Consolidation, step by step: from the oedometer to settlement-time curves

Saturated clay settles slowly because water has to escape from the pores before the soil skeleton can carry the load. Consolidation theory answers two questions: how much settlement will happen, and how long it will take.

1. The e–log σ′ curve

In an oedometer a small disc of soil is loaded in steps, and each step is usually doubled. Plotting the final void ratio of each step against the logarithm of effective stress gives a flat recompression branch and then a steep virgin compression line. The slopes are Cr and Cc. The kink between them is the preconsolidation pressure σ′p, the largest effective stress the clay remembers.

Settlement of a layer of thickness H follows directly. Where the final stress is above σ′p: ρ = H/(1+e0)·[Cr log(σ′p/σ′0) + Cc log(σ′f/σ′p)]. If the clay stays below σ′p, only the Cr term applies, and settlement is usually several times smaller. This is why σ′p matters more than any other number in the test.

2. How fast: cv and the time factor

Each load step also gives a dial gauge reading against time. Taylor's method plots settlement against √t. The early part is straight, and a second line with 1.15 times its slope cuts the curve at 90 % consolidation (t90). Then cv = 0.848·Hdr²/t90, where Hdr is the drainage path (half the sample height for double drainage).

In the field, time scales with the square of the drainage path. A 10 m clay layer drained top and bottom has Hdr = 5 m. With cv = 2 m²/year, reaching 90 % takes 0.848 × 25 / 2 ≈ 10.6 years. That is too long for most projects.

3. Vertical drains

Prefabricated vertical drains (PVDs) shorten the drainage path from metres to about half the drain spacing, and water flows sideways. Radial consolidation (Barron, Hansbo) is controlled by ch, the drain spacing and the smear around each drain. The combined degree of consolidation is U = 1 − (1 − Uv)(1 − Uh). Try it below by switching the drains on and changing their spacing.