Hello this is Professor Kitch. Welcome to this webcast which is the first
of two on section 10.5. This webcast covers the consolidation lab test
After this webcast, you should be able to describe the lab consolidation test
Explain why we generally use a semi-log plot of strain versus the log of effective stress
as the stress-strain curve for soils, rather than the arithmetic stress-strain curve used
for nearly all other materials. Once you have the strain versus log-sigma-prime
curve you should be able to identify the recompression curve, virgin curve and rebound curve
You need to be able to derive the relationship between strain and change in void ratio and
explain why we can plot consolidation data as either strain or void ratio versus the
log of effective stress You should be able to define the preconsolidation
stress and explain why we always see one in our laboratory data
And finally, you should be able to perform Casagrade method to estimate the preconsolidation
stress from lab data We discussed the basic consolidation process
in the previous section. Specifically we discussed how a change in total stress immediately generates
an excess pore pressure and that as that excess pore pressure dissipates, the soil consolidates
and the stress is transferred from pore pressure to the soil skeleton in the form of effective
stress. We're now starting sections that will allow
you to compute the magnitude of consolidation settlement. In understanding the magnitude
of consolidation settlement, it helps to start off by looking at the 1 dimensional consolidation
test. In the field, if we have a compressible layer,
shown here with a thickness of H-naught. And that layer is covered by a wide areal
fill we'll have one dimensional consolidation
and experience a consolidation settlement of delta-c
To understand what's happening in the field we can take a sample of soil from location
A, transport it to the lab, and put a specimen from that sample in a device that allows for
only one dimensional consolidation. We can then place a load, P, on the specimen
and it will consolidate one dimensionally. If we measure what happens in the lab, we
should be able to use that data to predict the field settlement.
This test is called the one dimensional consolidation test, or the oedometer test.
Three are two main types of consolidometers, the floating ring and the fixed ring. The
only one we'll discuss here is the floating ring consolidometer,
which is the most common type. In the center is a short cylindrical soil
specimen about the size and shape of a hockey puck.
It's usually about three quarters to one inch thick and 3 to 4 inches in diameter
The specimen is contained in a confining ring which is made of metal, is very stiff compared
to the specimen, and therefore prevents any lateral strain, thereby ensuring that we have
one dimensional consolidation. There are porous stones placed on the top
and the bottom of the specimen to allow drainage of pore water out of the specimen.
With porous stone on the top and bottom, the water can drain out from the center of the
specimen in both directions. A loading cap is place on top to distribute
applied forces over the entire area of the specimen
And a dial gage or digital device is used to measure the vertical displacement.
We place a load, P, on the top of the specimen and the loading cap distributes the load evenly
over the specimen The final effective stress that is applied,
is then P over A minus the pore pressure, u.
Since the specimen is so thin the average head of pressure is an inch or less
so we can assume the pore pressure is zero and the final effective stress is just equal
to P over A When the load P is placed on the cap, the
specimen starts to consolidate and we measure the vertical displacement, delta-z, versus
time When the sample is finished consolidating,
we can measure the final vertical displacement, delta-zf
We can then compute the vertical strain as the change in height over the initial height
or delta-z over H-naught We can then incrementally increase the vertical
stress several times, measuring the vertical deflection with each load.
From the data measured from each load increment we can create a table of vertical effective
stress versus vertical strain. Once we have our table of strain versus effective
stress, we can plot a stress-strain curve for our soil.
You're probably used to seeing such data plotted as stress versus-strain, but in geotechnical
engineering we generally plot the data as strain versus stress. We also generally plot
stress increasing downward because when soils compress they move down.
As you can see from the curve shown, soil stress-strain behavior is highly non-linear.
The portion of the curve from A to B to C is the initial loading curve for the soil.
Notice that the amount of strain from zero to 200
is more than that from 200 to 400 which is more than that from 400 to 600.
This indicates that the soil is always getting stiffer as it consolidates. This makes since.
As the soil consolidates, the soil particles get more and more tightly packed and as a
result, the soil skeleton gets stiffer and stiffer.
Interestingly, if we plot the strain versus the log of effective stress, the stress-strain
curve becomes much simpler as shown on the right. In this semi-log space, the curve is
very close to being composed of three straight lines
We call the portion from the beginning of the plot to the first brake, from A to B,
the recompression curve. The next portion of the curve from a bit past
B to C is called the virgin curve. and the final portion, which occurs during
unloading of the specimen, is called the rebound curve.
It may not be readily apparent, but we can also plot the curves as void ratio as a function
of effective stress rather than strain versus effective stress. Notice that the void ratio
decreases as the soil consolidates, which makes sense since the void volume decreases
as the soil skeleton compresses. The deformation of the soil during consolidation,
can be expressed either as strain or a change in void ratio.
Let's use our phase diagram to determine the relationship between void ratio change
and strain. On the left we have our initial conditions.
For convenience, we'll assume the volume of the voids is 1 unit.
Recalling that the void ratio is the equal to the volume of voids divided by the volume
of solids When the volume of solids is equal to 1, the
volume of the voids will simply be equal to the void ratio, e. In this case it will be
e-naught, the initial void ratio. Now, after loading and consolidation, there
will be a change in volume of the soils, and all of the change will be in the void space,
and therefore the change in volume will be equal to delta-e.
