Given the characteristic information from the two curves, it is now possible to
proceed with the calculations. The average drainage height,
, is computed using
Equation 17.18, with the root time value of
from the log construction.
The coeffi cient of consolidation based on the Log Time fi tting method is calculated
using Equation 17.21:
time to 50 percent consolidation for the increment (s)
time factor corresponding to 50 percent consolidation
The Log Time method is much more rigorous than the Root Time method because
it places more requirements on the shape of the consolidation curve. If a curve results
in the characteristic S-shape, then it is more likely that the material is conforming to the
theory. The price for this additional level of confi dence is time. Collecting enough infor-
mation to establish the linear secondary slope adds signifi cantly to the test duration.
Even on ideally shaped curves, the Root Time method yields a higher value of the
coeffi cient of consolidation in laboratory scale tests. The coeffi cient of consolidation
determined by the Square Root of Time method is usually about 2
/- 0.5 times the
value determined by the Log Time method. (Ladd, 1973, as appearing in Ladd et al.,
1977) The reason for this discrepancy is still a topic for research, but is likely due to
a combination of scale effects and the infl uence of secondary compression. In theory,
there is no end to primary consolidation. The log time construction generally results in a
slow transition into secondary compression, introducing concern as to what time to use
as the end of primary consolidation. For consistency with the interpretation of
time for the end of primary should be taken at the intersection point, as shown in
the fi gure.
In many situations, it is impossible to determine the end of primary consolidation for
a stress increment. This will happen in the consolidation test when using small stress
increments to better defi ne the compression behavior, and is extremely common when
consolidating test specimens in shear tests. The Root Time method will provide an esti-
mate of the end of primary consolidation, but there is no way to tell if this overestimates
or underestimates the time required for full pore pressure dissipation. The 3-t method
provides an effective solution to this dilemma. The strain data are plotted on a log time
scale and a line is drawn through the steepest portion of the data. A parallel line is drawn
shifted by a factor of three larger in time. The intersection of this shifted line and the
test data is taken as the strain at the end of primary consolidation. This method should
not be used to compute the coeffi cient of consolidation, but does provide a predictive
method to decide when to increment the load, to shear a test specimen, or obtain a strain
value. The method is illustrated in Figure 17.9.
Rate of Secondary
The rate of secondary compression is determined as the slope of the long-term portion
of the time curve for an increment, as measured over a log cycle of time past the end of
primary consolidation. An example of the determination of the coeffi cient of secondary
compression is included in the Log Time interpretation of the time curve, as shown in
Figure 17.8. The transition between primary consolidation and secondary compression
is often gradual. Data should be available for at least one log cycle of time beyond
the end of primary before accepting the slope as the rate of secondary compression.
The rate of secondary compression will be overestimated if interpreted too early on the
(a) Theoretical curve
Fig. 10.7 The square root of time ‘fitting’ method.
(a) Theoretical curve
- (b) Establishment oftg0
Fig. 10.7 The square root of time ‘fitting’ method.
of suitability. A consolidation test sample is always drained on both surfaces and in the formula H is taken as half the mean thickness of the sample for the pressure range considered. At first glance it would seem that cv could not possibly be constant, even for a fairly small pressure range, because as the effective stress is increased the void ratio decreases and both k and mv decrease rapidly. However, the ratio of k/mv remains sensibly constant over a large range of pressure so it is justifiable to assume that cv is in fact constant.
10.7 Determination of the permeability coefficient from the consolidation test
Having established cv, k can be obtained from the formula k = Cvmv7w. It should be noted that since the mean thickness of the sample is used to determine cv, mv should be taken as a/(l + e) where e is the mean void ratio over the appropriate pressure range.
10.8 Determination of the consolidation coefficient from the triaxial test
It is possible to determine the cv value of a soil from the consolidation part of the consolidated undrained triaxial test. In this case the consolidation is three-dimensional and the value of cv obtained is greater than would be the case if the soil were tested in the oedometer. Filter paper drains are usually placed around the sample to create radial drainage so that the time for consolidation is reduced. The effect of three-dimensional drainage is allowed for in the calculation for cv, but the value obtained is not usually dependable as it is related to the relative permeabilities of the soil and the filter paper (Rowe, 1959).
The time taken for consolidation to occur in the triaxial test generally gives a good indication of the necessary rate of strain for the undrained shear part of the test, but it is not advisable to use this time to determine cv unless there are no filter drains.
The consolidation characteristics of a partially saturated soil are best obtained from the triaxial test, which can give the initial pore water pressures and the volume change under undrained conditions. Having applied the cell pressure and noted these readings, the pore pressures within the sample are allowed to dissipate while further pore pressure measurements are taken; the accuracy of the results obtained is much greater than with the consolidation test as the difficulty of fitting the theoretical and test curves when air is present is largely removed. The dissipation test is described by Bishop and Henkel (1962).
Continue reading here: Consolidation during construction
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