Learn: 1D consolidation settlement — NC soil
A normally consolidated saturated clay layer can settle as increased effective stress compresses its soil skeleton. This one-dimensional estimate uses the compression index and a logarithmic change in effective stress.
What the formula is saying
The e–log10 σ′ relationship gives a void-ratio reduction proportional to Cc log10(σ′f/σ′0). Multiplying by H/(1 + e0) converts that reduction into layer shortening.
Read the symbols in plain language
- Cc
- Compression index
Compression index. Layer thickness is normalized by the initial solids-and-voids factor.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- H
- Layer thickness
Layer thickness. Layer thickness is normalized by the initial solids-and-voids factor.
mMetres measure length; 1 m = 1000 mm.
- e0
- Initial void ratio
Void volume divided by solid volume, not total volume. This ratio may exceed one.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- σ′f
- Final effective stress
Final effective stress. Use final divided by initial effective stress in matching units.
kPaOne kilopascal equals one kN/m² and 1000 Pa.
- σ′0
- Initial effective stress
Initial effective stress. Use final divided by initial effective stress in matching units.
kPaOne kilopascal equals one kN/m² and 1000 Pa.
- Sc
- Result to find
1D consolidation settlement — NC soil. Combine the logarithmic stress change with the representative layer scale.
m
Sort out the units first
σ′0 and σ′f are positive effective stresses in the same unit, here kPa. H is m, while Cc and e0 are dimensionless. Use the base-10 logarithm, not the natural logarithm.
Assumptions before calculating
Assume one-dimensional primary consolidation of a normally consolidated layer with representative uniform parameters. The final effective stress is at least the initial stress, and the compression index applies along that loading path.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find Sc and explain the result in the stated output unit.
- Cc · Compression index
- 0.3
- H · Layer thickness
- 5 m
- e0 · Initial void ratio
- 0.8
- σ′f · Final effective stress
- 200 kPa
- σ′0 · Initial effective stress
- 100 kPa
Find the effective-stress ratio
Use final divided by initial effective stress in matching units.
(200) ÷ (100) = 2Take the base-10 stress change
The compression index is defined for the e versus log10 effective-stress relationship.
log₁₀((2)) ≈ 0.3010299957Convert void-ratio change to layer shortening
Layer thickness is normalized by the initial solids-and-voids factor.
(0.3) × (5) ÷ (1 + (0.8)) ≈ 0.8333333333 mCalculate primary consolidation settlement
Combine the logarithmic stress change with the representative layer scale.
(0.8333333333) × (0.3010299957) ≈ 0.2508583297 m
Does this worked answer make sense?
Equal initial and final effective stresses give zero settlement. Doubling layer thickness doubles settlement only if the representative stress change and soil parameters remain the same.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- Cc · Compression index
- 0.25
- H · Layer thickness
- 4 m
- e0 · Initial void ratio
- 0.7
- σ′f · Final effective stress
- 160 kPa
- σ′0 · Initial effective stress
- 80 kPa
Find the effective-stress ratio
Use final divided by initial effective stress in matching units.
(160) ÷ (80) = 2Take the base-10 stress change
The compression index is defined for the e versus log10 effective-stress relationship.
log₁₀((2)) ≈ 0.3010299957Convert void-ratio change to layer shortening
Layer thickness is normalized by the initial solids-and-voids factor.
(0.25) × (4) ÷ (1 + (0.7)) ≈ 0.5882352941 mCalculate primary consolidation settlement
Combine the logarithmic stress change with the representative layer scale.
(0.5882352941) × (0.3010299957) ≈ 0.177076468 m
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- Cc · Compression index
- 0.32
- H · Layer thickness
- 6 m
- e0 · Initial void ratio
- 0.9
- σ′f · Final effective stress
- 240 kPa
- σ′0 · Initial effective stress
- 120 kPa
Find: Learn: 1D consolidation settlement — NC soil
A hint, not the answer
The e–log10 σ′ relationship gives a void-ratio reduction proportional to Cc log10(σ′f/σ′0). Multiplying by H/(1 + e0) converts that reduction into layer shortening.
σ′0 and σ′f are positive effective stresses in the same unit, here kPa. H is m, while Cc and e0 are dimensionless. Use the base-10 logarithm, not the natural logarithm.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the effective-stress ratio
Use final divided by initial effective stress in matching units.
(240) ÷ (120) = 2Take the base-10 stress change
The compression index is defined for the e versus log10 effective-stress relationship.
log₁₀((2)) ≈ 0.3010299957Convert void-ratio change to layer shortening
Layer thickness is normalized by the initial solids-and-voids factor.
(0.32) × (6) ÷ (1 + (0.9)) ≈ 1.010526316 mCalculate primary consolidation settlement
Combine the logarithmic stress change with the representative layer scale.
(1.010526316) × (0.3010299957) ≈ 0.3041987325 m
Avoid the common trap
Do not use total stress in place of effective stress. Do not use ln instead of log10, reverse the stress ratio or omit the 1 + e0 divisor.
When this method applies — and when it does not
Overconsolidated loading that crosses preconsolidation stress needs a split recompression/virgin-compression calculation. Secondary compression, time rate, layered integration, unloading and drainage path are not computed here.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: 1D consolidation settlement — NC soil. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.