Angle of phi

[dirtsqueezer]

This is a very green question, but could someone explain the angle of phi as it relates to soil mechanics? My textbook defines it as the angle formed by the normal stress v. shearing resistance. Does this in some way give you the actual angle that the sample will shear? Does the shear strength have something to do with the coefficient of friction between the two sliding masses? How do you measure the shearing resistance? Again, this wasn't offered at my university, I just picked up this book along the way. Any input would be appreciated. Thanks.

 

[jdonville]

dirtsqueezer,

The friction angle is determined experimentally in a shear box (for granular soils) or using a triaxial apparatus (for any soil). The normal stress vs. deviator stresses are plotted as a Mohr's circle (to graphically show the state of stress) at failure. The angle of the failure envelope tangent to the Mohr's circle is denoted as phi or phi', depending on whether effective stresses are being used.

Soils texts usually discuss this concept extensively, as the state of stress and failure criterion concepts are fundamental.

Jeff

 

[MRM]

Maybe this analogy will help:

Take a steel block sliding along a flat steel plate. To find "mue" the friction coefficient as used in a physics class, you'd raise the plate to the point where the block slides down it. That angle is analogous to the friction angle used in soils. (Also, to get "mue" of the block against the ramp, you'd take the inverse tangent of the resulting angle)

In soil mechanics, we're dealing with particulate materials. As jdonville mentioned, the friction angle is determined based on different testing such as the direct shear test. You find the maximum shear stress on a surface of the soil and observe how it increases with increaases in normal stress. Of course, there are other tests to determine it too.

In the case of loose dry sand, the angle of repose is about equal to the internal angle of friction, in that loose state. It would be different at different normal stresses, which is why another test method such as the direct shear test, must be used.

Regarding your other question: the friction angle is related to the angle at which the sample will shear, but it is not really in a direct way. Instead, you need to look at Mohrs circle and you will see how friction angle plays a role.

 

[dirtsqueezer]

Thanks for the replies. My soils book mentions something about C, or the y intercept. I understand the Mohr's circle to be something like a circle on the x-axis with a line tangent to it. This intercept 'C' is somewhat up from 0,0. How is this determined? It seems like such a simple concept on paper, but so many questions.

Also, that shear plane that develops in the tested soil sample, is that assumed to be 45 degrees? Is that how you determine the shear forces involved, and what if that angle is actually higher or lower? What if the sample is actually consolidating instead of shearing, as with a CH or ML? Again, so many questions. There must be some simple way of thinking about this. Thanks for your help.

 

[DarthSoilsGuy]

I agree with your concept that not enough attention is given to the phi angle in school. at my school we ran the triaxial tests but the professors were so concerned about advanced theoretical soil mechanics that they didn't push how many practical apps there are with the phi (or i would have paid more attention, instead of relearning it for my PE exam). There are so many soil design requirements that are based on that simplified number and there is a disconnect b/n this soil property and the others we usually mess with that are self-explanatory. i also have noticed a general creep towards higher phi numbers in MSE manufacturer published design literature over the last 10 years. The cynic in me believes there has been an upward shift to either limit potential design liability on the manufacturer side while still providing "technical resources" or to reduce the imagined cost of a typical cross-section of wall at first glance. There has also been an increase in caveots about global stability, but that's another topic.

As far as the shear plane, there is suppose to be a direct relation between the phi angle and failure plane with cohesionless soils in the triaxial test. But, as i recall it's more of a way of double-checking that the results from your Mohr circle analysis of the soils from the series of triaxial tests, and not the way to determine the phi alone.

 

[jdonville]

dirtsqueezer,

You should probably get a soils mechanics text that starts with a brief review of solid mechanics. G.N. Smith's Elements of Soil Mechanics does this. R.F. Craig's Soil Mechanics is more popular in North America, but seems to assume more knowledge at the outset of the discussion on shear strength.

Jeff