?
You can approximate by analyzing each compressible layer separately with its own parameters and drainage path, then summing settlements. For strong layering, stress-dependent parameters, or critical structures, use detailed analyses and confirm with monitoring.