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# Depth of Cohesionless Soil on Planar Slip Surface

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## Depth of Cohesionless Soil on Planar Slip Surface

(OP)
I have calculated that a particular slope is unstable (under seismic and static conditions based on a 2:1 slope. The soil in question is a well graded sand with silty gravel over an impenetrable bedrock. My soil properties are: unit wt. 100 pcf, cohesion 0 psf, and phi 30 degrees. As this is a cohesionless material, the FS for limit equilibrium is independent of depth of material.

A site recon was done and it could not be determined to what depth this material goes, but an assumption is being made that the SW-GM is parallel to the bedrock at 2:1. I need to calculate to what depth the SW-GM would be stable on the bedrock (1'?). I can consider compacting the material to obtain a higher friction angle, but depth still will not come into the equation under this situation.

Any ideas on how I might be able to evaluate this?

### RE: Depth of Cohesionless Soil on Planar Slip Surface

Not sure I understand the question.  Perhaps you could post a sketch, including phreatic and/or piezometric lines, which may not coincide.  (Link to do so appears just below the box where you will write the reply.)

Your calculations have shown the slope to be unstable, and if there really is zero cohesion, that result won't change by changing the depth to rock.  You would have to justify existence of some cohesion to change the conclusion, and phi' isn't terribly sensitive to changes in density.  Yes, it increases, but probably not enough to change the big picture.

Where is the phreatic/piezometric line?  I assume there must be one, at or pretty close to the surface, since 2H:1V is only 26 degrees, flatter than phi', and the slope is statically unstable.  Temporary cut slopes in unsaturated sand without pore pressure are routinely made at 1.5H:1V without problems.

Are the 100 pcf and 30 degrees measured values, or presumed?  30 seems pretty low for SW-GM, as does 100 even if it is the dry unit weight, not total.  This is some mighty loose stuff if phi' of SW-GM is only 30 (unless it's all shaped like marbles)!

BTW - You can't drill or get test pits?  And this is for your employment, not a school assignment, right?

The seismic analysis is another can of worms.  Be sure you need the slope to actually be stable under dynamic loading, and that you can't tolerate some limited dynamic deformation once every 200 or 500 years or whatever.

### RE: Depth of Cohesionless Soil on Planar Slip Surface

(OP)
Yes, this is an employment related question. My boss did a site recon on another island (which is where an active volcano currently is erupting and the seismic coefficient is 0.88). I cannot look at the site. I was given a hand drawn depiction and a very basic soil description. I assumed the above values. This is a slope along a highway and a retaining wall is being considered at this location.  We cannot drill due to difficult site conditions and the highway cannot be closed down.

I've had numerous conversations with my boss that depth isn't considered in a cohesionless soil, but I that I would have to assume some cohesion if he wants me to give him a "depth". He is adamant that he does not want me to consider any cohesion at all. There is no phreatic surface...

I'm not sure what to tell the guy because my hand calculations match what Slope/W outputs as well. I'll attach a hand drawn picture once I have some more time to do so.

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