Toe slope below cantilever wall

[GoodnightKiwi]

I'm curious as to what people do when designing a cantilever retaining wall with toe slope for the drained and undrained conditions. By cantilever, I mean say timber pole uprights at a 3 to 4 foot spacing, embedded by either driving or in concreted augered holes and with timber lagging/railing supporting the ground upslope. Embedment may be the same or more than the retained height.

For example, in undrained conditions I've seen the design retained height increased by [ 4 x pile dia x tan(toeslope) ], to essentially create a wall with level toe conditions.

 

[FixedEarth]

There is an equation for a descending passive soils coefficient (Kp) using Rankine method. Is that what you need?

http://www.soilstructure.com/

 

[GoodnightKiwi]

Yes, I've seen that method.

I don't have any particular problem that needs solving, rather I'm interested in what others are doing to account for a toe slope in doing their wall design - whether something like the Kp reduction, increasing the theoretical wall height to create 'level toe' conditions (and how this is done) or something else. I guess I was hoping for some general discussion.

 

[FixedEarth]

I noticed the following: If I use one friction angle for both the retained and the passive soils, there is no adverse effects for Kp when the backfill slope is level. However, when the backfill angle is inclined, the passive Kp automatically reduces (As Ka increases, 1/Ka or Kp reduces).

So recently I have been using two friction angles, two unit weights and two slope angles for the Active and Passive soils. As for the passive wedge or passive multipler, I never go as high as 4, I use 0.08(Phi) which ranges from 2 to 3 pier diameters.
For cantilever piles (timber, soldier beam, sheetpiles, etc), I always check the design embedment depth is where the pile tip defelction is very close to zero. You will notice the embedment depth is influenced by surcharges, so for example, you may get 1.5H or so if you have high vertical uniform surcharge and 1.2H if there are no surcharges at all.

http://www.soilstructure.com/

 

[RFreund]

It seems there are 3 different approximate approaches:

1. An empirical method which uses a 3:1 slope from the intersection of level ground up to the wall. Then half of this height is used.

2. Surcharge Method - The berm is converted to a uniform surcharge applied over the width of the passive failure wedge.

3. NAVFAC Method - This uses a trial wedge or the Rankine reduction as mentioned by FixedEarth above.

Or there is finite element I suppose.

I believe PileBuck which is/was a popular sheet pile program uses something similar to method 3 where they just input a negative value of the back slope into the coulomb or rankine or Terzaghi equations.

Supposedly Method 2 is overly conservative, method 1 is conservative and method 3 can be slightly non-conservative or should use a reduction/factor safety as mentioned by FE. He is some more information:

I'm not sure where to find this:

http://books.google.com/books/about/Design_Guidance_on_Soil_Berms_as_Tempora.html?id=QSVQYgEACAAJ

Thesis on the subject:

http://files.engineering.com/getfil...2-b493-053c406713d2&file=Thesis_-_See_for.pdf

Some further discussion:

http://www.mycrisp.com/publications... A BERM DURING TEMPORARY WORKS ACTIVITIES.pdf

EIT

http://www.HowToEngineer.com