Phi_constant volume

[Mccoy]

Hi all,
with the new year I'm back, sorry no football/soccer/cricket games reports, just ole plain geotechnical issues :-D
I'll promise I'll comment some jazz recordings though

Phi_constant volume, or Phi_critical state, you know it's the lower bound for the friction angle in a given material and it's a specific property of that material, function of mineralogy, shape, angularity and more.

Now, there is this engineering school in Italy, whose chief is professor Lancellotta (he wrote a coupla books), whose members state phi_cv is the value which should be used to design ground strenght.
Yes, even when calculating bearing capacity for foundations, and not just for sliding.
Their contention is that soil failure implies great deformations, that using peak strenght is dangerous since it's sort of a metastable condition, that phi_peak is a function of soil stress and not a constant, last but not least phi_cv is always a cautious estimate (unless phi_residual governs with very large strains).
Sometimes they'll say some vague 'post-peak' strenght value governs, never the peak value though.

Now, I've got a tough time taking all that. In my book, before large deformations are reached, interlocking forces contributing to peak strenght must be overcome. Besides, it would appear, from the few load tests on real-size footings (Briaud) that phi_peak and not Phi_cv governs vertical failure of a footing (Horvath)

I'd like your comments on that, if you ever used phi_cv for problems different from design in disturbed soil, existing slip surfaces...

 

[dgillette]

Hi McCoy.

I don't think I would accept that as universally true. If there is some reason to think that the ground could ever be sheared enough that the peak friction angle would be overcome so stability or bearing capacity needs to be assessed on post peak strength. In some seismic applications this would be true (where yield acceleration might be exceeded, and the slope still needs to have high factor of safety), and possibly for excavated slopes.

There have been a lot of foundations and slopes designed using peak friction angles, with few failures that could be attributed to a small difference in phi'. Can you name a single failure caused by the designer assuming that the friction angle was 36 degrees, when it should actually have been 33? Pretty near all of the failures I know about occurred due to total mischaracterization of the material, e.g., used drained strength when the material is plastic and contractive.

Reminds me of the risk analysis forum a year or two back, when Ron Law or someone was on a kick about medical errors being responsible for some startlingly large fraction of all deaths under age 40 or 45. But where were the bodies? (Habeas corpus?) I couldn't think of more than a few possible cases (and no certain cases) among my acquaintances and their acquaintances. I was able to list car, bicycle, and motorcycle accidents, leukemia, heart attack, suicide, homicide, plane wreck, mountaineering accidents, construction and industrial accidents, drug overdose, freezing, drowning, accidental asphyxiation, accidental poisoning, and so on. Where are the failure case histories from use of peak friction angle when the CV value was more important?

Best regards,
DRG

 

[moe333]

Strain compatibility may be one reason to use values lower than peak. If you are dealling with multiple materials that reach their peak strength at different strains, you would want to be cautious about the use of peak strength for all of the materials. This may also be handled with the Factor of Safety. I have often seen this intermediate post-peak strength referred to as the ultimate strength, and it is somewhat subjective.

 

[Mccoy]

Dave,
your point is pretty clear and I'll make sure to insist on the 'habeas corpus' aspect when, next week, I'll have to speak in the 'lion's den', the city where that engineering school is located and where 99% of the geotechnical engineers is still convinced phi_cv is the way to go.

moe333,
that's an interesting example, in that particular case as I see it you would have first to overcome peak strenght of the stronger layers (mobilized first) coupled to some undefined strenght of the weakers layers, then something like phi_peak (weak) and phi_CV (strong), would you try a different quantitative description?

 

[moe333]

It is a relatively complex system to be able to analyze with any accuracy. As an example, Consider a slope stability analysis with multiple soil layers with peak strengths at different levels of shear strain using Limit-Equilibrium methods. The strain level is not constant along a potential failure surface, and it would be very difficult to evaluate the strain level in each soil layer, and thereby assign a peak strength or a post-peak strength. You may be able to get to the strain levels using FEM. This uncertainty is one reason some people use post-peak strengths.

