Soil Mechanics / Laboratory and field testing

Consolidation and permeability tests

The oedometer curve and reading Cc, Cr and σ′c; measuring permeability.

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Why this matters

Settlement and its rate come from the oedometer (one-dimensional consolidation) test, and drainage from permeability tests. Reading the oedometer curve — extracting the compression indices and the preconsolidation stress — is one of the most common interpretation tasks in practice, and it is where the numbers for Module 10 come from.

In the oedometer a disc of clay is confined in a stiff ring (no lateral strain — exactly the 1-D condition of Module 10) and loaded in steps, each held until consolidation is complete. Two things are recorded: the final void ratio at each load, giving the e–log σ′ curve (from which $C_c$ , $C_r$ and $\sigma'_c$ come), and the time history of each step, giving $c_v$ (from which the rate comes).

Compression index from the curve

C_c = \dfrac{e_1 - e_2}{\log_{10}(\sigma'_2/\sigma'_1)}

What it calculates: the slope of the virgin line between two points on the e–log σ′ plot

C_c: compression index (use Cr on the recompression line)
$e_1,\ e_2$: void ratios at the two stresses
$\sigma'_1,\ \sigma'_2$: the two effective stresses (kPa)

In plain terms: Read Cc from two points on the steep virgin portion, Cr from the flat recompression portion. The preconsolidation stress σ′c is located at the break between them (Casagrande's construction).

Try it

Oedometer curve interpreter

Read the compression index off the virgin line, and see the preconsolidation stress at the break in the curve.

Soil

Upper reading point (σ′)1200 kPa

Anchor point: e=0.86 @ 150 kPa
Upper point: e=0.59 @ 1200 kPa
Compression index Cc: 0.299
Recompression Cr: 0.051
Preconsolidation σ′c: 150 kPa

How to read it

Cc is the slope of the steep virgin line; Cr the flat recompression line.
σ′c is prescribed at the break in this idealised curve. A Casagrande construction needs a tangent, horizontal and angle bisector, which are not shown here.
The same Cc then drives the settlement equation in Module 10.

Between 150 and 1200 kPa on the virgin line, Cc = 0.299. Below σ′c ≈ 150 kPa the curve is far flatter (Cr ≈ 0.051) — an overconsolidated clay settles little until the load passes σ′c.

Worked example

Reading Cc from an oedometer curve

Given

On the virgin line: at σ′ = 100 kPa, e = 0.92
At σ′ = 400 kPa, e = 0.75

Find

The compression index Cc.

Assumptions

Both points lie on the straight virgin (normally consolidated) portion of the curve.

Practice

On the virgin line of an oedometer curve, e = 1.05 at σ′ = 50 kPa and e = 0.90 at σ′ = 200 kPa. What is the compression index Cc?

Permeability is measured directly in a permeameter — constant-head for coarse soils, falling-head for finer ones (Module 7) — or inferred indirectly from the rate of the oedometer test through $c_v = k/(m_v\gamma_w)$ . In the field it is measured by pumping or in-situ tests. Because $k$ spans many orders of magnitude and is dominated by fabric and fissures, a single laboratory value on a small specimen often badly underestimates the mass permeability of the ground.

Summary

The oedometer imposes 1-D consolidation; its e–log σ′ curve gives Cc, Cr and σ′c, its time curves give cv.
Cc = (e1 − e2)/log10(σ′2/σ′1), read on the virgin line; Cr on the recompression line; σ′c at the break.
Permeability comes from permeameters (constant/falling head) or indirectly from cv.
Small specimens can badly underestimate mass permeability because fabric and fissures dominate it.