Consolidation Settlement Calculator

Formula for primary consolidation settlement

For a normally consolidated clay, the final primary consolidation settlement can be estimated as Sc = H × [Cc / (1 + e0)] × log10((σ0 + Δσ) / σ0).

In more compact text form:

Sc = H × [Cc / (1 + e0)] × log10((σ0 + Δσ) / σ0)

Definition of symbols

• $H$ – Thickness of the compressible clay layer (same length units as the settlement result, e.g. metres).
• $e_0$ – Initial void ratio of the clay at the in‑situ stress state, obtained from a consolidation test.
• $C_c$ – Compression index, the slope of the virgin compression line on the e–log $\prime$ plot (dimensionless).
• ${\sigma }_0$ – Initial vertical effective stress at the mid‑depth of the clay layer (kPa in this calculator).
• $\Delta \sigma$ – Increase in vertical effective stress at the same depth due to the new load (kPa).
• ${\log }_{10}$ – Base‑10 logarithm. Ensure your hand calculations, if any, also use base 10.

Because $C_c$ and $e_0$ are dimensionless and the logarithm is also dimensionless, the settlement $S_c$ has the same units as $H$. If you input $H$ in metres, the output settlement will be in metres; if you use millimetres, the output will be in millimetres.

How to use this consolidation settlement calculator

1. Choose the clay layer thickness, $H$ – This is usually the vertical thickness of the primary compressible clay stratum beneath the foundation. For a simple profile, you can take the full clay thickness from the top of the layer to the bottom.
2. Enter the initial void ratio, $e_0$ – Take $e_0$ from your oedometer (consolidation) test at the in‑situ effective stress level corresponding to the mid‑depth of the layer.
3. Enter the compression index, $C_c$ – Determine $C_c$ from the slope of the virgin compression line in the e–log $\prime$ plot. Use the portion of the curve beyond the preconsolidation pressure for normally consolidated behaviour.
4. Estimate the initial effective stress, ${\sigma }_0$ – Compute the vertical effective stress at the mid‑depth of the clay. This is typically the total overburden stress minus pore water pressure at that depth.
5. Estimate the added stress, $\Delta \sigma$ – Determine the increase in vertical effective stress at the same depth due to the proposed loading (for example, from a footing or embankment). Use your preferred stress distribution method to obtain $\Delta \sigma$ in kPa.
6. Use consistent units – Enter both ${\sigma }_0$ and $\Delta \sigma$ in kPa, and $H$ in metres to obtain settlement in metres.
7. Compute the settlement – After entering all inputs, run the calculation. The output is the estimated final primary consolidation settlement, $S_c$, for the specified clay layer.

Interpreting the results

The calculator returns a single value representing the final primary consolidation settlement of the specified clay layer. This is the long‑term vertical compression that occurs as excess pore water pressure dissipates and the soil skeleton takes the additional load.

A larger settlement indicates greater risk of serviceability issues such as differential movements, tilting, or cracking of supported structures. In design practice, the calculated $S_c$ is typically compared with project‑specific settlement criteria for the structure type (e.g. total settlement limits for buildings or embankments).

Keep in mind that the result reflects only primary consolidation under one‑dimensional conditions for a single, homogeneous clay layer. Actual field settlements may be greater or smaller due to factors such as layering, drainage boundary conditions, overconsolidation, and secondary compression (creep).

Worked example

Consider a building constructed on a 5 m thick normally consolidated clay layer. From laboratory testing and stress analysis, you have the following data:

• Layer thickness: $H=5.0$ m
• Initial void ratio: $e_0=0.9$
• Compression index: $Cc=0.25$
• Initial effective vertical stress at mid‑depth: $\sigma {\sigma }_0=100$ kPa
• Increase in vertical stress due to new load: $\Delta \sigma =50$ kPa

Step 1: Compute the stress ratio inside the logarithm:

Formula: (σ_0 + Δ σ_0) / σ_0 = (100 + 50) / 100 = 1.5

$\frac{{\sigma }_0+\Delta {\sigma }_0}{{\sigma }_0}=\frac{100+50}{100}=1.5$

Step 2: Compute the base‑10 logarithm of this ratio:

Formula: log_10 ⁡ 1.5 ≈ 0.1761

${\log }_{10}\left(1.5\right)\approx 0.1761$

Step 3: Compute the factor $\frac{C_c}{1+e_0}$:

Formula: C_c / (1 + e_0) = 0.25 / (1 + 0.9) = 0.25 / 1.9 ≈ 0.1316

$\frac{C_c}{1+e_0}=\frac{0.25}{1+0.9}=\frac{0.25}{1.9}\approx 0.1316$

Step 4: Multiply to obtain the settlement:

Formula: S_c = H × C_c / (1 + e_0) × log_10 ((σ_0 + Δ σ) / σ_0)

$S\_c=H\times \frac{C\_c}{1+e\_0}\times {log}_{10}\left(\frac{{\sigma }_0+\Delta \sigma }{{\sigma }_0}\right)$

Formula: S_c = 5.0 × 0.1316 × 0.1761 ≈ 0.116 m

$S\_c=5.0\times 0.1316\times 0.1761\approx 0.116\text{ m}$

So the estimated primary consolidation settlement is approximately 0.12 m (about 120 mm). Whether this value is acceptable depends on the type of structure and the project criteria. For sensitive buildings, 120 mm of settlement could be too large, particularly if there is potential for differential settlement between adjacent areas.

Comparison of key input parameters

The table below summarizes the main input parameters and their qualitative influence on the estimated settlement.

Assumptions and limitations

This calculator is based on a simplified one‑dimensional consolidation framework. It is important to understand where it applies and where it does not.

• Normally consolidated clay – The formula assumes the clay behaves as normally consolidated over the full stress range (that is, stresses exceed the preconsolidation pressure). Overconsolidated clays require separate treatment of recompression (using $C_r$) up to the preconsolidation stress, followed by virgin compression with $C_c$.
• Primary consolidation only – Secondary compression (creep) is not included. In soft organic clays and peats, secondary settlements can be significant and may need explicit modelling.
• One‑dimensional strain – Settlement is assumed to occur in one dimension only (vertical), with lateral strains neglected. This matches the conditions of standard oedometer tests but may not fully represent field conditions with 3D stress changes.
• Single, homogeneous clay layer – The method assumes a uniform clay layer with constant $e_0$ and $C_c$. For layered or variable profiles, engineers often divide the soil into sublayers and sum the settlements computed for each sublayer separately.
• Average stress at mid‑depth – The input stresses ${\sigma }_0$ and $\Delta \sigma$ are taken at the mid‑depth of the layer as an approximation. For more accuracy, the profile can be subdivided and stresses evaluated at several depths.
• Effective stress formulation – The stresses used should be effective stresses. If your inputs are total stresses, you must account for pore water pressure to convert them to effective stresses.
• Drainage conditions and time – The calculation gives the final primary settlement but does not estimate the time required to reach this settlement. Time rate of consolidation requires additional parameters, such as the coefficient of consolidation and drainage path length.

Professional use and disclaimer

The results from this tool are intended for educational purposes and preliminary design insight only. They are not a substitute for project‑specific analysis by a qualified geotechnical engineer using detailed subsurface data and appropriate design methods.

Actual field settlements can differ significantly from simplified estimates due to factors such as soil layering, variability in material properties, non‑uniform loading, construction sequence, drainage boundaries, overconsolidation, secondary compression, and three‑dimensional stress effects. Always verify critical design decisions with comprehensive analysis and professional judgement.