CIVL2410 Chap.11 Compressibility, stress history and settlement
Compressibility, stress history and settlement
This chapter asks what happens when the effective stress changes. Soil is not elastic: loading it beyond anything it has carried before produces large and largely irrecoverable compression, while reloading within its past experience produces far less. The dividing line is the largest effective stress in the soil's history, and locating that line is half of what a compressibility test is for.
The other half is the pair of slopes either side of it.
What this chapter covers
- 01
The oedometer, and why a rigid ring reproduces a field boundary condition
- 02
Why the applied stress in a drained oedometer is the effective stress
- 03
Plotting void ratio against the logarithm of effective stress, and what the corner is
- 04
Compression and recompression indices as the two slopes
- 05
Coefficient of volume compressibility as a secant, and the constrained modulus
- 06
Particle rearrangement, interparticle friction and crushing at the grain scale
- 07
Overconsolidation ratio, its categories and its geological and human causes
- 08
The two stage rule when the final stress crosses the preconsolidation pressure
- 09
Deriving the settlement relation from the constancy of the solid volume
- 10
When one dimensional analysis is legitimate, and summing over sublayers
- 11
The coefficient of earth pressure at rest, from Poisson's ratio and from Jaky
An overconsolidated clay pushed past its memory
- +1The final effective stress is 80 + 120 = 200 kPa, which exceeds the preconsolidation pressure of 140 kPa, so the calculation runs in two stages.
- +1Recompression from 80 to 140 kPa uses the flat slope: 0.05 x log10(140 / 80) = 0.05 x 0.243 = 0.0122.
- +1Virgin compression from 140 to 200 kPa uses the steep slope: 0.30 x log10(200 / 140) = 0.30 x 0.155 = 0.0465.
- +1The total change in void ratio is 0.0122 + 0.0465 = 0.0587.
- +1Settlement is that change times the thickness over one plus the initial void ratio: 0.0587 x 4.0 / 1.80 = 0.130 m.
Key terms
- Oedometer
- A cell in which a disc of soil is compressed vertically inside a rigid ring between porous stones, so vertical strain is allowed and lateral strain is prevented.
- Compression index
- The slope of the virgin compression line on a plot of void ratio against the logarithm of effective stress. Higher values mean a more compressible soil.
- Recompression index
- The slope of the reload or swelling line, usually a tenth to a fifth of the compression index. It governs settlement while the soil stays inside its stress history.
- Overconsolidation ratio
- The preconsolidation pressure divided by the current effective stress. A value of one means normally consolidated; higher values mean the soil has carried more in the past than it does now.
- Coefficient of volume compressibility
- The volumetric strain produced per unit increase in effective stress over a stated stress range. It is a secant rather than a constant, so it has to be quoted with the range it was measured in.
- Coefficient of earth pressure at rest
- The ratio of horizontal to vertical effective stress in ground that has not strained laterally. It runs about 0.4 to 0.7 in normally consolidated clays and can exceed one in heavily overconsolidated soils.
Compressibility, stress history and settlement FAQ
Why is the stress axis logarithmic?
Because it turns a featureless curve into two straight lines. Plotted against stress directly, the compression response is a smooth bend with no constant slope and no distinguishing feature. Plotted against the logarithm, the same data become a flat recompression line and a steeper virgin line meeting at a corner.
Straight lines can each be described by a single number, which is what makes the compression and recompression indices possible at all, and the corner becomes locatable by eye rather than by judgement.
Which parameter should I use, the index or the compressibility coefficient?
Either, provided the arithmetic is consistent with the choice. The indices go with a logarithmic stress change and are the natural parameters when the increment is large or when stress history matters, since they carry the corner in the curve. The coefficient of volume compressibility goes with a linear stress change and suits small increments, over which the curve is nearly straight. Both are on the data sheet.
What is not acceptable is carrying a compressibility measured over one stress range into a calculation over a much larger one, because that overpredicts the settlement.
Exam move
The decision that dominates this topic is where the final effective stress sits relative to the preconsolidation pressure, so make that comparison the first line of every answer. Learn the derivation of the settlement relation as one idea, that the solid volume does not change, because a question asking where it comes from wants that sentence and not the algebra.
When a profile has several layers, compute the stress change at the centre of each and sum the settlements rather than averaging the parameters, since the relation is nonlinear in stress. Finally, be honest about accuracy: predictions of this kind carry an uncertainty of tens of percent, which is a reason to test properly and monitor, not a reason to skip the calculation.
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