calculation of secondary consolidation

[AK92]

Hi all,

I'm calculating post-PVD secondary consolidation for a soil that is going to be improved using prefabricated vertical drains. Now the secondary consolidation equation goes like this: s = Ca/(1+e0) X log (t2/t1). The log (t2/t1) is bothering me a lot now, because I am using prefabricated vertical drains to accelerate the consolidation, it doesn't make sense that I would have significantly more secondary consolidation settlements just because I decreased the time period required for primary consolidation.

The equation implies that the settlement is heavily dependent on t1 (the time at the end of primary consolidation). For example for a time period of 100 years:

t1 = 4 years, t2 = 100 + 4 = 104 years, log(t2/t1) = log(104/4) = 1.42
t1 = 50 years,t2 = 100 + 50 = 150 years, log(t2/t1) = log(150/50)= 0.48

This is a difference in settlement prediction of a factor of 3!

Now I don't have that much experience but I think that the secondary consolidation settlement shouldn't depend on t1 at all. If the equation was log(t2-t1) instead of log(t2/t1) it would make a lot more sense.

Now another thing is that: If the soil is in an overconsolidated state during the working load, is it OK to ignore secondary consolidation and just use recompression settlements to calculate the residual settlement? My site is made mostly of marine clay with some limited areas where organic clays are present.

Thanks!

 

[fattdad]

According to the equation, which I happen to trust, the degree of secondary compression is affected by the time to end primary consolidation. If you are using wick drains and a surcharge though, you can drive off some of the secondary compression.

f-d

¡papá gordo ain’t no madre flaca!

 

[aeoliantexan]

I believe the reasoning is that if the time of primary consolidation is long, more of the secondary consolidation takes place along with the primary, so there is less secondary left to occur afterwards. why we don't factor up the primary consolidation settlement based on the time for primary is a puzzle to me.

Dr. Charles Ladd at MIT addressed reduction of secondary compression settlement through overconsolidating the soil with a surcharge. The "amount of surcharge" is the effective stress at the end of preloading minus the final effective stress in service, divided by the final effective stress and expressed as a percentage. If the amount of surcharge is say 20%, the average reduction in the rate of secondary compression is about 40%. So yes, overconsolidation reduces secondary compression, but does not eliminate it.

 

[AK92]

@fattdad

So let's say I put a fill on two adjacent areas with exact subsoil conditions. One is improved using vertical drains and one is not. The one improved by vertical drains finishes primary consolidation in 1 yr while the unimproved one requires 20 yrs.
Assuming equal ca values, if I compare the amount of secondary consolidation over a period of 20 years

improved area:
log(t2/t1)= log (21/1) = 1.32
unimproved area:
log(t2/t1)= log (40/20) = 0.30

This is a factor of 1.32/0.30 = 4.4 times.

So the secondary consolidation of the improved areas for 20 years after primary consolidation would be 4.4 times the primary consolidation for the one at the unimproved area.

Would that be true?

@Aeoliantexan

Where can I find that relationship?

Thanks for all your help!

 

[aeoliantexan]

All I have is a preliminary chart from a lecture Dr. Ladd gave about 1985. A note at the bottom says, "Ladd, 1975", but he may have updated it. A search under his name should produce it.

In your example, the amount of primary consolidation settlement depends on the thickness of the fill, the compression index, and the thickness of the clay. The secondary compression settlement depends on the coefficient of secondary compression, the thickness of the clay, and time. In most engineering cases the primary consolidation settlement is larger. The fact that the secondary compression settlement is independent of the load added is another of the mysteries I don't understand.

 

[BigH]

I would suggest that the OP pick up a copy of Terzaghi Peck and Mesri (1996) and see pages 101-103 and 108-110. This might give him a better understanding of secondary consolidation. In the area of the text (pages 224 and then on 231 where they discuss consolidation with wick drains.

 

[dgillette]

I believe aeolian is correct with his explanation of most of the secondary having already occurred during primary in the no-drain case. They are different mechanisms, one of which happens due to the increase in effective stress, with the other occurring more like creep under constant effective stress. Right at the drainage boundary, the soil feels the final effective stress right away, so it has 20 years of secondary consolidation already having occurred at the end of primary. That has less effect away from the drainage boundary, but you get the picture.

 

[AK92]

Thanks everyone!

@BigH and @dgillette Thank you for the references and explanations, those were very useful for me.

