Hello this is Professor Kitch.
Welcome to this webcast on section 10.8.
This webcast covers consolidation settlement computations
The first thing we'll cover in this webcast is computing consolidation settlement for
a single soil layer subject to a surcharge load.
That is there is no stress distribution and the change in vertical stress is the same
throughout the soil layer To do this it's critical that you be able
to distinguish between normally consolidated and overconsolidated condition in the field
And finally, you should be able to apply these techniques to multi-layered profiles and deal
with stress changes due either to fill placement or groundwater table changes.
When we place a fill on a compressible soil layer we're applying a change in vertical
stress, delta-sigma-z.
If the fill is wide compared to the soil thickness, then there is no stress distribution and the
change in effective stress everywhere in the soil layer will be the same, delta-sigma-z,
and this will be a one-dimensional problem.
In this case, the soil will consolidate, generating consolidation settlement, delta-c-ultimate
Just as with any engineering material, we compute the deformation as the strain integrated
over the length of the element, in this case epsilon-z dz, integrated from zero to the
thickness of the layer, H. Because we're engineers, and basically lazy,
rather than solving this integral, we'll approximate it by dividing the soil into sub-layers
and compute the settlement as the sum of the strain in each sub-layer times the thickness
of each sub-layer.
So let's look in more detail and the consolidation of a single sub-layer,
in this case we'll look at the ith layer, with thickness, h-sub-i
Before starting the computations, we must have the consolidation curve for the soil
stratum from which our sub-layer comes.
We'll know c-sub-c over one plus e-naught, c-sub-r over one plus e-naught, and the preconsolidation
stress, sigma-prime-c.
For this example we'll assume our soil is overconsolidated.
For the ith sub-layer, we'll calculate the initial vertical effective stress, sigma-prime-z-naught.
From the consolidation curve we can determine epsilon-naught.
And knowing the change in vertical stress, delta-sigma-z, we can determine the final
effective stress, sigma-prime-zf, and the associated strain, epsilon-f.
The total strain for the sub-layer will then be epsilon-sub-i
To simplify our computations, it will be helpful to divide this strain into that portion coming
from recompression, epsilon-r and that portion coming from virgin compression,
epsilon-v Both the recompression and virgin curves are
linear in the semi-log space we use for the consolidation curve,
so we can compute epsilon-r as c-sub-r over one plus e-naught times the log of sigma-prime-c
over sigma-prime-naught.
Similarly, we compute epsilon-v as c-sub-c over one plus e-naught times the log of sigma-prime-af
over sigma-prime-c.
Obviously, the total strain for the ith sub-layer is simply the sum of epsilon-r and epsilon-v.
The consolidation settlement of this sub layer, delta-sub-i, is simply epsilon-i times the
original height of the sub-layer, h-sub-i And if we factor out 1 over 1 plus e-naught
we have this equation for the consolidation settlement of one sub-layer.
Getting the consolidation settlement for the entire compressible layer is simply a matter
of summing up the contributions from each sub-layer.
And this is our equation for computing consolidation settlement.
We just showed the case of an overconsolidated soil to derive the equation for consolidation
settlement, but in reality, there are three possible cases that can occur in the field
The case we just used, we'll call overconsolidated case 2.
In this case, not only is the soil is overconsolidated, but the change in vertical effective stress
is large enough that the soil will be loaded past the preconsolidation stress, sigma-prime-c
So the stress path for the soil will first follow the recompression curve from sigma-prime-z-naught
to sigma-prime-c and then the virgin curve from sigma-prime-c to the final effective
stress, sigma-prime-zf.
The equation for consolidation settlement in this case is the one we just derived.
It has terms for both the recompression and virgin curves.
This is equation 10.25 in your text.
The second case, we'll call overconsolidated case 1.
In this case the soil is overconsolidated but the change in vertical effective stress
is small enough that the soil will not reach the preconsolidation stress, sigma-prime-c.
Sigma-prime-zf will be less than sigma-prime-c.
