Backfill Problem - Mononobe Okabe Equation

[X-Wing]

thread255-95878

Referring to previous post (link above) and other post that were closed, I have some clarifications about Lateral Earth Pressure

What is the remedy if the backfill slope is great in such the mononobe equation nor the coulomb equation be messed up?

 

[Doctormo]

The equation solutions do not solve when the back slope is steeper than the phi angle or the seismic factor reduces the maximum possible back slope for a given phi angle. A negative square root becomes the math problem.

Since slopes are rarely infinite like the equations assume, it is possible to use a trial wedge analysis that may converge on a solution when a slope breaks such that an answer can be obtained. It is also possible to physically limit a wedge search such as only considering a zone that goes back 100 feet for example.

A trial wedge solution will go back infinitely for an infinite slope and never converge on a solution which can be thousands of feet behind a wall. This is not very realistic as the failure surface is not planer but circular or log spiral in nature but it is the way a wedge analysis works.

The poor man's solution is to set the negative square root portion of the equations equal to 1 and get an answer. It is not correct but it is an answer which might give you a Ka = 1.2 or thereabouts.

One can also run a global stability analysis of an irregular back slope condition and determine the amount of thrust resistance the wall has to provide to arrive at a safe situation (FS > 1.5 or whatever), similar to the wedge analysis.

Then there is cohesive strength which the equations can not deal with either. It is a big headache that requires different approaches to get answers that make sense and not just grinding formulas.

 

[X-Wing]

Man, Geotechnical or simply, Soils are really so unpredictable. I didn't know about the trial wedge in college, only till now. I'll try to search on that, also, if you can give nice reference (bowles maybe?) about that, thanks sir!

 

[Doctormo]

Bowles has a section on Coulomb trial wedge as well as almost every other textbook that discusses lateral earth pressures. Some of the older texts discuss it better, especially those that deal with retaining walls.

The concept is simple, sweep a bunch of wedges and see which one provides the greatest thrust. The model gets complicated if there are many changes in back slope geometry which is why some prefer global stability analysis as those programs allow the input of irregular back slope conditions to analyze. However, they do not provide a direct solution to lateral earth pressure so you have manipulate the software to get an answer.

Soils are hard to deal with so the exercise is to get a reasonable magnitude of thrust on a retaining structure then provide enough resistance to be safe. Seismic analysis is a problem because loads are displacement related and yielding structures can absorb a lot of energy thus the pseudo-static loads are less than a more rigid structure.

 

[X-Wing]

Thanks for the reply!

Practically the other methods that can be used if the MO cant be used also include the generalzed limit equilibrium

 

[Doctormo]

GLE is just another method that AASHTO/FHWA throws around like it solves the world's seismic stability problems. They all suffer from the same problem if you truly have an infinite slope and phi-only soil with a significant pseudo-static acceleration force. The forces just do not resolve for the infinite condition. It is really the same thing as having a 26 deg backslope with a 25 deg material without worrying about seismic loads, just does not solve for the infinite condition.

However, a break in the slope and it solves, a little cohesion and it solves and so on. You just can not use equation solutions and have to use a method that reconciles force equilibrium in some manner that solves. Even when you do this, you may not like the answer but at least you have an answer to start tweaking from.

 

[X-Wing]

Thanks for enlighting me up with this problem, it really shows how unpredictable and hard it is to study soil/rock geotechnical in particular. Thanks!

Very Truly Yours,

- andru18