Sloped backfill - Culman's graphic method

[Okiryu]

I am trying to determine the active wedge zone for a sloped backfill retaining wall of 5 m height. I am considering that the backfill is cohesive soil (not ideal, but this material is normally used in my area)

I think that the approach for the failure line based on 45+(phi/2) from the horizontal at the base of the wall does not apply for sloped backfill retaining walls, so I am trying to check this with Culman's graphic method. Does anybody can provide a good reference for this?

Thanks for your help.

 

[BigH]

Terzaghi and Peck (1967) or Terzaghi Peck and Mesri (1995) pages 251-252

 

[oldestguy]

US Navy NAVAF Manual DM-7, available to view on Internet has several charts showing various affects of sloping backfill, straight or broken slopes.

 

[Okiryu]

Just curious, what is the approach when the sloped backfill has a larger angle than the angle of internal friction of soils (phi)? Coulomb

 

[Okiryu]

sorry, did not complete the post...Coulomb's equation will not work.

 

[Doctormo]

Coulomb (and Rankine) are based on homogeneous cohesionless soil (no cohesive strength component) and the infinite slope condition to provide an equation solution. This situation rarely exists in real life unless one is retaining a 100m tall sand dune. The only way the equation solution solves is for the slope angle to be <= phi angle.

When the equation solutions do not work, a "trial wedge" analysis or more complicated type of stability analysis is used that can consider breaks in slopes, cohesive components, different soil zones, and other real world considerations. While cohesion can be tricky to work with for the long term strength condition, if may be silly to ignore it if a soil strength is predominantly cohesive and one is only left with a 12 degree frictional component or a material zone is cemented in some manner and has no frictional strength. Most slopes break some distance behind a wall so the wedge analysis will provide an answer even when the phi angle is lower.

The practical limitation of any "mechanical" analysis is that they will consider an almost infinite failure scenario unless the engineer constrains the analysis to the some distance behind a wall. A 10' wall does not really feel anything from events happening 100' behind the wall but a wedge analysis may "see" this loading when the phi angle and slope angles are close. Same with stability analysis that looks a global stability scenarios. However, a landslide is often that exact situation that goes way beyond the wall influence zone but almost impossible to predict ahead of time by analysis.

In my opinion, Bowles is probably the best reference for these methods as Terzaghi does not go into much detail.

 

[Okiryu]

Thank you for your replies. I did some checks using the trial wedge analysis. I did the analysis in CAD and it was faster than I expected.

I tried with different "phi" angles for the cohesive fill behind the wall and realized that the results are sensitive against variation in "phi". In your opinion, is this tendency correct?

For instance, with a phi=5, the resultant is 442 KN, ka=1.3 and the angle of the failure plane with the horizontal is 32.
For phi=10, Pa=336 KN, ka=0.98 and the angle of the failure plane is 37.
For phi=20, Pa=185 KN, ka=0.54 and the angle of the failure plane is 45.

Please refer to the attached picture to see the geometry of the retaining wall.