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Settlement (Consolidation) Calculator

Estimate the primary consolidation settlement of a normally-consolidated clay layer under an applied load. Geotechnical engineers use it to predict how much a foundation, embankment or fill will settle as pore water is squeezed from the clay over time.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the compression index Cc (from an oedometer test) and the clay layer thickness H in metres.
  2. Enter the initial in-situ void ratio e0 and the initial effective overburden stress σ0' (kPa) at the layer mid-height.
  3. Enter the stress increase Δσ (kPa) caused by the new load; read the settlement Sc in millimetres and metres.

How it works

Terzaghi's one-dimensional theory gives the primary consolidation settlement of a normally-consolidated clay as Sc = (Cc·H / (1 + e0)) · log10((σ0' + Δσ) / σ0'). The term Cc·log10((σ0'+Δσ)/σ0') is the change in void ratio, and dividing by (1 + e0) converts it to vertical strain, multiplied by the layer thickness H.

The logarithm is base-10, not natural log — a common source of error. The formula applies to normally-consolidated soil. For over-consolidated soil whose final stress stays below the preconsolidation pressure σp', replace Cc with the recompression index Cr; if the load crosses σp' the settlement is split into a recompression part (Cr) and a virgin part (Cc).

Worked example

3 m clay layer under a 50 kPa surcharge. With Cc = 0.30, H = 3 m, e0 = 0.90, σ0' = 100 kPa and Δσ = 50 kPa: the stress ratio is 150/100 = 1.5, log10(1.5) = 0.1761, and Sc = (0.30 × 3 / 1.90) × 0.1761 = 0.4737 × 0.1761 = 0.0834 m ≈ 83.4 mm.

Common mistakes

  • Using natural log (ln) instead of base-10 log (log10) — the consolidation formula is defined with log10.
  • Applying the Cc formula to over-consolidated soil; below the preconsolidation pressure you must use the recompression index Cr, not Cc.
  • Reporting Sc as the total settlement — this is primary consolidation only, and excludes immediate (elastic) and secondary (creep) settlement.

Frequently asked questions

Is this normally-consolidated or over-consolidated settlement?

This is the normally-consolidated (NC) case using the compression index Cc. For over-consolidated (OC) soil where the final stress stays below the preconsolidation pressure σp', use the recompression index Cr instead; if the load crosses σp', split the settlement into a Cr part below σp' and a Cc part above it.

Does the formula use log base 10 or natural log?

Base-10 (log10). Consolidation theory defines Cc as the slope on a void-ratio versus log10(effective stress) plot, so the settlement equation uses log10 throughout.

What stress should I enter for σ0'?

The initial vertical EFFECTIVE overburden stress at the mid-height of the clay layer, i.e. total overburden minus pore-water pressure. Thick layers are best sub-divided.

Does this include immediate and secondary settlement?

No. It is primary consolidation only. Total settlement = immediate (elastic) + primary consolidation + secondary compression (creep). Add those separately where they matter.

Where does Cc come from?

From a laboratory oedometer (one-dimensional consolidation) test — the slope of the virgin compression line on the e–log σ' curve. As a rough check, Skempton's Cc ≈ 0.009·(LL − 10) can be used from the liquid limit.

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