friction angle vs depth 2

[translation314]

This is a hypothetical question:

Lets say we want to simulate the conditions of different sand samples at various depths in the ground, say 0-5meters via Triaxial test(setup the test so principle stresses match in-situ condition of sand at different depths).

Then lets say we take the principle stresses from the test at failure and calculate the friction angle of the failure plane of each sample.

My question is:

How would friction angle vary with depth? Would it simply increase or decrease?

 

[dgillette]

It wouldn't "simply" anything. There are at least two possibilities:

If the density and gradation are strictly uniform, you MIGHT see a SLIGHT decrease in phi' with depth, because the strength envelope is not really linear. Nineteen times out of twenty, it is inconsequential in analysis.

If the deposition process was completely uniform but the density increases with depth due to overburden (remembering that even very loose clean sand consolidates rather little with overburden), you MIGHT see a SLIGHT increase with depth. Twenty-three times out of twenty-four, it would be inconsequential in analysis.

DRG

Any variation that actually occurs would be very subtle, and it may well be overshadowed by the effect of sampling disturbance. (The effect of disturbance on undrained strength is vastly greater than the effect on drained strength.) Correcting for that has been the subject of several doctoral theses.

 

[escrowe]

Just try not to drop the sample on the floor.

 

[DRC1]

Friction Angle is a soil property, so technically for the same soil, the friction angle will not change. Since the soil strength is a function of friction angle and overburden pressure, soil strength will increase with depth.
However, friction angle is a function of many things such as mineralogy, angularity, and grain size. So with in a soil strata that would appear homogeneous, it is possible to have variation in friction angle.

 

[dgillette]

DRC1 - I must disagree - phi' is not an intrinsic property of the soil. The linear phi'-c' model that we use so much is just a convenient model. In reality, it is not strictly linear, so the value of phi' you would determine from tests of identical samples with different sigma' would vary with sigma'.

 

[escrowe]

With regard to the OP, your question seems to presume that stress increases uniformly with depth. Certainly a theoretical condition!

To DRC and dgillette, I suspect that you're both right, and suggest that the challenge of phi determination is a perpetual boondoggle.

We observe that shear resistance for a given material changes with material density, vertical stress, and pore pressure, and so phi can thereby be calculated for total and effective stress conditions: for example, an estimate of 'undrained' phi for a total stress analysis (as opposed to phi prime) will certainly change with pore pressure.

But consider that phi prime (effective phi, 'drained') is often determined graphically at the theoretical zero vertical stress condition based on direct shear tests under varying normal stress. These results are rarely linear, especially at lower confining stresses.

Even with triaxial equipment, creating and observing tests under the effective phi condition (zero excess pore pressure, zero vertical stress) is problematic especially for a non-cohesive material that will simply disperse when subjected to shear without confining stress.

So what is the 'real' effective phi for a given material? It is at best an average within a shifting range. Each measurement of phi is based on numerous grain interactions, and barring perfect uniformity, the range and average will tend to vary both with and independently of stress, and many other factors.

 

[dgillette]

"But consider that phi prime (effective phi, 'drained') is often determined graphically at the theoretical zero vertical stress condition based on direct shear tests under varying normal stress."

Please clarify this, escrowe. Phi' is simply the arctan of the slope, necessarily at sigma' > zero. In 24 years of practice and three university degrees in civil and geotechnical engineering, I have never seen it related to a condition of zero stress, nor would it make much sense to do so. Did you instead mean to say that c' is graphically determined for a theoretical zero stress condition?

 

[escrowe]

dgillette, I was not clear. And your comment is mathematically and procedurally correct, but theoretically problematic. Here's what I mean:

For a non-cohesive material, the failure envelope defined by the maximum stress values of a series of direct shear tests is presumed to pass through the origin of the sigma/shear resistance function. So we presume, theoretically, that shear resistance = 0 when sigma prime = 0, and c = 0, as would be the case for a non-cohesive material (sand): as you noted, the slope of the failure envelope and the calculated value of phi depends on this construction.

Understanding that this has little practical meaning or application, we are still left with a theoretical assumption expressed graphically that I have rarely seen confirmed with test data. In fact, I have often seen the direct shear failure envelope for sand trend toward the x axis somewhat short of the origin... Would that not suggest a negative shear resistance at sigma = 0? Or does it suggest that shear resistance approaches zero in advance of confining stress? The latter seems more likely, but still renders a precise (and consistent) determination of phi by this method even less likely.

[I put the 'failure envelope curve' in a box labeled 'interesting laboratory extraneaity,' along with the 'proctor curve tail' and other tendencies not readily explained by the theoretical assumptions upon which the tests are based.]

Now I've gone and hijacked this perfectly serviceable thread. Please forgive me translation314, I'm old.

 

[dgillette]

Here's where I disagree with you: There is no theoretical reason that the envelope should be linear, if one allows for particle crushing, interlocking of dense angular particles leading to variation in angle of dilation with confining stress, etc., but it generally works well enough for designing stuff. Forcing a linear strength envelope through (0,0) is strictly a convenience that we very often (almost always) employ for granular materials, not something that is directed by theory.

Even with granular materials, one may see nontrivial curvature in denser material at very low normals in triax tests. (Work done by NASA, U of Colo, and others for lunar soil mechanics.) We DON'T NECESSARILY have to force the strength envelope through (0,0). Doing so is not something theoretical; it is simply a practical thing to do, one that matters in practice very rarely. (It could introduce minor conservatism that isn't worth paying attention to.) You've probably seen a cut in rockfill that stood much steeper than 1:1 for some height, even vertical, even though phi' for the rockfill is likely no more than about 45 degrees under high confining stress.

If you are seeing the shear resistance dip toward zero before the vertical normal reaches zero, you wonder about a problem with the boundary conditions in the direct shear test at very low normals (assuming there is no issue with load cell zero point, platen hanging up slightly on grit between it and the box, or something like that). I don't believe you would find that in a triax or simple shear test. In undrained cyclic tests on very loose material, pore pressure ratios can get very close to 100%, without the shear resistance reaching exactly zero.

(Negative shearing resistance would probably violate the second law of thermodynamics, but if real, it could have potential in building a perpetual-motion machine. )

Don't worry about hijacking a hypothetical thread - see first sentence of the thread - with theoretical discussions. By the way, what's become of the OP? Whence the question in the first place?

 

[translation314]

thank you all for comments. now i realize that this hypothetical and possible vague question is not so simple!