Hello this is Professor Kitch.
Welcome to this webcast on section 10.2 through 10.4 which covers the consolidation process
After this webcast, you should be able to describe the three most common process that
can lead to changes in effective stress in the ground
You should be able to define excess pore pressure And for saturated soils, you should be able
to explain how any change in total stress is initially carried by the pore water creating
excess pore pressure.
And finally, you should be able to describe how this excess pore pressure dissipates and
is transferred to effective stress as the soil consolidates.
We learned earlier that consolidation settlement is caused by a change in effective stress.
The soil will start out at some initial effective vertical stress, sigma-prime-z-naught.
A change in vertical effective stress, delta-sigma-prime-z, will be caused by some process
Leading to a final vertical effective stress of sigma-prime-zf
This change in vertical effective stress generates the consolidation process
We will compute the initial vertical effective stress, sigma-prime-z-naught using our standard
techniques for computing geostatic stress.
But how we compute delta-sigma-z-prime will depend on the source of the effective stress
change Remembering our fundament equation that the
effective stress is equal to the total stress minus the pore water pressure, we can see
that the effective stress can be changed by either by changing the total stress or by
changing the pore water pressure.
There are three major sources of effective stress changes
Placement of a fill that covers a large area of the ground surface
Placement of load on a finite sized area such as square or rectangular footing
And changes in the groundwater table The first two sources change effective stress
by changing the total stress The third source uses a change in pore water
pressure to change the effective stress Let's look at how fill placement can change
effective stress.
We'll start out with a layer of compressible soil with thickness H-naught and unit weight
gamma.
The water table is at the ground surface.
If we consider point-A at a depth z below the ground surface.
The initial vertical stress will be the total stress, sigma-z, minus the pore pressure,
u.
Or in this case gamma times z minus gamma-water times z
Now we place a wide fill on the soil, with thickness H-fill and unit weight gamma-fill
By wide we mean that the width of the fill, W, is much greater than the thickness of the
soil layer, H-naught.
In this case the change in stress will be the same anywhere under the fill and this
will be a one-dimensional problem.
To compute the change in vertical stress, we only need to realize that this fill now
looks like just another soil layer and the change in vertical stress is simply the geostatic
stress due to the fill layer.
And the change in vertical stress, delta-sigma-z-prime is gamma-fill times H-fill
The final vertical effective stress at A will be gamma times z minus gamma-water times z
plus gamma-fill times H-fill Example 10.1 in your text illustrates this
concept for a slightly more complicated situation.
Now would be a good time to pause the webcast and work through this example problem.
Now let's look at stress changes due to finite sized loads
Our initial conditions are as with the previous example.
We're considering a point-A at a depth z below the ground surface.
The initial vertical effective stress will again be gamma times z minus gamma-water times
z But now instead of a wide fill, we'll place
a square footing of width, B, on the ground surface above point A.
The footing will apply a stress, q, to the ground surface and q will be equal to P divided
by B squared.
The change in vertical stress at A will now be equal to the applied stress, q, times I-sub-sigma.
We'll have to use the stress distribution techniques we learned in Chapter 9 to determine
I-sub-sigma.
We can use the chart solution shown here, or one of the equation solutions from Chapter
9.
No matter how we determine I-sub-sigma, the final effective stress at A will be gamma
times z minus gamma-water times z plus q times I-sub-sigma.
Unlike our previous wide fill example, this problem will be three-dimensional and the
change in vertical stress will be different and different points in the soil layer.
Now let's consider the case where the groundwater table changes.
Unlike our previous two examples, in this case the change in effective stress will be
due to the change in pore water pressure rather than a change in total stress.
We'll start with the same soil profile as our previous example.
And the initial effective stress will be the same
Now let's assume the groundwater table in the area permanently drops to some new lower
level at a height z-w above point A.
This could be due to pumping of groundwater from nearby wells, or a change in climate.
Rather than computing the change is effective stress due to the ground water table drop,
it's easier in this case to compute the final vertical effective stress directly, using
geostatic stress principles.
When the water table drops, the unit weight of the soil above the water table will decrease
somewhat, but we'll ignore that effect for this example and assume the unit weight is
the same above and below the groundwater table.
We'll compute the final vertical effectives stress as the total vertical stress, sigma-z,
minus the pore pressure, u.
And at point A the total stress will be gamma times z and the pore pressure will be gamma-water
times z-w.
If we want to know the change in effective stress, delta-sigma-z-prime, we can compute
it as the final vertical effective stress, sigma-zf-prime minus the initial vertical
effective stress sigma-z-naught-prime.
That will expand to the quantity gamma times gamma-z minus gamma-water times z-w, minus
the quantity, gamma times gamma-z minus gamma-water times z.
Which simplifies to gamma-water times the quantity z minus z-w
Which is simply the change in pore water pressure due to the drop in the water table.
So now you know how to compute both the initial vertical effective stress and the final vertical
effective stress at a point due to the most common loading conditions.
Which is to say we know where a soil element starts before consolidation and where it ends
up after consolidation.
Now we need to discuss what actually happens during the consolidation process.
Let's look back at our particulate soil model under the initial vertical effective stress,
sigma-z-naught-prime.
And its phase diagram We then add a change in vertical stress, delta-sigma-z.
It could be due to a wide fill or a finite loaded area like a footing.
Under this additional stress the soil particle rearrange, the soil skeleton compresses to
take on this additional stress.
And there is a decrease in the void volume.