@Aeolian
I found this document online, is this the one that you are referring to?

It gives a Cα'/Cα = 1.85 – 1.08 log (AAOS%) where AAOS is the "adjusted amount of surcharge" and the definition looks something like OCR - 1.

[URL unfurl="true"]http://users.ntua.gr/mpanta/Teaching_EN/LimerickCaseStudy/CalculatingSecondaryCompression[/url].doc

I am planning to use this equation as it is the easiest to use for me at the moment. I wonder if Prof. Charles Ladd has published his findings in a paper somewhere that I can reference to?

 

[AK92]

Oops I have a broken link in my post above. The link should be [URL unfurl="true"]http://users.ntua.gr/mpanta/Teaching_EN/LimerickCaseStudy/CalculatingSecondaryCompression.doc[/url]

 

[dgillette]

Over breakfast, I made a quick stab at finding a reference using scholar.google.com, but didn't get much. I put it in as: clay AND "secondary consolidation" AND ladd

The first hit I got back was Rheology and Soil Mechanics / Rhéologie et Mécanique des Sols
International Union of Theoretical and Applied Mechanics 1966, pp 273-304 "The Secondary Consolidation of Clay" by Robert L. Schiffman, Charles C. Ladd, Albert T.-F. Chen. Since Bob Schiffman was first author, it's probably heavy on the theory and light on the applicability. Bob was about 98 percent theoretician (which I knew because he was on my PhD committee, even though I wasn't working in clay consolidation).

Most of the rest that came up didn't seem directly relevant, although you might want to try work by Mesri at Illinois. He had some papers in the ASCE Jnl Geot Engr in the 1980s, and also "Primary Compression and Secondary Compression," from Symposium on Soil Behavior and Soft Ground Construction Honoring Charles C. "Chuck" Ladd, Cambridge, Massachusetts, United States, October 5-6, 2001. ASCE Special Geotechnical Publication #119. (I don't have it.)

Cheers!
DRG

 

[AK92]

@BigH

In the Terzaghi, Peck and Messi (1996) book it seems to show heave over time due to unloading, which reaches a turning point and proceeds to secondary consolidation. Now I realise that I have not actually considered heave in the design. If I calculate heave using the recompression index, it would be quite significant (>100mm)if I am using heavy surcharge loads. The site has strict differential settlement criteria and tight time limits with pavement construction is going to follow immediately after the ground improvement. I suppose that I really shouldn't be surcharging that much, so to avoid significant heave settlements which may cause pavement cracks, but still enough to avoid continuing primary consolidation settlements.

Is the above correct?

 

[fattdad]

after pore pressure dissipation from consolidation, any heave would result from an elastic response and would be quick!

If you truly using a surcharge in conjunction with wick drains, you'll benefit from the shorter drainage path and you'll realize consolidation settlement that's (to some extent) greater than would develop from just the final earthwork load.

Let's say you need to increase the grade over a soft clay by 10 ft, and that 10 ft of fill will produce 3 ft of consolidation. You install the wick drains and place 15 ft of fill and calculate that the 15 ft of fill will produce 4-1/2 of consolidation. You document the degree of consolidation and you show that you're at 95 percent for the earthwork load and the surchage load (i.e., about 4 inches of consolidation was yet to be realized, based on the load of the 15 ft of fill).

Let's say that for the 20 years after the 10 ft of fill is placed, you calculated 1-1/2 ft of secondary compression. Well the 5 ft of surcharge just drove off that 1'-2" of that secondary compression (it did it via consolidation however). Now that the surcharge has been removed, what amount of secondary compression should develop over time? The way I see it, you've just forced the soil to go about 20 years down the secondary compression time line, so you should retool the equation to set the time accordingly.

Maybe it's hard to type about. . .?

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Might want to read this. I haven't studied it in any detail - but it might give you some insight.

http://www.issmge.org/images/joomd/223-226.pdf

 

[AK92]

@BigH

I had a look at this paper along with a paper on oedometer surcharging tests on Bangkok clay done for a highway project. It seems that based on the oedometer surcharging tests I can construct curves of Ca''/Ca and tl/tpr similar to the work from Mesri and Feng and then use that to estimate the long term post-surcharge secondary consolidation settlement. Seems to me that this might be the most reliable way of calculation.

Thank you everyone for all the inputs.