In this case the soil will load only along the recompression curve from sigma-prime-naught
to sigma-prime-zf.
Our equation for consolidation settlement will have only a preconsolidation term and
that term will include the log of sigma-prime-zf over sigma-prime-naught since the stress path,
in this case, goes from sigma-prime-naught to sigma-prime-zf along the preconsolidation
curve.
This is equation 10.24 in your text.
The final case is the normally consolidated case.
In this case sigma-prime-naught is equal to sigma-prime-c.
And the soil loads along the virgin curve from sigma-prime-naught to sigma-prime-zf.
Our equation for consolidation settlement will have only a virgin curve term and that
term will include the log of sigma-prime-zf over sigma-prime-naught since the stress path,
in this case, goes from sigma-prime-naught to sigma-prime-zf along the virgin curve.
This is equation 10.23 in your text.
I've presented these equations backwards from the way they're presented in the text, but
I think it's easier to understand this way.
Really Case OC-2 is the general case with both recompression and virgin curve terms,
and Cases OC-1 and NC are simplifications of the OC-2 case with only one term each.
Be careful to put the right stresses in the right places in the equations or you'll miss
that question on your midterm.
So let's summarize the computation procedures The first step is to determine the stress
changes in our geologic profile.
They can come either from a change in total stress due to fill placement
or a change in the static pore water pressure from lowering the ground water table.
We then must identify each of the distinct soil stratum in our profile.
For each, we must determine it's consolidation properties, that is, c-sub-c over one plus
e-naught, c-sub-r over one plus e-naught, and, sigma-prime-m or OCR, whichever we're
using to characterize the degree of overconsolidation.
We then divide the profile into sub-layers.
If we're doing hand calculations 5 to 7 layers is sufficient to get a good estimate of the
settlement.
Remember that the more compressible layers will contribute more to the settlement, so
don't divide the sub-layers equally.
We generally use thinner layer near the surface where the most compressible soil is and thicker
layers lower.
If you develop a spreadsheet for doing this computation then can just use a large number
of equally thin sub-layers in your computations Next at the mid-point of each layer we compute
sigma-prime-z-naught, sigma-prime-c and sigma-prime-zf.
Then we choose the appropriate case (NC, OC-I, or OC-II) depending upon whether the soil
is normally consolidated or overconsolidated, and if over consolidated whether the loading
stays on the recompression curve or passes the preconsolidation stress and moves onto
the virgin curve.
Once we have the correct equation, we compute the consolidation for each sub-layer.
Finally, we sum all the sub-layer consolidations to determine the ultimate consolidation settlement
for the entire profile See, it's a piece of pie.
Easy as cake.
For hand computations, it's best to setup at table like this one to organize your computations.
Each line in the table represents the computations for one sub-layer.
And each column is one of the items you need for your computation.
Note that this particular computation has two different soil strata in it.
We can tell by the changes in the values of C-sub-r and C-sub-c.
Note that one layer in normally consolidated and the lower one is overconsolidated.
Also note that sub-layers are thinner at the top and gradually get thicker with depth.
So, let's summarize Remember that within a single soil stratum
we assume that c-sub-c over one plus e-naught, c-sub-r over one plus e-naught, and, sigma-prime-m
or OCR are constant but both sigma-prime-z-naught and sigma-prime-zf will be changing.
We must always divide the soil into sub-layers.
This is true even if the profile contains only one distinct soil stratum.
Use thinner layers near the surface where the soil is more compressible.
Be careful to identify the right case and use the right equation.
Also be careful to put the correct stresses in the correct location in each equation.
Don't forget that you can have all three cases in the same profile.
Finally always use a table for hand calculations, or, better yet, develop your own spreadsheet
to do the computations�it will leave more time for the important things in life.
Like hiking, SURFING,
BEER drinking, or just sleeping.
But before you go to sleep, you should do some of the example problems in your text.
There are four example problems on computing consolidation settlement 10.5 through 10.8.
If you're only going to do one I'd recommend doing
10.6.