Consolidation*
Consolidation is the settlement that occurs over time in fine grained soils. The amount of settlement is pro
strain caused by variation in the effective stress. The rate of settlement is a function of the soil type, the ge
consolidation, the length of the drainage path) and a mathematical solution between a time factor and the
occurred.
AMOUNT OF CONSOLIDATION - SETTLEMENT
The clay layer in Fig. 1 is shown as a phase diagram. If the total, solid and void volumes are divided by a
respective heights are determined. The void ratio of the soil is found by dividing the height of void by the
initial height of clay can be directly related to (1+eo).
Figure 1 - Clay Layer and Settlement Calculation
The volume of solid remains constant in the soil profile. Any change in height in the soil is equal to the ch
change in height of voids divided by the height of solids produces a change in void ratio. The strain that o
change in height divided by the original height, or
.
Finally, the change in height (or the settlement) is determined by
.
Note, H is the full height of clay layer.
Soil is an engineering material, that is, when the state of stress on the soil is changed, it undergoes strain.
the stress-strain curve is not linear but is logarithmic.
The stress-strain curve is determined in the laboratory. An undisturbed sample is taken from around the ce
is trimmed and placed in a device known as a consolidometer, shown in Fig. 2.
Figure 2 - Consolidometer
As the load, P, is increased, the void ratio of the soil decreases. For a soil which is being loaded for the fir
strain relationship is a curve while the log effective stress vs e curve is a straight line (Fig. 3). The void ra
effective stress can easily be determined from the curve. An example how this data is used is given in the
Figure 3 - Void Ratio versus Effective Stress Curve (e-log p)
Steps in Determining the Settlement in a Soil
1) Determine the initial effective stress. The effective stress is usually determined in the middle of the cla
2) Find the corresponding void ratio, eo from the e-log p curve.
eo = 0.870
3) Determine the final effective stress.
4) Find the final void ratio and change in void ratio.
5) Determine the settlement.
Is this value large or small? It depends on what is causing the settlement.
RATE OF CONSOLIDATION
When the soil is first loaded, it does not deform instantaneously. The void ratio remains constant indicatin
constant. However, because the total stress has changed, the water pressure must change by the same amo
or
.
The water pressure in the soil increases the total head, causing the water to flow out of the void space in th
decreases and eventually reaches zero. This causes the effective stress to increase until it finally reaches it
the settlement determined before.
The water flow out of the soil is described by the consolidation equation,
which relates the change of water pressure in space to the change in water pressure with time. The coeffic
hydraulic conductivity to the compressibility of the soil. It is equal to
where av is the coefficient of compressibility
, the slope of the void ratio vs. effective stress curve.
The change in water pressure which causes the settlement can be related to the Percent Consolidation, U,
where H is the final settlement just determined and Ht is the settlement occurring at time t. For examp
zero and U is zero. At long times, Ht approaches H and U approaches 100%. U can also be associated
given time.
A solution to the consolidation equation which gives the time to reach a given Percent Consolidation tU is
where cv is the coefficient of consolidation, H* is the length of the longest drainage path that a particle of
Factor which is related to the Percent Consolidation, U. The table below gives this relationship.
U (%)
U (%)
0
0
60
0.287
10
0.008
65
0.342
20
0.031
70
0.403
30
0.071
75
0.478
35
0.096
80
0.567
40
0.126
85
0.684
45
0.159
90
0.848
50
0.197
95
1.127
55
0.238
100
This table holds true as long as the initial change in water pressure with depth is described by a straight lin
which a uniform surface loading is applied or there is a change in water pressure at the clay boundary.
The length of the longest drainage path H* is the longest distance that a particle must travel to a drainage
D flow and H* can be determined by dividing the total height of the clay H by the number of drainage fac
.
These are shown in the two examples:
Single Drainage
Double Drainage
The coefficient of consolidation cv is a soil property which is determined from the same consolidation tes
it has the interesting units of [L2/t].
Example:
Using the same soil as before:
Assume single drainage and
Find: t50 at U = 50%.
From the table, at U = 50%, TU = 0.19
and
* from ( http://wwweng.uwyo.edu/classes/fa2007/ce3600/6_consolidation/consol.htm)