Undrained Shear Strength

[moe333]

Hi All,

Trying to come up with a shear strength to use in a seismic dam stability/deformation evaluation. I am using a simplified Newmark method so the shear strengths should start out at peak strength, then degrade to ultimate or residual strength as displacement accumulates through the seismic event.

It's a debris dam, so there is no water impounded and the soils will be moist, not saturated.

The core is well compacted clayey sand and low PI clay, and the shells are well compacted silty sand.

I will use drained strengths (friction only) for the silty sand shell materials. This will be conservative since there will likely be some apparent cohesion due to the suction from the partially saturated condition.

I'm wondering what strengths to use for the clayey sand (30% low PI fines), and the low PI clay.
They are not saturated, but the seismic loading will be fast enough that there should be no drainage. So I'm thinking an undrained cohesive strength. I don't have the option to run any lab tests so would base the strength on judgement. Since they are well compacted (92% mod. minimum), I'm thinking cohesion of 1,000 psf for a residual strength.

Any thoughts or references on this are appreciated.

Thanks

 

[BigH]

moe333 - I'll have some thoughts for you tomorrow morning (about 18h from now).

 

[BigH]

moe333: Further to your question, I have consulted (1) Terzaghi Peck & Mesri (1995) – article 20; (2) Canadian Foundation Manual, 4th Edition (2006); and Kramer’s Geotechnical Earthquake Engineering (1996).
For sands with fines content greater than 5%, TP&M suggest using the expression for undrained critical shear strength (Su-critical / effective O/B pressure) = 0.006*{N160 + ?N160} where ?N160 = 0 for 5% fines, 4 for 15% fines, 6 fro 25% fines and 7 for 35% fines where N160 or ?N160 is corrected for 60% energy and 100kPa pressure. Elsewhere they say that no corrections is needed if PI <20.
Kramer discusses a limiting cyclic stress ratio (my old professor at Cornell, Dr. Sangrey) whose work suggested that there was a critical ratio where the porewater pressures did not continue to increase with added cyclic loading – ranging from 0.05 for non-plastic silt to 0.55 for San Francisco Bay Mud. Thiers and Seed (1969 – ASTM paper) suggests that the (strength after cyclic loading for clays over original strength) would be about 0.9 for (peak cyclic strain over Failure strain in static test) of 0.5, 0.6 for 0.75, 0.4 for 1 and 0.2 for 1.5.
Canadian Foundation Manual discusses non-plastic silts Gravels and Sands, and then for silts and clays. They quote Boulanger and Idriss that a fine grained soil acts “sand-like” if PI<7 and “clay-like” if PI>7. In the end, they suggest that the residual strength
= remoulded shear strength if (wn/LL) >= 0.85 and PI<=12;
= 0.85*static undrained strength if (wn/LL) >=0.8 and PI between 12 and 20; and,
= Su if (wn/LL)<8 and PI>=20.
It appears that you do not have fine grained soils – it is a mix – but you can use this as a basis to estimate from a likely remoulded strength value – can estimate from liquidity index for Su and use Sensitivity of 2 or so . . .

From TPM, it seems appropriate to draw a graph for various effective O/B pressures and determine the critical undrained shear strength from their equation for likely N values. See attached.

The question, perhaps, is that since the embankment may not be “saturated” fully, then it might be sandy regardless of PI; if so, then TPM may be the choice.

Hope, my friend, that this helps a bit . . .

 

[BigH]

Here's a second scan

 

[moe333]

BigH,

Thanks much! I've been in jury duty for a couple days so just saw your posts. I'll take a look at these references.

 

[BigH]

By the way - the square box in my post is supposed to be the capital greek letter Delta!

 

[moe333]

Thanks for the references. The issues I'm struggling with is:

Is an undrained strength appropriate when the soil is not saturated?

And, given the anticipated deformation of 1 to 2 feet (which is acceptable), wouldn't that amount of deformation cause the soils to be at residual strength for at least a portion of the earthquake?

 

[dgillette]

Starting at the end:

If the soil is not saturated, the undrained strength would be practically the same as the drained strength, since the air in the voids is compressible. For saturated materials, the big difference between drained and undrained is because of incompressible pore water in a material that wants to contract. I'm not sure you need a sophisticated analysis accounting for strength degradation, especially if you are starting out with moderately conservative strengths.

If clayey material was compacted at optimum moisture +/- then loaded with enough overburden pressure, it may become saturated. How high is this thing? Above that point, it is reasonable to use a friction angle a bit less than the effective-stress friction angle, with a generous cohesion intercept, because of the capillarity. Design of Small Dams by USBR can give some guidance on specifics.

It is rather unlikely that 1-2 feet of deformation would cause much loss of strength, except maybe in the uppermost part of the core where the confining stress is low. Especially not if you are starting out assuming no cohesion in the SM shell. The compacted fill should be fine.

I see that BigH has provided correlations for residual undrained shear strength, but I think those are for liquefied foundation materials, not for compacted fill, which should be far too dense for that. Is there liquefiable material that I missed? How big is the design earthquake?

For a "gut check" on your results, try to find a paper by Jim Swaisgood, who collected settlement data from a large number of dams hit by earthquakes. He's published the data several different places with different correlation equations. You may be able to find it by Google. (I'm not wild about his correlation, but his data set is quite helpful.) The history of dams in the world is that, without liquefaction of foundation or embankment, they rarely deform more than a couple of feet in the most severe loadings.

Regards,
DRG

 

[moe333]

The dam is 60 feet high at most. It is within 2-5 km's of two M=6.9-7.0 faults, one of them being fairly active with a slip rate of 4mm/yr. Lots of other faults at greater distances.

