Lower and upper bounds for friction angle in sands

[Mccoy]

Dear friends,

I'm having this lingering idea to build a distribution model for friction angle in granular materials, based on beta distribution (as rightly suggested by Milton Harr).

This is sure more realistic than the usual normal distribution (may lead to overconservative design), since we know well values of Phi have a finite minimum and a maximum. As a downside, the beta distribution may be tricky to treat.

About the minimum: this is commonly identified with the Phi CV value. I read some literature on it, Bolton, Santamarina, and the recent paper from MRM. It would seem that Phi_CV = Phi_min could be reasonably placed at 32 or 33 ° for many natural clean sands.

Now, what about the MAX value? Which would be a reasonable upper bound for the friction angle of a natural, uncemented, non-engineered sand? Here I am at a loss: 45°? 50° ? 55°?

You are kindly invited to expose your considerations here, and eventual references to literature.

I'm also interested about expert opinions on the following generic soils :

silty sands: min and max values of phi

conglomerates, uncemented: min and max values of phi

breccias, uncemented: min and max values of phi

Again, the minimum value I'm especially interested into, since it governs conservative design.

I'm also aware size of clasts in breccias and conglomerates may influence significantly max phi value).

I spoke with a friend of mine who was owner of a testing lab until recently. He told me he had DSS tests of uniform. medium-coarse beach sand done, just put it into the shear box, and the result was 28°. This clashes enormously with the phi-CV cited by literature. Any clues as to the possible reasons for such anomalously low value? clasts are quartz-feldspar and carbonate particles, many organogenic ones.

Based on the results of this discussion I'm going to build a model and a relative spreadsheet, avalaible to all those who are interested. If feasible, I'm also going to write a paper on it (in English, besides Italian).

 

[fattdad]

There are several things in your post, I'm just not familiar with. Here's why I reply: The lower bound for "sand" or "silty sand" often implies that you are dealing with a primarily quartz sand grain. This is typically reasonable, but may not be the case. For the case that the soil includes appreciable mica, the mica grains often size out as "sand", but the behavoir is anything but "quartz-like". In Central Virginia we also have a miocene-age silty sand (in the Coastal Plain) that is very fine sand and elastic silt. The problem with ASTM is there is no soil description for elastic-silty sand, but this miocene-age soil behaves more like elastic silt than silty sand.



¡papá gordo ain’t no madre flaca!

 

[Mccoy]

papagordo,

the study would deal primarily with the 'usual' quartzose, feldspatic sand, where behaviour is not heavily influenced by particles with extreme deviations from the spherical shape.

But I would be interested as well in min and max from micaceous sand, if you have a whole dataset in such soil it would be most welcome (Phi values drawn from measurements in an homogeneous layer).

 

[Mccoy]

Just came across the following lecture frome Mike Duncan:

http://cee.ucla.edu/news/Duncan_Friction Angles.pdf

It would seem it answers some of my questions for sands and gravel.

Only, it's not always clear wether soils are engineered.
I gather we may assume up to 85% relative density as a treshold for non-engineered granular materials.

Measured values would indicate a 50-55° upper bound for sands, according to CU.

A lower bound in the region of 30-35° for sands seems to be confirmed by Duncan's report, always in relation to CU.

 

[fattdad]

What a great reference. I'll be sure to save it when I get back to the office!

I would think that non-engineered sand fill would have a much lower Dr than 85 percent. I would think non-engineered fill could easily be less than 50 percent relative density - much less actually. Now if you are meaning "relative compaction", I'd more likly agree with your 85 percent criterion. That said, 85 percent relative compaction may be actually only 25 percent relative density.

f-d

¡papá gordo ain’t no madre flaca!

 

[dgillette]

28 degrees: Could the platen for vertical load have gotten hung up on something? Happened to me once with some coarse, angular hard sand (crushed quartzite from commercial source) getting between platen and box. Or, are the carbonate particles soft enough to crush during shearing? Or, is he reporting a friction angle from a suite of tests that give a non-zero cohesion intercept?

Relative density of non-engineered fill: 85% RD would be very dense material. We commonly specify 70%, occasionally 75%, for dam filters and drains.

50% is about as low as you could get unless you really tried or placed it hydraulically. If the material is clean, I'd expect that or more if you just dumped the fill and spread it with a dozer.

Best regards,
DRG

 

[Mccoy]

I do not know if I misused the term 'engineered soil', what I mean is 'undisturbed soil in its natural density'.

So, the density is governed by sedimentary processes, in seismic areas by the densification effect of cyclic waves. I specifically ruled out cementation phenomena.


Dave, OK for the 70-75% very dense treshold.

As to the test, unfortunately my friend is no more owner of that lab, I may convince the new owner to do some careful testing. Some biogenic clasts may have crushed, but they are not the main component of that sand.

Papà grasso (that's Italian, how do you like it fat-dad?),
I'm aware I was not overly clear in my first post, what I'm trying to do is to estabilish some way of applying rigorous probabilistic methods, also useful to choose a reference for reasonably conservative design. An objective reference, rather than a subjective one.

Also, subjectivity has its role, and the dataset's extremes (min and max) might be chosen anytime according to the specific engineer's knowledge in that soil.

Pretty useful when you have very few data.