Consolidation Settlement Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Preconsolidation Pressure: About this input

The greatest vertical effective stress the clay has carried in the past, in kilopascals. It marks where the soil switches from the recompression to the virgin compression line.

Unit kPa Default 100 Range At least 0
Initial Void Ratio E0: About this input

The void ratio of the clay before loading, dimensionless, the ratio of void volume to solid volume.

Default 0.9 Range At least -1
Recompression Index Cr: About this input

The slope of the void ratio against log stress on the recompression line, dimensionless. It governs settlement while the stress stays below the preconsolidation pressure.

Default 0.05 Range At least 0
Time: About this input

The elapsed time since the load was applied, in years, at which the degree of consolidation and settlement are reported.

Unit yr Default 2 Range At least 0
Stress Increase Dsigma: About this input

The increase in vertical effective stress at the middle of the clay layer caused by the new load, in kilopascals.

Unit kPa Default 80 Range At least 0
Coefficient Of Consolidation Cv: About this input

The coefficient of consolidation of the clay, in square metres per year, which sets how fast pore pressure dissipates and settlement develops.

Unit m2/yr Default 2 Range At least 0
Clay Layer Thickness: About this input

The full thickness of the compressible clay layer, in metres.

Unit m Default 4 Range At least 0
Compression Index Cc: About this input

The slope of the void ratio against log stress on the virgin compression line, dimensionless. It governs settlement once the stress passes the preconsolidation pressure.

Default 0.3 Range At least 0
Initial Effective Stress: About this input

The vertical effective stress at the middle of the clay layer before the new load, in kilopascals.

Unit kPa Default 100 Range At least 0
Drainage: About this input

Whether the clay layer drains from one face or from both. Double drainage halves the drainage path and greatly shortens the time to settle.

Default Double Allowed Double, Single

Outputs

Primary Consolidation Settlement: About this output

The ultimate settlement from squeezing water out of the clay, in millimetres. It is primary consolidation only and excludes secondary compression (creep) and immediate elastic settlement. The tool is not a design or a check of one, and settlement assessment must be performed and sealed by a licensed engineer.

Unit mm
Settlement At Time: About this output

The settlement developed at the chosen time, in millimetres: the ultimate primary settlement multiplied by the degree of consolidation.

Unit mm
Time Factor Tv: About this output

The dimensionless time factor from the coefficient of consolidation, elapsed time and drainage path, used to read the degree of consolidation.

No unit declared
Overconsolidation Ratio Ocr: About this output

The preconsolidation pressure divided by the initial effective stress, dimensionless. A value near 1 is normally consolidated; larger values are overconsolidated.

No unit declared
Degree Of Consolidation: About this output

The fraction of the ultimate primary settlement reached at the chosen time, in percent.

Unit percent
Drainage Path Length Hdr: About this output

The longest distance water must travel to a draining face, in metres: the full thickness for single drainage or half of it for double drainage.

Unit m
Model Status: About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared

What it is

The Consolidation Settlement Calculator estimates how much a clay layer will settle under a new load, and how long it will take. It computes the ultimate primary consolidation settlement from the clay's compressibility and the stress increase you apply, then uses Terzaghi's one-dimensional theory to work out how much of that settlement has developed at a chosen time.

It works in SI units: metres for thicknesses, kilopascals for stresses, square metres per year for the coefficient of consolidation, years for time, and millimetres for settlement.

Use it for a first estimate of foundation settlement on a compressible clay layer. It models primary consolidation only, and the soil parameters it needs come from laboratory testing rather than from any default.

Methodology

Purpose and model boundary

This model estimates one-dimensional primary consolidation settlement of a clay layer and the portion of that settlement developed at an entered time. It distinguishes recompression below the preconsolidation pressure from virgin compression above it and applies the workbook's time-factor approximation for single or double drainage. It does not model immediate settlement or secondary compression.

The spreadsheet remains the calculation authority. The browser submits named inputs through the calculation service and presents the returned results without duplicating the settlement equations.

Inputs and units

Input	Meaning and unit
Layer thickness `H`	Compressible clay thickness, m.
Initial void ratio `e0`	Initial void volume divided by solid volume.
Compression indices `Cc`, `Cr`	Virgin-compression and recompression slopes on a base-10 void-ratio/log-stress plot.
Initial and preconsolidation stresses `σ'0`, `σ'p`	Effective vertical stresses, kPa.
Stress increase `Δσ`	Added effective stress applied to the clay, kPa.
Consolidation coefficient `Cv`	m²/year.
Time `t`	years.
Drainage	Single or double drainage.

Governing relationships

OCR = σ'p / σ'0. The ultimate primary settlement uses one of three stress-history branches:

when the final stress stays below σ'p: S = H Cr/(1+e0) × log10((σ'0+Δσ)/σ'0);
when loading crosses σ'p: S = H/(1+e0) × [Cr log10(σ'p/σ'0) + Cc log10((σ'0+Δσ)/σ'p)];
when the clay is normally consolidated: S = H Cc/(1+e0) × log10((σ'0+Δσ)/σ'0).

The workbook converts settlement from metres to millimetres. The drainage path is Hdr = H for single drainage and Hdr = H/2 for double drainage. Tv = Cv t / Hdr². Degree of consolidation U is evaluated with the workbook's standard early-time and later-time approximation to Terzaghi's one-dimensional solution, and S(t) = U × S.