The soil skeleton is now carrying both the initial effective stress and the additional
delta-sigma-z, so the final effective vertical stress, that stress carried by the soil skeleton,
sigma-zf-prime, is sigma-z-naught plus delta sigma-z.
It's very important to understand that the soil skeleton has to compress, has to undergo
some strain, in order to carry this additional stress.
Just like any solid material the additional stress comes with strain.
Now let's consider the same soil element, but this time it's saturated, all the voids
are filled with water.
And this is our phase diagram.
Since the soil is saturated we need to know the pore pressure, so we'll install a pressure
gage in the pore fluid.
And its initial reading will be the static pore pressure, u-zero.
The total stress at this time, sigma-z-naught, is sigma-z-naught-prime plus u-naught.
We again apply a stress increase to the sample, delta-sigma-z.
However, now things are different.
For the soil skeleton to compress and take on the additional stress, the water has to
flow out of the pores.
The problem is this doesn't occurring instantly.
Because of the finite hydraulic conductivity of the soil, it takes some for the water to
flow out of the soil.
So the instant delta-sigma-z is applied the total stress has increased by the same amount.
However, if the soil skeleton hasn't compressed, then it can't have taken on any additional
stress and there is no change in the effective stress.
So where has the addition stress delta-sigma-z gone to?
In order to keep our equation balanced there's only one place for it to go and that's the
pore pressure.
There must be an increase in the pore pressure which we'll call the excess pore pressure,
u-sub-e.
And it should be apparent that u-excess must be equal to delta-sigma-z.
So if we watch our pore pressure gage, it must jump up by u-e the instant the stress
delta-sigma-z is applied.
We call this increase in pore pressure, excess pore pressure, because it is temporary and
will go away as we'll see in just a moment.
Right now we're looking at a point frozen in time, the instant after the additional
stress has been applied.
However, time waits for no student, so we'll turn the clock back on, and as time goes on
after the application of delta-sigma-z, three things happen at the same time.
The soil starts to compress, the pore pressure decreases and as the soil skeleton compresses,
the effective stress increases.
The process continues until the pore pressure has return to the original static pore pressure,
u-naught By this time all the increased stress has
been transferred from pore pressure to effective stress and the final vertical effective stress,
sigma-z-f-prime, is the sum of sigma-z-naught-prime plus delta-sigma-z.
So when a soil is saturated, the consolidation process takes time, just as we saw in the
Kansai airport case history.
Initially when the stress is increases, all the additional stress is taken by the pore
pressure creating an excess pore pressure.
The excess pore pressure forces water out of the soil.
As the water leaves, the soil skeleton starts to compress taking on additional stress.
At the same time the pore pressure is decreasing.
This continues until all the additional stress is transferred from excess pore pressure to
effective stress.
We can also use the piston and spring analogy to explain consolidation.
In this analogy, we have piston and cylinder placed in a large water bath.
The piston has two small holes drilled in it with valves that can open and close.
Under the piston is a spring, and we have a pressure gage to measure the water pressure
in the cylinder In this analogy, the spring represents the
soil skeleton and carries the effective stress and the water inside the cylinder represents
the pore water.
We have a load on the piston which generates our initial conditions.
The total stress is sigma-naught The initial pore pressure is u-naught.
And the initial effective stress being carried by the spring, sigma-naught-prime, will the
sigma-naught minus u-naught.
We add an additional stress to the piston, delta-sigma, but the valves in the piston
are kept closed.
With the valves closed, no water can leave the cylinder so the piston does not move.
The spring cannot compress so the effective stress cannot increase.
Therefore the only way to balance out the increased stress is for an excess pore pressure
to be created.
The magnitude of the excess pore pressure will be equal to the stress increase, delta-sigma.
We then open the valves in the piston allowing water to flow out of the cylinder into the
larger reservoir.
However the holes are very small and restrict the flow, simulating the hydraulic conductivity
of the soil.
As the water slowly leaks out the holes, the pore pressure reduces, the piston moves down
and the spring takes up more stress.
That is stress is being transferred from the pore pressure to the spring.
Since the spring represents the effective stress in the soil skeleton, we see the effective
stress rise.
Eventually the pore pressure returns to u-naught.
All of the stress increase, delta-sigma, has been transferred to the spring, and the final
effective stress, sigma-f-prime, is equal to the initial effective stress plus delta-sigma.
And all the change in stress has been transferred from excess pore pressure to effective stress.
In the field, the process is very similar We have a compressible layer with initial
thickness H-naught At some point A in the soil there is an initial
total vertical stress, sigma-v-naught, pore pressure, u-naught, and effective stress,
sigma-v-naught-prime.
In the field, it takes time to construct the fill and, therefore, the load is applied over
some period of time rather than instantaneously.
Initially, the induced stress change, delta-sigma-v, all goes to excess pore pressure and there
is no change in effective stress.
After the fill is placed, the excess pore pressure starts to dissipate, the effective
vertical stress increases and the fill settles.
The total consolidation settlement is delta-c Let's summarize
Consolidation settlement is a process that starts with a change in total stress.
For a saturated soil with finite hydraulic conductivity, the change in stress must, initially,
be carried by the pore water creating excess pore pressure.
With time, water is forced out of the soil due to excess pore pressure.
As the water leaves, the pore pressure is reduced and the soil compresses.
As the soil compresses the skeleton is able to pick up the additional stress and the effective
stress increases.
In the end all of the increased stress will end up as effective stress.
The soil compressibility and hydraulic conductivity will control how fast the soil consolidates.
Example 10.2 in your text goes through the process of computing change in effective stress
during consolidation for the soil profile shown here.
You should go through this example before class.