Rankine versus Coulomb Earth Pressures 1

[MIBridgeEng]

AASHTO LRFD seems to flip flop in their cantilever retaining wall figures (Section 3 and 11) showing the inclination of the resultand active pressure to be at angle beta (parallel to backfill slope) or at angle delta (wall friction). This confuses me a bit. I've also seen several figures from random google searches that show the angle of inclination to be angle beta+delta. The link here shows an example of the beta+delta which is almost identical to some of the figures in AASHTO

http://www.engmath.dal.ca/risk/pubs/FHWA_Manual.pdf

Can somebody explain which is correct?

 

[kslee1000]

Per memory:

1. Rankine theory does not include wall friction, for sloping backfill, the resultant is parallel to the slope.
2. Coulomb theory considers wall friction and angle of slope, both are included in the equations for earth pressure constant K, the resultant force is making an angle, equal to the friction of the wall, from the plane normal to wall.

Remotely remember the case shown in the attachment, but the details are forgotten.

 

[kslee1000]

where are our geotech fellows ?

 

[dgillette]

If you are referring to the cover figure and page 4.33, something is fishy , or else delta is defined differently from what I've usually seen (friction angle of fill against wall material). I don't see a list of the coefficients there!! See page 4.20 of that same volume, for Mononobe-Okabe analysis. There, beta is the batter angle of the wall, so the force on the wall is inclined (beta + delta) from horizontal (and I think (beta+delta) is limited to no more than phi'). If you set Kv=kh=0, I think the MO model will reduce to the correct static active pressure.

kslee1000 - you are correct; the original Rankine model - remarkable for being developed on the basis of internal friction and failure state of soil decades before Terzaghi played in a sandbox - assumes frictionless walls and level fill. (For that case, it gives the same answer as Coulomb.) I believe, however, that it has been extended to the general case, allowing frictional walls and nonlevel fill. I think I saw that somewhere, but I would use Coulomb.

 

[kslee1000]

dgillette:

Thank you for responding to the call for help. You have clarified my memory - an advice from my geotech professor: do not count on wall friction unless it,s certain, and Coulomb method is used. Also, the use of wall friction shall take into account of the type of backfill materials and fluctuation of water table into account, the potential risks outweighs the gains when wrongfully applied.

 

[STVU]

Agree with all that Rankine neglects wall friction. Rankine method is also applicable to inclined slopes as long as it is not a broken slope.

Coulomb method does consider wall friction. Depending on the reference, friction between soil and concrete for granular soils is often 0.5 to 0.75 of phi. For flatter slopes like 3:1(h:v) or less, wall friction can also be equated to beta, the slope angle.

 

[BigH]

Rankine is really a "special" case of Coulomb (which came first, by the way). We had a discussion a while back as some texts use differing notations for the same thing - was confusing. About 6 to 8 months ago . . .

 

[dgillette]

I don't think I'd call Rankine a special case of Coulomb. Coulomb w/frictionless wall gives the same result as Rankine, but they have different bases - sliding wedges vs state of failure within the fill as a mass like we think of with a triax test (not just along the sliding surface), w/ sigma1 and sigma3 being vertical and horizontal, respectively, for active, and the reverse for passive. I've used that as a way to show someone how the Mohr circle relates to reality.

Coulomb is older by most of a century, but the concept of coefficient of friction on a sliding surface was already established by then. The rest is trigonometry. I think Rankine was so remarkable because, as far as I know anyway, that was the first, or certainly one of the first uses of the concept of internal strength of mass of soil.

I'm easily impressed by ideas that I would never even have thought about thinking up.

 

[BigH]

Well, then shouldn't we be using log-spirals? While the "states" may be a bit different and both don't match actual, numerically, it is so.

 

[kslee1000]

dgillette:

That was what I learned from school, glad to hear it again.

 

[dgillette]

In theory anyway, we probably should be using log spirals, but I have a feeling that the difference gets lost in the noise of phi, delta, whether the wall moves enough for active-pressure assumptions to hold, etc. I don't think it makes a whale of a difference in active, but at least with high phi', it can a bigger difference in Kp. We actually had a slightly bizarre case where a higher Kp was harmful, and we found out that Sokolovski's spirals made it higher than Coulomb's wedges.

 

[vulcanhammer]

I just put back into print two documents which discuss this issue in detail.

The first is The Seismic Design of Waterfront Retaining Structures. The second is Retaining and Flood Walls. The latter has two especially interesting comparisons of the relative conservatism (or lack thereof) of Rankine, Coulomb and Log-Spiral.

Both of these can be downloaded from

http://www.vulcanhammer.net/geotechnical/retaining.php

http://www.pz27.net

 

[BigH]

Thanks Don . . .