Calculation sequence

Validate thickness, stresses, void ratio, indices, time, Cv and drainage mode.
Compute OCR and select the recompression, crossing or normally consolidated settlement branch.
Determine drainage-path length and time factor.
Convert Tv to degree of consolidation.
Multiply the ultimate primary settlement by U and build the settlement-versus-time curve.
Return the workbook status and supporting values.

Outputs and interpretation

Primary consolidation settlement is the ultimate one-dimensional settlement from the entered stress change. Settlement at time is the developed portion at t. OCR indicates stress history; Hdr, Tv and U expose the time-rate calculation. These values do not address differential settlement, bearing failure or serviceability acceptance criteria.

Validation and status logic

Condition	Returned status
Thickness, effective stress or `1 + e0` is nonpositive	`NOT VALID: thickness, stress and (1+void ratio) must be positive`
Preconsolidation pressure is below the entered current effective stress	`CHECK: preconsolidation pressure below the current stress is inconsistent`
`Cr` exceeds `Cc`	`CHECK: the recompression index exceeds the compression index; check the two values`
Very little consolidation has developed at the entered early time	`CHECK: very early in consolidation; little settlement has occurred yet`
Inputs are usable and no warning branch applies	`OK`

Assumptions and limitations

One-dimensional primary consolidation, small strain and uniform layer properties are assumed.
Cc, Cr, e0, Cv, σ'0 and σ'p must come from appropriate laboratory and field interpretation.
The stress increase is treated as representative of the compressible layer; stress variation with depth is not integrated.
Immediate/elastic settlement, secondary compression, creep, nonlinear drainage, staged loading, radial drainage and soil improvement are omitted.
The time-rate approximation is close to, but not identical with, an exact infinite-series solution.

Restrictions and non-computing states

This calculator enforces declared numeric bounds and the authored drainage choices. Zero or negative thickness and stress states cannot produce a meaningful logarithmic settlement. Protected formula values shown with a NOT VALID status are not valid settlement results.

Errors and warnings

A rejected entry means the published input rules were not satisfied. NOT VALID prevents interpretation. CHECK identifies a calculated but internally unusual stress history, index relationship or early-time state. A connection or calculation-service error describes service availability, not soil behavior.

References

The workbook derives its relations rather than reproducing any table, chart or figure from a specification, standard or agency publication. The settlement expression is the standard logarithmic compression relation and the time rate is Terzaghi's one-dimensional consolidation theory.

United States Army Corps of Engineers. Settlement Analysis, EM 1110-1-1904. https://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-1-1904.pdf
Wikipedia. Consolidation (soil), for the mechanism and the primary and secondary phases. https://en.wikipedia.org/wiki/Consolidation_(soil)
Wikipedia. Terzaghi's principle, for the effective stress basis the theory rests on. https://en.wikipedia.org/wiki/Terzaghi%27s_principle

Compression and recompression indices, the coefficient of consolidation, the initial void ratio and the preconsolidation pressure must come from oedometer testing on undisturbed samples from the site. The values shipped with the workbook are illustrative and carry no authority.

Additional source notes migrated from Methodology

The workbook uses the conventional one-dimensional consolidation and time-factor relationships documented in its References sheet. Real settlement assessment requires site-specific testing, the governing standard and review by a licensed geotechnical engineer.

Frequently asked questions

Why does double drainage make so much difference to the time?

Because the drainage path is squared in the time factor. Double drainage lets water escape through both the top and bottom of the layer, so the longest journey is half the thickness rather than all of it, and halving a squared term divides the time by four, not two. It is the input most worth getting right, and it depends on whether the layers above and below the clay are actually permeable enough to drain it.

What is the overconsolidation ratio telling me?

Which stiffness regime the clay starts in. It is the preconsolidation pressure divided by the current effective stress. A value of 1 means the clay has never carried more than it carries now, so any new load is virgin compression and the softer `Cc` applies immediately. Above 1 the clay was preloaded at some point (by ice, by erosion since removed, by desiccation), and it behaves stiffly under the recompression index until your load exceeds that past maximum.

Is this the total settlement my structure will experience?

No. This is primary consolidation only. Immediate elastic settlement on load application is not included, and secondary compression (the slow creep of the soil skeleton after pore pressures have dissipated) is not computed at all. On organic or highly plastic clays, secondary compression can be a large fraction of the total over a structure's design life, and sometimes the larger part.

Why does the last part of the settlement take so long?

Because consolidation approaches completion asymptotically. The pore pressure driving the water out gets smaller as consolidation proceeds, so the process slows continuously and never strictly finishes. In the shipped example 93 percent arrives in two years; the remaining 7 percent takes considerably longer than the first 93 did. This is why practice designs around a target such as 90 percent rather than waiting for 100.

Where does the stress increase figure come from?

You supply it, and it is not the pressure your footing applies. The stress increase at mid-layer is the footing pressure after it has spread through the soil above, which decays with depth. Computing it is a separate calculation; the Effective Stress Calculator on this site does it by the 2:1 and Boussinesq methods. Entering the bearing pressure directly will substantially overestimate settlement for anything but a very wide load.

Can I use this for a layered profile?

Not directly. The tool models one uniform layer with one set of parameters and one stress increase applied at mid-layer. A real profile with several compressible layers has to be handled by treating each layer separately, with its own parameters, its own mid-layer stress and its own drainage path, and adding the results. The one-dimensional assumption also requires the load to be wide relative to the layer, so that the clay is laterally confined.

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