Tiered Retaining Wall Surcharge

[goose47]

Can anyone tell me the surcharge load that I should be applying?

I am looking into the design of a tiered wall system. The lower wall consists of a 26 ft high concrete cantilver retaining wall and the upper wall is a 23 ft high MSE. The set back distance is 9 ft.

I have currently used the Boussinesq equation for area loading a distance away from the wall. The surcharge that I calculated is (height of the upper wall X unit weight of soil) 2.875ksf. The distance my surcharge load is applied I assumed as 17ft(26-9, 1V:1H).

This is resulting in extremely large loads and a footing size that is not economical. Is there another way I should be analyzing this?

 

[RFreund]

I would create a spreadsheat and figure out the resultant location from the boussinesq analysis as this may help you. However I would also consider using the weight of the soil of the upper wall once my footing went back under the upper wall to help resit OT and sliding.

EIT

 

[goose47]

My footing geometry is limited due to a bridge abutment in close proximity. My heel width can only be 8ft while my toe can be as large as necessary.

I created a spreadsheet for assuming both a 1V:1H and ~2V:1H and my resultant is 21.5klf at 13.0ft and 6.98klf at 14.89ft, respectively. This load is acting over a 30.5 ft panel so the moments are extremely large for either case. The footing sizes are impractical or not possible.

 

[FixedEarth]

Your Boussinesq approach is correct, the 2.9 ksf is a little high. I did a quick check and I am getting about 820 psf at 7 feet depth. You can average this "question mark" shaped as approximately say 600 psf uniform stress which is about 1800 psf (600 psf x 3) or say 1800/120 = 15 ft of soil surcharge. I assumed a bearing pressure of 3,000 psf of the upper wall applied to a strip width of 9 ft and setback at a distance of 9 ft. The "3" is convert lateral stress back to vertical stress.

You did not say if the upper wall exists or both walls will be newly built concurrently. If both walls are new, you have few options to deal with the high lateral stresses.

 

[goose47]

Both walls will will be newly built construction. I guess I am not sure where your numbers are coming from. The 2.9ksf of surcharge is coming from the upper wall vertical soil stress. I then applied that as the surcharge for both a ~2V:1H and 1V:1H. I used the Boussinesq approach for both and obtained the resultants for each as stated above.

I am looking for the lateral load that is produced from the upper wall soil load for the design of my lower wall. Using the Boussinesq approach I took the area under the curve for the total load that is applied over the 30.5ft panel. See attached.

Another thought, if I were to use Rankines theory for surcharge right next to the wall I would get a total lateral load of 20.2klf @ 13ft. Why would this be less than when I use Boussinesq's appraoach at a 1V:1H or any other greater distance?

 

[RFreund]

Just so I'm understanding the 2V:1H and 1V:1H is how your defining the back of the strip load correct?

If the wall can tolerate some movement the force from the boussinesq may actually be half of the value. The factor of 2 in the equation seems to be pretty debatable see this link which has been posted before:

http://www.ejge.com/iGEM/Articles/FactorOf2/FactorOf2.htm

EIT

 

[FixedEarth]

Yor strip load dimension and setback distance should be fixed. In your calcs, your "a" distance is variable?

To compare exactly, I need the following 4 values:

Setback distance
Strip load width
Strip load intensity and
proposed lower wall height (including embedment depth)

 

[goose47]

RFreund - Correct. I assumed the "back" of my load strip ended somewhere along the top of wall within 26ft. 2V:1H was assuming an active failure plane and 1V:1H is the wall height.

If I lose the factor of 2 my loads are still very large, no problem though. I just want to make sure that the loads I am applying are realistic.

FixedEarth - My "a" distance was not variable. I calculated it looking at "a" going from the back of the upper wall to edge of the failure plane (~2V:1H) and 1V:1H. The values depicted represent a value for "a" of 4.53ft and 17.5ft respectively.

The setback distance is 9ft. The lower wall height is 26ft. The load intensity is 2.875ksf (23ft*125pcf). "a" would be 4.53ft assuming an active failure plane or 17.5ft for a 1:1. I guess this is where my question lies; what is the appropriate "a" dimension and what is the proper load intensity?

 

[FixedEarth]

The "a" dimension is the footing width of your upper wall. The setback is fixed and is measured from lower wall inside face to upper footing inside edge. I see your question. I only know of 3 ways to go about solving this. one way is have your "a" and setback values, then draw a 1:2 (H:V) from the inside edge of the upper footing and see where it hits the lower wall. Then just use footing stress distribution values for vertical componenet and solve for your lateral stress.

The other is to use the Boussinesq equation, like you did ina spreadsheet. The "a" and setback are fixed and you solve for your 3 angles and then the lateral stress directly. I prefer thsi method, since it is more direct approach. Attached is the solution I obtained.

The 3rd approach is to draw a 40 to 45 degree line from the upper footing and use an equation. This is how the older reference books solved it and they say if you are more than 1:1 influence away, then there no surcharges involved. This is not the case for strip, but is valid for line loads.

Try playing with your spreadsheet and get a feel for it.

 

[goose47]

My upper wall is MSE with a small (1'-6") leveling pad. Say it were a CIP wall, how can you only assume that the vertical soil pressure acts on the width of the upper footing? The soil pressure will still have an impact beyond that, I would think.

I went about the Boussinesq approach the exact same way as you did, using slightly different values though. Modifiying my spreadsheet to match yours I would still get a 250kip force acting at 14.7ft from the bottom of the footing, producing a very large moment. That is fine if it is the correct approach. Just seems to me like it is too large as my footing size, pile arrangement and stem backface reinforcement are not very realistic.

 

[RFreund]

For the situation you have described in your OP I get 7.2K (flexible) 14.4 (rigid) at about 14' from the bottom of the wall.
See attached - Ignore the Sliding and Overturning analysis section.

EIT

 

[RFreund]

I should say kips per foot of wall length not kips. And my "a" distance was 5.4'.

And the spreadsheat is pretty crude as I always say that I'm going to refine it and make if more user friendly but I'm usually always busy. I can post if for you if you'd like.

EIT

 

[goose47]

I'm guessing that the 5.4ft was using a friction angle of 32deg. I am required to use 35deg so thats where the difference is. I wasn't able to get the same values of stress that you did but I got it figured out.

I still am not confident in the way I chose to calc "a" but I'll have to dig into it more to see what is appropriate.

Thanks all for the input.

 

[RFreund]

I actually did not mean to use a=5.4 except that I saw fixedearth had used it. If you are using the bearing pressure of the upper retaining wall then I would use the width of the retaining wall base for CIP or MSE. If you are using the weight of the soil then I would do as you did and assume a failure plane angle and say that beyond that point the soil above does not effect the wall. Or you could use a large value for "a" which would yield a conservative result (or atleast I think it should).

EIT

 

[InDepth]

Why don't you use a micropile foundation to resist overturning and a battered micropile to resist the horizontal load....or just go full on concrete pile and pile cap baby...

Or a butress wall with micropiles.

 

[InDepth]

F the soil conditions are right you can also jet grout the whole shebang behind the reatining wall and thus modify the soil properties (reduce ohi and thus load) or essential create a gravity wall.

 

[BigH]

For wall stability why not carry out a Culmann graphical method as a check on those methods described above . . .