If our soil is in one dimensional compression, then the change in void ratio must come only
from vertical compression Therefore, we can write that the vertical
strain, epsilon-z will be equal to the change in length of our
soil element over the original length or delta-l over l-naught
If we look at the initial phase diagram on the left, we'll see that the original length
of the element is 1 plus e-naught. And from the phase diagram on the right, we
see that the change in length is delta-e Therefore the vertical strain epsilon-z is
equal to delta-e over one plus e-naught. That's why we can plot our consolidation curve either
as either strain versus log-sigma-prime, or void ratio versus log-sigma-prime. Epsilon-z
and delta-e are directly proportional to one another and the proportionality constant is
1 over 1 plus e-naught. So let's look at how the stress-strain curve
for soils gets its characteristic shape in semi-log space
To do this let's go back a few hundred thousand year, just a few minutes in geologic time,
and consider a point A just below the bottom of a Pleistocene ocean during a depositional
period. At this point the soil is under some very
small effective stress shown as point 1 on our semi-log stress-strain curve.
As the deposition continues the effective stress increases, the soil at point A consolidates
and undergoes strain. On our strain versus log effective stress plot it travels alone
a line from point 1 to point 2. If the deposition continued, the stress path
of the soil would continue down the dotted line shown. However, it doesn't. The deposition
at this location stops, and we enter the Holocene epoch.
Neanderthals go extinct, homo sapiens get bigger brains, the stone age gives way to
the bronze age then the iron age. Finally, the industrial revolution happens
along, we start spewing billions of tons of CO2 and other pollutants into the atmosphere.
A English teacher, a history teacher, and writer, open a coffee house in Seattle featuring
a two tailed mermaid in their logo. Three decades later barista turned Starbucks
CEO Howard Schultz, shows up at the empty lot above point A and decides to build yet
another Starbucks because the nearest one is over 200 feet away.
Schultz hires your geotech firm to do a site investigation.
Having read about the Kansai airport and knowing settlement might be an issue, you make a boring
at the site and take an undisturbed sample back to the
lab. In the process of taking the sample, the soil
is unloaded and it follows the stress path form point 2 to point 3. Notice that the soil
does not travel back along the original compression line from point 1 to point 2.
This is because soil is not elastic and undergoes unrecoverable plastic strain during consolidation.
So in unloading it's stiffer than in loading. We now take a specimen from our field sample
and place it in a consolidometer and perform a 1-D consolidation test.
During the initial part of the test, the stress path for the soil closely follows the rebound
curve from point 3 to 4. But when it gets near the original consolidation curve at point
4, the stress path turns down and follows the original depositional consolidation curve
or virgin curve to point 5 The consolidation test continues with unloading
during which the soil travels along the rebound curve from point 5 to 6.
However, realize that the only information you will have is the laboratory strain versus
log effective stress curve shown here. Due to plastic strain during consolidation,
it will have a recompression curve, a virgin curve,
and rebound curve. And the point where the recompression and
virgin curves meet is the preconsolidation stress, sigma-c-prime.
If we have a high quality specimen our testing is done very carefully, we'll get a strain
versus log effective stress plot with distinct breaks between different segments of the curve.
And it will be very easy to identify the recompression curve, the virgin curve,
and find the preconsolidation stress. However, we don't always have a high quality
sample. As samples get more disturbed due to poor sampling techniques or poor handling,
the lab test specimen quality is lower and the strain versus log effective stress plots
tend to soften and don't show a clear break between recompression and virgin loading.
This can make it difficult or impossible to determine the preconsolidation stress accurately.
If the specimen is of relatively good quality and tested properly, but doesn't show a
distinct preconsolidation point, as shown here,
We can use the method developed by Casagrande to estimate the preconsolidation stress.
The first step in the Casagrande method is to locate the point of maximum curvature on
the strain versus log effective stress plot. From this point you then draw a horizontal
line and a line tangent to the lab data curve
you then determine the angle between these two lines
and draw a third line bisecting that angle. Next you go to the lower end of the virgin
curve and draw a line tangent to the low end of the curve.
Now locate the point where this extension of the virgin curve intersects the bisector
line. That point is the location of the preconsolidation
stress. This method is based on Cassagrande's considerable
experience, but there's no theory behind it. It is however, a consistent method and
if followed carefully, will ensure some consistency in estimating the preconsolidation stress.
However if the specimen is highly disturbed such as the one show in red, there is now
way of accurately estimating the preconsolidation stress.
Schmertmann extended Cassagrande's method into a procedure to reconstruct an estimate
of the field compression curve from a moderately disturbed laboratory curve. This figure shows
a typical lab data curve and the corresponding reconstructed field curve using Schmermann�s
method. The procedures are outlined on pages 439 & 440 of your text.
It is important to note that the reconstructed field curve lies outside of the measured lab
data and therefore constitutes an extrapolation of the lab data. Extrapolation is always a
dicey endeavor and the accuracy of curves reconstructed by this method is questionable.
The best approach is to get high quality samples and use good lab techniques so you get a lab
curve that clearly show the preconsolidation stress and require little correction.
So let's summarize Soils have nonlinear stress-strain curves
and their stiffness increases during consolidation. We generally plot these curves as strain versus
the log of effective stress or void ratio versus the log of effective stress.
Plotting in this semi-log space makes the curves more linear
On unloading soil always exhibits plastic strain and unloads on a curve stiffer than
the loading curve We use the laboratory consolidation test to
determine our stress-strain curve Lab tests will always show both a recompression
and virgin curve, because the field sample is unloaded during the sampling process
The point where the recompression and virgin curves meet is the preconsolidation stress
and it represents the greatest effective stress the soil has ever experienced.
If we have high quality tests with high quality specimens, we can easily draw tangents to
the recompression and virgin curves and locate the preconsolidation stress.
When the lab data are moderately disturbed, you should use Cassagrande's method as a
consistent way to estimate the preconsolidation stress.
And finally, we can use Schmertmann's method to reconstruct field compression curves for
lab tests on disturbed samples. However, it's better to get a high quality sample and generate
a high quality lab curve.