Learn: Consolidation time
Settlement magnitude and the time needed to develop it are different questions. The consolidation time factor relates elapsed time to the drainage path and coefficient of consolidation for a chosen degree of primary consolidation.
What the formula is saying
Rearrange Tv = cv t/Hdr² to get t = Tv Hdr²/cv. Water must travel along the drainage path, so time depends on its square rather than on the layer thickness alone.
Read the symbols in plain language
- Tv
- Time factor
Time factor. The supplied dimensionless factor selects the intended degree of primary consolidation.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Hdr
- Drainage path
Drainage path Hdr, not automatically total layer thickness.
mMetres measure length; 1 m = 1000 mm.
- cv
- Coefficient of consolidation
Coefficient of consolidation. Squared distance divided by the consolidation coefficient has units of time.
m²/sUse m²/s as the base unit shown here. H is the drainage path Hdr in m, cv is m²/s and Tv is dimensionless. The result is seconds. For double drainage of a uniform layer, Hdr is half the full layer thickness; for single drainage it is the full thickness.
- t
- Result to find
Consolidation time. The supplied dimensionless factor selects the intended degree of primary consolidation.
s
Sort out the units first
H is the drainage path Hdr in m, cv is m²/s and Tv is dimensionless. The result is seconds. For double drainage of a uniform layer, Hdr is half the full layer thickness; for single drainage it is the full thickness.
Assumptions before calculating
Assume one-dimensional Terzaghi primary consolidation with compatible Tv, cv and drainage boundary conditions. The selected Tv corresponds to a target degree of consolidation established separately.
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 t and explain the result in the stated output unit.
- Tv · Time factor
- 0.848
- Hdr · Drainage path
- 2.5 m
- cv · Coefficient of consolidation
- 1e-7 m²/s
Square the drainage path
Use the longest relevant drainage distance, which may be half the layer thickness.
(2.5)^2 = 6.25 m²Find the drainage time scale
Squared distance divided by the consolidation coefficient has units of time.
(6.25) ÷ (1e-7) = 62500000 sApply the target time factor
The supplied dimensionless factor selects the intended degree of primary consolidation.
(0.848) × (62500000) = 53000000 s
Does this worked answer make sense?
Doubling drainage path multiplies time by 4. Doubling cv halves time. For the same layer and cv, double drainage takes one quarter of the single-drainage time for the same Tv.
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.
- Tv · Time factor
- 0.197
- Hdr · Drainage path
- 2 m
- cv · Coefficient of consolidation
- 2e-7 m²/s
Square the drainage path
Use the longest relevant drainage distance, which may be half the layer thickness.
(2)^2 = 4 m²Find the drainage time scale
Squared distance divided by the consolidation coefficient has units of time.
(4) ÷ (2e-7) = 20000000 sApply the target time factor
The supplied dimensionless factor selects the intended degree of primary consolidation.
(0.197) × (20000000) = 3940000 s
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.
- Tv · Time factor
- 0.848
- Hdr · Drainage path
- 1.5 m
- cv · Coefficient of consolidation
- 1.5e-7 m²/s
Find: Learn: Consolidation time
A hint, not the answer
Rearrange Tv = cv t/Hdr² to get t = Tv Hdr²/cv. Water must travel along the drainage path, so time depends on its square rather than on the layer thickness alone.
H is the drainage path Hdr in m, cv is m²/s and Tv is dimensionless. The result is seconds. For double drainage of a uniform layer, Hdr is half the full layer thickness; for single drainage it is the full thickness.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Square the drainage path
Use the longest relevant drainage distance, which may be half the layer thickness.
(1.5)^2 = 2.25 m²Find the drainage time scale
Squared distance divided by the consolidation coefficient has units of time.
(2.25) ÷ (1.5e-7) = 15000000 sApply the target time factor
The supplied dimensionless factor selects the intended degree of primary consolidation.
(0.848) × (15000000) = 12720000 s
Avoid the common trap
Do not use full layer thickness for a double-drained layer. Do not mix cv in m²/year with an assumed seconds output, and do not forget to square the drainage path.
When this method applies — and when it does not
This does not choose Tv from a target percentage or model variable permeability, staged loading, vertical drains, secondary compression or changing layer thickness. A laboratory cv may not represent all field stresses and drainage conditions.
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: Consolidation time. 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.