This is related to the concept of progressive failure where some layers are strained to post-peak strength, causing more load to be shed to other layers, potentially causing them to go to post-peak strength as well. This process can continue until all or many of the layers go to post-peak strength, potentially resulting in a failure if the conditions are right. The progressive failure is typically only a concern where stress levels approach the shear strenght of the materials (maybe within about 80%).

 

[dgillette]

The issue of strain compatibility in progressive failure can be a really big deal for undrained stability analysis, if for no other reason than that the difference between peak and post-peak (a.k.a. "softened") undrained strength is bigger than the difference between phi'_peak and phi'_cv. There can also be significant differences in the strains to reach and pass peak among extension, compression, and simple shear (maybe in Ladd's Terzaghi Lecture on SHANSEP??).

Of course, there is a lot more opportunity to just plain screw up undrained strength than drained strength.

 

[moe333]

I would think that you should consider strain compatibility for drained strenghts as well, particularly if they are brittle and show lower post-peak strenghts. This would include cemented sands among others.

 

[BigH]

McCoy: I would believe that the most important aspects to consider are not necessarily the strength levels but the serviceability limits. As you indicated, the school of thought is that this should also apply to foundations. I would think that there are only few cases (soft clays, for example) where the strength governs - in most cases, the design is based on limits placed by serviceability. In such cases, the operative strength parameter would be well under the peak strength values. As such, you would, in design, not be using peak strength which, interestingly enough might be closer to the phi_cv values although be "accident" only. Neither concept really takes into consideration strength gains due to the added foundation loading and hence consolidation/compression resulting in strength values higher than before the foundations went in.

For slopes, etc., again, a lot depends on the strains to be expected and the time frame. Long term creep forces the residual strengths to be considered (London Clay for example). My question is how does this fit in to "reliability" analyses and "load reduction factors" - the modifiers are based on something - what are most using?

 

[Mccoy]

BigH,
you're raising a pretty relevant issue here, which I'm sure has also its part in the reasonings of the Turin's geotechnical school.
Why bother at all with Phi_peak when most probably the bearing capacity calculated with such an output will fail the test of settlements?

We've partly already discussed on that.

I'll just say in the recent European codes (Eurocodes which are the basis of design in western and eastern europe, north africa, most ex-commonwealth countries, partly China and Japan),ultimate limit states and serviceability limit states must be treated separately.

Moreover, seismic ultimate states may well be more conservative than serviceability limit states.

Plus, there are more variables added into like approach designs and their multiple loading combinations which are different for static ultimate, seismic ultimate, serviceability short and long term, and so on.

It's not like it used to be, a single loading and you figure out bearing capacity and settlements based on that.

Strenght gains due to compressive loading and consolidation are not usually taken into consideration, you're right. I'm only aware of some qualitative estimates.

I'm not sure I understand your final question.

Loads in the eurocodes are usually increased, not reduced, whereas resistances are reduced, in a triple fashion:

1) find a characteristic value which is a cautious estimate of the value which affects the occurrance of the limit state (i.e.: failure, or excessive settlement). That's usually a 5th percentile of the distribution of the mean or the distribution of the sample (depending upon the signal's autocorrelation)

2) apply a partial safety factor to the characteristic value, which ranges from unity to 1.4, even 1.6 in intact rocks

3) apply a global safety factor to the bearing capacity output

Tath compares to LRFD which only uses a resistance-reducing model factor. But which underwent-case history calibration.

Phi_cv would be a particular case, since it's the minimum possible value of the distribution of phi in sands, hence it may be unrealistic to further reduce such a lower bound.

The eurocodes just ignore this problem.

 

[Mccoy]

I came out of the lion's den unhurt.

Colleaugues were more or less convinced of my explanations. I told them they are just about the only ones in the whole world who are designing the vertical bearing capacity of foundations by phi_cv

Professors weren't there though, a panel discussion would have been interesting.

It later occurred to me another reason they like phi_cv is probably because of the undetermined normal effective stress on the surface failure and how that affects phi_peak.

Phi_cv remains unchanged and that's sort of a comfy security in a world of change after all.