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# using rankine or coulomb for Ka

## using rankine or coulomb for Ka

(OP)
When calculating the active or passive earth pressure at retaining walls, if there is friction between wall and soil, and that friction angle is given , then we use coulomb formula (that long one) even if there is no incination of backfill or wall correct?

if so, in question 76 of six minute solutions of geotech, why did they use the simple rankine formula when calculating Ka - active earth pressure coefficient?

for those who dont have the book, it is just a simple rectangular retaining wall, with no inclined geometry or no inclined backfill but the question gives you a friction angle between soil and the wall. i used that long coulomb formula for calculating Ka because of that reason. but they used rankine and it makes a little difference of course. i didnt understand why they used rankine, although the question gave the angle of friction between the wall and soil.

### RE: using rankine or coulomb for Ka

That is tricky when the problem statement doesn't imply what to use. Usually if statement said assume wall is frictionless then Rankine active earth pressure would be appropriate.

The problem in your case gave enough info (beta = 90, alpha = 0) that makes it a candidate for Coulomb's Ka. However, I'm unclear about the solution's rationale.

### RE: using rankine or coulomb for Ka

The P.E. exam prep books should give you hints. If you are given a friction or adhesion between the backfill soil and the retaining wall, Rankine theory can't be used. So you default to Coulomb or Spiral wedge or other methods. So your hint is right - if wall/soil friction is given, Coulomb should be used. Agree with cloud69. See attached.

### RE: using rankine or coulomb for Ka

I second FixedEarth's attached PDF.

@FixedEarth: Is your pdf from a textbook? Are you able to give title? Thanks.

### RE: using rankine or coulomb for Ka

Don't forget there is also a log spiral solution

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