Oedometer Consolidation Test

Theory: Consolidation

How the oedometer test measures the soil's compressibility, how the preconsolidation stress and the compression indices are found, and how the readings with time give the coefficient of consolidation.

The test

An undisturbed specimen is confined in a rigid ring, between porous stones at the top and bottom, and loaded vertically in stages, usually doubling the stress each time. In each stage the height is read on the dial over time, for about 24 hours or until primary consolidation ends; the specimen may then be unloaded, also in stages.

With no lateral strain, every change of height is a change in the volume of the voids. The height of the solids stays fixed and gives the void ratio at each height:

H_s = \frac{M_s}{G_s\, \rho_w\, A}

M_s: dry mass · G_s: specific gravity of the solids · A: ring area · H: height at the end of the stage

Compressibility

On the e–log σ′ plot the virgin compression stretch is nearly straight, its slope the compression index; before it, in recompression, and in unloading, the curve is much flatter.

C_c = -\frac{\Delta e}{\Delta \log \sigma'}

C_c: compression index, from the virgin line · C_s: swelling index, from the largest stage to the last unloading

a_v = -\frac{\Delta e}{\Delta \sigma'}

a_v: coefficient of compressibility · m_v: coefficient of volume compressibility · e_i: void ratio at the start of the stage

Preconsolidation stress

The preconsolidation stress, σ′_p, is the largest effective stress the soil has borne; it marks the change from recompression to virgin compression. With the in situ effective stress it gives the overconsolidation ratio, OCR = σ′_p / σ′_v0.

Casagrande (1936): at the point of greatest curvature, draw a horizontal and the tangent to the curve; the bisector of the angle between them meets the extended virgin line at σ′_p.
Pacheco Silva (1970): extend the virgin line to the horizontal through e₀; from there drop a vertical to the curve and, from that point, run a horizontal to the virgin line. The abscissa where they meet is σ′_p.

Pacheco Silva's construction depends neither on the chart's scales nor on finding the greatest curvature, which is why it's the most used in Brazil. Sample disturbance rounds the curve and lowers σ′_p by both methods.

Coefficient of consolidation

By Terzaghi's theory, a stage's average degree of consolidation depends only on the time factor. Fitting the theoretical curve to the readings gives the time to a degree of consolidation and, from it, c_v:

c_v = \frac{T\, H_d^2}{t}

T: time factor · H_d: drainage path, half the stage's mean height with double drainage · t: time

Casagrande (log t): the corrected start d₀ comes from the initial parabola, adding to the reading at t its difference from the reading at 4t; the end of primary, d₁₀₀, where the tangent at the steepest stretch meets the secondary compression line. With t₅₀ at the reading halfway, c_v = 0.197 H_d² / t₅₀.
Taylor (√t): a line through the first readings gives d₀; another, with abscissas 15% larger, cuts the curve at t₉₀. Then c_v = 0.848 H_d² / t₉₀.

C_\alpha = \frac{\Delta e}{\Delta \log t}

C_α: secondary compression index, from the final line · k: coefficient of permeability

Limitations

The constructions are automatic and depend on how dense the readings are; check on the chart that the lines sit on the right stretches, and adjust the virgin line points or the greatest curvature if needed.
Terzaghi's theory leaves out secondary compression, which overlaps the end of primary in organic and soft clays.
Laboratory c_v often underestimates the field value, where sand lenses and horizontal flow speed up consolidation.

References

ABNT NBR 16853. Solo — Ensaio de adensamento unidimensional. Rio de Janeiro: ABNT, 2020.
ASTM D2435/D2435M. Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading. West Conshohocken: ASTM International.
Casagrande, A. The determination of the pre-consolidation load and its practical significance. In: International Conference on Soil Mechanics and Foundation Engineering, 1., 1936, Cambridge. Proceedings, v. 3, p. 60–64.
Pacheco Silva, F. Uma nova construção gráfica para determinação da pressão de pré-adensamento de uma amostra de solo. In: Congresso Brasileiro de Mecânica dos Solos e Engenharia de Fundações, 4., 1970, Rio de Janeiro. Anais, v. 2, t. 1, p. 225–232.
Taylor, D. W. Fundamentals of Soil Mechanics. New York: Wiley, 1948.
Das, B. M.; Sobhan, K. Principles of Geotechnical Engineering. 9th ed. Boston: Cengage, 2018.

Enter the specimen's data, the stress and final reading of each load stage and the readings with time to get the e–log σ′ curve, the compression and swelling indices, the preconsolidation stress by Casagrande and by Pacheco Silva and, for each stage, the coefficient of consolidation by Casagrande's (log t) and Taylor's (√t) methods, with m_v and the permeability.

e₀: 1.300
C_c: 0.549
C_s: 0.060
σ′_p Casagrande: 138 kPa
σ′_p Pacheco Silva: 127 kPa
OCR (Pacheco Silva): 1.95

Use in Settlement

Specimen

Initial height, H₀mmDiametermmG_sDry mass, M_sgInitial readingmmIn situ σ′_v0kPaPoints on the virgin lineσ′ of greatest curvaturekPa

H_s = 8.696 mm · e₀ = 1.300

The initial reading is the dial's before the first stage. With the in situ σ′_v0, the page gives the OCR; Casagrande's greatest curvature is found on the curve when left blank.

Load stages

#	σ′ (kPa)	Final reading (mm)	e
1			1.288
2			1.273
3			1.255
4			1.218
5			1.108
6			0.950
7			0.786
8			0.620
9			0.656
10			0.692
11			0.729

A stress below the one before is an unloading. With the final reading blank, the stage's last reading with time is used.

Readings with time

Stage 5 · 200 kPa

#	Time (min)	Reading (mm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

The time since the load was applied and the dial reading. Enter moves down a row and adds one past the last; blank rows are ignored. You can paste both columns from a spreadsheet into the time.

Drainage at the top and bottom, the drainage path being half the stage's mean height. Readings grow as the specimen compresses. The graphical constructions are made automatically on the points entered and should be checked on the chart; Casagrande's depends on the scales and is drawn in the chart's proportions.