Total and effective stresses in excavation

[Mccoy]

A colleague of mine asked my opinion for a practical case he is examining:
we have a NC clay with very low permeability, a shallow water table and an excavation with a face a few metres high. Everything into the same low-permeability formation, no conspicuos silty or sandy layers. Just after excavation, the unloading causes a state of negative pore pressures in soil within and around the active wedge. We verify excavation stability in terms of Su. The Mohr circle construction makes it evident that a total stress analysis is more favourable (less conservative) than one based upon effective stresses, but it governs the calcs in the short term, some time after the cut has been completed.
Yet, beyond end of construction stage, after a wall or wathever has been built to contain the face (or even after face has been left unconfined), a swelling phenomenon (the reverse of consolidation) is triggered, due to a water influx toward the active wedge region which tends to equalize pore pressure.
The question, at last, is the following: How long does it take to reach such a degree of swelling that effective stresses analysis will govern the excavation stability?
It is the reverse of the question: "how long before a NC clay layer underneath a foundation will consolidate enough to allow us to reason in terms of effective stresses, in this instance (this is a loading problem) more conservative than a total stress analysis?".
The foundation example of course has well defined boundary conditions, which is not usually the case for the excavation problem. Tomlinson reports cases in London brown clay where excavations of similar geometry took 1 to 6 months prior to collapse. If we construe collapse as reaching the effective stress state, that could be an answer. My only doubt is that our clay has a very low permeability. I would expect YEARS to reach pore pressure equalization. Can that time in the real world routinely be shortened by ubiquitous permeable and almost invisible layers? Or by (micro)cracks in the active wedge caused by unloading stresses?

Am I missing some relevant point?
What's your opinion (based on literature or hard evidence) about the time necessary to reach the effective stress state in the example situation?

 

[MRM]

I haven't responded to any posts in a while fellas, and fellettes. Sorry about that...

Mccoy, It seems to me that you're considering most of the salient points here.

You mentioned that the total stress analysis is more conservative as the reason for using it as opposed to the effective stress analysis. That may be true, but I would use the total stress analysis in this case for a different reason...namely, I haven't met a client yet who will wants to spend any money on soils engineering, let alone money on expensive effective stress methods!

Sometimes using Su may be more beneficial in that you can run multiple vane shears, penetrometers, and Torvanes for a very low cost. In looking at the long term stability issues (which would likely be the critical case in this instance) I usually estimate the effective stress friction angle according to the LL/PL tests that I've run. That is; a phi angle and no "cohesion" intercept.

When it comes to accounting for possible variables (silt lense, etc.) as they relate to time for consolidation to occur, I agree that is a good thing to consider. I typically assume that consolidation will happen more quickly than it would appear based on the fine soil appearance-especially in the case of temporary construction slopes. I can't quote any papers off hand, but I've seen many studies that suggest that consolidation occurs much more quickly than anyone could guess. This must be because there will always be higher permeability drainage paths that hasten consolidation.

I'm looking forward to more on this subject from others.

 

[GeoPaveTraffic]

In theory the time to reach complete effective stress should be the same to reach consolidation, all things being equal. However, as you pointed out, all things are seldom equal and it could occur fairly quickly. I have always used one to three months when talking to clients in situations like this one.

One thing to remember is that you don't need to reach complete effecitve stress conditions to reach the failure condition. As soon as the driving force over comes the resisting force, the stress state no longer matters. In fact the stress state maybe even more complex depending on relative loadings, since at some points along the failure (potential failure) surface the stress due to movement may cause consolidation, thereby moving toward effective stress conditions sooner.

 

[BigH]

McCoy - actually, I have been trying to find some hard references for you. I have a little bit from Malcolm Bolton's book on Soil Mechanics and will forward.
In fact, effective stress analyses always works - it is just that with the excavation - you get relief of stresses both in a horizontal relief with vertical pressure remaining the same and, in the base, vertical relief with horizontal stress remaining the same - effective stresses are not typically used, though - - - why? because of the extreme difficulty in determining the pore water pressure response due to the unloading. In normal vertical pressure placement, pwp response is to the 'left' of the drained condition (+u) for NC and LOC clays; for HOC, the pwp response is to the 'right' of the drained condition (whose slope is 3V:1H in the q-p space).
With the unloading, though, you have extension - and depending on the location of the of the soil point and the level of overconsolidation, you may have -p and +q, or -p and -q, etc. The "drained" lines are differnt - so the stress path has different directions both in the unloading and in the drainage.
Undrained shear would be used for the short term analysis and drained for the long term. I would suggest that you would "start" using the drained conditions, say, at an estimate of 85% to 90% of the drainage. Again, there is not "theoretical" time since effective stress is always acting. There is an interesting paper in one of the ASCE Geo-Journals a few years back calculating factors of safety of a slope (fill embankment) at various stages of its consolidation.
Bolton indicates that it is very difficult to estimate the time; but consensus does seem that it is in proportion to consolidation settlement.


Just finished ripping a Lena Horn and Charles Mingus CD - good stuff.

 

[VAD]

There are cases in London clay that took at least 70 years for pore water pressure equilibration and reported failures of motorway cuts that took a large number of years before failure occurred. These have been published and are well known. Many of these have been shallow slipouts. The environment has alot to play in the case of cuts. From my experience, many failures take the form of surficial sloughs in cut slopes and generally occur within a year or two and much pronounced during or after wet seasons.

The 6 month time period provided by others has been used to define a period for temporary slopes using undrained analysis. Some factor of safety relation ship exists to incorporate the months excavation is to be left as temporary, with the FOS increasing with the time of temporary slope.

No specific period is provided

The embankment time can be some how linked to the consolidation of the subsoil based on pwp dissipation. Instrumentation can help in this situation- pneumatic piezometers. For the slope case you may wish to explore the unsaturated soil mechanics end.

 

[Mccoy]

well, by now it's quite evident that unloading-swelling conditions sound more complex than loading-consolidation.
At least, so would appear to me.

Mingus remains one of the masters, I love his band with Jaky Byard at the piano and Eric Dolphy at the alto sax and bass clarinet. Some pretty peculiar tunes, pretty peculiar titles too, such that you don't easily forget: "Orange was the color of her dress but blue..."

 

[BigH]

VAD - if I remember correctly, some of the motorway cuts were of the very shallow cut (say 1 to 2 m) - and the resulting failure was defined by the residual friction angle (lower than the fully softened value). McCoy's question seems to be one that texts only talk about in esoteric terms with little or no details (that I have been able to find out).

 

[VAD]

Big H - You are partly correct based on my memory. I will check on some ino that I may have re the subject.

 

[BigH]

VAD - there was a very classical paper on the subject back from the 60s - likely Skempton or Bishop. I'll see, too, if I can find it.