Variation of the coefficient of consolidation with time

[Ben93]

Hello everybody,

Does anyone know anything about the variation of the coefficient of consolidation (Cv) with time (i.e. as consolidation is going on)?
My goal is to obtain a rough estimate of Cv when the consolidation process began, knowing its present value.
Has any study been performed on this question? I couldn't find anything in the literature.
Thank you for your help.

Ben

 

[dgillette]

It appears that you are talking about finite-strain theory of consolidation, of which Terzaghi's formulation is a special case in which Cv can be considered near enough to constant (which we know isn't exactly true). (Terzaghi might not have done it that way if he had access to a PC with a Pentium, or even an 8086.)

I haven't ever seen an analysis where Cv was considered as a variable. Instead, for finite-strain analysis of plastic mine tailings and dredge spoil, what I have seen is skipping the whole notion of Cv and working with permeability and compressibility directly as fns of void ratio (or K as a fn of e, and e as a fn of sigma'v). If that's what you need to do, I can dig out refs. (I worked with tailings and dredge spoil in the '80s, but that stuff is all in boxes.)

What's the situation you are analyzing?

 

[Ben93]

I'm actually trying to assess how much the soil (soft clay) has consolidated so far. The problem is that the overload (fill) was placed some 60 years ago and the only values that I have are from last year. I wonder if using the now-value of Cv to calculate T and U (with Terzaghi's theory) makes sense.
So I'm more looking for some sort of correlation between Cv(t=0) and Cv(t=t1).

 

[Erdbau]

How much fill? Was the clay normally consolidated before fill placement? From the consolidation data, how does Cv vary with increasing load? How much does it vary within your range of working loads, i.e. between prefill eff. stress and postfill eff. stress?

Cv will change depending on stress levels, so "age" isn't really going to change Cv all that much. It will vary with stress, and possibly signifcantly in the overconsolidated versus normally consolidated region, so it's important to look at it in the context of your case.

 

[dgillette]

First, I'd be a little bit surprised if there was still anything going on with consolidation 60 years after the fill was placed.

Second, I know of no way to project a different Cv backwards in time like that. To do that, you would need to somehow obtain estimates of K and m-v at the two different times. I suppose, you could do that, in theory anyway, if you knew the original void ratio and the present values of e, K, and m-v, plus some way of relating K and m-v to void ratio, but I wouldn't recommend that as a real-world solution.

Have you thought about shoving a vibrating wire piezometer into the center of the layer to check for excess pore pressure?

 

[Erdbau]

I agree with the piezometer. It's the only way of really (sort of) knowing what's going on. If the budget doesn't allow for one, then I'd bet that trying to figure out Cv vs. time is way beyond the level of effort required for what you're doing.

 

[BigH]

Have you done any consolidation testing? Comparing the "in situ" effective stresses to the test curve's precosolidation pressure can tell you if there is still more consolidation to do. I'd suggest that you use a loge vs logp plot as a check on the normal Casagrande method.

 

[Ben93]

CRS-tests have been performed at 3 different depths, and the clay appears to be underconsolidated (the OCR ratio is around 0.8). It might appear strange after so many years but the amount of fill that was placed is about 7m (another problem in this case in the lack of reliable information about the site history).
The Cv values obtained from the CRS-tests are fairly constant with the effective stress (between 10^-7 and 10^-8 m2/s).
Field investigations cannot be performed anymore in this case, but I'll consider it next time.