CIVL2410 Chap.13 Consolidation and the rate of settlement
Consolidation and the rate of settlement
The previous chapter said how much the ground settles. This one says when. Load a clay and nothing settles immediately, because water cannot leave: the increment is carried entirely by the pore water as excess pressure, which then bleeds away over months and years, transferring load to the skeleton as it goes.
Terzaghi's theory turns that process into a diffusion equation, and two dimensionless groups reduce every problem to one curve.
What this chapter covers
- 01
Consolidation defined, and the three triggers that cause it
- 02
The three stages, from fully undrained through to fully drained
- 03
Assembling Terzaghi's equation from continuity, Darcy and a compressible skeleton
- 04
The coefficient of consolidation, and the two properties it combines
- 05
Why releasing one assumption turns Laplace into a diffusion equation
- 06
The drainage path length, and the factor of four that hangs on it
- 07
Boundary conditions for one way and two way drainage
- 08
The time factor and the degree of consolidation as two dimensionless groups
- 09
Reading the master curve, and why the last few percent take so long
- 10
Root time fitting for the coefficient, and the permeability that falls out of it
- 11
The explicit finite difference form and its stability limit
- 12
Vertical drains, preloading and secondary compression
Scaling a laboratory result to a field layer
- +1The same degree of consolidation means the same time factor, and the same clay means the same coefficient of consolidation, so t over H squared is the same in both.
- +1The specimen drains from both faces, so its drainage path is half its thickness, 0.010 m.
- +1The field layer drains only upward, so its drainage path is the full 4.0 m.
- +1Scale by the square of the path ratio: 9 x (4.0 / 0.010) squared = 9 x 1.6 x 10^5 = 1.44 x 10^6 minutes.
Key terms
- Excess pore pressure
- The pore water pressure above the static value, generated by loading a soil that cannot drain fast enough. Its dissipation is what consolidation consists of.
- Coefficient of consolidation
- Permeability divided by the product of compressibility and the unit weight of water. It compares how fast water can leave with how much has to be expelled, and has units of area over time.
- Drainage path length
- The longest distance water must travel to reach a draining boundary. It is half the layer for two way drainage and the whole layer for one way, and it enters the time factor squared.
- Time factor
- The dimensionless group formed from the coefficient of consolidation, the elapsed time and the square of the drainage path. One curve of degree of consolidation against it serves every layer, every clay and every load.
- Degree of consolidation
- The proportion of the final settlement achieved so far. It says nothing about the magnitude of that final settlement, which is a separate calculation.
- Vertical drains
- Sand or prefabricated band drains installed on a close grid to shorten the drainage path, converting slow vertical drainage into fast radial drainage toward the nearest drain.
- Preloading
- Applying a temporary surcharge larger than the final load so that most settlement happens before construction and the soil is left overconsolidated relative to the real load.
Consolidation and the rate of settlement FAQ
Why does time scale with the square of the drainage path?
Because consolidation is a diffusion process rather than a flow at constant speed. Water near a draining boundary leaves quickly, but water in the middle of a layer must travel through soil whose own pore pressure is still elevated, so the driving gradient falls as the front advances. Doubling the distance therefore both doubles the journey and halves the average gradient driving it, and the two effects multiply.
It is also the reason vertical drains are so effective: cutting a nine metre path to one metre is roughly two orders of magnitude in time.
What does the theory not predict?
Secondary compression. Terzaghi's theory describes primary consolidation, the settlement caused by excess pore pressure dissipating, and it is finished when that pressure has gone. Real soils, particularly organic ones, continue to compress afterwards under constant effective stress, and nothing in the time factor anticipates it.
When a monitored settlement will not stop long after the predicted primary period, secondary compression is the usual explanation and it has to be estimated separately.
Can a consolidation test give a permeability?
Yes, and it is often the only practical route for a clay. The coefficient of consolidation obtained by root time fitting, multiplied by the compressibility from the same load increment and by the unit weight of water, returns the permeability at the stress level the soil will actually experience.
The limitation is that both parameters are assumed constant through the increment, so it is only reasonable if the increment is modest.
Exam move
Keep the two halves of a settlement question separate in your head: the magnitude comes from the compression parameters and the stress history, and the fraction achieved comes from the coefficient of consolidation, the drainage path and the time. They are multiplied only at the end, which also means an error in one does not contaminate the other and each can be checked alone.
Rehearse the drainage path decision until it is instinctive, since it is the input this topic most often loses. When a question offers a remedy for a slow site, ask what it does to the drainage path: only that changes the timescale, while staged construction buys stability instead.
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