There are no liquefiable materials. I would have thought the strengths would start out at about peak + some extra due to capilarity, then they would decrease down to residual (somewhere around 30 degrees for the SM, the clay strength is alittle tougher to guess at). I can't see how they could stay at peak or near peak strength after 1-2 feet of movement. The materials should strain-soften.

I was thinking of using some intermediate strength value between peak and residual to account for the degredation. Any other thoughts you may have on this are appreciated.

I think the deformations will be fine, just trying portray it so that everyone agrees with the parameters, analysis, and results.

Thanks

 

[dgillette]

Oh, serious earthquakes. PHA possibly as high as 0.7 at the site.

IF the displacement occurred only along a single distinct rupture surface, like a slickenside, you would get essentially infinite strain, and would likely get close to a residual or a remolded condition, depending on materials. However, that isn't what happens, in general. The strain tends to be distributed through a zone with strains of a few percent. See, for example, Elgamal, Scott, Succarieh, and Yan in ASCE JGE December 1992 for a review of performance of La Villita and El Infiernillo Dams in Mexico. Both underwent a number of earthquakes with dynamic deformation, but apparently did not show distinct rupture surfaces. I can also dig out references to studies by Idriss, and by Stark and Contreras of a slide in the 1964 AK earthquake. They were looking at a meter or so of displacement to get to remolded strength in a fairly sensitive saturated clay. With the frictional SM shells, the peak and post-peak strengths should not be very different - just a few degrees apart. Your clay core would tend to have a greater difference between peak and post-peak, but you would need to have a lot of displacement along a concentrated sheared zone.

If I were a regulator or outside reviewer, I would most likely be comfortable with assigning strength parameters that are a little conservative, as you've done for the shell, and use those values all the way through the Newmark analysis. Depending on the configuration of the core, and the confining stress, it might be unnecessarily conservative to use 1000 psf for the whole thing.

There was also a study by Hynes and Franklin (Franklin and Hynes?) of USACE WES, in which they did Newmark analysis of a number of dams with different earthquakes, and concluded that if the PHA is less than triple the yield acc, deformation would be below 1 m. This is consistent with the Swaisgood data base. I can find that ref also if you want to cite it.

 

[dgillette]

Short on detail, but free download with general info:

http://www.fema.gov/library/viewRecord.do?id=1573

 

[moe333]

dgillette,

What your saying makes sense, particularly about the strain being distributed in a zone rather than on a discrete surface. Otherwise, embankments would only be good for one strong earthquake and then the materials would be at residual strength.

I would like to review the papers by Stark and Elgamal. I may be able to locate them but if you have them handy I would appreciate it.

Thanks

 

[dgillette]

"Fourth Avenue Landslide During 1964 Alaskan Earthquake," Timothy D. Stark and Ivan A. Contreras, ASCE JGGE, v. 124, no. 2, February 1998, pp. 99-109.

"La Villita Dam Response During Five Earthquakes Including Permanent Deformation," A.W.M. Elgamal, R.F. Scott, M.F. Succarieh, and L. Yan, ASCE JGE, v. 116, no. 10, October 1990, pp. 1443-1462.

If you don't have the journals in your office or nearby library and you are in the States, try inter-library loan. You might be able to find something on Elgamal's or Stark's websites.

See also closure to discussion of "Seismic Analysis of Concrete-faced Rockfill Dams," G. Bureau, R.L. Volpe, W.H. Roth, and T. Udaka, ASCE JGE v. 113, no. 10, October 1987, pp. 1255-1264.

 

[dgillette]

Moe333 - I should add that those two papers are the "bookends." One is a well-compacted embankment (more like your case), and the other is a sensitive clay that goes to mush with large strain.

DRG

 

[Mccoy]

I'll take the opportunity to ask a related question:

A seismic event is triggered.

I'm wondering about the behaviour of saturated sands and clays in slopes.

Pore pressure starts to build up, but when exactly (I mean after how many signal cycles)is it going to reach its max value ?

Reason of my doubt is this: I have a moderate earthquake with not a large number of cycles N.

Can it happen I'll reach a max Delta_u when the event is over?

Can post-seismic conditions be more severe (from the standpoint of pore pressure-induced strenght degradation) than during-the-event conditions? And when (after how many significant cycles) ? # of cycles within 65% max intensity is often correlated to expected earthquake magnitude.

Any reference useful in practice?

 

[dgillette]

Yes, post-EQ can be the worst case if excess pore pressure can migrate or if individual particles can settle, leaving a looser zone after liquefaction. Recent work has shown that if a liquefied non-plastic material has an impervious cap layer, the settling of the sand below the cap can lead to formation of a film of water, or at least very low density at the interface. This governs the stability of the slope. It's been shown in centrifuge tests (Kokusho in Japan, Boulanger and others at U Cal Davis), and quite likely was involved in many of the more important flow slide case histories: Fort Peck, Mochi Koshi tailings, Kawagishi Cho apartment building, Lower San Fernando Dam, etc.

Plastic clays may need to be thought of with peak and post-peak (softened) undrained shear strength if there is enough
shaking. Worst case is sensitive clay.

Every time I turn around this stuff gets more complicated.

 

[Mccoy]

Dave,
the water film below the aquiclude you are describing is an interesting worst case scenario.

If we have non-liquefiable layers though, wouldn't you, as a conservative procedure, use post-peak strenghts, or degraded strenght anyway, to calculate the slope stability during the earthquake with its design horizontal and vertical unfavourable accelerations?

Sure the lower bound resistance value along the sliding surface is found when dynamic conditions and diminuished soil strenght overlap.