Consolidation Settlement Calculator (Primary Settlement of Clay & Time)
Calculate the primary consolidation settlement of a clay layer from Cc, Cs, initial void ratio and effective stresses — normally or overconsolidated — plus the time for 50% and 90% consolidation from cv.
How it works
Normally consolidated: S = Cc·H/(1 + e₀) · log(σ′f/σ′₀) · overconsolidated, σ′f ≤ σ′p: S = Cs·H/(1 + e₀) · log(σ′f/σ′₀) · overconsolidated, σ′f > σ′p: S = H/(1 + e₀) · [Cs·log(σ′p/σ′₀) + Cc·log(σ′f/σ′p)] · σ′f = σ′₀ + Δσ · time t = Tv·Hdr²/cv with Tv = (π/4)U² for U < 60% and Tv = 1.781 − 0.933·log(100 − U%) above (Tv50 = 0.197, Tv90 = 0.848).
When a saturated clay is loaded, the extra stress is first carried by pore water and the soil compresses only as that water drains out — primary consolidation. The final settlement depends on how much the void ratio falls along the e–log σ′ curve: steeply (Cc) on the virgin compression line, gently (Cs) when the clay is reloaded below the highest stress it has carried before (σ′p). Terzaghi’s one-dimensional theory gives the rate through the coefficient of consolidation cv and the longest drainage path. Use the stresses at the middle of the layer; split thick layers into sub-layers and add the settlements for better accuracy. Secondary compression (creep) is not included.
Worked example
A 4 m normally consolidated clay layer has e₀ = 0.9, Cc = 0.3 and σ′₀ = 80 kPa at mid-depth; a new fill adds 50 kPa. S = 0.3 × 4/1.9 × log(130/80) = 0.6316 × 0.2109 = 0.1332 m = 133.2 mm. With sand above and below (Hdr = 2 m) and cv = 2 m²/year, 50% of it happens in 0.197 × 2²/2 = 0.39 years and 90% in 0.848 × 2²/2 = 1.70 years.
Sources: FHWA — Soils and Foundations Reference Manual Vol. I, §7 (consolidation settlement) · Consolidation (soil) — Terzaghi theory
Frequently asked questions
What is the difference between Cc and Cs?
Cc (compression index) is the slope of the virgin compression line on an e–log σ′ plot, used when the clay is loaded beyond anything it has carried before. Cs (swelling or recompression index) is the much flatter unload–reload slope, typically one fifth to one tenth of Cc.
How do I know if my clay is overconsolidated?
Compare the preconsolidation pressure σ′p from an oedometer test (Casagrande construction) with the current effective stress. OCR = σ′p/σ′₀ above about 1.2 means overconsolidated; such clays settle far less until the load pushes the stress past σ′p.
What value of cv should I use?
From the oedometer test at the stress range of your load. Typical values are 0.5–5 m²/year for soft to firm clays and 10–100 m²/year for silty clays; field rates are often several times faster than laboratory values because of thin sand seams.
Why does drainage matter so much for time?
Consolidation time grows with the square of the drainage path. A layer drained top and bottom (Hdr = H/2) consolidates four times faster than the same layer on an impervious base (Hdr = H). Wick drains shorten the path further to speed up settlement under embankments.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.